The contents of this document are subject to configuration control and may not be changed, altered, or their provisions
    waived without prior approval of the LSST Change Control Board.
    1
    Large Synoptic Survey Telescope (LSST)
    Science Requirements Document
    Željko Ivezić and the LSST Science Collaboration
    LPM-17
    July 6, 2011
    This LSST document has been approved as a Content-Controlled Document by the LSST Change
    Control Board. If this document is changed or superseded, the new document will retain the Handle
    designation shown above. The control is on the most recent digital document with this Handle in the
    LSST digital archive and not printed versions. Additional information may be found in the LSST CCB
    minutes.
    Donald Sweeney CCB Chairman
    Sidney Wolff
    Charles Claver CCB
    Project Manager
    On behalf of the LSSTC Board
    System Engineer

    LSST
    Science Requirements Document
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    antgo ecdo, naflitgeurreadt, oir
    on thceoinr
    trporl ovainsd imoany s not be
    waived without prior approval of the LSST Change Control Board.
    i
    Change Record
    Version
    Date
    Description
    Owner name
    1
    10/5/05
    Initial Version
    LSST Science Council
    3.4.1
    10/10/05
    Updated initial version
    LSST Science Council
    4.3
    9/14/07
    Approved by LSST Board of Directors and LSST
    Change Control Board
    LSST Science Council
    5.1
    3/24/10
    Updated version 4.3; see Appendix E of this
    document for details
    ŽeljkIveo zić and the
    LSST Science
    Collaboration
    5.2.3
    7/6/11
    Updated version of 5.; 1see Appendix E of this
    document for details
    Željko Ivezić and the
    LSST Science
    Collaboration

    LSST
    Science Requirements Document
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    trporl ovainsd imoany s not be
    waived without prior approval of the LSST Change Control Board.
    ii
    Table of Contents
    Change Recor
    ................................
    d
    ................................................................i
    ................................
    1
    Introduc
    ................................
    tion
    ................................................................
    1
    ................................
    2
    The
    LSST
    Sci2
    Tehe nLScST e DDirverrs i
    ................................
    vers
    ................................2
    ............................
    2.1
    Constraining Dark E................................nergy and Dark
    ................................Matter
    3
    ........................
    2.1.1 Weak Lens................................ing Studies
    ................................................................3
    2.1.2
    Supernovae ................................................................................................5
    ................................
    2.2
    Taking an Inventor................................y of the Solar
    ................................System
    5
    ............................
    2.3 Exploring the Tr................................ansient Opti................................cal Sky
    7................................
    2.4 Mapping th................................e Milky Way
    ................................................................8
    3
    Detailed
    Descriptio
    ................................
    n
    of
    Science
    Re
    ................................
    quirement
    1
    0
    s
    ......................
    3.1 The Definitions
    of Spec................................ified Parameter................................s
    1 0
    ...........................
    3.2 Distinction between Single Image Specfici
    ations and thfoe
    rmFanucel
    .......................
    l Survey
    1 0
    Per
    3.3
    Single
    Image
    Specfici
    atio................................ns
    ................................................................1
    1
    3.3.1
    Filter
    Set................................
    Characterist................................ics
    ................................1 2
    3.3.2
    Image
    Depth
    and
    the
    Minimal
    Exposure
    Tim................................e
    ................................1 3
    ..........
    3.3.3 The Delivered Image Quali................................ty
    ................................................................1 6
    3.3.4
    Photometric
    Qualit................................y
    ................................................................1
    9
    3.3.5
    Astrometric Quality
    ................................................................................................23
    3.4
    The
    Full ficSaturio................................vey
    ns
    Speci
    ................................................................25
    3.5 Data Processing and Management Requiremen................................ts
    ................................32
    ...........
    3.6
    Further
    Improve................................ments
    and
    Chan................................ges
    33
    ................................
    Autho
    ................................
    rship
    ................................................................35
    ................................
    Appendix
    A: asTehe
    linLSe
    ................................
    SDT eBsign
    ................................................................36
    Appendix
    B:
    The
    Unive
    ................................
    rsal
    Cadence
    S
    ................................
    trategy
    38
    ...........................
    AppendiD:
    The x
    Seeing Dsitribution at the Cerro Pachón Site
    ................................................................39
    Appendix E:
    The
    Docum
    ................................
    ent
    History
    ................................................................
    40
    Parameters Specified in this Docum
    ................................
    ent
    ................................
    4
    ................................
    1

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    The LSST System Science Requirements Document
    v5.2.3, June 19, 2011
    1 Introduction
    The main purpose of this document is to define science-driven requirements for the data
    products to be delivered by the Large Synoptic Survey Telescope (LSST). The LSST is
    envisioned to be a large, wide-field ground based telescope designed to obtain sequential
    images covering over half the sky every few nights. The current baseline design would allow
    to do so in two photometric bands every three nights. This baseline design (for details see
    Appendix A) involves a 3-mirror system with an 8.4 m primary mirror, which feeds three
    refractive correcting elements inside a camera, providing a 10 deg
    2
    field of view sampled by
    a 3 Gigapixel focal plane array. The total effective system throughput (´etendue) is expected
    to be greater than 300 m
    2
    deg
    2
    , which is more than an order of magnitude larger than that
    of any existing facility. The survey will yield contiguous overlapping imaging of ∼ 20,000
    square degrees of sky in six optical bands covering the wavelength range 320–1050 nm.
    Detailed simulations that include measured weather statistics and a variety of other effects
    which affect observations predict that each sky location can be visited about 100 times per
    year, with 30 sec exposure time per visit.
    The range of scientific investigations which would be enabled by such a dramatic im-
    provement in survey capability is extremely broad and is summarized in detail in the LSST
    Science Book
    1
    . However, it is not feasible to make an exhaustive study of the scientific
    requirements appropriate to all of them. To define quantitative science drivers and resulting
    requirements, we therefore limit our attention in this document to four main science themes:
    1. Constraining Dark Energy and Dark Matter
    2. Taking an Inventory of the Solar System
    3. Exploring the Transient Optical Sky
    4. Mapping the Milky Way
    Each of these four themes itself encompasses a variety of analyses, with varying sensitiv-
    ity to instrumental and system parameters. It is our belief that the analyses encompassed
    by our four science themes fully exercise the technical capabilities of the system, such as
    photometric and astrometric accuracy and image quality. The working paradigm at this
    time is that all such investigations will utilize a common database constructed from an
    optimized observing program. An example of such a program is described in Appendix B.
    Below, we include short summaries of the science goals in each of these four theme areas
    and the assumptions that have been invoked in translating these into the minimum and
    design specification parameters. This document concludes with Tables of Science Require-
    ments, in which we have integrated the constraints from the different programs.
    1Available
    from http://www.lsst.org/lsst/scibook
    1

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    These science requirements are made in the context of what we forecast for the scientific
    landscape by the end of this decade. Clearly science will not stand still in the intervening
    time. Using current plans for smaller surveys and precursor projects one may calculate
    efficiencies and gauge the likely progress on a number of LSST-related scientific frontiers.
    Some advances in each area will be made, but the LSST remains the ultimate facility for each
    key area covered in this SRD. Indeed, LSST represents such a large leap in throughput and
    survey capability that in these key areas the LSST remains uniquely capable of addressing
    sharply these fundamental questions about our universe.
    2 The LSST Science Drivers
    The LSST collaboration has identified the aforementioned four science programs as the
    normative key drivers of the science requirements
    2
    for the project. Their selection was the
    result of discussions within the consortium and reflects the input of
    • the four National Research Council studies
    3
    that have endorsed the LSST,
    • the report of the LSST Science Working Group (SWG), an independent committee
    formed by NOAO to represent community interests
    • the scientific interests of the partners in the LSSTC
    • the physics and astrophysics community.
    The SWG report
    4
    (also known as the Strauss report), the LSST NSF MREFC proposal
    5
    ,
    the LSST Dark Energy Task Force report
    6
    , and the LSST Science Book should be consulted
    for a more detailed discussion of the major scientific advances that can be expected from
    the construction of a wide-field telescope that is dedicated to repeated, deep, multi-color
    imaging of the sky.
    For each of the four primary science drivers selected by the LSST collaboration, this
    Section briefly describes the science goals and the most challenging requirements for the
    LSST system that are derived from those goals (separate documents will deal with more
    detailed requirements
    7
    ). Tables are also provided in the subsequent Section, that integrates
    2The
    “normative key drivers of the science requirements” define the scientific product of the LSST mission
    which is realized during survey operations phase. Normative key drivers of the science requirements lead in
    turn to actionable engineering project requirements that must be achieved at the end of the construction
    phase. Please refer to the LSST System Requirements (LSST Document LSE-29) for a complete discussion
    of system requirements.
    3Astronomy
    and Astrophysics in the New Millennium, NAS 2001; Connecting Quarks with the Cosmos:
    Eleven Science Questions for the New Century, NAS 2003; New Frontiers in the Solar System: An Integrated
    Exploration Strategy, NAS 2003; New Worlds and New Horizons in Astronomy and Astrophysics, NAS 2010.
    4Available
    as http://www.lsst.org/Science/docs/DRM2.pdf
    5Available
    (to LSST) as http://docushare.lsstcorp.org/docushare/dsweb/Get/Document-10549
    6Available
    as http://www.lsst.org/Science/docs/050617c deftwp.pdf
    7The
    two high-level documents derived from this document and other constraints are the LSST System
    Requirements Document (LSE-29) and the LSST Observatory System Specifications Document (LSE-30).
    For an overview of high-level LSST documents, please see the LSST Document Tree (LSE-39).
    2

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    the detailed requirements of these four programs. If these requirements are met by the
    LSST – and indications of the preliminary engineering studies undertaken to date indicate
    that they can be – then the LSST will not only enable all four of these major scientific
    initiatives but will also make it possible to pursue many other research programs. Some
    examples are described in the LSST Science Book, but the long-lived data archives of the
    LSST will have the astrometric and photometric precision needed to support entirely new
    research directions which will inevitably develop during the next several decades.
    2.1 Constraining Dark Energy and Dark Matter
    Driven by observations, current models of cosmology require the existence of both dark
    matter and dark energy (DE). One of the primary challenges for fundamental physics is to
    understand these two major components of the universe. In addition to making a unique
    map of dark matter structure over half the sky, LSST will probe dark energy in multiple
    ways, providing cross checks and removal of important degeneracies. The primary DE sci-
    ence drivers for LSST come from a suite of two and three point cosmic shear tomography
    analyses coupled with galaxy power spectrum and baryon acoustic oscillation (BAO) data,
    as well as from the use of supernovae as standard candles. Due to its wide area cover-
    age, LSST will be uniquely capable of measuring 7 parameters related to DE: the lowest
    6 eigenmodes of the DE equation of state vs. redshift, w(z), and any directional depen-
    dence. Combining these probes, LSST will measure the comoving distance as a function of
    redshift in the redshift range 0.3–3.0 with an accuracy of 1-2%, and separately the growth
    of cosmic mass structure. A sample of about four billion galaxies with sufficiently accurate
    photometric redshifts is required. In order to achieve this comoving distance accuracy, the
    photometric redshifts requirements for this i < 25 flux-limited galaxy sample are i) the rms
    (σ) for error in (1 + z) must be smaller than 0.02, ii) the fraction of 3σ (“catastrophic”)
    outliers must be below 10%, and iii) the bias must be below 0.003. These requirements are
    primary drivers for the photometric depth of the main LSST survey. In addition, meth-
    ods for rejecting the majority of those outliers, and for characterizing their effects on the
    sample, must be developed. The calibration of photometric redshifts and their errors can
    be a combination of correlation with bright spectroscopic samples and spot-checks with
    many-band photometric redshift samples. Combining BAO with weak lensing of galaxies
    can significantly reduce sensitivity to bias systematics.
    DE exerts its largest effects at moderate redshift; LSST’s redshift coverage will bracket
    the epoch at which DE began to dominate the cosmic expansion. When combined with
    Planck CMB data, the LSST data will sharply test models of DE, whether due to new
    gravitational physics, vacuum energy, or other causes.
    2.1.1 Weak Lensing Studies
    Weak lensing (WL) techniques can be used to map the distribution of mass as a function of
    redshift and thereby trace the history of both the expansion of the universe and the growth
    of structure (see Chapter 14 in the LSST Science Book). These investigations use common
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    deep wide-area multi-color imaging with stringent requirements for the shear systematics
    in at least two bands and photometry in all bands. These requirements are covered in more
    detail in the LSST DETF report and references therein.
    The shear systematic errors can be mostly corrected by use of foreground stars. The
    spatially varying PSF within each exposure must be mapped, fit, and corrected. The
    precision of this correction depends on how many stars are available, and thus depends
    on the angular scale. The overall scale of the combined errors is set by the requirement
    of distinguishing models of the origin of DE: unique sensitivity to the cosmic shear power
    spectrum from arcminute to 100 degree scales and wide redshift range, the ability to probe
    at least six DE eigenfunctions, and any variation over the sky. This leads to an ´etendue
    requirement for areal coverage times depth (several billion source galaxies to z=3), as well
    as photometric precision and wide angular coverage (> 90 deg).
    The power of the LSST relative to existing weak lensing surveys derives from its ability
    to survey much larger areas of the sky to faint limiting surface brightness while maintain-
    ing exquisite control of systematic errors in the galaxy shapes. Characterizing dark energy
    places particularly strong requirements on the total area of sky covered, the depth of the
    stacked image, the number of revisits to each field, the ellipticity and sampling of the point
    spread function (PSF), and the choice of filters, which must be suited to allow accurate
    photometric redshifts to be measured. At least six bands are required. Photometric preci-
    sion of at least 1% is required, as well as quite accurate calibration of photometric redshifts
    over the redshift interval 0.3 – 3.
    The scale of residual shear errors should be set by the statistical error floors on the coad-
    ded data, not systematics. The two components of statistical shear errors vary oppositely
    with angular scale. On small angular scales (< few arcminutes) the source galaxy shear
    error is dominated by the random “shot” noise of the galaxy intrinsic ellipticities (about
    e=0.3 rms per galaxy) and the finite areal density of source galaxies. On large angular
    scales the source shear error is dominated by large scale structure cosmic variance. The
    cross-over point varies with source redshift. For all redshifts in projection, the two errors
    sum to nearly a constant statistical shear power of 3 × 10
    ? 7
    , or a source rms residual ellip-
    ticity of 0.001, over the range of angular scales for LSST WL science. The residual shear
    power systematics at all angular scales (after PSF corrections) must be less than 30% of
    the statistical shear power, including correlations between angle bins. To achieve this goal,
    the residual shear power systematics (after corrections) must be below the statistical errors
    by a factor of ∼ 3. While the statistical error is uncorrelated with angular scale (as source
    galaxies are randomly oriented), systematic errors are typically correlated. Statistical errors
    are reduced when averaged over many exposures and a broad angular band, but systemat-
    ics do not average down unless they are chopped or vary stochastically from exposure to
    exposure due to seeing. Thus there are two limiting angular regimes with different methods
    for reductions of systematics: (1) arcminute scale systematics in the residual PSF ellipticity
    correlation average down like the number of exposures [further tests are needed for large
    N], and (2) degree scale residual systematics can be reduced via chopping by dithering and
    rotating. In both cases further tests are needed to make sure residuals continue to average
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    down to the needed level.
    2.1.2 Supernovae
    Supernovae (SN) provided the first evidence that the expansion of the universe is acceler-
    ating. LSST will be a powerful SN factory (see Chapter 11 in the LSST Science Book).
    Operating in a standard mode of repeated scans of the sky with images taken every few
    days and with exposures of 30 seconds, LSST will discover of the order 10
    5
    Type Ia SN an-
    nually. Their mean redshift will be z ∼ 0.45 with a maximum redshift of ∼ 0.7. These data,
    when combined with priors from other experiments, can constrain the lowest eigenmode of
    w (i.e. the mean value) in the nearby universe to 1% (limited by systematics), and given
    the dense sampling on the sky, can be used to search for any dependence of w on direction,
    which would be an indicator of new physics. Some SN will be located in the same direction
    as foreground galaxy clusters; a measurement of the magnification of the SN will make it
    possible to model the cluster mass distribution. Core-collapse SN will provide estimates of
    the star formation rate during the epoch when star formation was changing very rapidly.
    Longer exposures (10-20 minutes/band) of a small area of the sky could extend the discov-
    ery of SN to a mean redshift of 0.7 with some objects beyond z ∼ 1. The added statistical
    leverage on the “pre-acceleration” era will narrow the confidence interval on both w and its
    derivative with redshift.
    Spectroscopic follow-up for so many SNe will be impossible. Exploitation of the data
    from the LSST will require light-curves which are well-sampled both in brightness and color
    as a function of time. This is essential to the search for systematic differences in super-
    nova populations which may masquerade as cosmological effects as well as for determining
    photometric redshifts from the supernovae themselves; the development of techniques for
    determining photometric redshifts from supernova light-curves is currently being pursued
    by several community groups. Good image quality is required to separate SNe photometri-
    cally from their host galaxies. Observations in five photometric bands will be necessary to
    ensure that, for any given supernova, light-curves in four bands will be obtained (due to the
    spread in redshift). Absolute band-to-band photometric calibration to 1% is adequate, but
    the importance of K-corrections to supernova cosmology implies that the calibration of the
    relative offsets in zero points between filters remains a serious issue, as is stability of the
    response functions, especially near the edges of bandpasses where the strong emission and
    absorption features from supernovae makes this more of a problem than for stellar spectra.
    2.2 Taking an Inventory of the Solar System
    LSST will provide data for millions of small bodies in our Solar System. Previous studies
    of these objects have led to dramatic changes in our understanding of the process of planet
    formation and evolution, and the relationship between our Solar System and other sys-
    tems. These small bodies also serve as large populations of “test particles”, recording the
    dynamical history of the giant planets, revealing the nature of the Solar System impactor
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    population over time, and illustrating the size distributions of planetesimals, which were
    the building blocks of planets (see Chapter 5 in the LSST Science Book).
    The Earth orbits within a swarm of asteroids; some small number of these objects
    will ultimately strike the Earth’s surface. The U.S. Congress has mandated that by the
    year 2008, 90% of the near-Earth asteroids (NEAs) with diameters greater than 1 km be
    discovered and their orbits determined. Impacts of NEAs of this size have the potential to
    change the Earth’s climate and cause mass extinctions, such as the one credited with killing
    the dinosaurs. A NASA report published in 2003 estimates conservatively that with current
    search techniques, about 70% of the NEAs with diameters larger than 1 km will have been be
    cataloged by 2008. This same report quantifies the risk of impacts by smaller bodies, which
    have the potential of causing significant ground damage, and recommends reduction of the
    residual hazard by another order of magnitude as a reasonable next goal. Achieving this
    goal would require discovery of about 90% of the potentially hazardous asteroids (PHAs)
    down to diameters of about 140 m. While it is unlikely that any other currently planned
    facility could achieve this goal within a decade or two, modeling suggests that the LSST is
    capable of finding 84% of the PHAs with diameters larger than 140 m within ten years.
    The search for PHAs puts strong constraints on the cadence of observations, requiring
    closely spaced pairs of observations two or preferably three times per lunation in order to
    link observations unambiguously and derive orbits. Individual exposures should be shorter
    than about 1 minute each to minimize the effects of trailing for the majority of moving
    objects. Because of the faintness and the large number of PHAs and other asteroids that
    will be detected, LSST must provide the follow-up required to derive orbits rather than
    relying, as current surveys do, on separate telescopes. The observations should be obtained
    within ± 15 degrees of the Ecliptic. The images should be well sampled to enable accurate
    astrometry, with absolute accuracy not worse than 0.1 arcsec for sources detected with the
    signal-to-noise ratio SNR > 10. There are no special requirements on filters, although
    bands such as V and R that offer the greatest sensitivity are preferable. The images should
    reach a depth of at least 24.5 (5σ for point sources) in the r band in order to probe the
    ∼ 0.1 km size range at main-belt distances. Based on recent photometric measurements of
    asteroids by the Sloan Digital Sky Survey, the photometry should be better than 1-2% to
    allow for color-based taxonomic classification.
    The LSST can also make a major contribution to mapping Kuiper Belt Objects (KBOs).
    The orbits of KBOs provide a fossil record of the early history of the solar system; their
    eccentricities and inclinations contain clues to past perturbations by giant planets. The sizes
    of the KBOs hold clues to the accretion events that formed them and to their subsequent
    evolution through collisional grinding, etc. The compositions of KBOs are not identical
    and are correlated with their dynamical state; the reasons for these differences are not
    known. Light curves can be used to constrain the angular momentum distribution and
    internal strengths of the bodies. A more complete sample of KBOs and determination of
    their properties can assist with selecting targets for future NASA missions. The survey
    for PHAs can simultaneously provide the joint color-magnitude-orbital distribution for all
    bright (r < 24) KBOs. The 100 or so observations obtained for each bright KBO can be
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    searched for brightness variations, but modeling will be required to determine how well
    periods can be extracted from observations made at random times. At the very least, it will
    be possible to determine amplitudes for many thousands of KBOs, and periods can likely
    be derived for many of them.
    Long exposures would be required to push the detection of KBOs to smaller sizes and
    reach the erosion-dominated regime in order to study the collisional history of various types
    of KBOs. KBO science would be greatly amplified if a small fraction of the observing time
    were devoted to hour-long observations in the ecliptic. This same mode of observation
    may have applications to the study of variable and transient objects. Apart from exposure
    time limits, the requirements for the KBO science are similar to the requirements for the
    detection and orbital determination for other Solar System bodies.
    2.3 Exploring the Transient Optical Sky
    The LSST will open a new window on the variable sky (see Chapter 8 in the LSST Sci-
    ence Book). Recent surveys have shown the power of variability for studying gravitational
    lensing, searching for supernovae, determining the physical properties of gamma-ray burst
    sources, etc. The LSST, with its repeated, wide-area coverage to deep limiting magnitudes
    will enable the discovery and analysis of rare and exotic objects such as neutron star and
    black hole binaries; gamma-ray bursts and X-ray flashes, at least some of which apparently
    mark the deaths of massive stars; AGNs and blazars; and very possibly new classes of tran-
    sients, such as binary mergers and stellar disruptions by black holes. It is likely that the
    LSST will detect numerous microlensing events in the Local Group and perhaps beyond.
    The LSST would provide alerts for concerted monitoring of these events, and open the
    possibility of discovering planets and obtaining spectra of lensed stars in distant galaxies as
    well as our own. LSST can also provide multi-wavelength monitoring over time of objects
    discovered by the Fermi Gamma-ray Space Telescope (formerly GLAST) and the Energetic
    X-ray Imaging Survey Telescope (EXIST). With its large aperture, the LSST is well suited
    to conducting a Deep Supernova Search in selected areas. LSST will also provide a pow-
    erful new capability for monitoring periodic variables, such as RR Lyrae stars, which can
    be used to map the Galactic halo and intergalactic space to distances exceeding 400 kpc.
    Since LSST extends time-volume space a thousand times over current surveys, the most
    interesting science may well be the discovery of new classes of objects.
    Exploiting the capabilities of LSST for time domain science requires large area coverage
    to enhance the probability of detecting rare events; time coverage, since light curves are
    necessary to distinguish certain types of variables and in some cases infer their properties
    (e.g. determining the intrinsic luminosity of supernovae Type Ia depends on measurements
    of their rate of decline); accurate color information to assist with the classification of variable
    objects; good image quality to enable differencing of images, especially in crowded fields; and
    rapid data reduction and classification in order to flag interesting objects for spectroscopic
    and other follow up with separate facilities. Time scales ranging from ∼ 1 min (to constrain
    the properties of fast faint transients such as those recently discovered by the Deep Lens
    Survey) to ∼ 10 years (to study long-period variables and quasars) should be probed over
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    a significant fraction of the sky. It should be possible to measure colors of fast transients
    on timescales of a few minutes, and to reach r ∼ 24 in individual visits. Fast reporting of
    likely transients to the community is required in order to facilitate followup observations.
    2.4 Mapping the Milky Way
    The LSST is ideally suited to answering two basic questions about the Milky Way Galaxy:
    What is the structure and accretion history of the Milky Way? What are the fundamental
    properties of all the stars within 300 pc of the Sun? (see Chapters 6 and 7 in the LSST
    Science Book).
    Standard models posit that galaxies form from seeds planted by the Big Bang with
    accretion over time playing a significant role in determining their structure. Detailed study
    of the Milky Way can provide rigorous tests of these ideas, and the LSST will be able to
    map the 3-D shape and extent of the halo of our Galaxy. Specifically, the LSST will detect
    F turn-off stars to distances of 200 kpc; isolate stellar populations according to color; and
    determine halo kinematics through measurement of proper motions at distances exceeding
    10 kpc. The LSST dataset can be used to identify streams of stars in the halo that are
    thought to provide a fossil record of discrete accretion events. The LSST in its standard
    surveying mode will be able to detect RR Lyrae variables and classical novae at a distance
    of 400 kpc and hence can explore the extent and structure of our own halo out to half the
    distance to the Andromeda Galaxy. The proper motions and photometric parallaxes for
    these stars can be used to characterize the properties of the dark matter halo in which the
    Milky Way is embedded. The LSST will survey a significant fraction of the Galactic plane,
    including the Galactic center, and will obtain unprecedented data for studies of star-forming
    regions.
    Is our solar system with its family of planets unique? Or are there many more that
    contain Earth-like planets within the so-called habitable zone? How do solar systems form?
    Detailed exploration of our local neighborhood is key to answering these questions. The
    LSST will obtain better than 3σ parallax measurements of hydrogen-burning stars to a
    distance of 300 pc and of brown dwarfs to tens of parsecs. These measurements will provide
    basic information on candidate stars that merit further study in the search for companions,
    including planets. Residuals from the fits for position, proper motions, and parallax will
    be searched for the signature of Keplerian motion to identify stars and brown dwarfs with
    companions and provide fundamental estimates of the mass of the primaries. LSST data
    will be used to determine the initial mass functions for low-mass stars and sub-stellar mass
    objects and to test models of brown dwarf structure. The age of the Galactic disk can be
    inferred from white dwarf cooling curves.
    Key requirements for mapping the Galaxy are large area coverage; excellent image qual-
    ity to maximize the accuracy of the photometry and astrometry, especially in crowded fields;
    photometric precision of at least 1% to separate main sequence and giant stars; stringent as-
    trometric accuracy to enable parallax and proper motion measurements; and dynamic range
    that allows measurement of astrometric standards at least as bright as r = 15. In order to
    probe the halo out to distances of 100 kpc using large numbers of main sequence stars, the
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    total depth (5σ for unresolved sources) has to reach r ∼ 27 (assuming 5% photometry in the
    r band at r = 25.5). To study the metallicity distribution of stars in the Sgr tidal stream
    and other halo substructures at distances out to at least ∼ 40 kpc, the coadded depth in the
    u band has to deliver 5% photometry at u ∼ 24.5. In order to constrain tangential velocity
    at a distance of 10 kpc to within 10 km/s with the most luminous main-sequence stars
    (low-metallicity blue turn-off stars with M
    r
    = 5.5), the proper motion accuracy has to be
    at least 0.2 mas/yr at r = 20.5 (1σ per coordinate). The same requirement follows from the
    decision to obtain the same proper motion accuracy as Gaia at its faint end (r ∼ 20). The
    LSST will then represent an “extension” of Gaia astrometric measurements to 4 magnitudes
    greater depth. In order to produce a complete sample of the solar neighborhood stars out
    to a distance of 300 pc (the thin disk scale height), with 3σ or better geometric distances,
    parallax measurements accurate to 1 mas (1σ) are required for stars with M
    r
    = 15. To
    obtain 3σ or better geometric distances for T9/Y0 brown dwarfs with z ? y colors measured
    with 10σ or better precision (in coadded data), parallax measurements for sources detected
    only in y band visits at 10σ significance must have an accuracy of 6 mas (1σ).
    In summary, these requirements imply that the LSST will enable studies of the distri-
    bution of numerous main-sequence stars beyond the presumed edge of the Galaxy’s halo,
    of their metallicity distribution throughout most of the halo, and of their kinematics be-
    yond the thick disk/halo boundary, and will obtain direct distance measurements below the
    hydrogen-burning limit for a representative thin-disk sample.
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    3 Detailed Description of Science Requirements
    The purpose of this Section is to lay out a common set of science requirements necessary
    to achieving a set of concrete scientific measurements, of specified accuracy, in the four
    main science areas described above. It will serve as the primary starting point for deriv-
    ing engineering project requirements to be placed upon the various technical subsystems
    that comprise the LSST. Note that some of these requirements are not fully independent
    of the existing baseline design (see Appendix A), and of realities such as seeing and sky
    brightness distribution at the selected site (Cerro Pach´on in Chile). While different sci-
    ence programs require broadly consistent datasets, the adopted values represent the most
    stringent requirements from the previous section.
    3.1 The Definitions of Specified Parameters
    For each quantity specifying a requirement, we identify two values: a minimum specification,
    and a design specification.
    The minimum specification shall represent the minimum capability or accuracy required
    of the system in order to achieve its scientific aims. If the design analysis clearly demon-
    strates that a minimum specification requirement cannot be met, the Science Council will
    reevaluate the science drivers that led to the specification, estimate the scientific impact of
    the failure to meet the specification, and report the findings to the Project Director and
    Project Manager.
    The design specification represents the system design point and will be used as the basis
    for developing engineering tolerances. At the time this document is written, we believe that
    the design specification should be achievable in the context of the existing baseline concept
    for the LSST. However, as development proceeds, it is conceivable that there may be some
    change in capability away from these values.
    In some cases, stretch goals are specified. These are desirable system capabilities which
    will enhance scientific return if they can be achieved. Stretch goals are to be pursued if they
    do not significantly increase cost, schedule or risk. To avoid complication and ambiguity, we
    do not list these in every instance; it remains understood that wherever improved capability
    is easily achievable, it should be pursued. Situations where enhanced capability beyond
    the design specification compromises cost, schedule, or other system parameters must be
    evaluated on a case-by-case basis to decide whether they make sense in the context of
    the whole system. In addition to numerical requirements, a brief reference to the science
    program that places the strongest constraints is also provided.
    3.2 Distinction between Single Image Specifications and the Full Survey
    Performance
    Detailed simulations show that the LSST will be capable of obtaining over 200,000 10
    deg
    2
    images per year, assuming 30 sec total exposure per image and realistic observing
    conditions for Cerro Pach´on. For each of these images, a decision involving at least three free
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    parameters (position on the sky and filter; assuming fixed exposure time and position angle
    of the field of view) must be made. With a simplifying assumption of only 2,000 allowed sky
    positions (i.e. a fixed grid of 10 deg
    2
    field centers tiling an area of 20,000 deg
    2
    ) and 5 filters,
    there will be over 10
    10
    different ways to execute the LSST observations over its projected
    10-year lifetime. Hence, the optimization of LSST observing strategies is a formidable
    problem that requires significant additional analysis. For this reason, only weak constraints
    for observing cadence are listed here (though integral quantities such as total depth and sky
    coverage are specified). The required properties of individual images (also known as visits,
    consisting of two co-added, back-to-back exposures), however, are specified in detail because
    they directly constrain the capabilities of the hardware and software systems. The detailed
    error budget distribution between the hardware and software systems is not considered here
    and will be addressed in a separate documents (the LSST System Requirements Document
    and the LSST System Architecture Document). As a general principle, the measurement
    errors for fundamental quantities, such as astrometry, photometry and image size, should
    not be dominated by algorithmic performance.
    3.3 Single Image Specifications
    The fundamental image properties specified in this section are
    • Bandpass characteristics
    • Image depth (attained magnitude at some fiducial signal-to-noise ratio)
    • Image quality (size and ellipticity)
    • Astrometric accuracy
    • Photometric accuracy
    There are several factors that increase the complexity of these specifications. Many of
    the image properties depend on quantities such as zenith angle (airmass), wavelength, sky
    brightness, relative positions on the sensor and within the field of view, and attained signal-
    to-noise ratio. Most of these quantities are actually distributions, and can be specified by
    a single number only in special cases, such as that of a perfect Gaussian distribution (with
    zero mean).
    We address these complexities as follows. For quantities with strong wavelength de-
    pendence, requirements are specified in each band. Where relevant, fiducial seeing and
    airmass are specified. For quantities with a strong dependence on the signal-to-noise ratio
    (SNR), requirements are specified at the bright end, defined here as the magnitude range
    between 1 mag and 4 mag fainter than the saturation limit (full well) in a given bandpass.
    Assuming that the faint end of this range corresponds to r = 20, and that 5σ depth is
    achieved at r = 24.5, the photon statistics limits on photometric and astrometric accuracy
    (SNR ∼ 200) are 5 millimag and 4 milliarcsec for a fiducial delivered seeing of 0.7 arcsec.
    Both of these limits are sufficiently small as to allow the required overall photometric and
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    astrometric accuracy described below (which include effects such as sky brightness and in-
    strumental noise, as well as various calibration uncertainties). About 1% of all the sources
    detected in a typical LSST image will be brighter than r = 20. At this magnitude, the sur-
    face densities of galaxies and high-Galactic-latitude stars are similar: about 1000 per square
    degree (implying a typical nearest-neighbor distance for stars of the order of 1 arcmin).
    We define “FWHM” as the full width at half maximum, and “rms” as the root-mean-
    square scatter. For a one-dimensional Gaussian distribution, FWHM = 2.35 rms.
    3.3.1 Filter Set Characteristics
    The filter complement (Table 1) is modeled after the Sloan Digital Sky Survey (SDSS)
    system because it has demonstrated success in a wide variety of applications such as pho-
    tometric redshifts of galaxies, separation of stellar populations, and photometric selection
    of quasars.
    Quantity Design Spec Minimum Spec Stretch Goal
    Filter complement
    ugrizy
    ugrizy
    ubgrizy
    Table 1: The filter complement.
    The extension of the SDSS system to longer wavelengths (the y band at ∼ 1 µm) is
    mandated by the increased effective redshift range achievable with the LSST due to deeper
    imaging, and the desire to study regions of the Galaxy that are obscured by interstellar dust.
    The optimal wavelength range for the y band is still under investigation. A narrow, blue b
    filter may increase the photometric redshift accuracy, but the quantitative effects of its addi-
    tion are also under investigation. The addition of the u band will improve the robustness of
    photometric redshifts of galaxies and stellar population separation, will enable quasar color
    selection and stellar metallicity estimates, and will provide significant additional sensitivity
    to star formation histories of detected galaxies (e.g. GALEX bands are redshifted to the u
    band for galaxies at redshifts of about 1, close to the median redshift for galaxies detectable
    in deep LSST images). The current design of the bandpasses is illustrated in Appendix C.
    The Number of Filters Used in a Night
    The number of filters, Nfilters, to be used on the same night is equivalent to the number
    of filters that can be simultaneously housed within the camera. It is assumed that any other
    filter from the filter complement can be inserted during the daytime, even on the shortest
    winter days.
    Specification: The number of filters available at any given time is specified as Nfilters
    (Table 2).
    Quantity Design Spec Minimum Spec Stretch Goal
    Nfilters
    5
    3
    6
    Table 2: The number of filters that can be housed simultaneously
    within the camera.
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    Specification: The maximum time allowed to switch filters already present inside the
    camera is specified as TFmax (Table 3).
    Quantity Design Spec Minimum Spec Stretch Goal
    TFmax (min)
    2
    10
    1
    Table 3: The maximum time, in minutes, allowed to switch filters already present inside
    the camera.
    The ability to rapidly switch active filters will allow more useful color measurements of
    fast transients.
    Filter Out-of-Band Constraints
    Specification: Beyond the wavelengths more than one FWHM from the filter center
    wavelength (including hardware and atmosphere), the mean transmission in any 10nm in-
    terval must be less than Fleak % of the peak value, and the integrated transmission at those
    wavelengths must be below FleakTot % of the overall transmission (Table 4).
    Quantity
    Design Spec Minimum Spec Stretch Goal
    Fleak (%)
    0.01
    0.02
    0.003
    FleakTot (%)
    0.05
    0.1
    0.02
    Table 4: Filter Out-of-Band Constraints (transmission in % of the peak value in any 10nm
    interval beyond one FWHM of the central wavelength, Fleak, and total transmission out of
    band, FleakTot).
    This requirement assures reasonable photometric accuracy for objects with extreme
    colors. For example, for a source with the color u ? i = 5, the effect of a u band red leak
    confined to the i band (e.g. see Appendix C) is limited to a 0.05 mag bias in the u band
    measurement (<0.01 mag for sources bluer than u ? i = 3).
    The temporal change of bandpasses (due to aging of the filters, changes in reflectivity
    of coatings, etc.) must be sufficiently small to enable the required photometric calibration
    accuracy (specified below, see § 3.3.4).
    3.3.2 Image Depth and the Minimal Exposure Time
    An exposure means a single readout of the camera (one of the two back-to-back exposures
    designed for cosmic ray rejection that together represent a visit to a target field). Image
    properties, such as depth (attained magnitude for point sources at some fiducial SNR, here
    taken to be 5), are defined per visit (not per exposure), and assume optimal count
    extraction algorithms (e.g. point-spread-function magnitudes). The image depth depends
    on total exposure time, bandpass, delivered image quality (dominated by atmospheric seeing
    as per image quality requirement), the sky brightness and its spatial structure, and the
    system efficiency. For a given exposure time, fiducial seeing, and sky brightness, the required
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    image depth is an indirect constraint on the system’s efficiency (assuming a fixed effective
    primary mirror diameter).
    The overall image depth distribution
    Specification: The distribution of the 5σ (SNR=5) detection depth for point sources
    for all the exposures in the r band will have a median not brighter than D1 mag, and no
    more than DF1 % of images will have a 5σ depth brighter than Z1 mag. The implication of
    many exposures only formally violates the paradigm of a single image specification in this
    section; this requirement can be understood as a probability distribution for the attained
    depth (DF1 is the fraction not of all exposures, but of those in the r band in good seeing on
    photometric dark nights and close to the zenith, corrected to the fiducial parameters listed
    in Table 5).
    Quantity Design Spec Minimum Spec Stretch Goal
    D1(mag)
    24.7
    24.3
    24.8
    DF1 (%)
    10
    20
    5
    Z1(%)
    24.4
    24.0
    24.6
    Table 5: Single image depth in the r band (SNR=5 for point sources). The D1 and Z1
    values are expressed on the AB magnitude scale and assume a source with spectral en-
    ergy distribution F
    ν
    =constant, fiducial seeing of 0.7 arcsec (FWHM), fiducial dark sky
    brightness of 21 mag/arcsec
    2
    , airmass of 1.0, and a total exposure time of 30 sec. The
    sky brightness is a conservative estimate corresponding to solar maximum. Solar minimum
    value may be 0.3-0.4 mag fainter, resulting in ∼ 0.2 mag deeper data. On the other hand,
    about ∼ 0.2 mag loss of depth is expected for data obtained at airmass of 1.4 (mostly due
    to seeing degradation).
    For a given exposure time and observing conditions, the required depths primarily con-
    strain the effective primary mirror diameter and overall (hardware + atmosphere) system
    throughput. The chosen exposure time per visit (2 × 15 sec) is a result of the survey op-
    timization and satisfies both the required final coadded depth, single visit depth, and the
    revisit time if the effective primary mirror diameter is 6.5m. The single visit depth is driven
    by transient sources and motion measurements (for both Solar System objects and stellar
    proper motions) and the coadded depth is driven by the required number of galaxies for
    cosmological studies (see § 3.4).
    The variation of the image depth (throughput) with bandpass
    Specification: The median 5σ (SNR=5) detection depth for point sources in a given
    band will not be brighter than DB1 mag (Table 6).
    The science drivers described in § 2 and the corresponding image depths listed in Ta-
    ble 6 have motivated the baseline design parameters listed in Appendix A. The assumed
    bandpasses are illustrated in Appendix C. Note that there is no requirement that exposure
    time be same for all the bands.
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    Designspec.
    u
    g
    r
    i
    z
    y
    DB1 (mag) 23.9 25.0 24.7 24.0 23.3 22.1
    Minim. spec.
    u
    g
    r
    i
    z
    y
    DB1 (mag) 23.4 24.6 24.3 23.6 22.9 21.7
    Stretchgoal
    u
    g
    r
    i
    z
    y
    DB1 (mag) 24.0 25.1 24.8 24.1 23.4 22.2
    Table 6: Specifications for the single visit depth (DB1) as a function of bandpass (the r-
    band value is identical to that listed in Table 5), assuming 2 × 15 sec exposures, a source
    with spectral energy distribution F
    ν
    =constant, airmass of 1.0, the r-band fiducial seeing
    of 0.7 arcsec (FWHM), and the r-band sky brightness of 21 mag/arcsec
    2
    (both seeing
    and sky brightness are converted to the appropriate band using standard expressions, as
    implemented in the LSST Exposure Time Calculator).
    If delivered system throughput would result in brighter limiting magnitudes for the nom-
    inal conditions, the required DB1 values could be maintained by increasing the integration
    time. For example, to account for 0.2 mag of loss in limiting depth (equivalent to about
    30% loss of throughput), the required additional survey time is about half a year for the
    u and g bands, and about 1 year for other bands, for a 10-year survey (assuming the time
    allocation per band discussed in § 3.4). However, while such strategy would deliver the re-
    quired coadded survey depth, it would have a negative impact on the single visit depth and
    time sampling frequency. The system throughput should never drop below values needed
    to meet minimum specifications for image depths listed in Table 6.
    The variation of the image depth over the field of view
    Specification: For an image representative of the median depth (i.e. with the 5σ
    detection depth of D1 mag), the depth distribution over individual devices will have no
    more than DF2 % of the sample brighter by more than Z2 mag than the median depth
    (Table 7).
    Quantity Design Spec Minimum Spec Stretch Goal
    DF2 (%)
    15
    20
    10
    Z2 (mag)
    0.2
    0.4
    0.2
    Table 7: Image depth variation over the field of view. These values apply to all bands.
    While the depth depends on the delivered image quality, the implied requirements are
    less stringent than the direct requirements on the image quality variation over the field of
    view specified below. The primary purpose of these image depth requirements is to define
    allowed variation in detector sensitivity.
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    The Minimum Exposure Time
    Specification: The shortest possible exposure time will not be longer than ETmin
    seconds (Table 8).
    Quantity Design Spec Minimum Spec Stretch Goal
    ETmin (sec)
    5
    10
    1
    Table 8: The minimum exposure time (in seconds).
    The minimum exposure time limits the ability to study fast temporal changes in bright-
    ness and position. The required specification will enable sampling of time scales three times
    shorter than the nominal exposure time. As an added benefit, it will enable an extension
    of the saturation limit ∼ 1 mag brighter than with the nominal exposures. Note that the
    requirement on relative photometric accuracy specified in Table 14 also applies to these
    shorter exposures.
    3.3.3 The Delivered Image Quality
    The delivered image quality depends on atmospheric seeing and distortions introduced by
    the system. It can be parametrized by the equivalent Gaussian width (see below) and
    the ellipticity of the delivered PSF. The deviations of the image profile from the implied
    Gaussianity are parametrized by the radii enclosing specified fractions of the total energy
    (light).
    The weak lensing studies are particularly sensitive to the delivered image quality (other
    science programs are only indirectly affected, e.g. through the dependence of the image
    depth on image size). As there is no particular threshold to be achieved in the plausible
    0.5–0.9 arcsec range, the benefit is a monotonic function of improvements in delivered image
    quality.
    The delivered image size distribution
    The delivered image size, hereafter “delivered seeing” (as opposed to atmospheric seeing),
    is expressed using the “equivalent Gaussian width” computed from
    seeing = 0.663 pixelScale
    n
    eff
    arcsec.
    (1)
    Here pixelScale is the pixel size in arcsec (0.2 for the baseline design) and n
    eff
    is the effective
    number of pixels computed from
    n
    eff
    =
    (
    ?
    f
    i
    )
    2
    ?
    f
    2
    i
    ,
    (2)
    where f
    i
    is the image intensity (i.e. the sum is over a bright star). In the limit of a
    perfect single Gaussian profile, the seeing computed using these expressions is equal to the
    FWHM (n
    eff
    = 2.27 (seeing/pixelScale)
    2
    for a single Gaussian). Note that this approach is
    insensitive to the detailed image profile, and accounts for the fact that atmospheric seeing
    cannot be described by a single Gaussian at the required level of accuracy ( ∼ 1%).
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    The image size is specified for three values of fiducial atmospheric seeing: 0.44, 0.60
    and 0.80 arcsec. These values are chosen as the three quartiles of the seeing distribution
    measured at the Cerro Pach´on site using DIMM at 500 nm, and corrected using an outer
    scale parameter of 30 m. The atmospheric seeing distribution at the Cerro Pach´on site is
    illustrated in Appendix D.
    Specification: The delivered seeing distribution across the field of view will have a
    median not larger than S1 arcsec, with no more than SF1 % of images exceeding SX times
    S1 arcsec (Table 9).
    Quantity Design Spec Minimum Spec Stretch Goal
    S1 (0.44)
    0.56
    0.59
    0.53
    S1 (0.60)
    0.69
    0.72
    0.67
    S1 (0.80)
    0.87
    0.89
    0.85
    SF1 (%)
    10
    10
    5
    SX
    1.1
    1.2
    1.1
    Table 9: The delivered seeing distributions for three fiducial values of atmospheric seeing
    (arcsec). These values apply to the r and i bands.
    The required image size is derived by assuming that the delivered image quality will be
    dominated by atmospheric seeing effects and not by the system. The design specification
    values reflect an error budget of 0.35 arcsec (for both telescope and camera, and including
    static and dynamic errors), which is added in quadrature. The minimum specification and
    stretch goal are computed using error budgets of 0.4 and 0.3 arcsec, respectively. The system
    contribution to the delivered image quality should not exceed 0.4 arcsec in any other band.
    The above design specification for the image quality requires that, for the median atmo-
    spheric seeing, the system contribution to the delivered image quality never exceeds 15%.
    This requirement should be fulfilled irrespective of the airmass, which limits the seeing
    degradation due to hardware away from the zenith (e.g. due to gravity load).
    Specification: The allowed seeing error budget due to system at airmass=2 is SXE
    arcsec (Table 10).
    Quantity Design Spec Minimum Spec Stretch Goal
    SXE
    0.52
    0.59
    0.45
    Table 10: The image quality error budget due to system at airmass=2 (arcsec).
    Assuming that the atmospheric seeing increases with airmass, X, as ∝ X
    0 . 6
    , the design
    specification for the allowed error budget due to the system (15% degradation in image
    quality) is defined at airmass of 2 and for the median seeing conditions (0.91 arcsec at
    X = 2). The minimum specification and the stretch goal are computed by scaling the
    design specification by 0.3/0.35 and 0.4/0.35, respectively, in analogy with specifications
    for the S1 parameter (see Table 9).
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    The Image Sampling
    Specification: The pixel size will be smaller than pixSize arcsec (Table 11).
    Quantity Specification
    pixSize
    0.22
    Table 11: The maximum pixel size (arcsec) to enable proper image sampling.
    The pixel size must be smaller than the first quartile of the delivered image size distri-
    bution (0.56 arcsec) divided by 2.5. This coefficient is motivated by the need to sample the
    point-spread function properly in the delivered images.
    The seeing spatial profile
    Specification: For a fiducial delivered seeing of 0.69 arcsec (S1 from Table 9 for the
    median atmospheric seeing), at least 80% of the energy will be encircled within a radius of
    SR1 arcsec, at least 95% of the energy will be encircled within SR2 arcsec, and at least 99%
    of the energy will be encircled within SR3 arcsec (Table 12).
    Quantity Design Spec Minimum Spec Stretch Goal
    SR1 (arcsec)
    0.74
    0.80
    0.70
    SR2 (arcsec)
    1.20
    1.31
    1.14
    SR3 (arcsec)
    1.66
    1.81
    1.59
    Table 12: The spatial profile (shape) for delivered seeing. These values apply to all the
    bands, as they are defined for a fiducial delivered seeing. For a different fiducial seeing, the
    SRx/seeing ratio, i.e. the shape of the delivered image, must be preserved.
    The specified values were computed using a double-Gaussian profile that is a good
    description of both typically-observed seeing profiles and that expected for Kolmogorov
    turbulence
    p(x) = G(0,σ) + 0.1G(0,2σ),
    (3)
    where G(µ,σ) is a two-dimensional Gaussian. For this profile, n
    eff
    is 31% larger than
    for a single Gaussian with the same FWHM. For a seeing of 0.69 arcsec described by this
    profile, the radii enclosing 80%, 95% and 99% of the energy are 0.67, 1.09, and 1.51 arcsec,
    respectively. Note that it would be grossly incorrect to assume that the seeing can be
    described by a single Gaussian, as the corresponding radii are 0.52, 0.71, and 0.89 arcsec.
    The design specifications were determined by multiplying the above radii by 1.1, and by
    1.2 for the minimum specifications. For the stretch goal specifications, the multiplication
    factor is 1.05. These requirements limit the deviations from the above canonical profile,
    and in particular, the amount of power in the expected power-law wings, due to the system.
    The power-law wings observed for free atmospheric seeing have a much smaller amplitude
    ( ∼ 10 times, relative to the central intensity) than the upper limit implied by the above
    requirements.
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    The image ellipticity distribution
    The image ellipticity is defined as e = (σ
    2
    maj
    ? σ
    2
    min
    )/(σ
    2
    maj
    2
    min
    ), where σ
    2
    maj
    and
    σ
    2
    min
    are, respectively, the 2
    nd
    moments of the best fit elliptical double Gaussian. The best
    fit elliptical Gaussian is used so as to minimize issues of truncation of intensity sums in noisy
    data. A double Gaussian is specified for consistency with the image size specifications above
    (the two components are assumed to have the same ellipticity and the same orientation).
    Specification: For a delivered seeing of 0.69 arcsec, in a field with a zenith distance of
    at most 10 degrees, the ellipticity distribution across the field of view for unresolved sources
    will have a median not larger than SE1, with no more than EF1 % of images exceeding the
    ellipticity of SE2 (Table 13).
    Quantity Design Spec Minimum Spec Stretch Goal
    SE1
    0.04
    0.05
    0.03
    EF1 (%)
    5
    10
    5
    SE2
    0.07
    0.1
    0.05
    Table 13: These values apply to the r and i bands.
    These values are motivated by observations showing that the ellipticity induced by
    atmospheric turbulence in a 10-second exposure in 0.69 arcsec will be in the range 0.01-
    0.02. The specification is set such that the telescope+camera system does not contribute
    appreciably to the ellipticity beyond the natural limit set by the atmosphere (e.g. tracking
    errors, jitter in the telescope). This specification does not by itself address weak lensing
    systematics, because there are schemes for removing the influence of an anisotropic PSF
    on the observed shapes of galaxies. However, it is known that these schemes leave smaller
    residuals if initially given isotropic PSFs to begin with, hence the specification that the
    telescope+camera not greatly degrade the natural limit. The overall image PSF ellipticity
    distribution is further discussed in Section 3.4 (see Table 27).
    3.3.4 Photometric Quality
    The photometric accuracy is specified through requirements on relative photometry (re-
    peatability), the system stability across the sky, color zero-points, and the transfer to a
    physical flux scale (i.e. calibration onto the AB magnitude scale).
    A broad-band photometric system, such as LSST, aims to deliver calibrated in-band
    flux
    F
    b
    =
    ?
    F
    ν
    (λ)φ
    b
    (λ)dλ,
    (4)
    where F
    ν
    (λ) is specific flux of an object at the top of the atmosphere and φ
    b
    (λ) is the
    normalized system response for the given band (the λ
    ? 1
    term reflects the fact that CCDs
    are photon-counting devices)
    φ
    b
    (λ) =
    λ
    ? 1
    S
    b
    (λ)
    ?
    λ
    ? 1
    S
    b
    (λ)dλ
    .
    (5)
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    Here, S
    b
    (λ) is the overall atmosphere + system throughput
    S
    b
    (λ) = S
    sys
    b
    (λ) × S
    atm
    b
    (λ).
    (6)
    Traditionally, the in-band flux is reported on a magnitude scale, and here we adopt AB
    magnitudes defined as
    m
    b
    = ? 2.5log
    10
    ?
    F
    b
    3631 Jy
    ?
    .
    (7)
    In order to interpret photometric measurements at the error level specified below (<1%),
    both S
    sys
    b
    (λ) and S
    atm
    b
    (λ) must be known with sufficient precision. Experience with pre-
    cursor surveys, such as SDSS, suggest that the dependence of both functions on wavelength
    have to be directly measured to break the 1% photometric error barrier (especially for
    sources with complex spectral energy distributions, such as supernovae). While the in-
    dividual normalizations of S
    sys
    b
    (λ) and S
    atm
    b
    (λ) are not required (c.f. eq. 5) to interpret
    measurements using eq. 4, the flux scale (calibration) errors affect the reported values of F
    b
    (i.e. m
    b
    ). Therefore, for each photometric measurement both F
    b
    and φ
    b
    (λ) will be reported,
    together with their estimated uncertainties. These two quantities will capture fundamental
    information included in LSST measurements, and will enable accurate transformation of
    F
    b
    to systems with similar φ
    b
    (λ) when the source spectral energy distribution is known or
    assumed. In particular, corrections to some standardized “average” LSST system, φ
    std
    b
    (λ),
    will be defined during the commissioning period for the most relevant spectral energy dis-
    tributions (such as main sequence stars and normal galaxies).
    The requirements for photometric calibration accuracy are specified using the following
    error decomposition (valid in the limit of small errors)
    m
    cat
    = m
    true
    +σ +δ
    m
    (x,y,φ,α,δ,SED,t) +∆
    m
    ,
    (8)
    where m
    true
    is the true magnitude defined by eqs. 4 and 7, m
    cat
    is the cataloged LSST
    magnitude, σ is the random photometric error (including random calibration errors and
    count extraction errors), and ∆
    m
    is the overall (constant) offset of the internal survey
    system from a perfect AB system (the six values of ∆
    m
    are equal for all the cataloged
    objects). Here, δ
    m
    describes the various systematic dependencies of the internal zeropoint
    error around ∆
    m
    , such as position in the field of view (x, y), the normalized system response
    (φ), position on the sky (α,δ), and the source spectral energy distribution (SED). Note
    that the average of δ
    m
    over the cataloged area is 0 by construction.
    This error decomposition decouples “internal absolute” calibration (i.e. producing an
    internally consistent system by minimizing δ
    m
    ), from that of “external absolute” calibra-
    tions (i.e. determining the six ugrizy ∆
    m
    values for the LSST survey). Furthermore, the
    deviation of the LSST system from a perfect AB system, ∆
    m
    , can be expressed relative to
    a fiducial band, say r,
    m
    = ∆
    r
    +∆
    mr
    .
    (9)
    The motivation for this separation is twofold. First, ∆
    mr
    can be constrained by con-
    sidering the colors (spectral energy distributions) of objects, independently from the overall
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    flux scale (this can be done using both external observations and models). Second, there are
    few science programs that crucially depend on knowing the “gray scale” offset, ∆
    r
    , at the
    1-2% level. On the other hand, knowing the “band-to-band” offsets, ∆
    mr
    , with such an ac-
    curacy is critically important for many applications (e.g., photometric redshifts of galaxies,
    type Ia supernovae cosmology, testing of stellar and galaxy SED models).
    The photometric repeatability (relative photometry)
    Specification: The rms of the unresolved source magnitude distribution around the
    mean value (repeatability) will not exceed PA1 millimag (median distribution for a large
    number of sources). No more than PF1 % of the measurements will deviate by more than
    PA2 millimag from the mean (Table 14).
    Quantity
    Design Spec Minimum Spec Stretch Goal
    PA1 (millimag)
    5
    8
    3
    PF1 (%)
    10
    20
    5
    PA2 (millimag)
    15
    15
    10
    Table 14: The specifications for photometric repeatability. The listed values apply to the
    g, r and i bands. The PA1 and PA2 values in the u, z and y bands may be 50% larger.
    This requirement, defined for bright, unresolved sources (i.e. those whose measurements
    are not dominated by photon statistics, see § 3.3), specifies the distribution of random pho-
    tometric errors, σ, and constrains both the repeatability of extracting counts from images
    and the ability to monitor (or model) the changes in normalized system response (φ). In
    practice, multiple visits will be used to compute the photometric rms for each individual
    star in each bandpass and then study its dependence on position on the sky and on the
    camera, stellar color, brightness, time, etc.
    The specified values are driven by the photometric redshift accuracy, the separation of
    stellar populations, detection of low-amplitude variable objects (such as eclipsing planetary
    systems), and the search for systematic effects in type Ia supernova light-curves. To verify
    that this requirement is fulfilled, samples of predominantly non-variable stars will have
    to be selected using appropriate color selection. Note that is sufficient to have only two
    observations to diagnose that this requirement is not fulfilled.
    The spatial uniformity of photometric zeropoints
    Specification: The distribution width (rms) of the internal photometric zero-point error
    (the system stability across the sky) will not exceed PA3 millimag, and no more than PF2
    % of the distribution will exceed PA4 millimag (Table 15).
    This requirement on the distribution of δ
    m
    (x, y, φ, α, δ, SED, t) primarily constrains the
    stability of the internal photometric system across the sky.
    The specified requirements are driven by the photometric redshift accuracy, the sep-
    aration of stellar populations, and the accuracy of inter-comparing distance moduli from
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    Quantity
    Design Spec Minimum Spec Stretch Goal
    PA3(millimag)
    10
    15
    5
    PF2 (%)
    10
    20
    5
    PA4 (millimag)
    15
    20
    15
    Table 15: The specifications for the spatial uniformity of photometric zeropoints. The
    values for PA3 and PA4 may be somewhat worse in the u band (but not by more than a
    factor of two).
    different supernovae. These requirements apply to both the bright and faint ends and con-
    strain the non-linearity of the flux scale. To verify that these requirements are fulfilled,
    samples of standard stars may be needed (an alternative is to track the shifts of morpho-
    logical features in color-color diagrams). Note that these requirements also place an upper
    limit on various systematic errors, such as, for example, a correlation of internal photometric
    zero-point error with the position on a sensor, and within the field of view.
    The band-to-band (flux ratio) photometric calibration
    Specification: The absolute band-to-band zero-point transformations (color zero-points,
    e.g. for constructing the spectral energy distribution, SED) for main-sequence stars must
    be known with an accuracy of PA5 millimag (Table 16).
    Quantity
    Design Spec Minimum Spec Stretch Goal
    PA5
    5
    10
    3
    PA5 (with u)
    10
    15
    5
    Table 16: The accuracy of color zero-points (in millimag). The second row applies to colors
    constructed using the u band photometry.
    These requirements on ∆
    mr
    are primarily driven by the desired accuracy of photometric
    redshift estimates. Note that an overall stable gray error in the absolute calibration of the
    system (∆
    r
    ) does not have an impact on the above requirements. Such an error is specified
    next.
    The overall external absolute photometry
    Specification: The LSST photometric system must transform to a physical scale (e.g.
    AB magnitude scale) with an accuracy of PA6 millimag (Table 17).
    Quantity Design Spec Minimum Spec Stretch Goal
    PA6
    10
    20
    5
    Table 17: The accuracy of photometric system transformation to a physical scale (in mil-
    limag).
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    The requirements on ∆
    r
    are driven by the accuracy of absolute determination of quan-
    tities such as luminosity and asteroid size for objects with well determined distances. Note
    that the internal band-to-band transformations, ∆
    mr
    , are required to be much more ac-
    curate as they may be calibrated and controlled by other means, and are not sensitive to
    errors in overall flux scale of photometric calibrators.
    Further notes on photometry
    The photometry of resolved sources of moderate size (effective radius ≤ 10 arcsec) must
    have comparable quality (not worse than a factor of 2 in an rms sense, with the same
    fraction of sources in the distribution tails, as per above requirements) to unresolved stellar
    sources. The photometric measurements for resolved sources (galaxies) have to include
    several standard magnitudes, such as Petrosian magnitudes, as well as appropriate model
    magnitudes.
    It is noteworthy that the technical aspects of how the required photometric precision
    and accuracy will be achieved (e.g. calibration schemes, flat-field determination, corrections
    for atmospheric effects) are purposely left out of this discussion as they belong to the
    Engineering Requirements Documents; for example, an all-sky cloud camera or new software
    algorithms (e.g. self-calibration, pioneered as u¨bercalibration by SDSS) may be needed to
    achieve the required photometric accuracy. The same approach is taken when specifying
    astrometric requirements, described next.
    3.3.5 Astrometric Quality
    The astrometric requirements are defined for bright unresolved sources (i.e. those whose
    measurements are not dominated by photon statistics, see § 3.3). The astrometric accu-
    racy is specified through requirements on relative astrometry (repeatability) and absolute
    astrometry.
    The relative astrometry
    Specification: The rms of the astrometric distance distribution for stellar pairs with
    separation of D arcmin (repeatability) will not exceed AMx milliarcsec (median distribution
    for a large number of sources). No more than AFx % of the sample will deviate by more
    than ADx milliarcsec from the median. AMx, AFx, and ADx are specified for D=5, 20 and
    200 arcmin for x= 1, 2, and 3, in the same order (Table 18).
    The three selected characteristic distances reflect the size of an individual sensor, a
    raft, and the camera. The required median astrometric precision is driven by the desire to
    achieve a proper motion accuracy of 0.2 mas/yr and parallax accuracy of 1.0 mas over the
    course of the survey. These two requirements correspond to relative astrometric precision
    for a single image of 10 mas (per coordinate).
    About 25% of blue stars (g ? r < 1) and 50% of red stars brighter than r = 20 have
    proper motions greater than 10 mas/yr. Thus, to verify that these requirements are met, it
    may be necessary to use quasars, which have a sky surface density of about 60 per square
    degree for r < 20 (implying a mean separation of ∼ 4 arcmin).
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    Quantity
    Design Spec Minimum Spec Stretch Goal
    AM1 (milliarcsec)
    10
    20
    5
    AF1 (%)
    10
    20
    5
    AD1 (milliarcsec)
    20
    40
    10
    AM2 (milliarcsec)
    10
    20
    5
    AF2 (%)
    10
    20
    5
    AD2 (milliarcsec)
    20
    40
    10
    AM3 (milliarcsec)
    15
    30
    10
    AF3 (%)
    10
    20
    5
    AD3 (milliarcsec)
    30
    50
    20
    Table 18: The specifications for astrometric precision. The three blocks of values correspond
    to D=5, 20 and 200 arcmin, and to astrometric measurements performed in the r and i
    bands.
    Specification: The astrometric reference frame for an image obtained in a band other
    than r will be mapped to the corresponding r band image such that the rms of the distance
    distribution between the positions on the two frames will not exceed AB1 milliarcsec (for a
    large number of bright sources). No more than ABF1 % of the measurements will deviate
    by more than AB2 milliarcsec from the mean. The dependence of the distance between the
    positions on the two frames on the source color and observing conditions will be explicitly
    included in the astrometric model (Table 19).
    Quantity
    Design Spec Minimum Spec Stretch Goal
    AB1 (milliarcsec)
    10
    20
    5
    ABF1 (%)
    10
    20
    5
    AB2 (milliarcsec)
    20
    40
    10
    Table 19: The requirements on the band-to-band astrometric transformation accuracy (per
    coordinate in arbitrary band, relative to the r band reference frame).
    The requirements on the band-to-band astrometric transformation accuracy are driven
    by the detection of moving objects, de-blending of complex sources, and astrometric accu-
    racy for sources detected in a single-band (e.g. high-redshift quasars detected only in the y
    band).
    The absolute astrometry
    Specification: The LSST astrometric system must transform to an external system
    (e.g. ICRF extension) with the median accuracy of AA1 milliarcsec (Table 20).
    The accuracy of absolute astrometry is driven by the linkage and orbital computations
    for solar system objects. A somewhat weaker constraint is also placed by the need for posi-
    tional cross-correlation with external catalogs. Note that the delivered absolute astrometric
    accuracy may be fundamentally limited by the accuracy of astrometric standard catalogs.
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    Quantity Design Spec Minimum Spec Stretch Goal
    AA1 (milliarcsec)
    50
    100
    20
    Table 20: The median error in the absolute astrometric positions (per coordinate, in mil-
    liarcsec).
    The time-recording accuracy
    Specification: The LSST system must record times (such as TAI) with an internal (rel-
    ative) accuracy of TACREL milliseconds and an absolute accuracy of TACABS milliseconds
    (Table 21).
    Quantity Design Spec Minimum Spec Stretch Goal
    TACREL(millisec)
    1
    1
    1
    TACABS (millisec)
    10
    10
    1
    Table 21: The requirements for the time-recording accuracy.
    The time-recording accuracy is driven by the linkage and orbital computations for solar
    system objects. An assumed nominal angular motion for a very fast object of 10 deg/day,
    and a limit on astrometric accuracy of 5 milliarcsec, yield a requirement of 10 millisec.
    The specification for internal accuracy is adopted as ten times smaller than for absolute
    accuracy.
    Auxiliary System Characteristics
    The weak lensing science may be jeopardized by systematics in shape measurements. The
    effects of ghosting, which can also contribute to systematics in the shape measurements,
    are partially addressed through photometric requirements (e.g. the fraction of objects with
    substandard photometry). The presence of ghost images which can be confused with new
    point sources and thus be a source of false transient detections must be minimized. Further
    constraints, such as maximum sensor area loss and up/down time, are addressed in the
    LSST System Requirements Document.
    3.4 The Full Survey Specifications
    By obtaining numerous images of the same area on the sky, LSST will be able to significantly
    extend the scientific reach of the single images described above. The required total number
    of images depends on each particular science program. Studies of LSST science capabilities
    performed to date have demonstrated that:
    1. It is possible to design a “universal cadence” that would result in a common database
    of observations to be used by all science programs (see Appendix B).
    2. The required survey lifetime is of the order 10 years. The strongest constraints on this
    lower limit come from the required number of images to perform robust weak lensing
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    analysis and from the minimum time baseline to obtain sufficiently accurate proper
    motion measurements. A somewhat less quantitative constraint on the upper limit
    for the survey lifetime comes from the desire to avoid “stale science” and to stay at
    the technological forefront.
    As a result of these studies, the adopted baseline design (see Appendix A) assumes a
    nominal 10-year duration with about 90% of the observing time allocated for the main LSST
    survey. The same assumption was adopted here to derive the requirements described below.
    Only visits that satisfy the requirements listed in the previous section are counted towards
    the specifications listed in this Section. For example, if the photometric accuracy falls
    below requirements due to complex atmospheric cloud structure, or due to extraneous noise
    sources inside the system, the data will not be counted. The remaining 10% of observing
    time will be used to obtain improved coverage of parameter space such as very deep (r ∼ 26)
    observations, observations with very short revisit times ( ∼ 1 minute), and observations of
    “special” regions such as the Ecliptic, Galactic plane, and the Large and Small Magellanic
    Clouds. A third type of survey, micro-surveys, that would use about 1% of the time, may
    also be considered.
    Note that some quantities relevant for science analysis are indirectly defined. For ex-
    ample, while the accuracy for photometric redshifts is not specified, it is one of the main
    drivers for the bandpass selection, required photometric accuracy per single visit, and the
    number of visits. Simulations show that the requirements described here will result in
    photometric redshift accuracy in the range 1-3% (fractional rms for 1+z over the redshift
    range 0.2-3.0, the fraction of catastrophic failures is still being investigated; also, a training
    sample of galaxies with spectroscopic redshift may be needed in order to limit systematic
    errors). This performance is consistent with the level required by the science drivers. Un-
    like photometric redshifts whose accuracy is not very sensitive to the distribution of visits
    in time, the proper motion and parallax accuracies can significantly deteriorate for some
    types of cadence strategies. Therefore, the requirements for the proper motion and parallax
    accuracies are explicitly listed.
    The sky area and distribution of visits vs. bandpass for the main survey
    Detailed simulations show that, during its nominal 10-year lifetime, LSST will be capable
    of obtaining over 2,500,000 10 deg
    2
    visits (using exposure time of 2x15 seconds). Assuming
    an effective sky area of 20,000 deg
    2
    (less than the maximum observable area from a given
    site because of airmass constraints), this implies that each position on the sky can be
    visited about 1000 times (ignoring field overlaps). The distribution of these visits among
    the bandpasses (filters) will have a direct impact on the science of the full LSST survey.
    The r and i bands should be preferentially selected over other bands because they will
    be used for shape measurements. Other bands cannot be neglected, however, because a
    broad wavelength coverage is required to achieve desired photometric redshift accuracy for
    galaxies and needed color information on transients such as supernovae. The impact of the
    visit distribution across bands can be gauged from the following two cases. If all 1000 visits
    were assigned equally to the r and i bands, their final depth, assuming
    N scaling,
    would
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    be 3.4 mag deeper than the single image depth (see § 3.3.2). If the visits were distributed
    equally over 6 bands, then the final depth would be 2.8 mag deeper than the single image
    depth. Note that the depth difference between these two scenarios is only 0.6 mag.
    Detailed simulations of LSST operations indicate that the following sky coverage and
    allocation of observing time per band satisfies a variety of science drivers at a nearly optimal
    level. However, the listed requirements should be understood only as an illustration of the
    LSST capabilities because the survey optimization is still in progress.
    Specification: The sky area uniformly covered by the main survey will include Asky
    square degrees (Table 22).
    Quantity Design Spec Minimum Spec Stretch Goal
    Asky (deg
    2
    )
    18,000
    15,000
    20,000
    Table 22: The sky area uniformly covered by the main survey.
    The design specification for the sky area uniformly covered by the main survey is a
    result of maximizing the number of galaxies detected at a fiducial signal-to-noise ratio,
    given a fixed total exposure time. The derived area corresponds to an airmass limit of 1.4
    (including accounting for the Galactic plane area and variable observing conditions), which
    assures that the delivered image size degradation as a function of airmass is not larger than
    the degradation induced by the system (see Table 9), and that the image depth degradation
    due to increased airmass is not larger than variations due to varying sky brightness.
    Specification: The sum of the median number of visits in each band, Nv1, across the
    sky area specified in Table 22, will not be smaller than Nv1 (Table 23).
    Quantity Design Spec Minimum Spec Stretch Goal
    Nv1
    825
    750
    1000
    Table 23: The sum of the median number of visits in each band across the sky area specified
    in Table 22.
    An illustration of the distribution of Nv1 is shown in Table 24. It is assumed that
    ∼ 10% of the total observing time is allocated to each of the u and g bands, and ∼ 20%
    to each of the rizy bands. These allocations reflect the dependence of the desired final
    coadded depths on bandpass, as well as a minimum number of visits in the r and i bands
    to enable exquisite control of image shape systematics. The bandpass dependence of the
    coadded depths is optimized using a mean galaxy spectral energy distribution at a redshift
    of ∼ 2. The adopted depths are also well matched to spectral energy distributions of blue
    stars ( main sequence stars will enable kinematic and metallicity studies all the way to the
    presumed edge of the Milky Way halo) and low-redshift quasars, and to those of very red
    objects (e.g., high-redshift quasars and galaxies, the coldest stars, highly reddened stars in
    the Milky Way disk). The simulations assume an exposure time of 30 seconds per visit,
    which is a result of the survey optimization using simultaneous constraints for the single
    visit depth, the number of visits, the revisit time, and the surveying efficiency (see Section
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    2.2 in the LSST overview paper, arXiv:0805.2366).
    Quantity
    u
    g
    r
    i
    z
    y
    Nv1 (design spec.) 56 (2.2) 80 (2.4) 184 (2.8) 184 (2.8) 160 (2.8) 160 (2.8)
    Idealized Depth
    26.1
    27.4
    27.5
    26.8
    26.1
    24.9
    Table 24: An illustration of the distribution of the number of visits as a function of band-
    pass, obtained by detailed simulations of LSST operations that include realistic weather,
    seeing and sky brightness distributions, as well as allocation of about 10% of the total
    observing time to special programs. The median number of visits per field for all bands is
    824. For convenience, the numbers in parentheses show the corresponding gain in depth
    (magnitudes), assuming
    N scaling. The last row shows the total idealized coadded depth
    for the design specification median depth of a single image (assuming 5σ depths at X = 1
    of u = 23.9, g = 25.0, r = 24.7, i = 24.0, z = 23.3 and y = 22.1, from Table 6), and the
    above design specification for the total number of visits. The coadded image depth losses
    due to airmass greater than unity are not taken into account. For a large suite of simulated
    main survey cadences, they are about 0.2-0.3 mag, with the median airmass in the range
    1.2-1.3.
    The coadded image depth losses due to airmass greater than unity are not taken into
    account because they depend on cadence details. For a large suite of simulated main survey
    cadences, they are about 0.2-0.3 mag, with the median airmass in the range 1.2-1.3. Table 24
    specifies the median number of visits. The actual number of visits may vary across the sky.
    For example, the regions close to the Ecliptic may benefit from longer exposures to improve
    the size and distance limit for distant solar system objects. These regions may also require
    a larger than median number of visits to improve the completeness level for small asteroids.
    On the other hand, the Galactic plane regions may have smaller than median number
    of visits (e.g. very deep images may be confusion limited). Details of such variations
    are not specified here, with an understanding that the adopted observing strategy will not
    jeopardize the goals of any of the four main science themes (e.g. the full avoidance of the
    Galactic plane would have a severe impact on the Galactic structure studies). For the same
    reason, minimum specification and stretch goal values per band are also not specified. The
    median total number of visits (824 here) is expected to be uncertain by about 10% due to
    unpredictable observing conditions and details of the final adopted observing strategy.
    Distribution of visits in time
    The LSST will be capable of observing 20,000 deg
    2
    of the sky in two bands every three
    nights. While the data obtained with such a cadence will contribute greatly to studies of
    optical transients, it is desirable to explore much shorter scales, down to 1 minute. This
    can be achieved with frequent revisits to the same field, or by utilizing field overlap. The
    details of the revisit time distribution, and its dependence on the covered area, will greatly
    depend on the adopted observing strategy and here only rough guidance is provided.
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    Specification: At least RVA1 square degrees will have multiple observations separated
    by nearly uniformly sampled time scales ranging from 40 sec to 30 min (Table 25).
    Quantity Design Spec Minimum Spec Stretch Goal
    RVA1 (deg
    2
    )
    2,000
    1,000
    3,000
    Table 25: The minimum area with fast (40 sec – 30 min) revisits.
    The requirements are derived using the universal cadence described in Appendix B as a
    minimalistic scenario. It shows that ∼ 10% of the total area can be revisited on short time
    scales by utilizing field overlaps.
    Strong constraints on the distribution of visits in time come from the goal of accurately
    measuring stellar parallax and proper motion (see Section 2.4). Irrespective of the deliv-
    ered astrometric precision, parallax measurements will not be of sufficient accuracy if the
    majority of visits are clustered around the same epoch. Similarly, proper motion measure-
    ments require that a large fraction of the observations are spread over as long a baseline as
    possible.
    Specification: The median trigonometric parallax accuracy across the main survey
    area for unresolved sources with r = 24 must be at least SIGpara mas. The median proper
    motion accuracy per coordinate across the main survey area for such sources must be at
    least SIGpm The median trigonometric parallax accuracy across the main survey area for
    unresolved sources detected only in the y band (at 10σ) must be at least SIGparaRed mas.
    (Table 26).
    Quantity Design Spec Minimum Spec Stretch Goal
    SIGpara (mas)
    3.0
    6.0
    1.5
    SIGpm (mas/yr)
    1.0
    2.0
    0.5
    SIGparaRed (mas)
    6.0
    10.0
    3.0
    Table 26: The required trigonometric parallax and proper motion accuracy.
    These requirements constrain the distribution of visits in time and are derived from
    the requirements for proper motion accuracy of 0.2 mas/yr at r = 20.5, trigonometric
    parallax accuracy of 1 mas at r = 22.4, and trigonometric parallax accuracy of 6 mas for
    red sources with only 10σ y-band detections, per Section 2.4. Detailed simulations show
    that the baseline cadence can deliver this performance for main sequence stars (Section
    3.3.3 in the LSST overview paper, arXiv:0805.2366), if the astrometric requirements from
    the previous section are met.
    Additional constraints on the distribution of visits in time come from the requirement
    to efficiently detect and characterize moving Solar System objects. In addition to their
    own science drivers, this requirement is driven by the fact that they may significantly
    contaminate samples of transients (see Section 2.3). In order to enable robust inter-night
    linking of their detections, the current baseline cadence assumes two visits per night (see
    Appendix B).
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    Distribution of visits vs. observing conditions
    Observing conditions include, but are not limited to, seeing, sky brightness (affected by
    lunar phase and time of night), transparency, and airmass. Designing a cadence which will
    optimize performance on the mixed science goals described in this document will necessar-
    ily involve some compromises between conflicting goals. The algorithm employed by the
    observation scheduler will balance these goals, take advantage of current conditions, and
    maintain as uniform coverage as possible in both time and location on the sky.
    It is assumed that the observing strategy will follow standard practices as much as pos-
    sible when selecting the bandpass and sky location of a particular visit (e.g. blue exposures
    should preferentially take place around the new moon, and bright time observations will
    avoid the moon as much as possible). However, for some transient science, especially high-
    redshift supernovae, it is critical to sample the z and y bands throughout the light-curve,
    and this will necessitate altering these standard practices to some extent. Weak lensing
    science mandates that the r and i band observations be performed in the best seeing nights,
    and at low airmass. It also requires a large range of angles between the pupil, detector, and
    sky to minimize possible systematic errors.
    Galaxy shear measurement accuracy, and PSF ellipticity residuals
    The important angular scales for weak lensing two-point shear correlation probes of dark
    energy are 10 arcminute to several degrees, where the cosmic shear correlation signal can
    get as small as 10
    ? 6
    at low redshift and several degree scales. The hemisphere sky coverage
    of LSST is needed in order to achieve the required statistical precision in these shear corre-
    lations, and to suppress cosmic variance. As explained in section 2.1, for the LSST “gold”
    sample of 4 billion galaxies (defined by i < 25.3), the resulting random component of the
    shear cross correlation noise level is about 3 × 10
    ? 7
    over this angular range up to several
    degrees. It is thus important that the systematic component be less than about 30% of this
    noise (to become negligible when added in quadrature). The requirement then is that the
    galaxy shear extraction algorithm (and system hardware) be capable of delivering this level
    of galaxy shear systematics residual. Because of the dominant galaxy shape shot noise, the
    shear errors in a large sample are dominated by PSF errors at the galaxy positions (together
    with errors in model fitting given the PSF). This then leads to a requirement on the residual
    PSF ellipticity correlations on these angular scales.
    A limit to the effectiveness of the PSF-correction schemes is our knowledge of the de-
    livered PSF within each image, which is sampled at high Galactic latitude roughly three
    times per square arcminute by a high S/N ratio star and must be interpolated at the posi-
    tions of the galaxies. (There is a color dependence, such that the stellar PSF must also be
    interpolated to the colors of the galaxies, but we do not address that issue here.)
    To address these systematics, we first define ellipticity components
    e
    1
    =
    σ
    2
    1?
    σ
    2
    2
    σ
    2
    1
    2
    2
    ,
    (10)
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    and
    e
    2
    =
    2
    12
    σ
    2
    1
    2
    2
    ,
    (11)
    where σ
    2
    1
    and σ
    2
    2
    are the 2nd moments of the stellar image along some set of perpendicular
    axes, and σ
    2
    12
    is the covariance (again, for the best-fit elliptical Gaussian). A PCA fit to
    the ellipticity components dependence on the position within each CCD is made, and we
    examine the residuals. It is the correlation of these residuals δe
    1
    and δe
    2
    , not their mean
    size, which sets the level of weak lensing systematics. We define the residual ellipticity auto
    and cross correlation functions
    E
    1
    (θ) = ? δe
    ( i )
    1
    δe
    ( j )
    1
    ? ,
    (12)
    E
    2
    (θ) = ? δe
    ( i )
    2
    δe
    ( j )
    2
    ? ,
    (13)
    and
    E
    X
    (θ)= ? δe
    ( i )
    1
    δe
    ( j )
    2
    ? ,
    (14)
    where angle brackets indicate averaging over all pairs of stars i and j at a given angular
    separation θ. Again, we use the natural limit of the atmosphere as a guide. Observations
    indicate that the residuals E
    1
    , E
    2
    , and E
    X
    are ∼ 10
    ? 4
    at scales of an arcminute and smaller
    for a 10-second exposure at 0.7 arcsec delivered seeing, falling below shot noise levels at
    θ = 5 arcmin. It is a requirement that LSST images not degrade this quality significantly.
    The defocus spectrum from atmosphere induced seeing, combined with optics astigmatism
    and FPA (focal plane array) non-flatness, produces so-called “B mode” shear (non-zero E
    X
    ).
    Using as priors the measured FPA non-flatness, the wavefront curvature measurements for
    that image, and the optics astigmatism vs. defocus data, one can optimally fit the PSF
    over the image. Similarly, requirements on these instrument parameters can be deduced
    from the science requirements on the residual ellipticity correlations.
    Specification: Using the full survey data, the E
    1
    , E
    2
    , and E
    X
    residual PSF ellipticity
    correlations averaged over an arbitrary FOV must have the median less than TE1 for θ ≤ 1
    arcmin, and less than TE2 for θ ≥ 5 arcmin. No more than TEF % of images will have
    these medians larger than TE3 for θ ≤ 1 arcmin, and TE4 for θ ≥ 5 arcmin (Table 27).
    Quantity Design Spec Minimum Spec Stretch Goal
    TE1
    2 × 10
    ? 5
    3 × 10
    ? 5
    1 × 10
    ? 5
    TE2
    1 × 10
    ? 7
    3 × 10
    ? 7
    5 × 10
    ? 8
    TEF
    15%
    15%
    10%
    TE3
    4 × 10
    ? 5
    6 × 10
    ? 5
    2 × 10
    ? 5
    TE4
    2 × 10
    ? 7
    5 × 10
    ? 7
    1 × 10
    ? 7
    Table 27: These residual PSF ellipticity correlations apply to the r and i bands.
    The residual ellipticity correlations vary smoothly so it is sufficient to specify limits
    in these two angular ranges. On 1 arcmin to 5 arcmin scales, these residual ellipticity
    correlations put LSST systematics a factor of a few below the weak lensing shot noise, i.e.
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    statistical errors will dominate over systematics. On larger scales, the noise level imposed
    by nature due to shot noise plus cosmic variance is almost scale-independent, whereas the
    atmospheric contribution to systematics becomes negligible. Therefore the specifications
    on 5 arcmin scales apply to all larger scales as well (as per section 2.1.1). On scales larger
    than the field of view, sources of systematic error have less to do with the instrumentation
    than with the operations (due to the seeing distribution), software, and algorithms. It is
    recommended that the scheduler attempt to match the seeing distribution in each patch
    of sky, so that at the end of the survey at most a small fraction of patches will have
    substantially better or worse seeing than average.
    3.5 Data Processing and Management Requirements
    Detailed requirements on data processing and management will be described in the LSST
    System Requirements Document (for example, specifications for catalog completeness and
    reliability). Here, only a rough guidance is provided. There will be three main categories
    of data products:
    • Level 1 data products are generated continuously every observing night, including
    alerts to objects that have changed brightness or position.
    • Level 2 data products will be made available as annual Data Releases and will include
    images and measurements of positions, fluxes, and shapes, as well as variability in-
    formation such as orbital parameters for moving objects and an appropriate compact
    description of light curves.
    • Level 3 data products will be created by the community, including project teams,
    using suitable Applications Programming Interfaces (APIs) that will be provided by
    the LSST Data Management System. The Data Management System will also provide
    at least 10% of its total capability for user-dedicated processing and user-dedicated
    storage. The key aspect of these capabilities is that they will reside “next to” the
    LSST data, avoiding the latency associated with downloads. They will also allow the
    science teams to use the database infrastructure to store their results.
    One of the most fundamental advantages of LSST survey is the use of individual im-
    ages and corresponding modeling of varying observing conditions (such as seeing and the
    background emission) in order to reduce systematic errors in measured parameters. Many
    types of systematic errors (those that do not decrease with exposure time or source bright-
    ness; e.g., errors in photometry due to imperfect point-spread-function modeling or due to
    flatfield errors) that will be present in individual visits will be uncorrelated between dif-
    ferent observations (for example, seeing will be uncorrelated; the data taking strategy will
    include dithering). These uncorrelated systematic errors can be significantly reduced by
    appropriate processing of data that utilizes the full knowledge of varying observing condi-
    tions. Substantial benefits of such error reduction for LSST science, together with a general
    principle that the measurement errors for fundamental quantities should not be dominated
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    by algorithmic performance, lead to the following requirements for the image processing
    software.
    Minimum Specification: observing conditions, such as point-spread function and
    background level, will be evaluated and known for each visit, and for all objects detected in
    deep coadded data and in difference images. The object properties, such as positions, fluxes,
    and shapes, will be measured for all these objects in each visit. These measurements must
    meet the design specifications from this document; more complex issues, such as deblending
    of overlapping sources and galaxy photometry, will be addressed with the best existing
    algorithms.
    Design Specification: a flexible and robust software framework that can process data
    using methods which preserve information from individual exposures, and use it to constrain
    best-fit model parameters, will be developed. This framework will not assume, nor be
    dependent on, a specific set of processing algorithms. The algorithms to be ultimately
    deployed must model point-spread function, basic extended source parameters (such as
    galaxy shapes), source blending, the impact of observing conditions and other effects, at
    least at the level required to meet the SRD design specifications for the relevant parameters.
    Stretch goal: a set of improved algorithms will be developed, meeting a general prin-
    ciple, specified at the end of section 3.2 in this document, that the measurement errors
    for fundamental quantities, such as astrometry, photometry and image size, should not be
    dominated by algorithmic performance. In other words, whenever LSST data will support
    a better performance than required by the SRD design specifications, various algorithmic
    improvements which will deliver such performance will be undertaken within the project
    resource boundaries. These algorithmic improvements will be prioritized by the project,
    guided by input from the LSST Science Council and the LSST Science Collaborations.
    Specification: Images and catalog data will be released to publicly-accessible reposi-
    tories as soon as possible after they are obtained. This latency, and the exact form of the
    data to be continuously released, are left unspecified at this time pending further discus-
    sion within the project. Data on likely optical transients, however, will be released with a
    latency of at most OTT1 minutes.
    Acknowledging that science thrives on repeatability of results, however, it is recognized
    that specific, fixed “snapshots” of the data should periodically be released so that data
    used in published analyses can unambiguously be referenced. The object catalogs in these
    snapshot data releases will include an extensive list of measured properties that will allow a
    variety of science analyses without the need to reprocess images. These catalogs and images,
    corrected for instrumental artifacts, and photometrically and astrometrically calibrated, will
    be released to public every DRT1 years (Table 28). The catalogs and images will be released
    for both single visits and for appropriately co-added data (such as those optimized for depth
    and for weak lensing analysis). The catalog data in these releases may be more extensive
    (i.e. reflect more analysis) than that released on a continuing basis. The catalogs will be
    released in a format that will allow efficient data access and analysis (such as a database
    and query system).
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    Quantity Design Spec Minimum Spec Stretch Goal
    DRT1 (year)
    1.0
    2.0
    0.5
    OTT1(min)
    1.0
    2.0
    0.5
    Table 28: Requirements for the data release cadence and for the transient reporting latency.
    The requirement on the data release cadence is a compromise between “too often”, which
    may have an impact on the system’s efficiency, and “too slow”, which may have an impact
    on the system’s science outcome and its perception within the community. The requirement
    on the transient reporting latency is essentially driven by the total exposure time, which
    sets an intrinsic scale for the time resolution of transient sources.
    The fast release of data on likely optical transients will include measurements of position,
    flux, size and shape, using appropriate weighting functions, for all the objects detected
    above transSNR signal-to-noise ratio in difference images (design specification: 5). The
    data stream will also include prior variability information and data from the same night,
    if available. The prior variability information will at the very least include low-order light-
    curve moments and probability that the object is variable, and ideally the full light curves
    in all available bands.
    Specification: The system should be capable of reporting such data for at least transN
    candidate transients per field of view and visit (Table 29).
    Quantity Design Spec Minimum Spec Stretch Goal
    transN
    10
    4
    10
    3
    10
    5
    Table 29: The minimum number of candidate transients per field of view that the system
    can report in real time.
    The users will have an option of a query-like pre-filtering of this data stream in order to
    select likely candidates for specific transient type. Users may also query the LSST science
    database at any time for additional information that may be useful, such as the properties
    of static objects that are positionally close to the candidate transients. Several pre-defined
    filters optimized for traditionally popular transients, such as supernovae and microlensed
    sources, will also be available, as well as the ability to add new pre-defined filters as the
    survey continues.
    3.6 Further Improvements and Changes
    A number of LSST-related design and scientific studies are under way that may affect
    the requirements described in this document. In addition, it is quite possible that further
    specifications may be requested during the process of distilling this document into the LSST
    Engineering Requirements Document. Any such changes to this document will need to be
    brought to the attention of the LSST Science Council, who will review the case and, if
    appropriate, propose changes to the LSST Change Control Board. Please report such, and
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    any other, concerns and comments to Zˇeljko Ivezi´c
    8
    .
    4 Authorship
    This document is the result of deliberations by the members of LSST Science Council, listed
    below, who also benefitted greatly from input from a variety of people, including, but not
    restricted to: Neil Brandt, David Burke, Kem Cook, Gregory Dubois-Felsmann, Daniel
    Eisenstein, Peter Garnavich, Perry Gee, Richard Green, Alan Harris, Lynne Jones, Tod
    Lauer, Jeremy Mould, Knut Olsen, Phil Pinto, Steve Ridgway, Abi Saha, Don Schneider,
    Mike Shara, Chris Smith, Nick Suntzeff, David Wittman, Sidney Wolff, and Dennis Zaritsky.
    The members of the LSST Science Council are: Tim Axelrod, Chuck Claver, Andy
    Connolly, Gregory Dubois-Felsmann, Kirk Gilmore, Zˇeljko Ivezi´c (chair), Lynne Jones,
    Mario Juri´c, Steve Kahn, Sebastian Lopez, Robert Lupton, Dave Monet, Don Schneider,
    Michael Strauss, Chris Stubbs, Don Sweeney, Alex Szalay, and Tony Tyson.
    8E-mail:
    ivezic@astro.washington.edu
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    Appendix A: The LSST Baseline Design
    The following tables includes excerpts from the March 16, 2010 LSST Baseline Design
    Summary (available from http://www.lsst.org/lsst/science/survey requirements) that are
    most relevant to this document.
    Excerpts from the Baseline Design Summary
    Quantity
    Baseline Design Specification
    Optical Configuration
    3-mirror modified Paul-Baker
    Mount configuration
    Alt – Azimuth
    Final f-Ratio
    f/1.234
    Field of view area
    9.6 deg
    2
    Aperture
    8.4 m
    Effective aperture
    6.68 m
    Effective ´etendue (AΩ)
    319 m
    2
    deg
    2
    Plate Scale
    50.9 microns/arcsec (0.2 arcsec pix)
    Pixel count
    3.2 Gigapixel
    Wavelength Coverage
    330 – 1070 nm
    Standard exposure sequence 41 sec total for 2x15 sec exposure
    (with slew, without filter change)
    Table 30: The LSST March 2010 Baseline Design Parameters.
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    Appendix B: The Universal Cadence Strategy
    Strict optimization of each of the numerous science programs that LSST will enable
    would certainly result in the same number of observing strategies. However, thanks to the
    large ´etendue, it is possible to design a universal cadence that would result in a common
    database of observations to be used by all science programs. An example of such a cadence
    is described here and presented as a “proof of concept” rather than as a specific requirement
    on the observing strategy. It does not address the possibility of deeper, or more frequent,
    KBO and SNe surveys discussed in § 3.4.
    This, so-called “universal cadence”, has a number of desirable properties, and in par-
    ticular, samples a wide range of time scales that are necessary for time domain science.
    Equally important, the proposed cadence is invariant to time translation and reversal, a
    feature that is desirable for a massive steady-state synoptic sky survey. More details about
    this proposal are available in the LSST Science Working Group report, and here only its
    essential characteristics are described.
    The strategy proposes two revisits closely separated in time (15-60 min) to enable a
    robust and simple method for linking main-belt asteroids (MBA). Their sky surface density
    is about two orders of magnitude higher than the expected density of potentially hazardous
    asteroids (PHA), and thus MBAs must be efficiently and robustly recognized in order to
    find PHAs. MBAs move about 3-18 arcmin in 24 hours, which is larger than their typical
    nearest neighbor distance at the depths probed by LSST (2.3 arcmin on the Ecliptic). Two
    visits closely separated in time enable linking based on a simple search for the nearest
    moving neighbor, with a false matching rate of only a few percent.
    With this cadence, it is possible to observe 20,000 deg
    2
    of sky in about three nights,
    with two visits per field. The colors of transients (such as SNe) and moving objects can
    also be measured by using two different filters for the two visits (with a preference given to
    the r band).
    Due to the proposed overlap between successive fields of view, about 17% of the observed
    area represent multiple observations with a variety of time scales. With a representative
    choice of various free parameters, about 5% of the observed area would be revisited within
    25 sec. Another 10% of the area would be reobserved with a fairly uniform sampling of
    time scales ranging from 25 sec to 15 min.
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    Appendix C: The LSST Bandpasses
    300
    400
    500
    600
    700
    800
    900
    1000
    1100
    Wavelength (nm)
    0.0
    0.2
    0.4
    0.6
    0.8
    1.0
    Throughput (%)
    LSST = solid
    Airmass 1.0
    u
    g
    r
    i
    z
    y4
    Figure 1: The current design of the LSST bandpasses (thick lines: the full throughput,
    including the atmosphere and idealized system, described by S
    b
    (λ) from eq. 6). The thin line
    shows the throughput for a standard atmosphere at airmass X = 1.0 used in computations
    (S
    atm
    (λ) from eq. 6).
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    Appendix D: The Seeing Distribution at the Cerro Pach´on site
    Figure 2: The seeing distribution measured at the Cerro Pach´on site using DIMM at 500 nm
    (red histogram), and corrected using the outer scale parameter of 30 m (blue histogram).
    For details about the outer scale correction see Tokovinin 2002 (PASP, 114, 1156). The
    lines show best-fit log-normal distributions, with the best-fit parameters as shown in the
    inset (computed by C. Claver).
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    Appendix E: The Document History
    1. Version 4.3 (September 2007) The first version approved by the LSST Board,
    placed under the Change Control Board, and made public.
    2. Version 5.1 (May 2010) The most important changes, relative to v4.3, are:
    • Incorporated references to the LSST Science Book
    • Made listed science drivers normative
    • Listed expected performance for photometric redshifts of galaxies
    • Improved quantitative drivers and specifications for trigonometric parallax and
    proper motion
    • Adopted a general principle that software algorithms should not dominate mea-
    surement errors
    • Relaxed minimum requirements for single-image depth (by 0.2-0.3 mag)
    • Made it explicit that the system throughput function is a part of photometric
    data products
    • Removed specifications for ghosting
    • Removed specifications for modeling residuals for single-image ellipticity
    • Added specification for time-recording accuracy
    • Made explicit mini and micro surveys
    • Made explicit the three levels of data products
    3. Version 5.2 (June 2011) The most important changes, relative to v5.1, are:
    • Added the first paragraph in section “Galaxy shear measurement accuracy, and
    PSF ellipticity residuals” (see Table 27).
    • Added requirements for the image processing software in Section 3.5.
    • Updated Science Council membership list.
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    Parameters Specified in this Document
    AA1
    The median accuracy of the astrometric transformation from the LSST system to an
    external system (milliarcsec). p. 24
    AB1
    The maximum rms distance between images in r and in other bands (milliarcsec). p.
    24
    AB2
    At most ABF1 % of rms distances between images in r and in other bands will be
    greater than this value (milliarcsec). p. 24
    ABF1
    The maximum fraction of rms distances between images in r and in other bands
    greater than AB2 (see AB1)(%). p. 24
    ADx
    AFx of the astrometric distances will deviate by more than this (see AMx, AFx)
    (milliarcsec). p. 23
    AFx
    The maximum fraction of astrometric distances which deviate by more than ADx
    milliarcsec (see AMx) (%). p. 23
    AMx
    The maximum rms of the astrometric distance distribution for stellar pairs with sep-
    arations of D arcmin (repeatability) (x=1,2,3 → D=5, 20, 200 arcmin) (milliarcsec).
    p. 23
    Asky
    The sky area uniformly covered by the main survey. p. 27
    D1
    The brightest median 5σ (SNR=5) detection depth for point sources for all exposures
    in a given band (mag). p. 14
    DB1
    The median 5σ (SNR=5) detection depth for point sources for all exposures in a given
    band (mag). p. 14
    41

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    waived without prior approval of the LSST Change Control Board.
    DF1
    The fraction of images with 5σ depth brighter than parameter Z1 (%). p. 14
    DF2
    The maximum fraction of images Z2 mag brighter than the median depth over indi-
    vidual devices (%). p. 15
    DRT1
    The maximum interval between public releases of “snapshot” catalog and image data
    (years). p. 33
    EF1
    The maximum fraction of ellipticities exceeding an ellipticity of SE2 (%). p. 19
    ETmin
    The minimum required exposure time (sec). p. 16
    Fleak
    The maximum permitted out-of-band flux for filters (defined as flux, normalized by the
    peak value, in any 10nm interval at wavelengths beyond those where the transmission
    curve decreases to below 0.1% of its peak value for the first time) (%). p. 13
    FleakTot
    The maximum integrated out-of-band filter transmission at all wavelengths beyond
    those where the transmission curve decreases to below 0.1% of its peak value for the
    first time (%). p. 13
    Nfilters
    The number of filters that can be housed simultaneously within the camera. p. 12
    Nv1
    The median of the distribution of the number of visits across the sky in a given band.
    p. 27
    OTT1
    The minimum latency for releasing data on optical transients (minutes). p. 33
    PA1
    The maximum rms of the unresolved source magnitude distribution around the mean
    value (repeatability) (millimag). p. 21
    42

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    waived without prior approval of the LSST Change Control Board.
    PA2
    At most PF1 % of magnitudes may deviate by more than this from the mean (mil-
    limag). p. 21
    PA3
    The maximum rms of the internal photometric zero-point error (the system stability
    across the sky) (millimag). p. 21
    PA4
    At most PF2 % of internal photometric zeropoint errors may exceed this value (mil-
    limag). p. 21
    PA5
    Color zero-points for main-sequence stars must be known to this accuracy (millimag).
    p. 22
    PA6
    The transformation from the LSST photometric system to a physical scale must be
    at least this accurate (millimag). p. 22
    PF1
    The maximum fraction of magnitudes deviating by more than PA2 from mean (%).
    p. 21
    PF2
    The maximum fraction of internal photometric zero-point errors exceeding PA4 (%).
    p. 21
    pixSize
    The maximum pixel size (arcsec). p. 18
    RVA1
    The minimum area of sky with multiple observations separated by nearly uniformly
    sampled time scales ranging from 40 sec to 30 min (square degrees). p. 29
    S1
    The maximum delivered median seeing (arcsec). p. 17
    SE1
    The maximum median ellipticity across the field of view for unresolved sources (ellip-
    ticity). p. 19
    43

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    waived without prior approval of the LSST Change Control Board.
    SE2
    EF1 % of the ellipticities may exceed this value (see EF1) (ellipticity). p. 19
    SF1
    The maximum fraction of images with median seeing exceeding S1 ∗ SX arcsec (see S1,
    SX) (%). p. 17
    SIGpara
    The trigonometric parallax error for a r=24 source (mas). p. 29
    SIGparaRed
    The trigonometric parallax error for 10σ y-band only detections (mas). p. 29
    SIGpm
    The proper motion error for a r=24 source (mas/yr). p. 29
    SR1
    The 80% encircled energy diameter for median seeing (arcsec). p. 18
    SR2
    The 90% encircled energy diameter for median seeing (arcsec). p. 18
    SR3
    The 99% encircled energy diameter for median seeing (arcsec). p. 18
    SX
    A scale factor on S1 used in defining SF1 (see S1, SF1). p. 17
    SXE
    The allowed error budget due to system at airmass=2 (arcsec). p. 17
    TACABS
    The absolute time-recording accuracy (millisecond). p. 25
    TACREL
    The internal (relative) time-recording accuracy (millisecond). p. 25
    TE1
    The maximum value for the median ellipticity correlation function on ≤ 1 arcmin scale
    for unresolved bright sources using the full survey data (hereafter ellipticity). p. 31
    44

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    waived without prior approval of the LSST Change Control Board.
    TE2
    The maximum value for the median ellipticity correlation function on ≥ 5 arcmin scale
    for unresolved bright sources using the full survey data (hereafter ellipticity). p. 31
    TE3
    At most TEF % of ellipticities for unresolved bright sources using the full survey data
    may exceed this value on ≤ 1 arcmin scales (see TE1). p. 31
    TE4
    At most TEF % of ellipticities for unresolved bright sources using the full survey data
    may exceed this value on ≥ 5 arcmin scales (see TE3). p. 31
    TEF
    The maximum fraction of ellipticities for unresolved bright sources using the full
    survey data exceeding TE3 or TE4 (%). p. 31
    TFmax
    The maximum time allowed to switch filters already present inside the camera (min-
    utes). p. 13
    transN
    The minimum number of candidate transients per field of view that the system can
    report in real time p. 34
    transSNR
    The minimum signal-to-noise ratio in difference image for reporting detection of a
    transient object p. 34
    Z1
    DF1 % of images will have a depth brighter than this value (used to describe the tail
    of the distribution) (mag) (see DF1). p. 14
    Z2
    DF2 % of images on different devices will be this much brighter than the median
    depth (mag) (see DF2). p. 15
    45

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