Dark Energy Task Force Whitepaper

A Whitepaper prepared for the
Dark Energy Task Force Committee
Rocky Kolb, Chairman

The Large Synoptic Survey Telescope (LSST)

i. Personnel and Institutions: *Brookhaven Nat'l Lab: Aronson, Haggerty, Kuciewski, Li, Lynn, Mahler, May, O'Connor, Radeka, Rehak, Takacs, Throwe Tsang; Carnegie-Mellon Univ: Kubica; Columbia Univ: Haiman; George Mason Univ: Borne; Google Corp: Pike, Rosing; *Harvard Univ/CfA: Geary, Oliver, Protopapas, Stubbs; *Johns Hopkins Univ: Nieto-Santisteban, Szalay, Thaker; *Lawrence Livermore Nat'l Lab: Abdulla, Asztalos, Baker, Brase, Carrano, Cook, Dossa, Garlick, Goldstein, Hale, Matarazzo, Miller, Nikolaev, Olivier, Phillion, Rosenberg, Seppala, Sweeney, Whistler; LSST Corp: Jacoby, Kantor, Schaefer; Microsoft Corp: Gray *Nat'l Optical Astronomy Observatory: Allsman, Barr, Claver, Isbell, Krabbendam, Liang, Mighell, Mould, Neill, Saha, Schumacher, Sebag, Smith, Upton, Warner, Wolff; Princeton Univ: Lupton; *Research Corp: Gasch; *Stanford Univ: Blandford, Kahn; *Stanford Linear Accelerator Center: Althouse, Becla, Brachmann, Burke, Gilmore, Hanushevsky, Huffer, Innes, Kim, Langeveld, Lee, Luitz, Marshall, Perl, Peterson, Rasmussen, Schindler, Thurston; STScI: Figer, Hanisch, Harris; Tohoku Univ: Takada; *Univ of Arizona: Axelrod, Barnard, Burge, Efrat, Kingsley, Moon, Pinto, Strittmatter; Univ of California-Berkeley: Franklin, Jernigan, Liu; *Univ of California-Davis: Fassnacht, Knox, Margoniner, Reese, Roat, Tyson, Wittman, Zhan; Univ of California-Santa Cruz: Schalk; Univ of Chicago: Song; *Univ of Illinois/NCSA: Beldica, Butler, Crutcher, Daues, Fleming, Pennington, Plante, Thaler, Williamson; *Univ of Washington: Becker, Carey, Hawley, Hogan, Ivezic, Owen, Silvestri; Univ of Pennsylvania: Jain; Univ of Pittsburg: Connolly; US Naval Observatory: Monet *Member Organization of the LSST Corporation

ii. Overview of Goals and Techniques of the LSST: The prime goal of LSST is a precision measure of the nature of dark energy though a suite of techniques using a homogeneous imaging dataset. Central of these is weak lens shear of galaxy shapes to z=3 by mass at z<3, giving a unique probe of dark energy. This will be done through a combination of deep-wide multi-band imaging data over 20,000 sq.deg. in a weak lensing survey of unprecedented sensitivity x volume and quality. By measuring the gravitational lens distorted shapes of billions of galaxies as a function of angle on the sky and photometric redshift out to z=3, and using galaxy P(k) from these same data together with WMAP and Planck data, LSST will constrain six eigenmodes of the dark energy equation of state parameter. The shear power spectra and 3-point correlations depend on the growth function and angular diameter distances, which are both sensitive to the equation of state of dark energy. The technique used in our forecasts is lensing tomography with the auto and cross power spectra of the lensing shear. LSST will also measure with record precision: baryon acoustic oscillations, hundreds of thousands of SNe, and clusters of galaxies - three additional cosmological diagnostics providing independent constraints on dark energy.

iii. Description of the LSST Baseline Proposal: LSST will be a large, wide-field ground-based telescope designed to obtain sequential images of the entire visible sky every few nights. The optical design involves a 3-mirror system with an 8.4 m primary, which feeds three refractive correcting elements inside a camera, providing a 10 square degree field of view sampled by a 3 Gpixel focal plane array. The total effective system throughput, A &Omega = 318 m2 deg2, is nearly two orders of magnitude larger than that of any existing facility. The survey will yield contiguous overlapping imaging of 20,000 - 23,000 square degrees of sky in 6 optical bands covering the wavelength regime 350-1100 nm.

Required LSST precursor projects

The design of LSST has benefited from experience gained with a number of current and previous moderate-scale, multi-color imaging surveys (SDSS, DLS, ESSENCE, SuperMaCHO, etc.). Many of the key developers of those projects are members of the LSST team. While LSST represents a substantial increase in size and statistical precision, we believe that most of the basic aspects of its design are sufficiently well understood at this stage that the development of additional intermediate scale precursors is not required for it to proceed forward.

However, there are some calibration issues that still need to be studied. By and large, these can be addressed with existing facilties. Of highest priority will be obtaining a deep training set for LSST grizy and ugrizy color redshifts. Spectroscopic surveys at faint limits may be plagued by selection effects that limit their utility. A good way to proceed, which we are presently pursuing, is to use ultra deep ten-band photo-z fields (like the Spitzer deep field) to calibrate LSST photo-z's. Completeness and selection effects will need to be simulated, measured, and modeled for this study.

In addition, our requirement for photometric calibration at the sub-1% level is a challenge. We are designing in an extensive calibration effort for LSST at the component level, and will use these data coupled with the sky data to derive our ultimate calibration database. In addition, we have developed an innovative radiometric calibration technique which can be performed at the system level on the mountain. This is being tested now at CTIO. Initial results look very encouraging. Since the LSST camera sensors are likely to be new devices which have not been used before for astronomy, we will also build a prototype camera early in the program, and test this at an existing telescope.

Finally, the 3D matter power spectrum needs to be calibrated in order not to degrade the cosmological errors. Figure 1 shows how the random errors in P(k) increase the errors in cosmological parameters, indicating that P(k) has to be calibrated with accuracy of ~2% in order not to degrade the error in w0 by less than 10-20%. While current accuracy in Monte Carlo calculations of P(k) on relevant scales is about 5-10%, the required level of 2% accuracy will be achievable with future numerical resources.

Error budget, sources and magnitude of systematic errors, priors

The high optical throughput of LSST enables unprecedented control of photometric and shear systematics. In addition, LSST is being designed to minimize and control system-induced systematics. The following systematics are being addressed:

The LSST survey is characterized by the following parameters: Total solid angle surveyed = 20,000 sq.deg, shear rms = 0.22, number density of galaxies = 50 per sq.arcmin. Our analysis assumes the Planck priors. The LSST imaging goal is a sky noise limited stack of at least 300 images per filter band for every patch of sky. Several billion source galaxies will be detected. The goal for the shear-redshift database is for our shear statistics to be limited primarily by the shot noise of 50-60 randomly oriented source galaxies per square arcminute. This puts constraints on the LSST telescope, camera, and survey which are being addressed in our current design effort. Systematic errors in redshifts or shear affect the precision obtainable for dark energy parameters (Huterer et. al. 2005). We briefly describe our plans for testing and controlling for systematics at the level necessary to reach our combined goal of 1% for w0.

Shear systematics

The twin requirements of LSST are (1) control of systematic shear errors, and (2) sufficient optical throughput to cover the entire visible sky multiple times per month in multiple filter bands. These are related. We know that we can achieve (1) because of weak lensing surveys already underway [see Appendix I]. The DLS data already reach a shear systematics floor within a factor of 5 of that required for LSST. New technology telescopes in good sites are routinely delivering superior image quality.

There are both multiplicative and additive shear systematics. Multiplicative systematics arise from the convolution with a finite PSF. These systematics are a function of galaxy size, requiring robust estimates of size relative to PSF (see Appendix I on DLS). For each redshift bin the shear error must be calibrated and the residual must be kept below 0.0001 shear. Additive shear systematics arise from anisotropic PSFs and also depend on galaxy size. There are two keys to controlling both of these. The first is a sufficiently large PSF correlation angle such that there are many stars at high latitude on that scale which may be used as local PSF calibrators. Together with the atmosphere fluctuations, this correlation requirement leads to a large telescope aperture (see Appendix II). The second is having hundreds of deep exposures in each passband used for shear measurement for each sky area. This enables multiple chops against the several sources of shear systematics. An advantage of the Alt-Az design is that the field rotates on the focal plane. Also, the pupil image rotates, but at a different rate. These two dimensions for chopping, each with bins of seeing, imply that at least ~200 images need to be obtained for each field. This can only be accomplished in a timescale less than ten years for an optical etendue > 300 m2 deg2. The LSST is the only facility which has yet been proposed that meets that requirement.

Color-z systematics

We require < 0.002(1+z) precision for the mean redshift of galaxies in each redshift bin. With our grizy+u band survey, estimates of color-z precision vary depending on assumptions and on technique. For LSST Connolly did n-body simulations in this system and found color-z bias ~0.003(1+z) and random error ~0.04(1+z) per galaxy, while Margoniner [see Appendix IV] used the HDF data, degraded to LSST, to find bias ~0.01(1+z) and random error ~0.07(1+z) per galaxy using all galaxy types. Much higher precision is reached using red galaxies. Here we adopt the worst case scenario. A training set of 30,000 galaxies (see section 3) per z-bin gives a sigma of 0.0004(1+z), sufficient to calibrate the mean to 0.002(1+z). Selection functions vs. magnitude are vastly different for each spectroscopic technique. Slitlet spectroscopy as a training set for 10-band color-z is a method for obtaining a wide redshift and magnitude range with good possibility of controlling and understanding the selection function.

Simulations

Based on recent data from new-technology 8 m telescopes and operations simulations [See Appendix V] using actual records from potential LSST sites, the LSST will cover 20,000-23,000 square degrees of sky with a source density of 50 per square arcminute, and a shear error floor of 0.0001. We have also performed extensive simulations of the effects of atmospheric seeing on PSF ellipticity correlations have been done [see Appendices II and III], and the results for our 8.4 m aperture are encouraging. A complete end-to-end simulator for LSST is currently under development.

Subaru and Gemini deep imaging at 15 sec per exposure: validation of shear systematics

As a further check on our ability to control shear systematics, we have recently obtained short exposures on 8 m telescopes (Gemini and Subaru). Because of the large aperture the PSF ellipticities are correlated over large angles (several arc-minutes). We have found that the improved imaging of these telescopes also results in far smaller shear systematics, even in individual images. Figure 2 shows a single Subaru image processed through our existing PSF interpolation and correction pipeline, giving residual mean shear of 7 ppm on 10 arcmin scales. Several hundred such images from a telescope built to control PSF at even greater precision will enable the control of PSF shear systematics at a level far below that required for our weak lensing goals.

E-B mode decomposition

There is information beyond tangential shear. The lensing signal is caused by a scalar potential in the lens and therefore should be curl-free. We can project each correlation function into one that measures the divergence and one that measures the curl: the so-called E-B mode decomposition. While we cannot correct the E-mode data with the B-mode, the existence of a B-mode is a useful diagnostic of systematic shear error. The current generation of weak lens surveys show significant power in the B-modes. However, the new generation of optical telescopes provide sufficient PSF control to eliminate optics induced B-modes. The LSST lensing pipeline software will deliver B-mode diagnostics live, for automated quality assurance.

LSST observational windows on dark energy

Observables in weak gravitational lensing are in principle predictable ab initio given a cosmological model. Measurements are limited mainly by instrumental systematics rather than unknown astrophysics. LSST is uniquely capable of addressing the underlying physics by exploiting a diversity of cosmic probes. LSST's multi-color deep imaging survey will provide photometric redshift information of distant galaxies to z=3. This additional information is extremely valuable in that it allows us to recover redshift information on weak lensing by subdividing galaxies into several redshift bins - i.e. to perform lensing tomography (Hu 1999, Huterer 2002, Hu 2002, Takada & Jain 2004, Takada & White 2004, Song & Knox 2004). If the galaxies can be separated into n multiple redshift bins, then we can create n shear maps. The most interesting statistical properties of these maps are the two-point functions. These n(n+1)/2 unique shear power spectra can be written as projections of the matter power spectrum along the line of sight out to some redshift. Jointly, these correlations contain enough information to break degeneracies and determine cosmological parameters, including dark energy parameters.

Weak lensing has high information content. A big advantage for lensing over CMB measurements is this ability to do tomography. The rich cosmological harvest from the CMB to date comes from measurements at a single redshift of 1100. If we know distances to source galaxies, the mass distribution and cosmic geometry can be measured as a function of redshift. WL thus has sensitivity to the evolution of dark energy. Weak lensing can be pursued from the ground because the maximal effects of dark energy occur at modest redshift around 0.5, and galaxies at z=0.5 are well resolved in deep optical imaging. The light deflection by a foreground mass is given by a product of the mass inside the impact radius and a dimensionless ratio of distances. Both of these terms are affected by dark energy and other cosmological parameters. Combining lensing data with CMB data breaks degeneracies and enables separate direct investigations of the growth of dark matter structure and multiple probes of the geometry from z~1 to the present.

The large-angle cosmic shear power spectrum

In shear-shear tomography the shear of background galaxies, binned in redshift, is cross correlated. There are tens of such co-spectra. These are quantities that can be measured as a function of cosmic time using photometric redshifts. Combining these results with those from the CMB allows constraints on the physics of dark energy (Hu & Keeton 2002). Adding cross-correlations with foreground galaxies increases the precision significantly (Hu & Jain 2004). The resulting tens of shear cross correlations vs redshift are very powerful independent probes of the expansion history (see Figure 3). It is clear that the unparalleled survey area of LSST allows a significant detection of the power spectra over a wide range of angular scales, from degree scales to arcminute scales. The source redshift dependence of the power spectra is very sensitive to cosmological parameters including the equation of state parameters of dark energy. Using galaxy P(k) from these same data together with WMAP and Planck data, LSST will usefully constrain six eigenmodes of the dark energy equation of state (see Figure 4). There is a striking difference in the modes for Type 1a supernovae vs. the modes for LSST weak lensing: Those for LSST stretch out to higher z. The reason for this is that lensing is less sensitive to the growth factor at the lower redshifts where the source density in a given redshift bin is small and the lensing window (for sources at higher z) is also small. Thus the supernovae are better at detecting changes in w(z) at lower z and LSST shear tends to be better at detecting changes at higher redshift. LSST and planned supernova surveys also have strikingly different eigenvalue spectra. The error on the amplitude of the best determined mode is quite similar for each ~0.03. But for the supernova surveys, the spectrum is much steeper. LSST has seven modes with errors smaller than unity, whereas the supernova survey has four.

The non-Gaussian information in the shear field

Another advantage of lensing over CMB measurements is that recent and/or small-scale fluctuations are non-Gaussian, so there is information present beyond the power spectrum. Research is in progress to see how much cosmological information can be extracted from higher-order behavior: N-point correlations, bispectrum, etc. For all these data analysis techniques a large number of source galaxies and coverage of a significant fraction of the sky are crucial. For large numbers of source galaxies, three-point correlations of shear vs redshift become feasible. Takada & Jain (2003) show that the bispectrum information from an LSST-scale survey is as powerful as the power spectrum in constraining dark energy parameters. Curiously, the resulting constraints on dark energy are independent of those from the other WL analyses and are subject to somewhat different systematic errors. Large data sets, such as only LSST could produce, are required. The expected errors with LSST are shown in Figure 5 (without CMB) and in Figure 6 (with CMB).

Weak lensing measurements on small scales are limited by the noise from the intrinsic ellipticities of the background galaxies. To average down this shot noise one wants deep images to maximize the number of resolved galaxies per unit area on the sky. On larger scales, one is limited by cosmic variance; we therefore need to maximize the sky coverage of the survey. A very deep survey of a significant fraction of the visible sky in enough wavelength bands to allow photometric redshifts, will enable multiple cosmological tests to be carried out. No other existing or planned observatory would be capable of such a survey.

Baryon Acoustic Oscillations

Features in the matter power spectrum, such as baryon acoustic oscillations (Peebles & Yu 1970; bond & Efstathiou 1984; Holtzman 1989; Hu & Sugiyama 1996; see Figure 7), can serve as CMB-calibrated standard rulers for determining the angular-diameter distance r(z) and constraining dark energy (Eisenstein, Hu, & Tegmark 1998; Linder 2003; Seo & Eisenstein 2003, hereafter SE03). The lowest k peak in the series of baryonic oscillations has been observed in spectroscopic redshift surveys (Eisenstein et al. 2005; Cole et al. 2005), but the samples are not large enough to provide sufficient precision for significant constraints on r(z).

Several papers have studied the prospects of measuring the baryon acoustic oscillation from photometric surveys (SE03; Blake & Bridle 2005; Glazebrook & Blake 2005). The main advantage of a photometric redshift survey, such as the LSST, is the wide coverage, which reduces the sample variance error, and deep photometry, which leads to more galaxies and lower shot noise. One may quantify this advantage with the effective survey volume Veff = &int d3r n2(r)P2(k) [1 + n(r)P(k)]-2 (Feldman, Kaiser, & Peacock 1994; Tegmark 1997), where P(k) is the power spectrum, and n(r) is the galaxy number density. Figure 8 compares the effective volumes of several existing surveys with that of the LSST. One sees immediately the unparalleled large effective volume the LSST probes.

The challenges include photometric redshift errors, dust extinction, galaxy bias, nonlinear redshift distortion, and nonlinear evolution. Despite the complexities, these uncertainties do not produce oscillating features in the power spectrum. Thus it is possible to use a photometric redshift survey to measure the angular-diameter distance accurately.

We divide the LSST photometric redshift galaxy survey into 10 bins of roughly equal width from z = 0.5 to 3.0, and then combine the 12-parameter [including r(z)] Fisher matrix of each bin with the 7-parameter CMB Fisher matrix to infer the errors on the angular diameter distance and dark energy equation-of-state parameters w0 & wa. The errors on r(z) are shown in Figure 9; they are typically around one percent. Baryon acoustic oscillations from the LSST can put constraints of roughly 0.1 on w0 and 0.25 on wa (see Figure 10), which is consistent with SE03 and Glazebrook & Blake (2005).

LSST Supernovae

LSST will find supernovae in two ways. The first is as a result of its normal operating mode providing frequent, all-sky coverage. The baseline observation strategy for the LSST survey will discover roughly 250,000 Type Ia SNe per year. This SNe Ia sample will have a mean redshift of about 0.45 and extend to 0.7. The lightcurves will typically have a sampling of approximately an observation every 5 days in the main search filter (nominally r) and 2 observations each month in other filters (e.g., g, b, and i). Such an enormous sample of SNe, and color redshifts and morphology of the host galaxies, will provide an unprecedented opportunity to search for hints to the nature of the type Ia progenitors and to search for "third parameters," especially by correlating with environmental properties. A small fraction of LSST operational time will be devoted to producing a second supernova sample, from a "staring mode" search of a more limited area of sky. After ten years, ten minutes per night spent staring at a single field will yield (with no rate evolution) 60,000 supernovae with lightcurves of unprecedented detail, typically with more than 100 photometric points per supernova in five bands. This sample will have a mean redshift of 0.75 and extend to beyond z=1.4. Such detailed lightcurves will allow fitting for photometric redshifts from the supernovae themselves; simulations show that such SN photo-zs have a typical error well below 0.01 in z. These can in turn be combined with host-galaxy photo-zs, and since the area on the sky is limited, multi-object spectroscopy can be obtained for many of these. The effect of joint SN plus shear-shear constraits is shown in Figure 11.

Discriminating the physics of acceleration with cosmic shear

Cosmic shear data provide us with an opportunity to discriminate between two very different explanations for the observed acceleration. This ability is due to the sensitivity of cosmic shear data not just to the history of the expansion rate, H(z), but also to the rate of growth of the large-scale density field. Cosmic shear depends on the mass density field as a function of redshift, since the density field is what does the lensing of background galaxies, and it depends on the history of the expansion rate, since that determines the distance-redshift relation and therefore how length scales at a given redshift project into angular separations on the sky today.

One can model the observed cosmic shear power spectra as a function of redshift by varying both g(z) and the distance-redshift relation, D(z), as independent functions. The cosmic shear power spectra are capable of constraining both separately with the same data [Song 2004]. This ability allows for a very important test. In Einstein gravity with dark energy, these two functions are not independent. With the dark energy properties adjusted to give the observed D(z), a prediction can be made for g(z). Theories of gravity with modified force laws on Mpc and larger scales will generally have different predictions for g(z). [Knox et. al. 2005]

Other LSST diagnostics of dark energy

The LSST database can also be used to address DE in yet other ways. We consider these to be secondary to the above, but they will be important diagnostics and consistency checks. Through the ultra-deep shear probe LSST will find and weigh 100,000 clusters out to z=1 which are so massive that 3-D tomography and optical confirmation (see Appendix I) ensures good completeness. Cuts vs mass(r) will enable the studies of the mass function and sample completeness necessary to extract DE parameters on which N(mass,r,z) depends exponentially. Another DE diagnostic is the time of arrival of AGN flares in multiply lensed source galaxies. In 20,000 sq.deg LSST will find ~100 such special alignments behind massive clusters, and some of these will have their mass distribution sufficiently well understood to constrain ratios of angular diameter distances for flaring sources.

LSST strengths

The LSST is the largest etendue multi-color optical imaging survey ever proposed, and as described above, it will enable a wealth of complementary analyses for constraining the properties of dark energy. LSST is unique in that it will pursue multiple probes of dark energy discussed above simultaneously. Of course, a survey of this magnitude will also enable a host of other astronomical investigations. Particularly exciting examples include: a systematic search for moving bodies in the solar system, a census of optical transients on a variety of timescales, and an astrometric map of the outer regions of the Milky Way galaxy. For these reasons, the project has wide support within both the astronomy and high energy physics communities. Several influential NAS reports (Astronomy and Astrophysics in the New Millenium, Connecting Quarks to the Cosmos) have explicitly endorsed the LSST by name. In addition, the project is highlighted in the recent Physics of the Universe report released by the Office of Science and Technology Policy.

While other smaller scale experiments may contribute to our understanding of dark energy over the next few years, we believe that none will have as sweeping and as multi-faceted an impact as the LSST. Given the present state of our ignorance on this topic, it seems well-advised to pursue the tightest constraints on the cosmological expansion that can be derived. We believe that the LSST project is well-conceived that its design is well-understood, and that it can be brought on-line by 2013 if sufficient funding is made available.

Risk Areas and pre-construction R&D

LSST's large etendue and broadband photometric accuracy requirements make non-negligible demands on current technology. Below we highlight briefly some of the key risk areas and our planned R&D program to mitigate these risks.

Telescope and site risks and development program

The LSST is a very dynamic machine, requiring novel alignment, control and robotic features not common in previous astronomical facilitiesThe LSST development program is currently focused on refining the system and component requirements, developing sound design concepts, and performing the design trade studies and analyses needed to support the chosen designs.

Telescope siting presents no special risks, but candidate sites are being considered which have limited sets of characteristic data. A program to systematically acquire consistent and comparable site data at each candidate site has been initiated and will continue throughout the pre-construction period.

The planned four year construction schedule requires significantly complete design work during the pre-construction development phase and requires that all three mirrors be purchased early using private funds under the management and technical coordination of the core Telescope and Site development team.

Camera risks and R&D program

The LSST Camera focal plane contains a large array of imagers. The risk area is the development of imagers which meet LSST's specifications on pixel size, QE, flatness, dead area and readout speed. All the specifications have been achieved in previously used CCD arrays; the development task involves integrating all the required features into a single sensor.

The risk is being mitigated in a number of ways. First, we are pursuing two different technologies - both CCD and hybrid PIN-CMOS sensor arrays. Both have the capability of meeting LSST specs and both have potential vendors interested in the required development. Second, we are proceeding in a stepwise approach with all potential vendors, to explore the key risk areas for both technologies in an LSST Sensor Development Program, which is now under way. This program and its associated R&D are described in section f.1 below.

LSST's fast optics produce a very narrow depth of field which requires that the focal plane be flat within 10 µm. The R&D program for the LSST camera will focus on understanding the best techniques to employ to keep the focal plane flat to the high precision tolerances required. Initial studies will include the development of various motion control scenarios to actively maintain flatness of the raft (3x3 detector array) under a variety of thermal and mechanical conditions. The integrating structure(s) will be subjected to rigorous mechanical and thermal tests to identify and isolate any potential problem areas.

LSST filters present special fabrication challenges to achieving spatially uniform passband characteristics necessary to do <1% photometry. These include achieving the necessary thermal and mechanical stability. A development program with an industrial partner is planned, with the goal of fabricating a full-scale prototype which demonstrates the necessary performance characteristics over the full field. This planned work includes collaboration with PanStarrs and other current programs.

Data management risks and development program

LSST will produce about 15 terabytes of high quality science image data per night (uncompressed). Key risk areas to be addressed by the data management development program include: achieving required precision in PSF and photometry estimation and reconstruction; achieving a suitably low false alarm rate for transient alerts; establishing scalability in object association pipelines; establishing the requisite frameworks and infrastructure for handling and delivering the high precision high rate data to the science pipeline processing; and designing effective algorithms for extracting the desired science output data sets in a manner which keeps up with the high data rate and adapts to evolving definitions of the technical systems and the desired science output.

The data management team's goals during the pre-construction development period include developing an organization which can analyze the risks and develop and demonstrate effective solutions. In addition, the data management team will develop subsystem requirements, architecture and design, and validate their functionality, scalability and extensibility with demonstration prototypes. These prototypes will be based on extensions of existing technology and integrate pre-cursor data, pipelines and infrastructure.

The proposed LSST meets the requirements for the LST

The LSST clearly is a candidate for the "LST" slot which has been identified in the DETF charge as a long-term goal for addressing dark energy science. In fact, the acronym LST is now used to refer to the project called "LSST" in various NAS and other reports. Those reports call for an optical imaging survey instrument with an etendue of > 250 m2 deg2. As presently designed, the LSST will have an etendue of 318 m2 deg2. As detailed below, the LSST build schedule will enable first light in 2013.

Related facilities

The LSST project has been able to use existing observatories and facilities to enhance the expected performance of the LSST and reduce risk. Our twelve member institutions and extensive scientific collaboration gives us access to a broad range of related facilities. Of course, we rely on (and many of us work on) the precursor projects discussed elsewhere.

For example, the LSST project has just completed a coordinated campaign using the SOAR and Gemini South telescopes, the CTIO weather station, DIMM and MASS instruments on Cerro Pachon to capture simultaneous atmospheric data to validate our model of atmospherically-induced PSF shape systematics. As discussed elsewhere, we have collected short-exposure data from the Subaru telescope to understand the effect of aperture size on atmospheric residual shear. We are using Don Figer's laboratory at the STScI and Mike Lesser's laboratory at the Steward Observatory to characterize our CCD and Hybrid CMOS focal plane sensors. All of the facilities at Kitt Peak, CTIO and Cerro Pachon are available, with modest conditions, for our use. We have already made extensive use of the Mayall, Blanco, and WIYN telescopes. We also have limited-scope collaboration agreements with Pan-Starrs and TMT. With Pan-STARRS we are working together on software for dynamic scheduling; with TMT we are sharing site data on a common site candidate. These early collaborations will grow and further leverage all our capabilities.

LSST schedule

As shown in Figure 12, the LSST schedule calls for first light by the end of 2012. This is a reasonable technical schedule if the funding schedule is also maintained. Since major funding from the government is years away (4+ years before NSF construction funding), the key is early private funding to jump-start critical-path items in technology and construction.

The overall budget for the construction of the LSST is $270M in 2004 base-year dollars. That funding will come from the NSF and the DOE and $50M from private sources. We currently have reason to believe NSF will begin funding our Design and Development Proposal this fiscal year. Plans call for NSF MREFC funding to begin in calendar year 2009; this requires submission of the MREFC proposal by the end of 2006. Three national laboratories (SLAC, BNL, and LLNL) are already spending DOE lab funds to develop the baseline LSST camera design. We have reason to believe the DOE Office of Science will initiate a Phase 0 statement of mission need for a ground-based dark energy observatory.

Private sources provide the key jump-start funding to realize first light in 2012. Current private funding includes $10M from the Research Corporation to operate the project office and enable essential long-lead design and development. Richard Caris, an Arizona philanthropist, has committed a minimum of $10M to purchase the LSST primary mirror. The primary mirror will be cast by the end of 2005 and be completed by about 2011. A generous private gift by the founder of the Las Cumbres Observatory is funding a commercial R&D effort to develop our required focal plane sensors. This critical-path project is discussed elsewhere in the paper.

Finally, the LSST has already teamed with the National Center for Super Computer Applications at the University of Illinois (an NSF Center) to provide data processing and data storage. The LSST does not need to schedule or fund building its own world-class computer facility.

REFERENCES

FIGURES

Figure 1 This plot shows how the random errors in P(k) increase the errors in cosmological parameters &)megade, w0 and &sigma8, relative to the marginalized error. The results indicate that P(k) has to be calibrated with accuracy of a few percent (1% for &sigma8, 5% for &Omegade and 2% for w0) in order not to degrade the cosmological error by more than 10-20%. In other words, most information on dark energy parameters come from the lensing geometric factor, provided the redshift distribution of galaxies is known (Huterer, Takada et al. 2005). While current accuracy in P(k) on relevant scales is about 5-10%, the level of 1-2% accuracy will be achievable with future numerical resources.

Figure 2 This plot shows the stellar PSF in a 10-second i-band Subaru exposure (one chip), taken with the guider off, at three stages of processing. On the left is the raw PSF shear of the stars in the field - average value 0.03. Black dots are e =0. In the middle, the common mode trailing was taken out. Some shear correlations remain. On the right application of a smoothly position-dependent rounding filter reduces the mean shear on 10 arcminute scales to 7 ppm. With good guiding, and especially the crisp optics of LSST, the starting PSF asymmetry will be much lower. This is confirmed in our recent Gemini imaging. See Appendices II and III for more discussion.

Figure 3 This plot shows the lensing shear power spectra constructed from 5 redshift bins. Only the 5 auto-power spectra of each redshift bin among the available 15 spectra are displayed, and the solid curves show the predictions for the concordance ΛCDM model. The power spectrum amplitude increases with lensing of galaxies at higher redshift. The boxes show the expected one-sigma measurement error due to the sample variance and intrinsic galaxy ellipticities (the sample variance is dominant at about l<1000, while the intrinsic ellipticities are dominant at l>1000).

Figure 4 Eigenvalues and first three eigenmodes of the w(z) error covariance matrix for LSST WL+Planck and JDEM 2000 SNe+Planck. The best-determined mode for each dataset has a standard deviation of about 0.03. This error rises quite slowly with increasing eigenmode number for the lensing data, reaching one only by the 7th mode. The eigenmode shape differences indicate that lensing is better at probing higher z while supernovae have their chief advantage at lower z.

Figure 5 68% C.L. constraints in two parameter space for the dark energy density parameter &Omegade and its equation of state parameters given by w(a)=w0+wa(1-a). The ΛCDM model is assumed for the fiducial, angular models of 50

Figure 6 Similar to Figure 5 except that Planck priors were used. It is clear that the bispectrum tomography improves parameter constraints by a factor of 2 compared to just power spectrum tomography, reflecting that the non-Gaussian signal in weak lensing provides additional cosmological information that cannot be extracted by the power spectrum. (Hu 2002; Takada & Jain 2004; Song & Knox 2004).

Figure 7 Baryon acoustic oscillations. Left panel: Expected results for 5 of the 10 redshift bins from the LSST survey. We use a galaxy distribution of n(z) = 640 z2 e-z / 0.35 arcmin-2, which gives rise to a projected galaxy counts of 54.4 per arcmin2. To avoid nonlinear effects, we only consider k ranges where fluctuations in logarithmic k-bins are less than 0.25, i.e. &Delta2(k) < 0.25. Upward shifts in increments of 0.1 are added for better readability. Each slice is 400-500 h-1Mpc thick and is centered at the redshift shown. The rms photometric redshift error takes the form of &sigmaz = &sigmaz0 (1 + z). The statistical errors are dominated by the sample variance on large scales, which is more pronounced at low redshift, and the shot noise and rms redshift error on small scales, which becomes more noticeable at high redshift. Right panel: The same as the left panel, but for a spectroscopic survey over 1000 deg2.

Figure 8 Effective survey volumes. The survey data except that of the LSST are from Eisenstein et al. (2005). The LSST survey parameters are the same as in Figure 6. The curve labeled with 0.01n(r) applies to the case where a sub sample of galaxies is selected for statistics.

Figure 9 Error forecasts for the angular diameter distance r(z). Following Seo & Eisenstein (2003, SE03), we combine CMB priors from the Planck mission in the Fisher matrix analysis. The resulting distance errors in 10 redshift bins from the LSST are shown for different survey qualities: the same as that in Figure 6 (solid line), twice the rms photometric redshift error (dotted line), and a tenth of the galaxy density (dash-dotted line). The error is roughly proportional to &sigmaz01/2, in agreement with SE03. For comparison, we include errors for the spectroscopic survey in the right panel of Figure 6 (S1000, dashed line) and the baseline survey in SE03 (solid circles). We also scale the baseline survey in SE03 to the LSST (open circles) with a scaling of (&sigmaz0Veff)-1/2. Since we calculate the scaling factor conservatively at the maximum wavenumber of each redshift bin, the resulting errors are a little larger than those of the LSST with &sigmaz0 = 0.04.

Figure 10 Error forecasts for w0 & wa in two cosmologies. One sigma error contours in the w0-wa plane for LSST simple shear-shear power spectrum tomography (dashed contours), LSST baryon acoustic oscillations (solid contours), and JDEM 2000 SNe (dash-dotted contour), where w(z) = w0 + wa(1 - a). LSST results combine CMB priors from the Planck mission in Fisher matrices. One may significantly increase the constraining power in this plane and on w(z) generally by combining CMB, baryon oscillations, weak lensing (shear-shear and also bispectrum), and SNe together, though investigations must be carried out to address the cross-correlation between baryon oscillations and weak lensing statistics before quantitative conclusions can be reached. As an example of joint constrains, Figure 10 shows this for the case where we combine only the WL shear-shear spectra and SNe.

Figure 11 w0 & wa error forecasts for combining SN and simple shear-shear power spectrum observations only. One sigma error contours in the w0-wa plane for LSST shear survey (G2&Pi), JDEM 2000 SNe, and the combination. The dashed curve is for LSST with the source density uniformly decreased by a factor of 2. With the over 50,000 SNe which will be followed by LSST in the first few years, the size of the joint error is competitive with the shear-shear plus shear bispectrum tomography limits, but with uncorrelated systematics. Adding LSST bi-spectrum and baryon acoustic oscillation observations will significantly shrink the errors. But the main advantage of this suite of LSST dark energy probes will be as a cross-check on low level systematics.

APPENDICES

Appendix I

LSST Precursor: Deep Lens Survey

The Deep Lens Survey (DLS, Wittman et al. 2002) is a significant LSST precursor in several ways. Observationally, it is a ground-based survey going to roughly LSST depth in a similar range of passbands (BVRz for DLS, grizy for LSST) and with similar observing strategy (multiple visits to each field, observing in one filter reserved for lensing analysis during periods of good seeing). Scientifically, it proves some of the techniques which LSST will employ on a much more massive scale (~20,000 deg2 rather than 20 deg2). A key difference to keep in mind, though, is that DLS was conducted as a guest program on decades-old facilities (the CTIO and KPNO 4-meters), while LSST is a modern, purpose-built facility engineered from the start to minimize systematics and able to keep them minimized on an ongoing basis. In addition, the better angular resolution of LSST (already reached by modern facilities such as Subaru and Magellan) means that more of the distant galaxies are resolved, increasing the lensing information content even at the same photometric depth.

Cluster Counting

After five years, the DLS has almost finished taking data and some early science results are coming out. The most relevant of these is the shear-selected cluster sample. Recall that cluster counts as a function of mass and redshift are an important constraint on dark energy through its effect on the growth of structure. Dark energy scenarios which are degenerate under WMAP can be distinguished with a sample as small as a few hundred clusters (Hennawi et al 2001). However, this assumes that the relation between the predictable quantity (mass, from theory or n-body simulations) and the observable (typically X-ray or optical emission) is well characterized. This relation has been the weak point of traditional cluster surveys; the observable depends on star formation history, dynamical state, baryon content, or a combination of these factors. Shear selection should provide a very clean comparison with theory, because it is based only on mass and redshift. The weakness of shear selection, in principle, is that it is susceptible to line-of-sight projections. To date, however, there are no shear-selected samples, only scattered serendipitous discoveries.

In a paper soon to be submitted, Wittman et al (2005) show that of eight shear-selected clusters in the first installment of the DLS sample, seven correspond to real clusters with X-ray emission and spectroscopically confirmed redshifts, and only one is a projection.

This proves that shear selection is a viable technique and will be an important tool for constraining dark energy from a deep, wide optical imaging survey. Furthermore, Wittman et al (2001,2003) introduced tomography as a verification technique. That is, shear around a given cluster candidate must increase with source redshift in a particular way, if the candidate is a real cluster. It is not yet known if tomography would have accurately diagnosed the one projection in the DLS sample, but that will soon be known.

In most cases the agreement between shear and X-ray observations is excellent.

In addition to a verified cluster sample, one can constrain dark energy through counts of shear peaks, regardless of their status as true three-dimensional clusters. This preserves the clean comparison with theory that is a virtue of shear selection, while discarding some redshift information. And of course, one can do optical cluster selection from the same imaging data taken for the shear selection. Optical selection is in fact much easier in terms of demands on the imaging, because it looks at the member galaxies rather than background sources, and at photometry rather than shapes. If the shear-selected sample proves that the optically-selected sample is not biased toward low mass-to-light ratio, or has a bias that is calibratible and correctable, then the larger optically-selected sample can be used. Those analyses are currently being carried out on the DLS data (figure below).

From the first installment of the DLS shear-selected sample, we estimate that ~2 clusters deg-2 can be detected with 5&sigma confidence in the DLS data. LSST goes roughly as deep, so 40,000 shear-selected clusters is a conservative estimate for LSST. The estimate is conservative because LSST will have better image quality, thus resolving more galaxies and reducing shot noise. The redshift range covered by the DLS sample is 0.19 to 0.68.

Cosmic Shear

An entirely complementary analysis of the same shear dataset is cosmic shear. This is perhaps the more compelling science goal for LSST, but for DLS the clusters came first because they could be done incrementally. Now that the DLS dataset is essentially complete, analysis is shifting to cosmic shear. In Margoniner et al (2005) we presented our first detection of cosmic shear and demonstrated that it rose with source photometric redshift in roughly the way that is expected. We are in the process of calibrating the shear and estimating the systematics. A rough indication of the level of systematics to expect can be seen from Jarvis & Jain (2005), who introduced a new method of interpolating the point-spread function (PSF) which reduced their systematics to a level which is zero within the shot noise. Their survey was conducted at CTIO, on the same 4-meter which took 60% of the DLS data. However, a substantial fraction of their data was taken with an earlier camera with significantly worse PSF systematics. Therefore it is entirely reasonable to expect that DLS systematics can also be controlled to a level comparable to the shot noise. For much larger survey, however, the shot noise level is much lower, and controlling systematics to that much-reduced level will be a major challenge, for which an appropriate response is designing and building a new facility from the ground up.

Algorithms

The DLS differs from other current weak lensing surveys in having 20 exposures on each piece of sky in each filter. In this respect it is somewhere between most current weak lensing surveys which have just a few, and LSST, which will have hundreds. Because seeing varies with each visit, it is natural to ask how to get the most information out of this dataset in the presence of variable seeing. With better seeing, more galaxies are resolved and more lensing information is available. The usual method of producing a "stack"---essentially taking the mean of the exposures to produce a single higher signal-to-noise image---and measuring galaxy properties on the stack, does not preserve all this information.

The first step in controlling this is during the observing: the DLS observes in R band only when the seeing is better than 0.9", and uses only the R band for the lensing shape analysis. The LSST will have a similar strategy for r and i bands, with a cutoff of 0.7" to match the better median seeing of a modern facility with carefully controlled "facility seeing" (local effects not due to the free atmosphere).

Still, there will be some variation in seeing even in the lensing-dedicated bands, and one would like to use the shape information contained in the "non-lensing" band data taken in seeing which is not too far above the threshold. Therefore we are developing a scheme for the DLS which is entirely applicable to the LSST: for each galaxy, fit for a model galaxy shape which, when convolved with the n different PSFs, bets matches the n different observations. The initial list of galaxy positions and starting shape estimates is extracted from a first-pass stack, which need not be of superbly high quality because it only provides the starting point. This scheme is illustrated in the figure below.

This scheme will maximize the information retrieved from ground-based lensing surveys with variable seeing. In addition, it has the great virtue of converting systematic PSF errors into random ones. That is, with the stack method, there is one measurement of the galaxy shape and one estimate of the PSF. Mis-estimation of the PSF is then a systematic error. With this method, mis-estimation of the PSF will occur independently for each of the n exposures, and will behave as a random error for the fitter.

References

Appendix II LSST Science End-to-End Simulator: Implications for Weak Lensing

Simulator Purpose and Design:

We have developed a science end-to-end simulator for the full LSST system. The organization of the models for each component is based on a Monte Carlo history of each photon emitted by sky objects such as galaxies or stars. The input to the simulator is a model of the sky composed of galaxies and stars with their associated spectral energy distributions in the form of images with a fine spatial resolution much better than the LSST resolution. Multiple versions of the models can be simultaneously realized as a series of photons with precise sky locations and wavelengths. The final synthetic sky can be as simple as a grid of stars or as complex as a series of shells in z that comprise a 3D cosmological model composed of nearby stars, galaxies at intermediate z associated with dark matter and distant galaxies at high z that are distorted by the gravitational lensing of the emitted photons as they pass through dark matter at intermediate z. This versatility supports simulations of many types ranging from evaluation of PSF effects of the atmosphere on the images of stars and galaxies to the simulation and full analysis of a particular cosmological model. Also space-based images with fine angular resolution can be used directly as input sky models. The concept end-to-end refers to the history of the photons from the sky model, through the layers of the atmosphere, into and through the optics of LSST, and finally the conversion of the photon into an electron that diffuses in the depletion layer of a Si detector that is readout as charge detected in a single pixel. The wavelength dependence of the photons is modeled at all stages of the simulation process. The fidelity of the current version of the simulator is designed to include all details that affect science performance with an emphasis on weak lensing. Future versions will include details to support other science topics and secondary effects on weak lensing.

The atmosphere is modeled by a series of layers each with an independent 3D Kolmogorov model that is averaged into an equivalent screen with refractive index variations in 2D (Figure 1). Each layer has an outer scale, a random realization of gaussian amplitude phase independent Fourier modes with a seeing for each layer set by the Fried parameter R0. The time dependence of the atmospheric seeing is modeled by the frozen translating screen approximation with a wind velocity and direction. The single photon history is traced through each layer of the atmosphere via a newly invented technique that avoids the need to do Fourier transforms of the wavefront perturbations. The approach is only valid for large aperture telescopes with exposure times of at least 10-20 seconds. A practical weak lensing simulation requires this approach since each photon from a faint galaxy (only 1000s) in a single integration (15 seconds) occurs at a different time within the exposure window for which the atmospheric structure has changed significantly. We can avoid Fourier transforms because the diffraction effects are averaged over a modest exposure (15 seconds) and over a large aperture (8 m). The figure below shows an example of a single Kolmogorov phase screen that spans a region of the atmosphere much larger than the aperture of the telescope. This allows for wind drifts during the exposure and for full wide field (3.5 degree diameter) images.

Fig 1: Phase screen of atmospheric turbulence

We have constructed a geometric raytrace code for the LSST design optics. The raytrace handles reflection/refraction after calculating ray intercepts. The full wavelength-dependent refraction and filter transmission effects as well as stray light are included. Figure 2 shows the current LSST design and shows rays being reflected and refracted through the optics: the three mirrors, three lenses, the filter, and detector. On the surfaces of all the mirrors we currently apply a set of perturbations consisting of a set of orthogonal functions with a power spectrum resembling realistic perturbations found with the Kitt Peak 4m telescope when the active optics control system was operating. This model is designed to mimic the surface perturbations expected from thermal and mechanical distortions while a modern control system is being used.

Fig 2: Raytrace of LSST optics

The current detector model built into the simulator treats conversion of individual photons into charge carriers collected at the channel. Each ray is refracted into the silicon according to its wavelength and incidence angle. The photon either interacts or doesn't interact, depending on its absorption range (dependent on wavelength and temperature of the silicon). The charge diffuses laterally during the time it takes to drift to the channel. The amount of diffusion is dictated by the strength of the electric field at the point of interaction.

The resulting PSF has limiting behavior in the two extremes of the instrument's band. The short wavelength achromaticity is broadened further by shallow interaction distribution in the CCD (contributing ∧=4∧m in each lateral dimension). On the long wavelength end, the PSF is dominated by the beam's refraction through the thick (100∧m) silicon, combined with the large interaction length.

Figure 3 shows a simulation of the Hubble Ultra Deep Field simulated through the LSST end-to-end simulator. Every photon was raytraced using complete wavelength-dependent effects through 12 layers of atmospheric turbulence, the complete LSST designed optics, and the detector. Stars and galaxies were simulated from the UDF and sky noise background was added. Fields such as this are being used to practice analysis algorithms and evaluate the performance of the design of LSST for weak lensing systematics. The complete end-to-end simulation of a 800"x800" image (one CCD chip) takes only 20 hours on a single workstation due to extensive effort to make the code run as fast as possible. Approximately 3x108 photons were simulated. Important simulation results are highlighted in the following section.

Fig 3: A small piece of a simulation of the Hubble UDF through the atmosphere and LSST optics and detector.

Implications for Weak Lensing Systematics:

The ellipticity of the point spread function (PSF) of any ground based telescope depends both on the properties of the atmosphere and the design and operation of the telescope and detector. Understanding the ellipticity of the PSF and its correlation across the field is critical to the success of weak lensing measurements. In particular, any residual uncorrectable ellipticity represents a floor that prevents the detailed measurements of arbitrarily low shear values.

Our simulations demonstrate that the ellipticity may receive similar contributions from the optics and the atmosphere (1 to 2% for each), which is similar to the shear from a massive foreground cluster of galaxies. The optics contribution to the ellipticity of the PSF, however, is highly correlated on several hundred arcsecond scales. This is due to the fact that the secondary and tertiary mirrors in the LSST optics chain are relatively close to the pupil plane. Photons emitted from all points in the field of view see a similar part of the surfaces of all the mirrors. Every perturbation, therefore, affects the PSF across the field of view in a similar way. While it is important to control the overall ellipticity induced by the optics in the design of LSST, it is anticipated from these simulations that the optics contribution the ellipticity of the PSF will be easily correctable, since it is highly correlated. Studies are continuing to identify other instrumental problems that could affect weak lensing measurements.

Figure 4 demonstrates the expected PSF function when we turn on various parts of the simulator. The upper left image shows the PSF due to the optics alone with the mirror perturbations. The second image shows the PSF after the detector simulator is included. The lower left image shows the PSF when the atmosphere with no wind is included. The lower right shows the same but with wind. Clearly, the effect of wind reduces the ellipticity due to a larger part of the atmospheric turbulence that is being averaged.

Fig 4: Simulated PSF of optics (upper left), optics+detector (upper right), atmosphere (lower left), atmosphere with wind (lower right). The colors represent where the photons hit the LSST aperture (red is the outer annulus, blue is the inner). The images are 120x100 microns, which is 2.4x2 arcseconds.

We have studied the effect of the atmosphere by generating grids of stars where the photons have been refracted by the atmospheric turbulence screens. Figure 5 shows the ellipticity vectors measured from a set of stars produced on an 18 arcsecond grid. One can see that the ellipticity is fairly well correlated from one point to the next even if this grid is only sparsely sampled by calibration stars. The simulations have shown that the decorrelation of the ellipticity as a function of angle depends on the overlap of projected telescope apertures at a given altitude such that the decorrelation angle is roughly equal to the telescope diameter over the layer height. Larger aperture telescopes will have a correlated ellipticity over larger angles.

Fig 5: Ellipticity vectors of a grid of stars simulated through the atmosphere

Figure 6 shows a scatter diagram in which each dot represents a random pair of stars derived from grids of stars like those in Figure 5. Each pair has a separate angle and the magnitude of the ellipticity difference, [(e1-e2')2 + (e2-e2')2]0.5, where each star has a vector ellipticity (e1,e2) and (e1',e2'). The weak lensing metric is defined as the capability to accurately interpolate the PSF ellipticity at any arbitrary location in the field of view where a galaxy might be located based entirely on random calibration stars that are sufficiently bright. Figure 6 shows a comparison scatter diagram of data taken from a Gemini image (similar to LSST) and a simulated image with atmospheric effects included. This particular visualization emphasizes PSF difference effects on short angular scales (a few arc minutes) that are dominated by atmospheric effects. The telescope control system induces ellipticity effects in the PSF that vary over angles larger than 10 arcminutes. We are continuing a program to validate the atmospheric model with many different comparison tests with actual data. This particular visualization is just a sample to indicate the qualitative comparison of the PSF effects of the atmosphere both real and simulated.

Note the large variance of the ellipticity differences at every angular scale and the clear expected reduction in the average magnitude for angles approaching zero. We have developed PSF interpolation procedures (not shown here) that fit the indicated ellipticity difference for angles less than 1 arc minute typical of the scale of separation of bright calibration stars at the Galactic poles. These interpolation methods reduce differences in ellipticities of ~10-2 to ~10-3 for single simulated image patches a few square arc minutes in size. The performance of the PSF interpolation schemes is similar for both simulated and real data. This performance means that Galaxy ellipticities can be corrected in single exposures at the ~10-3 level.

Fig 6: Vector ellipticity difference as a function of angle for simulations (bottom) and Gemini data (top). Gemini data was taken from a single 15 s exposure with the SLOAN r filter and the GMOS instrument. 243 stars were used in the 5.5x5.5' field of view.

The scatter diagram is useful for a visual comparison of PSF effects on short angular scales dominated by the atmosphere. The region near the origin for scales less than 1 arc minute indicates the correlation of the PSF that is required for the interpolation correction of the PSF for galaxies nearby calibration stars. We now consider a different metric that directly reveals the science performance for weak lensing measurement averaging over all atmospheric details. Figure 7 shows the shear correlation of a simulated atmosphere calculated in an identical way as described in the Subaru data appendix. The simulations demonstrate a similar decorrelation angle and lower shear residual. Further studies will validate the realism of the particular atmospheric model and the effect of the telescope on the residuals. The results are qualitatively similar. In summary, our simulations confirm what we find using 15 sec exposures on new technology 8-m telescopes: PSF shear calibration can be done over the full range of angles LSST probes to the precision required in several hundred images.

Appendix III

Weak-lensing Systematics from the Atmosphere: Experiments on 8-m Telescopes

LSST will have so much statistical power for weak lensing (WL) that it is fair to ask what systematics might impose a floor. The primary systematic in current weak lensing surveys is uncorrected point-spread function (PSF) variation due to instrumental effects such as imperfectly aligned optics. Recent breakthroughs in PSF interpolation have reduced these systematics to below the statistical noise in current surveys (Jarvis & Jain 2004, Jarvis et al 2005). Furthermore, LSST will limit this problem before it starts, with wavefront sensors and closed-loop corrections to the optics, a huge advantage over current WL surveys. In this appendix, we address a more subtle systematic, ellipticity correlations induced by the atmosphere, which are inherently uncorrectable with wavefront sensors and the like. What are the limits to WL accuracy imposed by the atmosphere on a ground-based telescope?

We start by asking what systematics are imposed on LSST by the atmosphere in a single exposure, to set the baseline which will then be reduced by the analysis of hundreds of exposures. For that purpose, we have analyzed a set of 10- and 30-second exposures taken by the Subaru 8-m telescope with its prime-focus camera SuPrimeCam. These exposures were retrieved from the Subaru archive because they are well-matched to the LSST: 8-m telescope, short exposures, and 0.65" seeing, while the instrument was pointed at a dense star field to map the PSF finely. We have also analyzed a set of 15-s Gemini exposures and found similar results. For simplicity, we present only the Subaru results here.

We simulate an LSST analysis as follows. We choose a small fraction of the stars, somewhat less than one per square arcminute, to act as PSF diagnosis stars. (This is a conservative estimate for a high-latitude field; it is what current surveys get with worse-than-LSST seeing, which makes it harder to separate stars and galaxies, and without using color information.) The majority of the stars are designated as "galaxies" and their ellipticities are corrected using a fit to the PSF stars, just as in a real observation. A strong caveat regarding this approach is that it will surely leave some unmodelled instrumental effects, as we are not familiar with SuPrimeCam and have made no attempt to model it in any detail. So these results should be regarded as upper limits to the size of the atmospheric effects.

As an estimate of the spurious power induced by the atmosphere, we plot the shear correlations of the "corrected galaxies" in Figure 1, for both 10-second (black) and 30-second (red) exposures. The two shear components are shown separately, one in solid and the other in dotted lines, to give a feel for the sample variance. Although single exposures are shown, they are quite representative of the larger dataset; the power is fairly constant across exposures of a given duration.

For vanishing angular separation, the quantity plotted in the figure is equivalent to the mean-square value of the residual atmospheric shear. For n independent realizations of atmospheric turbulence, we expect this to go as n-1, i.e., the rms goes as n-1/2. The improvement from 10-s to 30-s exposure time is more modest than a factor of 3, possibly because the atmosphere has not completely decorrelated in the 30 seconds. Perhaps it would be better to accumulate a longer exposure time by taking multiple short exposures, alternating fields so that the atmosphere is completely decorrelated by the time a field is revisited. To investigate this possibility, we examined a set of five consecutive 10-second exposures. The SuPrimeCam read time is long enough (~120 seconds) that it is a fair comparison to LSST, with its fast read time and point/settle time, doing several fields and coming back for a revisit. For any reasonable atmosphere, it should provide complete decorrelation. For each "galaxy", we took the mean of the five corrected shapes

Figure 1 Residual shear correlations after PSF correction for 10-second (red) and 30-second (black) exposures on the Subaru telescope. The two shear components are shown separately, one in solid and the other in dotted lines, to give a feel for the sample variance.

as its final shape estimate. The result is shown in Figure 2, now zoomed in to small separations where the correlations are detectable. The improvement is indeed a factor of five, apart from the innermost two bins where the improvement is somewhat smaller. This is possibly due to unmodelled instrumental effects. Extrapolation to the hundreds of exposures provided by the LSST dataset is left to the reader.

To set the scale of the lensing signal, the expected shear correlations are ~5 x 10-5 at 3' separation, increasing at smaller separation and decreasing at larger separation. In other words, it does not even enter the space covered by Figure 2.

Figure 2 Decrease of residual shear correlations from a single exposure (black) to five exposures (red), for a set of 10-second Subaru images. LSST will have 200 exposures in each filter for each location on the sky. Multiple exposures separated in time by as little as 120-s (the SuPrimeCam read time) are better than a single long exposure.

As a sanity check, we compare with ray-tracing simulations of the atmosphere and telescope/instrument PSF for 0.7" seeing. We repeat the analysis for a single exposure, shown in Figure 3, now going out to the largest separation covered by the simulation, and again plotting the components separately. The residual correlations are an order of magnitude less (in units of shear squared) than for the Subaru data. We cautioned that the Subaru analysis would provide only an upper limit, and this analysis probably provides a lower limit, given that the stars have been measured with no noise, the optics are in good alignment, etc.

In summary, we have measured correlations induced by the atmosphere and found that, after PSF correction using current algorithms and a conservative density of PSF stars, and using 400 independent exposures, the residual correlations will be four orders of magnitude less than the signal and comfortably less than the shot noise. The measurements were made at scales of several arcminutes, but this statement is not very scale-dependent. The atmospheric correlations and the shot noise both decline with scale in roughly the same way, until the size of the LSST field is reached. At that point, we expect a very sharp decline in atmospheric correlations, as the telescope is repointed and the photons travel through an entirely different column of air. More extensive simulations would have to be conducted to prove that point, but it is likely not important since cosmic variance picks up in importance at those larger scales. At very small scales, theoretical uncertainty in predicting the shear power spectrum, not atmospheric correlations, will be the dominant systematic.

Another atmosphere-related error is shear calibration. Even if the PSF is circular everywhere, the larger the seeing-induced FWHM, the more it dilutes the shear signal. The dilution correction has recently been the subject of a blind analysis by roughly a dozen lensing groups around the world (the STEP project, Heymans et al 2005). The best methods in the STEP analysis reached a shear calibration accurate to 1%. LSST can do 20 times better, even with today's methods, because we will have 400 exposures, each with an independent shear calibration. A new method, developed by Roat, does a good job of estimating the true shear of the galaxy by fitting to all images of it.

References

Appendix IV
Estimating the Photometric Redshift Distribution and Accuracy for LSST
by Vera E. Margoniner

To estimate the photometric redshift accuracy and final galaxy redshift distribution for 23,000 square degree LSST survey we degrade the Hubble Deep Field North (HDFN) to match the expected LSST depth. The HDFN is deeper than any of the current or planed (DES, Pan­Starrs, LSST) surveys and has reliable photometric redshifts (Fernandez­-Soto et. al. 1999, 2001) derived from 7­band (HST UBVI and ground based JHK) photometry, as well as spectroscopic redshifts for 148 galaxies (Cohen et. al. 2000). We choose UBVIJ as the 5 HDF photometric bands that more closely resemble the future LSST filter set, and degrade the images to match expected resolution and noise levels.

First, we convolve the HDF­N UBVI space images (Williams et. al. 1996) with a 0.7" FWHM gaussian to simulate seeing conditions. Then, we re­pixelize, add noise, and catalog the images to match the expected data quality for the final full­depth stack of 800x10s coadded exposures. The final stack will go to 26.7m and 25.4m (10­σ and 30­σ) in the i band. The J image is left unchanged, because it was taken from the ground with the 4­m KPNO telescope and has resolution and seeing very close to what is expected for LSST.

The photometric redshift technique used here, bestz (Margoniner 2005), is based on SED fitting, and on a magnitude prior. The SED fitting is computed with the publicly available hyperz code (Bolzonella, Miralles and Pello' 2000). This code computes a χ2 from the comparison between observed fluxes of an object and the fluxes derived from spectral energy distributions (SEDs) of different galaxy types, at a range of redshifts:

χ2(z)=Σ{ [Fobs,i(z) - b X Ftemp,i(z)]/ σi }2

where Fobs,i, Ftemp,i and σi are the observed and template fluxes and their uncertainty in filter i, and b is a normalization constant. From hyperz's χ2 and the number of degrees of freedom, r, a redshift "color" probability, pc(z), is derived:

pc(z)=Pr(χ2)= χ2 (r-2)/2)e-χ2/2/ (&Tau(r/2)2r/2)

The magnitude prior, pm(z), is determined from the redshift distribution derived from the HDFN 7­band, full­depth, high resolution data. We sliced the data in magnitude bins and fitted an analytical function to each redshift distribution:

N(z)=az2e-z/z0

where 2z0 indicates the peak of the distribution and a is a normalization constant. The magnitude dependent redshift distribution and fits for the full depth HDFN data are shown in Figure 1 (blue). The red points and fits show how the distribution is affected by a brighter surface brightness detection (simulating a shallower survey). The top panel shows how the integrated redshift distribution has a lower mean redshift if a brighter cut is used, but within a given magnitude slice near the limiting magnitude (panels 6 and 7), galaxies of all redshifts are apparently equally missed and the mean redshift of that bin remains the same.

Figure 1: HDFN redshift distribution as a function of I814 magnitude. The blue points and fits represent the full depth data. Red indicates the decreased number of detections in a slightly shallower survey (1m brighter detections).

We then fit an analytical function to the parameter z0 which characterizes N(z):

z0(m)= 1 / (1 + e(-m+26.06)/3.36)

where m is the magnitude in the I814 band. The magnitude prior, pm(z) is N(z), and the final redshift probability distribution for an object is the product pc(z).pm(z).

In the Tables 1 and 2 below we summarize our results regarding the photometric redshift accuracy estimated for the LSST 8000 sec LSST. We present statistics for the 65 objects with spectroscopic redshifts that are detected in the simulation, as well as for the 62 "best" objects, after 3 worst outliers are excluded. In Table 1 we quote the 1­σ scatter of the quantity (zphot­zspec)/(1+zspec), and in Table 2 its the mean (or bias). For comparison we also present the results for the full depth 7­band photometry of these galaxies. HDFN7 indicates redshifts derived from the full depth UBVIJHK dataset: zphotfsHDFN7 is the photometric redshift from Fernandez­-Soto (2001); zphotHDFN7 is hyperz's; and bestzHDFN7 is the result with the added magnitude prior. LSST8000 indicates results from the UBVIJ degraded data: zphotLSST8000 is hyperz's photometric redshift using the, and bestzLSST8000 is the redshift with the added magnitude prior.

Table 1: 1­σ scatter of (zphot­zspec)/(1+zspec) using all galaxy types.

  all 65 objects 62 objects (95%)
zphotfsHDFN7 0.149 0.086
zphotHDFN7 0.170 0.078
bestzHDFN7 0.137 0.065
zphotLSST8000 0.380 0.081
bestzLSST8000 0.091 0.067

Table 2: Mean of (zphot­zspec)/(1+zspec) using all galaxy types.

  all 65 objects 62 objects (95%)
zphotfsHDFN7 0.03 0.02
zphotHDFN7 0.03 0.01
bestzHDFN7 0.03 0.01
zphotLSST8000 -­0.06 0.01
bestzLSST8000 0.01 0.01

When comparing these results with others in the literature it is important to note that different authors quote different statistics. Some quote the rms of (zphot­zspec)/(1+zspec), and others the rms of (zphot­zspec), but most discrepancies come from the fact that authors often clip their results, excluding a fraction of outliers and dramatically decreasing the quoted errors. Usually 5%­10% of objects with discordant photometric redshifts are excluded from the rms computation, and at times a much higher fraction. Hsieh etal, for example, quote a σ(zphot­zspec) < 0.11 for 0.0 < z < 1.5 from BVRz ground photometry, but this error can only be achieved after the 32% worst outliers have been excluded.

The final, full­depth, redshift distribution for LSST can be directly computed from the photometric redshifts of all galaxies detected in the simulation, and is shown in Figure 2.

Figure 2: LSST 8000 sec estimated redshift distribution for 1­σ. The plot is noisy because it is based on the small HDFN field of view.

References

Appendix V
LSST Operations Simulator

The LSST will image large areas of the sky frequently and to great depth by repeatedly making short exposures as the telescope tiles the sky. The cadence of these observations, the order in which different fields of view are observed in each color and the frequency with which they are revisited, is an essential part of the design of the LSST system. It will determine just how much sky will be covered, to what depth, and with what sampling in time and passband. This in turn will determine the extent to which LSST data will satisfy its diverse science requirements.

We have developed an operations simulator to answer the question: can the proposed telescope design and site(s) deliver the required science? There are many distinct science goals for the LSST. The Weak Lensing Survey, the Solar System Survey, and the Galactic and Transient Science programs (in particular supernovae) all have different spatial, temporal, and color sampling requirements, but the common theme is that all require many visits to the same field spread out over time. We are employing the operations simulator to optimize observing cadences and strategies to maximize the science return from a single set of observations. This tool also informs the telescope design by allowing us to assess the effects of variations in such parameters as the etendue of the optical design, exposure times, and the speed of detector readout and filter changes (to name only a few) on the overall science capability. The operations simulator also plays a central role in examining proposed sites for LSST, assessing the impact of site data on the attainment of science goals by simulating years of operation with historical weather and seeing data.

The current operations simulator is based upon an open source simulation language, SimPy. This provides the infrastructure for event based activities and time-keeping. The design is highly modular, with separate science programs described as separate python modules. There is a sophisticated telescope module with all motions parametrized for ease of testing different telescope capabilities, e.g. the effect of acceleration capabilities of various motors on science output. We use the Krisciunas and Schaeffer (1991) sky brightness module and various SlaLib routines to track the sun, moon and planets. A model of sky background due to light pollution will soon be added to further gauge the effects of future development near candidate sites.

All important parameters for the telescope, the site, and the science programs are easily accessible in configuration files. Each scientific goal is embodied in a "proposal," an algorithm which ranks potential observations based upon the extent to which they satisfy a particular goal's scientific demands. Potential observations from different science programs are currently ranked by a simple, linear weighting of the internal rank of an observation within a science proposal multiplied by an adjustable parameter for the priority of the proposal. A "greedy" algorithm is used to select the final sequence of observations. While this is not the optimal algorithm (the art and science of scheduling is considerably more advanced), it provides a useful lower bound to what can be accomplished. Work is under way to include the more sophisticated optimization techniques which will ultimately be employed in the operational scheduler.

We have generated weather and seeing data for four possible LSST sites. Weather data is derived from satellite observations of cloud cover, and local seeing data comes primarily from DIMM measurements. The DIMM coverage is not as complete as one would like for any of the sites, so continuous seeing data was generated by matching the power spectrum of the available, real data.

When the simulator is run, details from simulated observations are stored in an open source database, MySQL. This database is also used to store the weather and seeing input data. For each observation, we store 34 attributes including sky conditions, filter, seeing, airmass, the time it took the telescope to move from the previous pointing, the date, and the position of the camera with respect to the telescope and the sky.

While simulation research is actively under way, early simulation runs have investigated the impact of the system field of view on the success of multiple science programs undertaken simultaneously. These simulations used real seeing and weather data from CTIO, a site which is not under consideration but which is not too much worse than that of proposed sites. Figures 1, 2 and 3 below show the sky coverage for a single simulation with a 3.5 degree FOV with three simultaneous science goals. The Weak Lensing (WL) survey requires a minimum of 15, 15, 15, 25, 25 visits per field in g, r, i, z, and y throughout the sky, with the best seeing possible and minimum effects of sky brightness. To chop most effectively on ellipticity systematics, these observations must be widely distributed in the angles of the camera and of the pupil on the sky and in telescope orientation. The Near Earth Asteroid survey is limited to within 10 degrees of the ecliptic. A successful search sequence requires 3 sets of 2 visits per night in each lunation, with nightly visits separated by 30 minutes and each of the 3 sets separated by 5 nights. In the Supernova survey, each field requires a visit every 3 days for 60 days and sampling in all filters with as much uniformity as possible.

Figure 1 shows the total visits per field achieved in this simulation, Figure 2 shows visits which could be used for the WL survey, and Figure 3 shows fields which had completed supernova or NEA sequences.

Figure 1 Three program coverage (WL/SN/NEA) of the sky from Cerro Pachon using real CTIO seeing corrected to Cerro Pachon and CTIO weather.

Figure 2 Field coverage for those fields satisfying the Weak Lensing program requirements for 339 days with WL/SN/NEA programs running simultaneously. Y and z band fields are covered more frequently to obtain equivalent depth for photometric redshift determinations.

Figure 3 Transient science fields (both NEA and SNe) with completed sequences for 339 days with WL/SN/NEA programs running.

The panels in Figure 4 show the sampling achieved when running simulations for 3.0 and 3.5 degree FOV focal planes performing simultaneous weak lensing (WL), supernova (SN) and near earth asteroid (NEA) surveys using minute-by-minute, CTIO seeing and cloud data. The plots are histograms of the number of visits per field in each filter where that field has a minimum of the required visits in each filter. The visit set of 15, 15, 15, 25, 25 per year in g, r, i, z, y, is the minimum needed for the WL science. It is apparent from the figures that even the 3.0 degree field does not meet these requirements. It is also apparent that there is little competition between the three science programs for telescope time - LSST can effectively achieve multiple science goals from the same images.

Figure 4 Distribution of visits per field in five filters for simulations using a 3.0 degree FOV (left panel) and 3.5 degree FOV (right panel). For multiple science programs, the 3.0 FOV barely meets (does not completely cover the accessible area) the WL visit requirement, while the 3.5 degree FOV covers the available area with some visits to spare.

Appendix VI
Focal Plane Sensor Development Plan

Overview

The principal goal of the LSST Sensor Development Program is to arrive at a viable production-ready sensor prototype, in one or both device technologies, before the start of the LSST construction, presently set for Jan 2009.

The device technologies being developed are the next generation of CCDs with deep overdepleted substrate and segmented readout, and the hybrid PIN-CMOS. The program has two remaining phases, Sensor Technology Study Contracts (Phase II, 1 year), and Production-Ready Prototype Development Contracts (Phase III, 2 years). Phase I, a testing program to evaluate the state of presently available devices has been completed. These Sensor Technology Study Contracts will address specific technology issues, where most of the technology required to satisfy LSST sensor requirements may exist, but a specific issue needs to be addressed in order to provide a complete technology base for the subsequent prototype development in Phase III. Phase II shall produce test devices with all essential characteristics for LSST (QE, PSF, read noise, readout time), but may be in a smaller format than the required 4kx4k. Phase III shall result in production-ready prototypes.

Key Milestones for Technology Selection, Deliverables and Testing

Appendix VII
LSST Project Structure and Management

The LSST Corporation was founded in 2003 to promote building the LSST. Today the corporation has 12 Institutional Members1 and has headquarters in Tucson, Arizona. Members of the LSSTC share a common interest in building, operating, and participating in the science of the LSST. The LSSTC management structure is shown below.

LSST Management Structure

The LSSTC Board of Directors is the highest level of authority in the LSSTC. The Board ensures that project reviews are conducted and monitors the overall performance of the project. Among its many duties, the Board selects the President, Director, and Project Manager.

The President (John Schaefer) is the Chief Executive Officer of the Corporation. The President leads private fund raiser and the principle public spokesperson for the project. While the President is not responsible for the scientific or engineering leadership of the project, he does have ultimate authority and implements the policies of the Board.

The Director (Anthony Tyson) is the scientific leader of the project. The Director defines and approves the scientific requirements of the LSST.

The Project Manager (Donald Sweeney) is responsible for the engineering and financial management of the project. The Project Manager is responsible for the day-to-day operation of the project. The Project Manager is responsible for preparing, defending, and providing the project schedule and budget.

The System Scientist (Zeljko Ivezic) is the principle leader of scientific studies for the project and monitors the day-to-day scientific activities of the project. His role extends over the entire project to ensure consistency of the scientific capability of the LSST. The System Scientist maintains an accurate and complete Science Requirements Document and associated supporting documentation.

The System Engineer (William Althouse) is the chief technologist in the project. He is especially concerned with the engineering design and construction of the LSST required to assure meeting scientific performance specifications. He is responsible for development of system design specifications based on scientific requirements.

The three Sub-system Project Scientists and their counterpoint Sub-system Project Managers work in close collaboration. Together they have ultimate responsibility for ensuring their sub-system is designed and constructed to meet the overall LSST specifications. There are currently three sub-system Project Scientists and companion Project Managers in the project: (1) Camera (Kahn, Gilmore), (2) Telescope/Site (Claver, Krabbendam) and (3) Data Management (Axelrod, Kantor).

Additional components shown in the diagram include the Science Council chaired by the System Scientist. This Council is composed of scientific leaders in the project who advise the Director on scientific issues. The Science Advisory Committee is composed of interested scientists from the community; they recommend and review the project as requested by the Director. The Simulation and Data Challenge Department (Philip Pinto) organizes the end-to-end science and engineering simulations of the LSST. Among other things, his group generates data challenges for the Data Management team. Education and Public Outreach (Suzanne Jacoby) is an important part of the project and the specifications of the LSST are designed to have a strong educational component.