4 Target Selection

4.1 Summary of Targeting Requirements

The primary science goal for the BigBOSS survey is to measure with high precision the baryon acoustic feature imprinted on the large-scale structure of the universe, as well as the distortions of galaxy clustering due to redshift-space effects. The survey will achieve this science goal through spectroscopic observations of three distinct classes of extragalactic sources: luminous red galaxies (LRGs), star-forming emission line galaxies (ELGs), and quasi-stellar objects (QSOs). Each of these categories will require a different set of selection techniques to provide sufficiently large samples of spectroscopic targets from available photometric data. Further, to ensure high efficiency, the methods used must select objects with spectral features that will produce a reliable redshift or Ly-α forest measurement within the BigBOSS wavelength range.

The targeting requirements for each of the BigBOSS targets is summarized in Table 4.1. The requirements table includes the spectral feature of interest, the desired redshift range, volume density, and the projected areal density summarized from the following target selection discussion. The volume density values in the table are the minimum required densities; we expect to achieve substantially higher target densities over much of the redshift range. Figure 4.1 shows the target redshift distributions resulting from the strategies discussed in this chapter. The distributions have been smoothed to show the general shape and redshift range of the target samples, and the total areal densities are scaled to match the values in Table 4.1. These distributions represent the raw galaxy populations that would be tar geted by BigBOSS before inefficiencies (such as placing a fiber on the target or measuring a spectral feature of sufficient signal-to-noise) are taken into account.

The lowest redshift sample of BigBOSS targets will be composed of LRGs. These luminous, massive galaxies ceased star formation more than a billion years before the time of observation, and therefore have evolved, red composite spectral energy distributions (SEDs). The BOSS survey is targeting these objects to z < 0.6 using SDSS gri colors and measuring spectroscopic redshifts using the prominent 4000Å break continuum feature. BigBOSS will measure the same feature but extending to z < 1.0; as a result, other selection techniques will be required. In particular, we will select LRGs using the prominent 1.6µm (restframe) “bump”. This feature corresponds to the peak of LRG SEDs and provides a strong correlation between optical/near-infrared (NIR) color and redshifts at z < 1. We will use 3.4µm photometry from the space-based Wide-Field Infrared Survey Explorer (WISE) to efficiently select LRGs in the redshift range of 0.6 < z < 1.0.

Figure 4.1: The general BigBOSS target redshift distributions summarized from the targeting discussion and scaled to match the areal density values in Table 4.1. The distributions represent the expected underlying galaxy populations for the BigBOSS targets before losses (such as targeting effciency and fi ber completeness) are taken into account. In the case of the LRGs, the target distribution is subsampled to meet the volume density requirement.

The majority of the spectroscopic redshift measurements for BigBOSS will come from emission-line galaxies at redshifts 0.7 < z < 1.7. These galaxies possess high star formation rates, and therefore they exhibit strong emission lines from ionized HII regions around massive stars as well as SEDs with a relatively blue continuum spectrum shape. One of the most prominent features of ELG spectra is line emission from the [OII] 3727Å doublet, which consists of a pair of emission lines separated in wavelength by 2.8Å. The spacing of this doublet provides a unique signature, allowing for definitive line identification and secure redshift measurements even if it is the only feature observed. The doublet feature is a key tool for measuring redshifts in several smaller-area spectroscopic surveys (such as DEEP2 and WiggleZ); as a result, the properties of strongly line-emitting galaxies have been well studied. The goal of the BigBOSS ELG target selection will be to provide a large sample of ELGs with sufficient [OII] line flux to obtain a redshift detection and measurement out to z < 1.7. We will use forthcoming large-area optical photometric datasets to select these targets.

The highest-redshift target sample will consist of QSOs. We will be able to measure large-scale structure using the foreground neutral-hydrogen absorption systems which make up the Ly-α forest at 2.2 < z < 3.5. Unfortunately, QSOs have SEDs and magnitudes very similar to blue stars, which generally leads to inefficient and incomplete targeting for spectroscopic samples. BOSS selects quasars with a combination of techniques that depend critically on SDSS u-band measurements, resulting in 40 targets deg−2; roughly 50% of those targets prove to be QSOs at an appropriate redshift for Ly-α absorption studies. BigBOSS will achieve twice the BOSS target density by using variability information from time-series photometric surveys and allocating a portion of the BigBOSS survey to high-redshift QSO identification. BigBOSS will provide redshifts for QSOs over a wide redshift range (z < 3.5), but only obtain long exposures on confirmed z > 2.2 quasars in order to measure the Ly-α forest.

For the purposes of the following targeting discussion, we define a few terms which we will use to describe the effectiveness of our selection techniques.

These measures are separate from considerations of what fraction of objects selected as targets are actually placed on fibers, defined at fiber completeness and discussed in Chapter 6.

In this chapter, we will show that the combination of time-series photometry in forthcoming wide-area surveys and simple color selections can achieve all the target density requirements of Table 4.1. We also provide expected redshift distributions of the targeted samples based upon tests of strawman target selection algorithms. Elements of several other sections have relevance here. For instance, Chapter 5 details the design of the BigBOSS instrument, which informs a spectral simulator presented in Appendix A. This detailed spectral simulator aids in the design of the targeting strategy (such as magnitude limits), calculates exposure times, and estimates redshift measurement efficiencies. Given the expected target densities and exposure times, the overall survey strategy is developed in Chapter 6. Included in the survey strategy is an optimized method to tile the sky that maximizes the area covered and number of target redshifts obtained, while minimizing the overall time required for the survey. Chapter 6 also outlines a strategy for fiber allocation and calculates the total usage of available fiber exposure times. The main results of these chapters are summarized in Table 2.2 and are used to calculate the DETF Figure of Merit in Table 2.8.

4.2 Photometric Surveys

Selecting extragalactic sources for BigBOSS will require the use of imaging data for targeting. Therefore, the success of the survey is predicated on the availability of photometry over the entire BigBOSS footprint to sufficient depth to achieve our target number density requirements (after taking selection efficiency into account). Large area surveys with more than 10,000 deg2 of extragalactic sky coverage are rare. However, there are several ongoing surveys in the Northern Hemisphere that will deliver multiband photometry in the BigBOSS footprint within the next few years. These forthcoming datasets will serve as the backbone for BigBOSS target selection. We describe these surveys in more detail below.

4.2.1 SDSS

The Sloan Digital Sky Survey [Abazajian et al., 2009] has served as an excellent photometric data source for wide-field studies. SDSS includes multiband (ugriz) photometry which can efficiently separate a wide variety of stellar and extragalactic sources using their optical spectral energy distributions (SEDs). The 5σ magnitude depths for the SDSS ugriz bands are 22.0, 22.2, 22.2, 21.3, and 20.5, respectively. SDSS covers a 10,000 deg2 footprint with contiguous coverage over the North Galactic Cap and partial coverage of the South Galactic Cap. The BOSS survey is designed to take advantage of this photometry, targeting both LRGs and Ly-α QSOs selected using SDSS imaging.

The main SDSS photometric sample will largely not be deep enough to be useful for spectroscopic targeting in BigBOSS. However, we can use the well characterized properties of SDSS spectrophotometry to help calibrate the spectroscopic properties of BigBOSS. For example, the relative spectral calibration of SDSS F-stars can readily be used by BigBOSS to calibrate relative throughputs and to monitor variable sky transmission. Further, the results of the BOSS QSO survey and variability studies in the deeper Stripe 82 will inform the BigBOSS QSO target selection and reduce the number of stellar contaminants in our quasar survey. SDSS photometry and spectroscopy will provide a well-tested data source to calibrate with and compare samples against throughout the BigBOSS survey.

4.2.2 PanSTARRS

The PanSTARRS 3π survey [PanSTARRS website , 2010] is a transient-sensitive survey designed to observe 30,000 deg2 of sky over 12 epochs in each of the five grizy survey filters. The multiband photometry generated from the co-added exposures will reach depths that exceed that of SDSS and will serve as a source database for BigBOSS target selection. PanSTARRS has been designed to be a staged experiment, with additional telescopes scheduled to come online in the next decade. However, only the first of those telescopes (PS1) is currently taking survey data and will accomplish 360 seconds of total exposure time in three years of operation. Upon completion of this survey, we expect that the PanSTARRS co-added data will be released for public consumption and use for spectroscopic followup.

Additional targeting information could also come from PS1 time-domain photometry, but the public availability of the time variability information is uncertain at this time.

4.2.3 Palomar Transient Factory

The Palomar Transient Factory (PTF) [Law et al., 2009] is a photometric survey designed to find transients over 12,000 deg2 in the Northern Hemisphere. PTF is using the 1.2m Oschin Telescope at Palomar Observatory with the CFH12K camera to conduct this survey. Thus far, PTF has focused on obtaining Mould R band photometry with a nominal 5 day cadence and 60 seconds of exposure time, as well as shallower coverage in the g’-band. Four years of survey operations will yield a total of three hours’ exposure time in R over the entire survey footprint. We project that the R-band depth of the final co-added data will be ~ 0.5 magnitudes fainter than PS1 r and therefore more valuable to our ELG target selection (see Figure 4.1). The PTF collaboration will be releasing data within two years of observation. LBNL is a member of this collaboration.

4.2.4 Ground-based Photometric Error Model

Our strawman plan for BigBOSS ELG target selection will focus on the co-added gi bands from the PS1 survey and the co-added R band from PTF. Since neither PS1 nor PTF have completed their surveys, we must model the photometric errors that match the depths expected from each survey. The error model can then be applied to synthetic magnitudes generated from galaxy SED templates convolved with the PTF and PS1 filter bands to reasonably represent the photometric quality of the surveys. The photometric signal to noise ratio for various telescope parameters is modeled with the equation

where mAB is the source magnitude, msite is the site-dependent sensitivity, t is the total exposure time, and ω is the FWHM of the source in arcseconds. Each filter band an independent value of msite which is solved for from the survey-reported 5σ depth shown in Table 4.2 . Figure 4.2 shows the photometric error versus source magnitude for the gri bands from PS1 and R band from PTF. For these estimates, we use a mean galaxy half light radius of 0.3" to represent the extended ELG galaxy objects observed at high redshift.

Figure 4.2: Assumed magnitude errors for the Palomar Transient Factory and PanSTARRS 3π survey.
4.2.5 WISE

Ground-based photometry will not always be optimal for selecting all targets of interest. In such cases, we can additionally make use of space-based surveys, which can obtain deep imaging at infrared wavelengths much more efficiently. The experiment of greatest utility for BigBOSS is the WISE (Wide-field Infrared Survey Explorer) satellite, which is conducting an all-sky survey at wavelengths of 3.4, 4.6, 12 and 22µ m [Wright et al., 2010]. In the course of its 10-month mission (to be completed in 2010), 99.99% of the sky will be imaged at least 8 times, while regions near the ecliptic poles will be observed more than 100 times.

The key WISE channel for BigBOSS is 3.4µ m, which will go the deepest for galaxy populations of interest, with 5σ limit estimated to be somewhat better than the WISE goal of 120µJy in the least-covered areas. In this proposal, however, we will use 100µJy (18.9 mag AB) as a conservative estimate of the actual WISE limit, and only reaching the confusion noise limit of 63 µJy (19.4 mag AB) in the deepest regions (E. Wright, priv. comm.). The final WISE public data release is scheduled to occur in March 2012, providing ample time for optimizing BigBOSS target selection.

4.2.6 Other Imaging Surveys

For reference, we list below other wide field imaging surveys which, if available and well documented by the time of the BigBOSS survey, could be used to help define our targets.

A. U-band Surveys

The South Galactic Cap U-band Sky Survey [SCUSS website , 2010] is a joint project amongst the Chinese Academy of Sciences, its National Astronomical Observatories unit, and Steward Observatory, with observations planned to begin in September 2010. Using a mosaic of four 4K×4K CCDs covering a one square degree field, the survey plans to observe a 3,700 square degree field within the South Galactic cap using the 90-inch (2.3m) Bok telescope at Kitt Peak (belonging to Steward Observatory). Given the expected survey exposure time of 5 minutes per field, the limiting magnitude reached is estimated to be u ~ 23 (5σ).

A complimentary survey to SCUSS could also be performed in the Northern Hemisphere. A collaboration of French and Canadian astronomers have proposed a u-band CFHT Survey which would cover a minimum of 5,000 square degrees in the Northern extragalactic sky. A Pilot Survey, which should start in 2011, will observe the ~800 sq. degree region covered by the CFHT Red Cluster Sequence-2 (RCS2) survey with MegaCam. Upon completion of this Pilot Survey, the CFHT u-band survey could then continue to partially cover the SDSS and PS1 footprint. The exposure times are expected to be about 10 minutes per field and the limiting magnitude will reach roughly u ~ 24 (5σ).

B. DES

The Dark Energy Survey (DES) [Abbott et al., 2005] will use a new wide-field camera for the 4-meter Blanco telescope at CTIO, the Dark Energy Camera (DECam), to probe dark energy via a wide-area photometric survey (as well as a smaller-area survey focused on detecting type Ia supernovae; as the latter will only cover ~ 40 square degrees, it is of little relevance for BigBOSS). The camera is scheduled to be installed in 2011. In total, DES will cover 5000 square degrees, primarily in the Southern sky, over the course of 525 nights of observations over five years. The survey will deliver griz imaging is expected to deliver 5σ (point source, 0.9" seeing) limiting magnitudes of g = 26.1, r = 25.6, i = 25.8, z = 25.4, considerably deeper than BigBOSS requirements. The DES footprint is expected to have ~ 500 deg2 overlap with the BigBOSS footprint, primarily in the equatorial SDSS Stripe 82 region.

C. LSST

The proposed Large Synoptic Survey Telescope (LSST) [Ivezic et al., 2008] will conduct a deep, 6-band (ugrizy) photometric survey covering over 20,000 square degrees (primarily in the Southern sky) focused principally on studies of dark energy. By combining a large field of view camera (observing 9.6 square degrees at a time) with a large-aperture (8.4-meter diameter) telescope, LSST is designed to rapidly survey the sky to deep depths. This will enable studies of faint transients and asteroids as well as yielding extremely deep co-added images by combining roughly 1000 observations of each area of sky over 10 years. For the main survey, a single visit to each field will yield 5σ magnitude limits of u = 23.9, g = 25.0, r = 24.7, i = 24.0, z = 23.3, and y = 22.1; co-added depths will reach 26.3, 27.5, 27.7, 27.0, 26.2, and 24.9, respectively. Each patch of sky will be visited about 1000 times in ten years with a camera that covers 9.6 square degree field of view. The main survey will also extend well into the Northern Hemisphere (Dec < +33 for 2.2 airmass limit) to cover the entire Ecliptic plane. Therefore, we expect that there will be significant overlap between the BigBOSS footprint and LSST, perhaps as large as 6,000 deg2 . Once LSST starts survey operations in 2018, inclusion of their photometry from the first year of operations could rapidly improve target selection for BigBOSS in the overlapping area.

4.3 Luminous Red Galaxies

4.3.1 Target Properties

The largest volume surveys of large-scale structure to date have targeted the highest mass galaxies in the z < 1 universe, a population commonly known as luminous red galaxies (LRGs) [Eisenstein et al., 2001]. These objects are luminous and red in the restframe optical bands due to their high stellar mass and lack of ongoing star formation. They are commonly found in massive galaxy clusters today, and therefore they exhibit strong clustering and a relatively high large scale structure bias ([Eisenstein et al., 2005], [Ho et al., 2009], [Kazin et al., 2010]). Because of their strong 4000Å breaks and the correlation between their apparent magnitudes and luminosity distance, LRGs at z < 0.6 can be selected efficiently and their redshifts estimated based on SDSS-depth photometry [Padmanabhan et al., 2007], while the strong absorption features around the break allow redshifts to be identified definitively in spectra of modest signal-to-noise. They have therefore formed the cornerstone of the BOSS spectroscopic redshift survey.

Surveying LRGs at higher redshifts is beneficial for studying cosmology as their strong biasing to the underlying dark matter halos leads to a greater power spectrum amplitude, aiding BAO measurements. However, LRGs are increasingly difficult to select at higher redshifts as the 4000Å break passes into the i band (at z ~ 0.75) and imaging at longer wavelengths (e.g. z, J, H, or K-band) is required to estimate LRG redshifts. At sufficiently high redshifts, an additional difficulty is that LRGs will be less common simply due to galaxy evolution. At these early times before their star formation has ceased, they will have bluer restframe SEDs, lower stellar masses, and weaker absorption breaks than local LRGs ([ Faber et al., 2007], [Brown et al., 2007]). Only a small subset of the massive red galaxy population was in place as early as z ~ 2 ([Daddi et al., 2005], [L´ opez-Corredoira , 2010]).

At z < 0.55, the BOSS LRG sample selection yields a number density above 3 × 10−4 galaxies per h−3 Mpc3, sufficient to achieve the BigBOSS science goals. Therefore, at lower redshifts, we will either use existing BOSS spectroscopic samples or apply the BOSS target selection in regions not yet covered. The BOSS selection will yield 119 LRGs per deg2 . At higher redshifts, however, we require different selection techniques, taking advantage of near-infrared imaging from space. The remainder of this section will focus on the strategy we will use in this domain.

4.3.2 Selection Technique

The spectral energy distributions of cool stars exhibit a local maximum at a wavelength of roughly 1.6µm, corresponding to a local minimum in the opacity of H ions [John, 1988]. This feature, commonly referred to as the “1 .6µm bump” dominates the near-infrared spectra of stellar populations with ages above ~ 10 Myr, and represents the global peak in fν for populations older than ~ 500 Myr [Sawicki, 2002]. Since they possess few young stars, luminous red galaxies at z ~ 0.5−1 will therefore exhibit relatively large near-infrared to optical flux ratios at wavelengths of ~ 2 − 4µm.

The lowest-wavelength channel in WISE, centered at 3.4µm, is nearly optimal for selecting these objects as it overlaps the bump at redshift z ~ 1. The infrared-to-optical flux ratio of LRGs rises monotonically with redshift as z approaches 1, then will decline beyond

Figure 4.3: An optical/near-infrared color-color diagram for galaxies observed by the CFHT Legacy Survey, Spitzer IRAC, and the DEEP2 Galaxy Redshift Survey. In this and below figures, r indicates CFHT LS r-band magnitude, i indicates CFHT LS i, and [3.6] indicates IRAC 3.6µm AB magnitude. Galaxies with LRG-like SEDs at z > 0.55 are indicated by red points; those with 3.6µm magnitudes brighter than 18.9 (a conservative estimate of the WISE 5-σ detection depth in the [3.4µm] band) are indicated by larger symbols.

z ~ 1.1. As a consequence of both the increased rarity of LRGs and the greater luminosity distance, LRGs at z > 1 are uncommon at the magnitudes BigBOSS will survey. A simple cut in r -[3.4µm] color should therefore select LRGs effectively while adding in information from more optical bands can help in rejecting non-LRGs. WISE data is particularly well-suited for this application, as its survey depth was designed specifically to be able to detect L* red-sequence galaxies to z = 1; LRGs are generally significantly brighter than this limit.

To test selection techniques, we have employed publicly-released data from the AEGIS survey [Davis et al., 2007], which incorporates pan-chromatic imaging and spectroscopy from the DEEP2 Galaxy Redshift Survey [Davis et al., 2003]. In particular, we use optical catalogs derived from CFHT Legacy Survey data [Gwyn, 2008], NIR imaging catalogs from Spitzer IRAC [Barmby et al., 2008], and redshifts and restframe colors from DEEP2. All magnitudes used are on the AB system. In our tests, we use IRAC 3.6µm magnitudes as a proxy for WISE 3.4µm photometry and hereafter refer to the 3.6µm band; actual BigBOSS target selection will be optimized using WISE itself. At z < 1.25, 3.6µm lies on the long-wavelength side of the bump, so the measured IRAC flux should be lower than 3.4µm flux for a given galaxy; as a consequence, estimates from [3.6µm] < 18.9 or < 19.4 sample sizes from this analysis will be conservative. As seen in Figures 4.3, 4.4, and 4.5, galaxies with red restframe colors (restframe UB > 0.9) at redshift z > 0.55 are almost entirely confined to a limited region in an optical/near-infrared color-color plot. A strawman LRG selection criterion is shown by the solid lines in this figure.

Figure 4.4: As Figure 4.3, with objects color-coded according to their redshift and symbol sizes determined by [3.6µm] magnitude.

Since the 1.6µm bump is present in all but the youngest stellar populations, a pure cut in infrared-to-optical ratio (or equivalently r −[3.6µm] color) is effective at selecting objects in the target redshift range, but roughly 15% of the selected objects will be bluer than LRGs. By making the selection cut dependent on an optical color (both gr and ri have been tested and prove to be equally effective), these blue interlopers can be partially rejected; even a crudely optimized box (as shown in Figs. 4.3 – 4.5) improves the LRG redshift window efficiency to 90%.

4.3.3 Sample Properties

There are 420 objects per square degree within the depicted selection box with [3.6µm] < 18.9 (a conservative limit), or 1120 with [3.6µm] < 19.4; we adopt these as two fiducial scenarios for BigBOSS LRG samples. As these target densities are based on a 0.4 square degree region within the Extended Groth Strip, these source densities are subject to sample (or ”cosmic”) variance as well as Poisson uncertainty; they are uncertain at the 10-15% level as a result.

We use DEEP2 redshifts to estimate the redshift distributions we will obtain from our z > 0.55 LRG target selection, though given the limited area covered by DEEP2, CFHT LS, and IRAC, both sample/cosmic variance and Poisson variance are large within small 0.1Δz bins. We consider two scenarios: a shallow sample selected to have [3.6µm] < 18.9 (a conservative estimate of the WISE survey depth) and i < 21.5; and a deeper sample with [3.6µm] < 19.4 (a more optimistic estimate) and i < 22. These samples yield 380 and 670 targets per square degree, respectively.

Figure 4.5: As Figure 4.3, with objects color-coded according to their restframe UB color. Objects with UB > 0.9 generally have spectral energy distributions similar to LRGs.

In Figure 4.6, we plot the redshift distributions of the resulting samples, along with the overall redshift distribution of all galaxies in our LRG selection box and the number density goal of 3 × 10−4 objects per h−3 Mpc3 . Both of these samples are larger than the LRG population assumed in Section 2.2. However, as seen in the figure, we have more than enough targets at z < 0.8 and will downsample at those redshifts accordingly. The apparent magnitude of LRGs is strongly correlated with their redshift as they are on the exponential tail of the luminosity function, allowing us to sculpt the LRG redshift distribution efficiently. Even using conservative assumptions about the depth of WISE photometry, we find that we can select a sufficiently large sample of LRGs to meet BigBOSS survey goals.

Our spectral feature efficiency for z > 0.55 LRGs will primarily be a function of optical magnitude, a fact that will strongly affect the signal-to-noise we achieve in the spectrum of a given galaxy and determine whether or not we can detect absorption lines. We therefore will only target WISE-selected LRGs down to some r or i-band magnitude limit, which will correspond to a limit in spectral signal-to-noise.

Figure 4.7 shows the effect changing this limiting magnitude will have on the surface density of selected targets, assuming either a [3.6µm] < 18.9 or [3.6µm] < 19.4 sample. We find that a limiting magnitude of r ~ 22.5 or i ~ 21.5 should produce a volume density sufficient for the BigBOSS LRG sample. Given the photometric survey magnitude limits of PTF and PS1, we expect that the optical spectral flux will be highly accurate at these

Figure 4.6: Redshift distributions for z > 0.55 LRG samples, estimated using data from DEEP2, CFHT LS, and Spitzer IRAC. Due to the small area covered and LRG sample sizes, both sample/cosmic variance and Poisson variance are large within small 0.1Δz bins. Distributions for two possible scenarios are plotted: a shallow sample selected to have [3.6µm] magnitude < 18.9 (a conservative estimate of the WISE depth) and i < 21.5 (solid black histogram); and a deeper sample with [3.6µm] < 19.4 (a more optimistic depth estimate) and i < 22 (dot-dashed purple histogram). We also plot the redshift distribution of all galaxies in the LRG selection box (blue dashed line), renormalized to match the average number of galaxies per square degree from the other two samples. The dot-dashed red curve corresponds to the LRG number density goal of 3 x 10-4 objects per h-3 Mpc3; this goal is easily achievable to z = 0.8, and we are within 30% of the goal to z = 1.

limits (~ 0.05% magnitude error), and therefore the overall target selection efficiency will be dominated by the LRG redshift window efficiency of 90%. Based on our experience with BOSS, we expect to obtain redshifts for 95% of all LRGs down to our chosen magnitude limit (which is designed to achieve BOSS-like levels of signal-to-noise).

In Table 2.2, the total LRG target selection efficiency is the product of the LRG spectral feature efficiency (~ 100%) and the fraction of selected objects that lie in our detection window (90%). The final rate of redshift completeness – the product of fiber completeness, target selection efficiency, and redshift measurement efficiency – for the BigBOSS LRG target sample presented here is estimated to be ~ 68%; this is the fraction of potential LRG targets which will be actually targeted by a fiber, will turn out to be in the desired redshift range, and will yield a redshift. This is significantly higher than for ELG samples, largely because redshift success for a given LRG may be predicted from its magnitude much more easily.

Figure 4.7: Surface densities of z > 0.55 LRGs as a function of limiting r and i-band magnitude. We consider samples to two possible WISE depths, a conservative depth of [3.6µm] < 18.9 and the extended mission depth [3.6µm] < 19.4. Target LRG sample sizes are readily achievable so long as satisfactory signal-to-noise is obtained from spectroscopy down to r ~ 22.5 or i ~ 21.5.

4.4 Emission Line Galaxies

4.4.1 Target Properties

The largest sample of galaxies that will be selected by BigBOSS are emission line galaxies, typically composed of the brightest late-type spirals. The composite rest-frame colors of these galaxies are typically bluer than those of evolved galaxies such as LRGs due to their active star formation in the recent past; however, as they can exhibit a wide range of internal dust properties, their colors can be significantly dependent on inclination effects. In the local universe, ELGs of a constant emission line luminosity threshold are much less numerous than at high redshifts (z > 1). This predominantly reflects the fact that the overall star formation rate of the Universe was ~ 10× higher at that time [Hopkins & Beacom, 2006]. The correlation of emission lines to star-formation is established well enough to measure the star-formation rate (SFR) to z ~ 2, around the peak of the cosmic SFR [Kennicutt, 1998 ; Moustakas, Kennicut & Tremonti, 2006; Hopkins & Beacom, 2006].

In regions where star formation has recently occurred, short-lived, blue massive stars will provide large numbers of energetic photons into the local interstellar medium, resulting in ionized HII regions. As ions and electrons in these regions recombine, a variety of emission lines will result; the most luminous lines in the optical are members of the Hydrogen Balmer series or are emitted by oxygen ions. The total rate of ionizations and recombinations from

Figure 4.8: A template star-forming, emission line galaxy spectrum at z = 1.4 sampled at a constant 0.76Å per pixel interval, similar to the resolution provided by the BigBOSS visible and red spectrographs. The inset gure shows that the [OII] doublet is resolved at this sampling frequency and is split almost evenly between the line components, as is generally observed.

a galaxy will be proportional to the total number of massive stars; hence, emission line fluxes provide a useful diagnostic of a galaxy’s star formation rate.

Figure 4.8 shows an example synthetic z =1.4 emission line galaxy spectrum constructed from a star-forming template SED [Bruzual & Charlot, 2003] with emission line fluxes calibrated to match zCOSMOS observations at lower redshifts (see Section 4.4.2 for details). The strongest of the emission lines are typically the Hα line at 6563Å rest-frame and the forbidden [OII] doublet transitions at 3727Å. Additional strong lines include Hβ λ4861 and the [OIII] λ4959 + 5007 doublet. Of all the emission lines, the [OII] doublet will be most useful for probing the redshifts required by BigBOSS (z < 2) without requiring observations beyond 11000Å where the near-IR sky background increases rapidly. An additional benefit to [OII] is that it is a doublet closely spaced in wavelength (220 km/s FWHM). Each component line contributes roughly one half of the total line flux, since electron densities typically range from 100-1,000 ecm−3 for star-forming galaxies [Pradhan et al., 2006; Kewley & Ellison, 2008].

The doublet nature of [OII] 3727Å emission provides a unique signature for line identification in observations of sufficiently high resolution. If both components are robustly identified, a secure redshift results, in contrast to single-line redshifts which can correspond to a number of possibilities in the absence of other detected features. The DEEP2 survey [ Davis et al., 2003] recognized the unique features of the [OII] emission line and used it (as well as the 4000Å break prominent in older stellar populations) to conduct a redshift survey focusing on the regime 0.7 < z < 1.4. To date, the survey has resulted in 33,000 confirmed redshifts, most of them obtained via the [OII] doublet, measured in four different survey fields totaling ~3 deg2 . Experience from DEEP2 shows that the resolution required to nominally split the [OII] doublet is sufficient to produce two recognizably separate line features for the bulk of emission line galaxies, providing high confidence in the line identificatio n [Weiner et al., 2005]. Only a small fraction of galaxies contain sufficiently high rotational velocities to blend the doublet, and those massive galaxies typically exhibit continuum absorption features from the Balmer series or Ca H & K. Further, [OIII] and Hβ emission lines will be detectable at wavelengths below 11000Å to z ~ 1, providing additional certainty to redshifts when the lines have sufficient flux to be detected. The success of the DEEP2 survey in identifying and measuring emission-line redshifts serves an excellent test of strategies for BigBOSS.

4.4.2 [OII] Luminosity Function

With large [OII] datasets as DEEP2, it is possible to measure the number density of objects as a function of both [OII] luminosity and redshift. Since surveys of line luminosities are generally limited in completeness at either the faintest or brightest luminosities due to choice of survey characteristics, it is important to include multiple samples that cover a wide range of luminosities. Figure 4.9 shows a compilation of the [OII] luminosity functions produced from multiple emission line datasets at a mean redshift of z ~ 1.2, including the DEEP2 Galaxy Redshift Survey [Zhu, Moustakas & Blanton, 2009] and narrow-band filter observations of the Subaru Deep Field and the COSMOS field [Ly et al., 2007; Takahashi et al., 2007].

We find that the composite [OII] luminosity function is best represented by an Abell function (rather than a Schecter function) to match the power law behavior measured by DEEP2 at the bright end of the luminosity function. We parameterize the luminosity function according to

where Nb and Lb characterize the luminosity function behavior as a function of redshift with

The redshift dependence of this LF model is derived from observations in multiple redshift bins available from SDF and DEEP2. The result of the model function is displayed in Figure 4.9 for z ~ 1.2. Another interesting feature is that for a fixed space density, the [OII] luminosity is greater at higher redshifts; this is a result of the ~ 10× larger mean star formation rates in blue galaxies of all types at z ~ 1 compared to today. To project line fluxes for redshifts at z > 1.4, we adopt a conservative scenario in which the star-formation rate remains constant from 1.4 < z < 2 (roughly 1Gyr of cosmic time) and no more evolution occurs in the [OII] line luminosity (J. Moustakas, priv. comm.).

Figure 4.9: The [OII] luminosity function measured from photometric and spectroscopic surveys near z ~ 1.2. The luminosity function from DEEP2 spectroscopic measurements behaves as a power law on the bright end and shows good agreement with previous work in the Subaru Deep Field (SDF) and COSMOS field [Ly et al., 2007; Takahashi et al., 2007; Ilbert et al., 2009]. Note that each survey has incompleteness at both the bright and faint ends but the model luminosity function tracks the best sampled data in a given regime.

The black triangles in Figure 4.9 correspond to a catalog of [OII] line luminosities available from the COSMOS survey [Ilbert et al., 2009]. This catalog is composed of photometric redshifts (measured over 30 photometric bands), best-fit galaxy templates, and synthetic magnitudes generated from the Le Phare photometric redshift software [Arnouts et al., 2002; Ilbert et al., 2006]. The COSMOS templates also incorporate emission lines calibrated based on [OII] fluxes from VVDS spectroscopic measurements [Lé Fevre et al., 2005]. For z > 1.4, the [OII] fluxes are calibrated by the M(UV)-[OII] relation [Kennicutt, 1998]. This calibra tion of the [OII] flux with redshift is accurate to 0.2 dex, and this scatter is maintained in the catalog for those objects where the calibration is implemented.

As a check of the COSMOS [OII] flux calibration, we compare the LF measured from the catalog to other [OII] LFs in Figure 4.9. We find that the COSMOS luminosity function is in good agreement with our model Abell function. The COSMOS LF includes more objects than DEEP2 at low luminosities largely because it is based on a photometric-redshift sample (with [OII] emission assigned according to the heuristics described above), and hence includes objects fainter than the DEEP2 limit of R = 24.1. However, the DEEP2 LF, which has been based upon spectroscopic redshifts, appears to better track the observed LF from the deepest narrow-band imaging (SDF) at higher line luminosities. It appears that the methods used to assign [OII] fluxes to objects with photometric redshifts from COSMOS may break down at the highest luminosities, possibly due to the VVDS calibrators consisting predominantly of redder galaxies lying at z < 1 and the applied i = 22.5 magnitude limit.

Figure 4.10: Comparison of redshift distributions at three limiting [OII] line fluxes as predicted from COSMOS photometric redshift and restframe spectrum fits calibrated with VVDS [OII] line flux data [Ilbert et al., 2009] and from the model [OII] luminosity function depicted in Fig. 4.9. The agreement is extremely good save at the highest fluxes, for which we would expect the COSMOS estimates to be low based on the previous figure.

By integrating the model luminosity function above a given flux limit, we can construct redshift distributions representative of the ELGs available for targeting by BigBOSS (Figure 4.10). As an additional check on the COSMOS catalog and our model LF, we also plot the redshift distribution resulting from applying the same cuts to the COSMOS sample. We find that the two methods predict similar redshift distributions over a range of [OII] flux limits near the minimum detectable line flux for BigBOSS. This result is reasonable since the bulk of the sample comes from objects in the range where the LFs are in good agreement, having L[OII] ~ 1041.5 − 1042.5 (ergs s−1). The agreement between the model luminosity function and COSMOS predictions increases our confidence that the number density of bright [OII] emitters is well measured up to z < 1.4 and conservatively estimated for 1.4 < z < 2.

Linear Bias. The linear clustering bias of bright emission line galaxies relative to their dark matter halos is a matter of current study, but several sources have made relevant measurements. DEEP2 looked at the bias as a function of restframe color at a median redshift of z=0.9 ([Coil et al., 2008], hereafter C08). They found that the blue galaxies, those with the strongest star-formation and [OII] emission line measurement, had an absolute linear bias of b =1.28 ± 0.04 over a scale length of 1 − 10h−1 Mpc at z =0.9. C08 also found that this clustering strength is consistent with similar ELG bias measurements from other samples [Marinoni et al., 2005] and that the absolute linear bias at z ~ 1 is greater than that in the nearby universe.

Other studies have looked at the clustering as a function of [OII] luminosity to investigate whether there is any correlation between halo mass and line brightness. Using Subaru X-ray Deep Field and semi-analytic models of the relationship between baryonic gas mass and dark matter halos, Sumiyoshi et. al. (2009) estimated the linear bias for various UV-calibrated [OII] flux limits over three redshift bins between 0.5 < z < 1.7. They found that the bias was largely insensitive to their [OII] flux estimates except for the very brightest objects (F[OII] > 1 × 10−15 ergs s−1 cm−2) but the overall bias increased with redshift. For our initial BigBOSS projections, we assume that the bias increases with redshift to preserve a constant clustering amplitude; this assumption provides a rough fit to measured galaxy correlation function amplitudes for blue star-forming objects at redshifts from z ~ 0 [Zehavi et al., 2010] to z ~ 3 [Steidel et al., 2010; Adelberger et al., 2005]. Based on the clustering of z ~ 1 samples, we adopt the model b =0.76/g(z) where g(z) is the cosmological growth function normalized by a factor of 1/(1 + z).

4.4.3 Selection Technique

Because the vast majority of spectroscopic targets for BigBOSS will be ELGs, the overall survey efficiency will largely depend on the efficient selection of ELG targets from photometric data. Given that DEEP2 efficiently selects ELGs with z > 0.7 using broadband optical photometry, we expect that BigBOSS can use similar methods to select objects in a similar redshift range with a high confidence in success. We will therefore first describe the methods applied for DEEP2 and then discuss how they may be adapted for BigBOSS.

Figure 4.11 shows the expected CWW and Kinney-Calzetti tracks [Coleman, Wu & Weedman , 1980; Calzetti et al., 1994] over the redshift range 0 < z < 2 in CFH12K Mould BRI photometry for a range of galaxy spectral energy distributions (SEDs). As can be seen from this figure, galaxies of all types have BRI colors that rapidly become redder in RI as the 4000Å break transitions into the R-band at z ~ 0.7. This effect is strongest for red galaxies and weakest for starbursts. This allows an efficient division between z < 0.7 and z > 0.7 objects; the dot-dashed line in the figure shows the color selection actually used by DEEP2, which was optimized for completeness at z > 0.75 using redshifts of objects in the Extended Groth Strip (where no color preselection is applied). Star-forming galaxies with z > 0.75 – roughly equivalent to our emission-line sample – occupy a region in color space below and to the right of the dashed line. The DEEP2 selection had a selection completeness of 97% for galaxies at z > 0.75 (i.e., 97% of z > 0.75 galaxies pass the color cut) and a redshift window efficiency (i.e., fraction of the selected sample which has z > 0.75) of 85%.

Due to the depth limits of available photometric surveys (see Section 4.2) and differ ing survey goals, BigBOSS will likely use a shallower imaging dataset than DEEP2 with a smaller color selection box to maximize the probability of obtaining [OII] detections. To simulate the expected photometry, we have generated synthetic magnitudes from the COS MOS fit galaxy templates for the photometric redshift sample described in 4.4.2 in both the Sloan gi bands (PS1) and the Mould R band (PTF). Here we choose PTF over PS1 because we expect PTF to have deeper co-added photometry than PS1 in R. We also add random magnitude errors onto the synthetic magnitudes based upon the models described in Section 4.2.4.

Figure 4.11: BRI color-magnitude diagram illustrating the target selection techniques applied for the DEEP2 Galaxy Redshift Survey utilizing CFH12K photometry. The colored tracks are the trajectories of objects with CWW and Kinney-Calzetti [Coleman, Wu & Weedman , 1980; Calzetti et al., 1994] template spectra through this color space over the redshift range 0 < z < 2. Red lines correspond to early-type elliptical galaxies, magenta lines to intermediate spiral galaxies, and blue to late-type starbursting galaxies; dots indicate intervals of 0.1 in z. The black line (dot-dashed) shows the DEEP2 color selection applied, which has been optimized using observed redshifts in the Extended Groth Strip (where no color cut is applied) to select z > 0.75 objects below and to the right of this line.

Figure 4.12 shows the location of objects in the gRi color plane using the COSMOS synthetic photometry and the expected PTF and PS1 photometry to RAB < 23.4. The figure also color codes galaxies which have [OII] flux above 9 × 10−17 ergs s−1 cm−2 in three redshift bins: 0.7 < z < 1.2, 1.2 < z < 1.6, and 1.6 < z < 2. 0 (refer to Appendix A for a calculation of the expected BigBOSS [OII] line flux limit). As was also seen for the DEEP2 BRI selection, low-redshift star-forming galaxies have bluer (Ri) colors than z ~ 1 objects, but the SEDs migrate towards bluer colors as redshift increases. We also show an illustrative color selection box which we will use to predict BigBOSS sample properties in the next section. This selection is not unique; one can choose a variety of other selections that will generally modify the target densities at z ~ 1 as opposed to higher or lower redshifts.

Figure 4.12: Emission line galaxy color selection using synthetic photometry for the 1.3 deg2 COSMOS sample described in §4.4.2, applying PTF R and PS1 gi magnitude errors estimated as described in §4.2. The gray contours indicate all galaxies with R < 23.4 and the data points indicate those galaxies which have an [OII] flux greater than 9 × 10−17 ergs s−1 cm−2. The black box indicates a simple color cut that would select the brightest [OII] emission line galaxies with z > 0.7 with high efficiency.
4.4.4 Sample Properties

Figure 4.13 shows the redshift distribution (based on COSMOS photometric redshifts) for objects located in the simple selection box shown in Figure 4.12. The selection produces a distribution of ELGs with a redshift range of z > 0.7 where the number density of targets exceeds the BigBOSS requirements (Section 4.1) to a redshift of z =1.7. Our initial optimization studies have shown that the FoM is optimized best when the greatest volume of the Universe can be sampled with the greatest efficiency and number density in the allotted survey time, in line with previously FoM studies [Parkinson et. al., 2010]. The particular shape of the redshift distribution is a second order effect in optimizing the dark energy FoM.

Based on the redshift distribution shown in Figure 4.13, we estimate a redshift window efficiency of 70% for selecting [OII] ELGs in the BigBOSS target range of 0.7 < z < 1.7. A full 92% of the objects reside at z < 1.7, where BigBOSS will have sensitivity to [OII] and other prominent emission lines (e.g., Hα,Hβ, and [OIII]). The redshift window efficiency is therefore significantly affected by the high redshift tail of the distribution and may be improved by reducing the magnitude limit of the selection (at the expense of overall target density), by including additional color information, or by pushing the selection box redder in Ri.

Figure 4.13: The predicted redshift distribution of objects found in the ELG color selection box in Figure 4.12, based on COSMOS photometric redshifts and synthetic photometry. The red line represents a constant volume number density corresponding to the minimum target goal of n =1 × 10−4 h−3 Mpc3 and the blue line corresponds to n =2.5 × 10−4 h−3 Mpc3 . Our target selection meets the minimum density goal at z < 1.7 and the higher volume density at z < 1.5.

In Figure 4.14, we plot the total surface density of ELGs that have F [OII] > 9 × 10−17 ergs s−1 cm−2 within the gRi color selection box as a function of R-band magnitude limit. In order to use the focal plane fibers with > 80% efficiency, we project that the ELG target density should be ~ 20% higher than the fiber density (cf. §6), or about 2300 ELGs deg −2 . We see that the ELG selection provides this target density for an R-band limit of R< 23.4. Figure 4.14 also shows the color-selected fraction of objects that will have [OII] line fluxes above various limits as a function of the limiting R magnitude.

We find that the fraction of objects lying in the selection box that have F [OII] > 9 × 10−17 ergs s−1 cm−2 is roughly 70%; this will be our expected spectral feature efficiency for ELGs. It should be noted that objects with [OII] fluxes below this limit may well yield redshift measurements, but they will have a lower signal-to-noise than the require S/N=8 per line. Higher values of spectral feature efficiency could be obtained by lowering the magnitude limit of the selection, resulting in a loss in the total number density of selected targets unless the color selection box is revised. However, even if an object intrinsically possesses a line flux of F [OII]> 9 × 10−17 ergs s−1 cm−2, we will not always successfully obtain a redshift for it from a BigBOSS observation due to bright sky emission lines. Based on tests with the spectral simulator (Appendix A), we estimate that we will fail to obtain redshifts 10% of the time, yielding a redshift measurement efficiency of 90%.

Figure 4.14: top: The fraction of color-selected objects in Figure 4.12 having [OII] flux above a certain value, as a function of limiting R magnitude. The overall spectral feature efficiency for our expected F [OII] > 9 × 10−17 ergs s−1 cm−2 flux limit (see Appendix A), assuming an R-band limit of R < 23.4, is therefore ~70%. bottom: Cumulative ELG target density as a function of R-band magnitude limit after applying the F [OII]> 9 × 10−17 ergs s−1 cm−2. The BigBOSS survey requires ~2300 total ELG targets per square degree to efficiently use the focal plane fibers.

In Table 2.2, we record the total ELG target selection efficiency as the product of the ELG spectral feature efficiency (70%) and the fraction of selected objects that lie in our detection window of z < 1.7 (92%). The total ELG target selection efficiency is therefore 65%. The final rate of redshift completeness – the product of fiber completeness, target selection efficiency, and redshift measurement efficiency – for the BigBOSS ELG target sample presented here is estimated to be ~ 47%; this is the fraction of potential ELG targets which will be actually targeted by a fiber, will turn out to be in the desired redshift range, and will yield a redshift. Although this may seem low at first glance, it significantly exceeds the redshift completeness of the DEEP2 survey (as DEEP2 had a redshift window efficiency of 82%, was able to observe 70% of potential targets, and yielded redshifts for 70% of objects observed, yielding 40%) or of zCOSMOS-bright (which has a redshift window efficiency of ~ 100%, obtains spectra of ~67% of potential targets, and gets secure redshifts for 61% of objects with spectra, yielding 41%). The BigBOSS rate of redshift completeness is therefore not unusual for a color-selected survey within the z ~ 1 universe.

4.5 Quasi-Stellar Objects

4.5.1 Target Properties

Quasi-stellar objects (QSOs) are extremely luminous extragalactic sources associated with active galactic nuclei (AGN). QSOs are fueled by gravitational accreation onto supermassive black holes (SMBHs) at the centers of these galaxies; almost all continuum and broad-line emission originates within a few parsecs of the SMBH. Even in the nearest QSOs, the emitting regions are too small to be resolved, so QSOs will appear as point sources in images, in contrast to the extended, more easily resolved emission from a galaxy’s stars and gas. QSOs commonly exhibit hard spectra in the X-ray wavelength regime, bright Ly-α emission in the rest-frame UV, and a power-law spectrum behaving as Fν ν−α in the mid-infrared bands [Stern et al., 2005]. The specific physical processes that trigger high-luminosity QSO-mode emission in galactic nuclei is a ongoing topic of study, though the basic requirements (a high-mass black hole to have nonnegligible Eddington luminosity, with an ample fuel supply to reach a high Eddington ratio) are well-understood; a variety of scenarios can duplicate this [Hopkins et al., 2006; Croton, 2009] and match observed properties of the QSO population [Croom et al., 2005; Ross et al., 2009]. Similar to the very blue star-forming galaxy population, the number density of quasars was much greater in the distant past, peaking at z ≈ 2 − 2. 5 [Richards et al., 2009].

Although broad-line (Type 1/unobscured) quasar spectra exhibit characteristic features that separate them from typical star-forming galaxy SEDs, their point-like morphologies, relatively bright apparent magnitudes, and exponential frequency dependence give them photometric characteristics that mimic faint blue stars in optical wavelengths. Figure 4.15 shows how QSOs overlap the stellar locus for several Sloan ugriz color-color planes. The greatest separation from the stellar locus comes from ugr colors where the “UV excess” in u − g produces bluer colors than that of most stars. However, the UV excess is less strong for z > 2 quasars, for which the Ly-α forest dampens the hard QSO spectrum. While sophisticated neural-network algorithms have been developed to utilize all available SDSS color information to produce quasar photometric redshifts [Yeche et al., 2010], the simpler photometric selection used by BOSS to target Ly-α QSOs from 2.2 < z < 3.5 already reaches a 50% targeting efficiency. The BOSS selection produces 20 measured Ly-α QSOs deg−2 down to the SDSS photometric limit of g < 22.1.

To increase the number of Ly-α forest sightlines over those measured in BOSS, the BigBOSS target selection goal is to deliver a highly-complete Ly-α QSO sample to a fainter magnitude limit. This selection goal presents multiple photometric targeting challenges. First, there is a larger uncertainty in the form of the faint end of the underlying QSO luminosity function. Figure 4.16 shows the integrated surface density for 2 .2 < z < 3.5 QSOs from the Jiang et al. (2006, hereafter J06) luminosity function. At g = 23, it is predicted that a complete sample would give 45 QSOs / deg2 in this redshift range, whereas the luminosity function used to make predictions for LSST [Hopkins et al., 2007b; Abell et al., 2009] predicts 85 QSOs / deg2, almost a factor of two more. To reach the same number of targets with an incomplete QSO sample, one must go to even fainter magnitude limits. In that case, the multiband photometric data used in the selection must be deeper than that of SDSS but cover a similar area on the sky. While the PTF and PS1 co-added survey data will fulfill this requirement, neither of the surveys will acquire deep u-band photometry, which is vital for specifically selecting z > 2 QSOs.

Figure 4.15: The ugriz colors of SDSS objects photometrically classified as stellar point-like objects (PLO) and those spectroscopically classified as QSOs (see Yeche et al. [2010]). For the BOSS Ly-α QSO selection, a neural-network algorithm uses available SDSS colors and spectroscopic templates to select the objects most likely to be QSOs with z > 2.2.
4.5.2 Selection Technique

Efficient selection of QSOs based on integrated photometry will be difficult without deeper u-band imaging than SDSS obtained. The availability of such deep imaging is possible but uncertain (cf. §4.2); in its absence, BigBOSS will exploit the intrinsic variability of QSOs to target them. Because the accretion region around a quasar is highly compact, its luminosity can vary on timescales ranging from days to years.

Figure 4.16: Surface density of quasars (objects per sq. deg.) in the redshift range 2.2 < z < 3.5, derived from the Jiang et al. [2006] luminosity function (thin line). We also plot a second line with surface density 33% smaller, illustrating the source counts expected for a 67% complete sample (thick line) .

The time-variability of astronomical sources can be described using a structure function, a measure of the amplitude of the observed variability as a function of the time delay between two observations; the structure functions of quasars and variable stars differ strongly from each other. Selecting quasars by their structure function has been successfully tested in the QUEST survey [Rengstorf et al., 2004; Bauer et al., 2009].

QSO-variability selection techniques have recently been refined by incorporating a model of the structure function which is a power law in observed time lag (as opposed to the more commonly-used rest-frame lag, which requires a known redshift to compute; [Schmidt et al., 2010], hereafter S10). This model can be parameterized in terms of A, the mean amplitude of the variation on a one year time scale (in the observer’s reference frame) and γ, the logarithmic slope of the variation amplitude with respect to time. Figure 4.17 shows the structure function selection cuts for PanSTARRS-like data defined by S10. This selection was determined using SDSS Stripe 82 data down-sampled to match PS1 observations for objects with known spectroscopic classifications. The S10 selection is effective in separating QSOs from typical stellar contaminants such as F/G stars and RR Lyrae variables, while selecting 75% of all known QSOs in the field.

While structure function information can be drawn from multi-epoch data a single deep band (such as PTF R), a similar variability selection can be be obtained by measuring the structure function separately in multiband (gri) temporal data. Figure 4.18 shows the structure function derived from SDSS Stripe 82 gri co-added data for z > 2.2 QSOs;

Figure 4.17: An illustration of the QSO variability-based selection from Schmidt et al. [2010]. The plotted parameters A and γ describe the amplitude and logarithmic slope of the time variability structure function of each object. The points indicate the positions of 15,000 spectroscopically-classified objects in SDSS Stripe 82 in this plane, determined using structure functions measured from griz SDSS photometry which has been down-sampled to 6 epochs, matching expectations for PS1 3π survey. The gray points are for F/G stars, the red points are RR Lyrae stars, and the aqua points are confirmed QSOs. The solid lines illustrate a selection in the amplitude-slope (A − γ) plane which efficiently targets quasars rather than stars.

this data has photometric limits similar to those expected for the PS1 survey. In the overplotted fit curves, the amplitude A of the structure function in each band is allowed to vary independently, while the amplitude variation γ is simultaneously fit from all bands. An efficient selection algorithm has been developed which begins with a loose selection of all blue point sources with (g − r) < 0.9 and iAB < 23.5. Three-band structure function information is then fed to a Neural Network (NN) to separate QSOs from stars, employing the global structure function fits in the process [Palanque-Delabrouille et al., 2010]. This method is currently being tested in BOSS in SDSS Stripe 82 and will produce results soon.

By employing a broad color cut followed by rejection of stars using variability information, we can select a QSO sample with a high degree of completeness. For the strawman selection algorithm described above, Figure 4.19 shows the fraction out of all z > 2.2, g < 23 QSOs that are included in the BigBOSS QSO sample (“completeness”) as a function

Figure 4.18: Structure functions measured in SDSS Stripe 82 data for z > 2.2 QSOs with (g − r) < 0.9 and iAB < 23.5, determined for each of the g, r, and i bands separately. The solid curves have been simultaneously fit to all three bands, with the amplitude in each band varying but the power-law slope (γ) required to be the same. These models are then used in a neural network-based algorithm to separate QSOs from stars, with results shown in Figs. 4.19 and 4.20.

of the restrictiveness of the QSO targeting algorithm. If only the highest-confidence objects are selected (corresponding to a low surface density), a significant fraction of the useful targets would be rejected. A high completeness (80–90% out of all optimal QSOs) may be reached by targeting 180–250 targets deg−2 . As is illustrated in Figure 4.20, the estimated QSO completeness as a function of redshift is relatively flat; this selection technique is effective throughout the desirable redshift range.

However, roughly 75-80% of the ~ 250 objects deg−2 selected as candidate Ly-α QSOs will either not lie in the desired redshift range or are interloping variable stars. Since each Ly-α QSO must be observed multiple times to achieve adequate signal-to-noise, targeting such a high surface density of objects with a ~ 25% success rate would have a significant adverse impact on the LRG and ELG samples. We can increase the effective redshift window efficiency by using the first tiling pass of the survey to determine redshifts to all QSOs (which requires much less signal) and then rejecting low-z objects (see §6 for details). In this way, we can minimize the impact of Ly-α QSO targeting on other BigBOSS science programs and still achieve 90% completeness in z > 2.2 QSO targeting sample.

4.5.3 Sample Properties

Assuming an average of the J06 and LSST QSO luminosity functions and 80-90% selection completeness, we expect there to be ~ 65 Ly-α QSO targets deg−2 to g < 23 suitable for repeated BigBOSS observations. We may estimate the redshift distribution of this sample

Figure 4.19: The fraction of all z > 2.2, g < 23 QSOs targeted (“QSO completeness”) as a function of the looseness of the selection criteria (parameterized by the number of objects selected per square degree). This plot results from tests of a new color-variability algorithm applied to SDSS Stripe 82 data. BigBOSS will target roughly 250 QSOs per square degree in its first visit to each field, and use the resulting redshifts to reject low-z objects for all return visits. In this way, a large fraction of all desired targets will be observed, while spending relatively little time on variable stars and low-redshift QSOs.

by using the confirmed QSO redshifts from the BOSS survey and rescaling the distribution to the expected total areal density. The resulting BigBOSS Ly-α QSO redshift distribution is shown in Figure 4.21. While the redshift distribution for BOSS may differ from that for BigBOSS because the selection criteria are different, we expect that the BOSS sample should only be more weighted towards low redshifts than BigBOSS, given that the QSO selection for the former depends heavily on relatively shallow u-band photometry. Figure 4.21 should therefore be considered a conservative estimate for the redshift distribution of BigBOSS Ly-α quasars, particularly at higher redshifts extending to z > 3.5. The final redshift distribution, after accounting for losses to fiber completeness and redshift measurement failures, is recorded in Table 2.4.

The proposed selection scheme will initially target any objects that have similar colors and intrinsic variability as Ly-α QSOs. We expect that the largest contaminant population will be faint horizontal branch stars. It is likely that there will also be a significant fraction of z < 2 QSOs targeted in the first pass. The extent to which we will sample Ly-α QSOs, as opposed to lower-redshift objects, using the color-variability technique is currently being tested via a BOSS ancillary targets program; we expect to have a complete sample in Winter of 2010 (early results are quite promising). Based on such tests, we will be able to optimize our target selection algorithms, potentially reducing the number of candidate QSOs that must be tested in the initial targeting pass compared to the estimates above. An example of one possible optimization method, incorporating near-infrared data from the WISE satellite, is presented at the end of this section.

Figure 4.20: The QSO completeness as a function of redshift for samples with two different overall QSO target density levels, based on the same data as Figure 4.19. For target sample sizes similar to those which BigBOSS will use, the QSO selection completeness is relatively at with redshift.

The g < 23 limit chosen for the BigBOSS QSO sample should ensure sufficient signal-tonoise to detect Ly-α forest correlations from co-adding 5 observations; hence, the sample’s spectral feature efficiency should be ~ 100%. We conservatively estimate that we will fail to obtain redshifts for QSO targets in the first visit 10% of the time, yielding a redshift measurement efficiency of 90%. Since ~ 75% of objects selected by our strawman algorithm are at z < 2.2, our redshift window efficiency will be ~ 25% in the first pass over a region. Hence, in this initial visit, the rate of redshift completeness – the product of fiber completeness, target selection efficiency, and redshift measurement efficiency – will yield ~ 18%. However, in the remaining four visits, the target selection efficiency and redshift measurement efficiencies will be ~ 100% as objects which are not known to be at z > 2.2 will not be re-observed. This scheme will yield an 80% redshift completeness for the targeted z > 2.2 QSOs in the subsequent observed tiles. The average redshift completeness over all visits will be 67%, comparable to the LRG sample and significantly greater than the completeness for ELGs.

4.5.4 Identifying Low-redshift QSOs

Our proposed target selection techniques can achieve a highly complete QSO sample without the use of u-band dropout information. However, because the color cut used is relatively broad ((g − r) < 0.9), it will also select QSOs over a wide redshift range. Additional information from other bands could be used to sculpt the redshift distribution as desired.

In particular, many z < 2 QSOs can be identified using mid-IR photometry from the WISE satellite. The constraints from WISE can be used either to veto these QSOs from the BigBOSS survey sample or to help select a wider range out of the overall QSO population to benefit ancillary science.

Figure 4.21: Estimated BigBOSS redshift distribution for Ly- QSOs. This sample is taken by rescaling the confirmed BOSS quasar redshift distribution and rescaling to the surface density of targeted BigBOSS Ly- QSOS with 2.2 < z < 3.5. The targeted surface density is ~ 65 deg-2 (cf. Table 2.2).

To determine the utility of WISE photometry for selecting z < 2 QSOs, we used data from the Spitzer observations of the Böotes Field of the NOAO Deep Wide Field Survey, the so-called Spitzer Deep Wide-Field Survey (hereafter SDWFS; [ Ashby et al., 2009]). SDWFS reaches 80% completeness limits of 18.2, 18.1, 16.8 and 16.1 Vega mag in the 3.6µm, 4.5µm, 5.8µm and 8.0µm bands respectively over an area of over 9 deg2, and is essentially complete at depths corresponding to the WISE 5σ point source limits.

The IRAC four-band color-color diagram for those SDWFS sources with flux densities brighter than the WISE 5σ point source limits in the 3.6µm and 4.5µm bands (hereafter, the SDWFS/WISE sample) is shown in Figure 4.22. The dashed lines show the “AGN wedge” as dened by [Stern et al., 2005], which is highly effective at discriminating AGN from IR- bright galaxies. While WISE will not provide photometry near 5.8 or 8.0µm, one could construct a similar four-color diagram using all of the WISE bands (3.4, 4.6, 12 and 22µm). However, this would restrict any WISE-selected sample to only sources that are detected in all four bands. Instead, a simple two-color cut of [3.6]-[4.5]≥0.6 results in selecting the bulk of the sources in the “AGN wedge”, and relies on the bands for which WISE photometry goes deepest.

Applying this selection to the sample in Figure 4.22 (i.e., SDWFS/ WISE) results in 407 sources, which corresponds to a surface density of ~ 50 deg−2 . Of these sources, 91% lie within the AGN wedge and 98% have IV ega < 22. The main contaminants are likely to be very low-redshift star-forming galaxies with strong PAH emission and a few high-redshift obscured galaxies.

Figure 4.22: The Spitzer/IRAC color-color diagram for those SDWFS sources [Ashby et al., 2009] which would be detectable by WISE at both 3.6µm and 4.5µm (i.e., the SDWFS/ WISE sample). The dashed lines show the \AGN wedge" as dened by [Stern et al., 2005], which is highly effective for selecting bright AGN. Note that the bulk of the wedge AGN may be selected using a simple color cut of [3.6]-[4.5]≥0.6.

The former could be easily excluded using a star-galaxy separation based on ground-based optical survey imaging, while the latter are rare at bright optical magnitudes.

Approximately 62% of the objects in the SDWFS/WISE sample have spectroscopic redshifts from the AGN and Galaxy Evolution Survey (AGES; Kochanek et al. (2010), in preparation; see also [Kochanek et al., 2004]) and other spectroscopic campaigns using the W. M. Keck Observatory telescopes. The redshift histogram in Figure 4.23 shows that 46% of the objects with redshift information have z ≥ 1 and only ~3% have z ≥ 2.2. We find that the magnitude distributions of sources with and without spectroscopic redshifts is roughly similar, and so we can expect that the redshift distribution of the full sample would be comparable. Thus, by employing WISE photometry to reject low-redshift AGN, we can reduce the number of objects that must be sifted through in the first-pass search for Ly-α QSOs by ~ 20% (from ~ 250 objects deg−2 to ~ 200), at the cost of rejecting ~ 1.5 Ly-α QSOs per square degree. More sophisticated techniques may be able to sculpt the redshift distribution with smaller loss; we will explore these with actual WISE photometry when it becomes publicly available.

Figure 4.23: Redshift distribution of the SDWFS/WISE sample of sources, based on spectroscopy from the AGES [Kochanek et al., 2004] survey and the Keck telescopes. 46% of the sources lie at redshifts z ≥1, but only ~3% are at z > 2.2.