|Figure 2.1: Forecast 68% CL constraints on dark energy (w0, wa) and structure growth () parameters from DES weak lensing alone (blue), redshift space distortions alone (purple), the combination of the two without spatial overlap (red) and with spatial overlap (yellow, i.e., DES+DESpec). In the last case, the lensing measurements include shear-shear, galaxy-shear, and galaxy-magnification correlations. Each two-parameter combination is marginalized over the third parameter. We use Planck and Stage-II priors. From Gaztanaga, et al. (2011).
In this calculation, the DESpec survey is assumed to obtain redshifts for 1000 galaxies per sq. deg. to limiting magnitude of iAB=22.5, with a mean redshift of about 0.6. RSDWL (DES+DESpec) improves the (marginalized over ) DETF FoM for w0, wa by a factor of about 4.6 compared to DES weak lensing alone. The spatial overlap of RSD spectroscopy with WL photometry is found to improve the DETF FoM compared to non-overlapping surveys. The improvement is around a factor 5-10 when one combines weak lensing and galaxy clustering (see Gaztanaga, et al. 2011) but note that this target selection choice does not optimize the survey strategy. Figure 2.2 shows which redshift bins are most important for the constraints, which in turn informs the optimization of target selection. Later (Section 3), we will consider more elaborate methods of selecting galaxies to demonstrate how the FoM can be further enhanced. We will also show how we reach similar conclusions with different assumptions and observables.
Figure 2.2: Percentage change in joint constraint on dark energy (w0, wa) and structure growth () for the WL+RSD (DES+DESpec) combination when we remove information from a particular redshift bin (relative change per unit redshift) for a DESpec survey limited to iAB <23.0 (black dashed curve) and iAB<22.5 (solid blue). The largest contribution to this FoM comes from information around z=0.7, which corresponds to the peak of DES weak-lensing efficiency. The next largest contribution comes from the highest redshifts, which sample the largest volumes, especially for iAB <23.0. We can use this type of analysis to optimize DESpec target selection (see Section 3).
A similar forecast has been done by Cai & Bernstein (2012), who focused on the growth parameter . Fig. 2.3 shows their comparison of the modified gravity FoM for surveys combining WL and RSD in separate volumes (non-overlapping) with those in the same volume (overlapping sky). For DES, we expect an effective lensing source density of Nlens=10 galaxies/arcmin2; in this regime, Fig. 2.3 shows a gain of a factor of about 1.5-1.8 in the modified gravity FoM compared to non-overlapping surveys if the spectroscopic survey targets of order one galaxy per halo in all halos down to Mmin ~ 1013 Msun. In the redshift range z~0.5-1, this corresponds to a spatial target density of about 10-4 (h-1 Mpc)-3 or an areal density of ~300 per sq. deg. Luminous Red Galaxies (LRGs) would be ideal targets for this population. The same-sky enhancement in the growth parameter precision is more modest than the gains in the dark energy parameters but still significant.
Figure 2.3: Ratio of RSD+WL modified gravity Figure of Merit for non-overlapping vs. overlapping spectroscopic+photometric surveys. The design strategies for the DES and DESpec surveys correspond to a gain of a factor 1.5-1.8 in the MG FoM for overlapping vs. non-overlapping surveys. From Cai & Bernstein (2012).
2.C Large-scale Structure and Baryon Acoustic Oscillations
The large-scale clustering of galaxies contains a feature at ~110 h-1 Mpc, detectable as a slight enhancement in the two-point correlation function on that scale or as periodic wiggles in the power spectrum. This scale is set by the sound horizon, the distance that acoustic waves in the photon-baryon plasma travelled by the time that ionized hydrogen recombined 380,000 years after the Big Bang. This BAO feature is imprinted dramatically on the cosmic microwave background anisotropy as a characteristic angular scale of ~1 degree in the size of hot and cold spots in the CMB temperature map. It is a more subtle feature in the galaxy distribution, since structure formation is driven primarily by gravitational instability of dark matter. First detected in the distribution of LRGs in the SDSS redshift survey (Eisenstein et al. 2005), its measurement is the primary aim of the on-going SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), which is targeting 1.5 million LRGs over 10,000 sq. deg. to redshift z~0.6 (Eisenstein et al. 2011, Dawson et al 2012, Anderson et al. 2012). A number of next-generation BAO-centric redshift surveys are under construction (e.g., HETDEX) or have been proposed (e.g., BigBOSS, WEAVE, VXMS, SUMIRE, EUCLID, WFIRST). The BAO feature is useful for dark energy studies, because it acts as a standard ruler (e.g., Blake & Glazebrook 2003, Seo & Eisenstein 2003). Photometric surveys such as DES and LSST will probe the BAO feature in angular galaxy clustering, measuring the angular diameter distance DA(z) and thereby constraining the expansion history. Redshift surveys improve the accuracy on DA(z) and, in addition, measure BAO in the radial direction, which provides a direct measure of H(z) (Gaztanaga, Cabre, & Hui 2009, Kazin, et al 2010). Greater precision in these geometric measures over a range of redshifts translates into greater precision in the dark energy equation of state.
The SDSS LRG BAO measurement constrained H(z) and DA(z) to ~4% and 1.6% precision at redshift z~0.35. BOSS is expected to determine these over a range of redshifts up to z=0.6, with its best precision of ~2 and ~1% at the upper end of that range. DES will probe DA(z) via angular BAO with a precision of about 2.5% but over a larger redshift range, to z~1.3. A DESpec survey that targets Emission Line Galaxies to z~1.5 over 5000 sq. deg. would reach a statistical precision of ~2.5% in H(z) and 1.5% in DA(z) at z~0.9 but with useful measurements over the entire redshift range. Extending the DESpec ELG survey to 15,000 sq. deg. by targeting LSST galaxies in addition would improve the precision on H and DA to about 1.5 and better than 1%; this precision would be achieved by BigBOSS as well. Combining DESpec and BigBOSS BAO would be expected to further improve each of these constraints by ~40% and give an independent check on systematic errors.
In designing a BAO survey, the precision of the H and DA measurements (and therefore of the DE constraints) is set by the relative statistical uncertainty in measuring the large-scale galaxy power spectrum, , where Veff is the effective volume of the survey,
Vsurvey is the survey volume, and n is the survey galaxy number density. To minimize cosmic variance errors, the survey should cover large volume Vsurvey; to minimize the impact of Poisson errors, the galaxy sampling density should satisfy To reach large effective volume, we wish to select galaxies with adequate sampling density out to high redshifts, z~1.5, which leads one to preferentially target Emission Line Galaxies (ELGs), as described in Sec. 3. Given the ELG large-scale power spectrum amplitude, the desired number density is very roughly n> 310-4 h3 Mpc-3; for a 5000 sq. deg. survey to that redshift, the survey volume is of order 21010 h-3 Mpc3, which implies an approximate total of N=nVsurvey~6 million ELG redshifts, with an areal density of 1200 per sq. deg. This figure sets the survey design of Sec. 3. For a wider-area BAO survey that also targets LSST galaxies, one would seek to maintain the same target density, resulting in ~18 million ELG redshifts over 15,000 sq. deg.
2.D Galaxy Clusters
DES will measure the abundance of massive galaxy clusters to redshift z~1.3 and use it to probe DE. The abundance of dark matter halos with mass and redshift, dN(M,z)/dzd, is sensitive to DE through the expansion history, which determines the volume element, and to the growth rate of structure, which determines the intrinsic halo density as a function of time. In this technique, clusters serve as proxies for massive dark matter halos. DES will determine cluster redshifts photometrically with sufficient precision for this test. However, since the masses of dark matter halos are not directly observable, this technique relies critically on the ability to determine the relation between cluster observables (such as the number of red galaxies above a certain luminosity) and the underlying halo masses; in particular, the mean and scatter of the mass-observable relation must be determined either internally (e.g., via self-calibration or weak lensing) or externally, by performing other measurements that constrain the relation. Clearly, external measurements that help reduce the uncertainty in the cluster mass-observable relation will strengthen the resulting DE constraints (Cunha 2009, Wu, Rozo, & Wechsler 2010). DESpec can provide such external information for DES clusters by providing dynamical cluster mass estimates: measuring redshifts for several tens of galaxies in a cluster provides an estimate of its velocity dispersion and therefore of its mass. Well-designed spectroscopic follow-up could improve the DES cluster DE FOM by a factor of several even if carried out over a subset of DES clusters. Targeting for this sample would synergize with the LRG targeting for RSD and BAO studies but would likely require additional cluster-optimized exposures as well.
The DES Supernova Survey will measure high-quality light curves for ~4000 type Ia supernovae to redshifts z~1 through repeat imaging of a 30 sq. deg. region over the course of the survey. Given limited spectroscopic resources, only a fraction of those will have follow-up spectroscopy while the supernovae are bright enough to detect. For the rest, follow-up spectroscopy of the host galaxies will be needed to precisely determine the SN redshift, which is important for increasing the precision of the SN Hubble diagram and reducing contamination from non-Ia SN types. The spectroscopic measurement of SN Ia host-galaxy properties (star-formation rates, gas-phase metallicities, etc) has become even more important with the results of recent studies (Kelly et al. 2010, Lampeitl et al. 2010, Sullivan et al. 2010, Gupta et al. 2011, D'Andrea et al. 2011) indicating that SN Ia luminosities (and therefore distance estimates) are correlated with host-galaxy properties. This correlation must now be taken into account in order to control SN cosmology systematic errors due to evolution of the mix of host-galaxy types (Sullivan, et al. 2011).
DESpec could contribute significantly to this program by measuring host-galaxy spectra of a large fraction of the DES SN Ia sample. Different science goals can be achieved, depending on the depth of the spectroscopic observations. At the lowest S/N ratio of ~3-5 in the continuum, we can measure accurate redshifts and star-formation rates of most emission-line host galaxies. Approximately 30% of the hosts in this category are brighter than r=22 mag, which can be achieved with DESpec in 30-minute exposures. A more ambitious observing program can measure redshifts of emission-line galaxies as faint as r=24 mag with total integration times of several hours. This will provide redshifts of ~90% of all SN Ia host galaxies from DES. The SNLS group, for example, has demonstrated the efficient use of the 4m Anglo-Australian Telescope and the AAOmega multi-object spectrograph for measuring SN Ia host galaxy redshifts down to r=24 mag with 60 ksec exposures (Lidman et al. 2012).
At S/N of ~10 in the continuum, we can measure the gas-phase metallicities of the hosts, which is an important parameter that is correlated with the Hubble residual at z<0.15 (D'Andrea et al. 2011). DESpec can study this correlation at z<0.4 (r=22 mag limit) and z<0.7 (r=24 mag limit) and will allow us to check for possible evolution. We can also measure average stellar population ages and metallicities with the use of Lick indices (Burstein et al. 1984), which requires much higher S/N of at least ~30-50. This can be achieved at the lowest redshifts (z<0.2) or by stacking the spectra in several SN Ia luminosity bins.
2.F Photometric Redshift Calibration
All four DE probes in DES rely on accurate estimation of galaxy photometric redshifts using color and other information from the DECam grizY images. The DES survey strategy is designed to optimize galaxy photo-z measurements to redshifts z>1, and the synergy of DES with the near-infrared (JHK) ESO Vista Hemisphere Survey will improve the photo-z precision of the survey. The weak lensing and galaxy clustering measurements in DES in particular rely on accurate estimation of the galaxy redshift distribution, N(z), and therefore require accurate estimation of the photo-z error distribution as a function of redshift. Uncertainties in the variance and bias of the photo-z estimates lead to systematic errors that degrade DE constraints (Huterer et al. 2005, Ma, Hu, & Huterer 2006).
Determining the error distribution as well as training empirical photo-z estimators requires spectroscopic samples of ~104-105 galaxies that cover the range of galaxy properties (colors, redshifts, flux limits, etc) of the photometric sample. While such spectroscopic samples in the DES survey footprint exist to approximately the DES depth, they are incomplete at the faintest magnitudes DES will reach.
The DESpec survey could aid in DES photometric redshift calibration in several ways. First, it will provide a large number of additional redshifts for training, validation, and error estimation for empirical photo-z methods, although not to the flux limit of the DES. Second, such a large sample of galaxy redshifts overlapping the DES footprint can in principle enable new methods that can augment traditional photo-z estimates at faint magnitudes. In particular, since galaxies are clustered, the angular cross-correlation between overlapping spectroscopic and photometric samples spanning the same redshift range can be used to estimate the redshift distribution of the photometric sample, calibrating the true redshift distribution for DES galaxies in photo-z slices (Newman 2008, Matthews & Newman 2010). Reducing the uncertainty in N(z) leads directly to improved dark energy constraints from the photometric sample. Initial estimates indicate substantial improvement in DES photo-z calibration from the technique for a spectroscopic survey covering ~60% of the DES area. Third, for a spectroscopic survey that completely overlaps DES, one can potentially take advantage of the fact that a faint galaxy in the DES photometric survey that is near on the sky to a brighter galaxy with a DESpec redshift will have a reasonable probability of having the same redshift as the spectroscopic galaxy. The DESpec redshifts therefore act as informative redshift priors for neighboring DES galaxies (Kovac et al. 2009); the utility of this approach for DE photometric surveys is under active study.
2.G Galaxy Evolution
While cold dark matter cosmologies provide a powerful framework to describe the formation and evolution of galaxies, we still have a poor understanding of key aspects of galaxy evolution including gas accretion and star formation processes, the mechanism for star formation quenching, relative roles of major and minor galaxy mergers, galaxy mass growth, and the role of the environment. Because of the complexity of these physical processes driving galaxy formation, progress in observational studies of galaxies can only be made through a comprehensive mapping of galaxy properties over a large range of time. DESpec will deliver this. The DESpec spectroscopic data set will create an enormous legacy value for a large range of additional science including studies of galaxy formation and evolution. Spectra of over one million luminous red galaxies out to redshifts z~1 will leverage the exploitation of the DES imaging data set and will lift the currently ongoing galaxy evolution studies of SDSS-III/BOSS data to a new level by pushing to larger look-back times.
DESpec will allow us to analyze stellar population properties, chemical enrichment histories, gas physics, dark matter content, structural properties, galaxy mass functions, merger rates, and number densities for a variety of galaxy types as a function of environment and look-back time to ultimately constrain the formation and assembly histories of galaxies. The large volume of the DESpec observations will allow the exploitation of a large and diverse parameter space of galaxy environment, type, color, luminosity, mass and size. The accurate spectroscopic redshifts produced by DESpec will boost the analysis of the DES imaging data set significantly. The legacy value of DESpec spectroscopy will go well beyond the use of spectroscopic redshifts. The typical signal-to-noise ratio will be sufficient to make measurements of fundamental galaxy properties such as stellar and gas kinematics. The true power, however, will lie in the possibility of stacking hundreds and thousands of spectra to produce a spectroscopic data set of galaxies up to z ~ 1 with data quality unmatched by any of the existing spectroscopic galaxy surveys. From stacked DESpec spectra we can derive accurate stellar masses, ages, and element abundances ratios by fitting state-of-the-art stellar population models (Thomas et al. 2011; Maraston & Strömbäck 2011), which allows us to tap into the fossil record of galaxies and derive accurate formation and chemical enrichment histories (Thomas et al. 2005, 2010). DESpec will clearly open a new chapter in observational galaxy evolution.
2.H Opportunities for Community Science
The Sloan Digital Sky Survey (SDSS) demonstrated the extraordinary value of combining photometry with spectroscopy, where high-precision photometry is used to select targets for spectroscopy. The SDSS was designed around a focused set of scientific requirements (large-scale structure in the galaxy distribution, and quasars), yet its legacy data products have became one of the most widely used astronomical archives ever created, leading to thousands of publications spanning from the Solar System to cosmology. One can confidently predict that the photometric surveys in the southern hemisphere (DES, VISTA, LSST, and others), in concert with DESpec spectroscopic targeting, will have at least comparable impact for the world astronomical community.
DESpec will be a facility instrument at CTIO, providing open access to wide-field spectroscopy in the southern hemisphere. The southern hemisphere features unique astrophysical environments in the Galactic center, the Magellanic Clouds, and star-forming regions elsewhere in the southern Milky Way. Importantly, DESpec will see the same sky as LSST, which will produce a deep, high-precision, time-resolved map of the southern sky. The source catalog generated by LSST will have unprecedented value, and as such, DESpec's capability to follow up sources discovered and characterized by LSST will yield enormous scientific leverage. Put differently, spectroscopic follow-up is required to fully exploit LSST imaging, and DESpec on the Blanco Telescope responds to that need.
The DESpec reference design can be modified or enhanced to enable more community science – we are open to community input about design priorities. For example, the fiber-positioning technology we will pursue allows additional fibers to be placed in the focal plane. These additional fibers could observe "community targets" in parallel with the DESpec cosmological survey, or, with the reference-design fiber density, fibers can be used for community targets with a proportional increase in the total number of nights allocated to the DESpec cosmological survey. There are a number of other options for community access, including standard PI-directed use of the instrument where all the targets are selected for a specific observing program. Alternatively, one could combine several target classes from different programs, each with similar requirements on exposure time. In effect, several surveys can run in parallel: since DESpec can observe 1000 targets per square degree, this mode is equivalent (say) to having 10 SDSS-like spectroscopic surveys packaged together, each with 100 targets per square degree.
An example of a potential DESpec community program is follow-up spectroscopy of stars measured by Gaia for proper motion (an idea that motivates ESO’s proposed 4MOST multiple-object spectrometer). Gaia will produce an astrometric catalog to V = 20, faint enough to guarantee that all of the DESpec fibers are subscribed. DESpec stellar radial velocities will be accurate to better than 4 km/sec (based on SDSS), and stellar abundances can be determined to better than 0.25 dex, again using SDSS experience. Such a survey would densely sample the position-velocity-abundance phase space for millions of stars in volumes not accessible in the northern hemisphere, altogether providing basic information about the history of the stellar build-up of the Milky Way.