**3.E Survey Strategy**
This section gives the outline of how the survey might acquire the spectra. The constraints are the field of view of the focal plane (2.3 degrees in diameter), the number of fibers (~4000), and the total survey time available in allocated nights, N, which is to be determined. For this exercise, we assume 80% of the allocated nights are astronomically useable and an average of 7.7 hours on the sky per useable night, both based on historical CTIO weather data. If the DESpec fibers span the full instrument circular FOV of 3.8 sq. deg. (as in Fig. 4.4 below), one could cover the 5000 sq. deg. DES footprint with, e.g., 1667 circular tiles, with 27% of the area covered by two tiles, similar to what was done for the SDSS spectroscopic survey. This would enable one in principle to place more fibers in dense regions of large-scale structure or to reach longer cumulative exposures on objects in the overlap regions; in this case, for 4000 fibers, the fiber density per tile on the sky is 1050 targets per sq. deg., and the average distance between fibers is 6.2 mm. This surface density of fibers per tile is comparable to the desired surface density of successful galaxy targets for BAO and RSD studies to redshift z ~ 1.7 (Secs. 2.B and 2.C). As an example, let us assume 65% combined targeting and redshift success rate for 800 flux- and photo-z selected ELG targets per sq. deg. and 80% efficiency for 140 LRG targets per sq. deg. for 30-minute cumulative exposures per target, with ~10% of the fibers left for sky background or other science targets per tile. We would obtain redshifts for ~8 million galaxies (~6.6 M ELGs and ~1.4 M LRGs) over 5000 sq. deg. in about 300 allocated nights, allowing for 20% loss to weather and 10% overhead. This would require target-selection strategies which would have at least 1800 ELG's available per square degree and 250 LRG's available per square degree. From the above strategies we have showed that this is possible. With, e.g., 15-minute individual exposures, this strategy would also provide some flexibility to adjust the target list over time, according to which galaxies had already achieved sufficient signal-to-noise ratio to yield a redshift. Since the source list of targets will be high (there are of order 10,000 galaxies per square degree brighter than i = 22.5), this approach can also help accommodate tile-to-tile fluctuations due to large-scale structure. For example, in underdense regions, additional galaxies can be added that comprise a different complete sample, and in overdense regions, having multiple visits per tile will help to achieve the required completeness (or calibrate the incompleteness). One could cover 15,000 sq. deg. (the bulk of the extragalactic sky for LSST) with ~24 million redshifts in ~900 allocated nights. These numbers are all approximate and require more detailed simulations to refine. The large reservoir of potential targets provides considerable latitude in designing the survey strategy.
The impact of altering the observed sample is demonstrated by some initial results in Section 3.G. At present we have limited ourselves to two populations, Luminous Red Galaxies (LRGs) down to a magnitude of i<22 and Emission Line Galaxies (ELGs) down to a magnitude of i<23.5, and only alter the ratio of LRGs to ELGs. We consider three cases of LRG/ELG: 10%/90%; 33%/67% and 50%/50%. We assume that the whole survey area adopts this ratio for the entire observing time. A number of more detailed results, which allow the type of observed galaxies to vary with redshift and observed position on the sky, will be presented in Jouvel et al. (2012).
**3.F Projected Angular Power Spectra Analysis**
In this section we introduce forecasts for joint constraints from DES+DESpec using a formalism entirely composed of projected angular power spectra, *C(l)s*, in redshift shells, using the above selection criteria. This technique is common in weak lensing and photo-z work but spectroscopic galaxy surveys usually use a full 3D power spectrum analysis. While the *C(l)* approach can lose small-scale information through projection effects, the benefit is a very elegant way of including cross-correlations between weak lensing and galaxy clustering, including all the off-diagonal elements of the covariance matrix. On scales of interest for our forecast, Asorey et al. (2012) have shown that this approach can in fact recover the full 3D clustering information. It is also much simpler to examine the impact of the galaxy distribution function, n(z), on galaxy clustering measurements, which is important when considering target-selection strategies. This approach is complementary to the work of Cai & Bernstein 2012 and Gaztanaga et al. 2012 described in Section 2.
We assume two fiducial survey designs. We model DES as a cosmic shear survey with photometric-quality redshifts, measuring cosmic shear of ~300 million galaxies over 5000 deg^{2} out to redshift 3. We assume DESpec will measure spectroscopic redshifts for ~10 million galaxies over 5000 deg^{2} out to redshift 1.7. We analyse the DES survey using five unequally spaced tomographic bins in redshift with roughly equal galaxy number density in each. The higher quality redshifts in the DESpec survey allow us to use 30 bins of equal redshift spacing. We include the effects of Redshift Space Distortions in our *C(l)* framework using the formalism introduced by Fisher et al. (1994). We examine both surveys independently, forecasting constraints through the Fisher Matrix (FM) formalism, as well as joint constraints from both surveys assuming that they observe different patches of sky (simply adding the FMs) or the same patch of sky (including all galaxy-shear cross-correlations). We exclude nonlinear scales from all observables that include galaxy clustering. Galaxy bias, b_{g}(z), is assumed to be scale-independent with fiducial value 1, parameterized by an overall amplitude normalisation and three nodes in redshift. The amplitude of these four nuisance parameters is allowed to vary and is marginalised over in our results. For galaxy-shear results, the cross-correlation coefficient is assumed to be unity at all scales/redshifts, r_{g}(k, z) = 1.
**igure of Merit**
the mentioned above in Sec. 3.E
, Q_{0} and R_{0,}zz,zThis one-parameter model has the advantage of being able to detect the presence of anisotropic stresses on cosmological scales but is otherwise complementary to the one-parameter MG model discussed above in Sec. 2.
igure of Meritcosmic shear (galaxy clustering (), DES+DESpec + *nn* (different sky), and DESxDESpec + *n* + *nn* (same sky, including galaxy-shear cross-correlations).
It is clear that combining both probes (weak lensing and galaxy clustering) improves the constraining power on Dark Energy and on Modified Gravity. Going from DES to DES+DESpec + *nn* improves the DETF FoM by a factor of 2.4. What is also very evident is that the additional cross-correlation information gained from having two surveys on the same patch of sky is very significant. The improvement in going from DES+DESpec + *nn* to DESxDESpec + *n*+ *nn*, i.e., from different skies to same sky, is more than a factor of 4 in the DETF FoM. This is understandable when we consider the extra control of galaxy biasing provided by the galaxy-shear cross-correlations.
The results for MG are similar. If we define an analog to the DETF FoM for MG (roughly the inverse of the area under the Q_{0}, Q_{0}(1+R_{0})/2 contour), we see a factor of 5.7 improvement in going from DES to DES+DESpec + *nn*. This gain is more pronounced than the DE case due to the strong degeneracy between the metric potentials, which can be broken by joint use of weak lensing and galaxy clustering. Even so, the improvement in going from different sky to same sky is still more than a factor of 5.
**Figure 3.12:*** 95% confidence contours for DES cosmic shear (**** [blue lines], DESpec galaxy clustering (nn) [cyan lines], DES+DESpec **** + nn (different sky) [green lines], and DESxDESpec ****+ n****+ nn (same sky) [black lines]. Top panel: Constraints on the equation of state of dark energy, w*_{0}* and w*_{a}*. Bottom panel: Constraints on deviations from GR parameterized by Q*_{0}* and R*_{0}*. All other cosmological parameters and nuisance parameters are marginalised over. These results are initial findings and a full investigation will appear in Kirk et al. (2012).*
**Table 3.1.*** Relative Figures of Merit for both DE and MG as a function of LRG/ELG ratio. DE and MG constraints are each independently normalised to the FoM for galaxy-galaxy clustering (including RSD) from a DESpec-type survey only. Columns show constraints for DESpec alone (nn), joint independent DESpec and DES constraints (nn + ****, and joint constraints assuming DES and DESpec are in the same patch of sky, including all cross correlations (****+ n****+ nn) . Rows show results for different ratios of LRGs to ELGs as target selection strategies are changed.*
Table 3.1 summarizes the FoM variation as a function of LRG/ELG ratio. Looking at these relative FoM numbers shows us that, even for the simple scenarios we consider, altering the type of galaxy selected can change FoM results by up to 70% for DESpec alone. Obviously the addition of the (unchanging) DES survey mitigates this variation in the joint constraints, but we still see differences at the 20% level for the joint constraints including all cross-correlations. These results are preliminary findings, but they demonstrate the importance of considering the details of target selection for a DESpec-type survey. A more detailed investigation will appear in Kirk et al. (2012).
In summary, Fig. 3.12 and Figs. 2.1 and 2.3 illustrate the potential for substantial improvement in our knowledge of DE and MG with respect to what will be achieved by DES. The combination of DES and DESpec can improve the DETF figure of merit on cosmic acceleration by factors well above 5, depending on the probes and assumptions used. A similar gain can be achieved simultaneously on the cosmic growth history or modified gravity models. We have also illustrated how we can use DES photometric information to select spectroscopic targets to optimize the survey science.
These results have assumed basic target selection strategies for a DESpec-type survey. We are pursuing R&D work on survey optimization. In particular we will optimize the relative number of galaxy targets of a given type at different redshifts (see Table 3.1). Different galaxy types differently trace dark matter halos of different mass. Higher-redshift galaxies sample larger volumes, but 3D dark matter information is better recovered at intermediate redshifts, where DES weak lensing information peaks (see Fig. 2.2). We will combine these theoretical considerations with those related to the spectrograph design to forecast results based on different design specifications, particularly wavelength coverage. This more detailed work is in progress and will be presented as part of the continued R&D development of DESpec.
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