Steeling Weak Lensing Source Galaxy Samples against Systematics using Wide Field Spectroscopy

Abstract

We investigate the cosmological constraining power of combined weak galaxy lensing and galaxy clustering probes, i.e. $3\times2$-point analyses, assuming flexible models for redshift uncertainty, and Lagrangian perturbation theory and hybrid effective field theory models for galaxy intrinsic alignments, galaxy bias and baryonic physics. In this context, we provide a detailed accounting of the limiting systematics on $3\times2$-point analyses. Our main finding is that in the presence of current levels of uncertainty on baryonic physics, the information content of weak lensing analyses saturates on quasi-linear scales, allowing the use of source galaxy samples that are significantly less dense, e.g. with number densities of $5\rm \, arcmin^{-2}$, without sacrificing constraining power, provided that redshift distributions can be calibrated at the $σ(\langle z\rangle)=0.005$ level. We show that for sufficiently narrow lens and source redshift distributions, intrinsic alignment contributions can be largely self-calibrated, though sufficient flexibility must be given to the redshift and scale dependence of this signal. The near optimality of such relatively sparse source galaxy samples opens the possibility to directly calibrate the redshift distributions and intrinsic alignment contamination of such a sample using a spectroscopic instrument like DESI, thus mitigating the dominant systematics in weak lensing analyses.

Figures (17)

• Figure 1: ( Left) Cosmic shear power spectrum for the highest redshift Steel sample bin (solid) compared to shape noise contributions per mode for different source number densities (dashed), roughly corresponding to the densities assumed throughout this paper for Steel (black) and Gold (orange) samples. ( Right) Fisher forecasts for $\sigma(S_8)$ as a function of $\ell_{\rm max}$ without shape noise, marginalizing over photo-$z$ and shear calibration uncertainties and fixing IA uncertainties to zero (blue) or IA and baryon uncertainties to zero (green). The vertical lines indicate where the lensing signal is greater than the shape noise for the two source densities plotted on the left. When baryons are marginalized over, the vast majority of the constraining power on $\sigma_8$ comes from scales where the cosmic shear signal is not shape noise dominated, even for relatively low source number densities. This is seen by the relatively small improvement in $\sigma(S_8)$ between the scales that are shape noise dominated for the two different densities, as indicated by the blue arrow. When baryons are fixed, more information can be extracted from high $\ell$, although even in this case the rapidly decreasing lensing signal at high $\ell$ limits the advantage of very high number densities.
• Figure 2: Redshift distributions (arbitrarily normalized) assumed for LSST sources (colored lines) for Gold (left) and Steel (right) samples constructed as described in Section \ref{['sec:lsst']}. The BGS and LRG lens bins (greyscale; §\ref{['sec:desi']}) are the same in both panels. Note that the Steel sample $n(z)$ are more compact, but have negligible support above $z=1.6$, where [O ii] redshifts out of the DESI spectrograph wavelength range.
• Figure 3: Impact of source number density on $S_8$ constraining power under various modeling assumptions for the Steel redshift distributions (black) for $3\times2$-point (solid), and $2\times2$-point (dashed) analyses compared to $3\times2$-point constraints from the Gold sample (orange band; with $\bar{n}_{\rm source}=27.7\,\mathrm{arcmin}^{-2}$). The upper end of the Gold sample constraining power corresponds to stage III levels of redshift calibration while the lower limit corresponds to the levels required by the SRD, analogous to $\sigma(\Delta z)=0.001$. The dashed orange line shows the most pessimistic Gold scenario where we must discard the highest redshift source bin. The left panel shows forecasts for our fiducial modeling assumptions. The middle panel simplifies the IA treatment to use the NLA model with linear redshift evolution per source bin. The right panel shows a case with this simplified IA model and the impact of baryons reduced by a factor of 10, such that there are only $0.5\%$ baryonic effects at $k=0.4\, h \, {\rm Mpc}^{-1}$.
• Figure 4: Illustration of the IA self-constraining power of $3\times2$-point analyses even in the presence of flexible IA redshift evolution. The shaded regions in the top two rows show constraints on $c_s^{i}(z)$ for Steel (blue) and Gold (orange) for each source bin in the various columns. The lines show the uncertainty in the fractional IA contribution to the total signal in the cosmic shear auto-power spectrum at $\ell=200$ as a function of redshift. The top row shows the case of our fiducial IA redshift evolution model with a correlation length of $\Delta z=0.5$. The middle row assumes a linear spline per source bin, i.e. $\Delta z=3.0$. The bottom row shows the source galaxy redshift distributions (blue and orange for Steel and Gold respectively) as well as the lens redshift distributions (grayscale). The $2\times2$-point data tightly constrains the IA amplitudes in both IA redshift evolution scenarios which mitigates IA contamination to cosmic shear.
• Figure 5: $p$-values for $\nu$ degrees of freedom (top left) and Fisher bias calculations in units of the uncertainty for $S_8$ (top right), $\Delta z_{\rm core}^1$ (lower left) and $A_s$ (lower right) as a function of $\Delta z_{c_s}$, the spline node spacing for $c_s$. $p$-values are for fitting the "Biased IA$(z)$" scenario for Steel (black) and pessimistic Gold (orange) samples, varying only the IA sector. Fisher uncertainty forecasts are shown as dashed lines with the right $y$-axis of the three 'bias' panels, with Fisher bias values the solid lines with the left $y$-axis. Generically, we see that models that only allow for a constant amplitude per source bin, denoted as "Const." on the $x$-axis, provide very poor fits to the "Biased IA$(z)$" model, and that biases decrease quickly as model complexity increases.