Dark energy constraints from cosmic shear power spectra: impact of intrinsic alignments on photometric redshift requirements

TL;DR

This study quantifies how intrinsic alignments (II and GI) impact cosmic shear constraints on dark energy, using a fiducial non-linear intrinsic alignment model and a flexible multi-parameter IA framework. It shows that ignoring IA biases the dark energy equation of state and that IA degrades the dark energy figure of merit, necessitating more tomographic redshift bins and tighter photometric redshift control. Priors on IA and redshift distributions can mitigate degradation and enable recovery of information, highlighting the need for external IA measurements and spectroscopic calibration in future surveys. The results inform survey design and redshift-quality requirements to robustly constrain dark energy with cosmic shear.

Abstract

Cosmic shear constrains cosmology by exploiting the apparent alignments of pairs of galaxies due to gravitational lensing by intervening mass clumps. However galaxies may become (intrinsically) aligned with each other, and with nearby mass clumps, during their formation. This effect needs to be disentangled from the cosmic shear signal to place constraints on cosmology. We use the linear intrinsic alignment model as a base and compare it to an alternative model and data. If intrinsic alignments are ignored then the dark energy equation of state is biased by ~50 per cent. We examine how the number of tomographic redshift bins affects uncertainties on cosmological parameters and find that when intrinsic alignments are included two or more times as many bins are required to obtain 80 per cent of the available information. We investigate how the degradation in the dark energy figure of merit depends on the photometric redshift scatter. Previous studies have shown that lensing does not place stringent requirements on the photometric redshift uncertainty, so long as the uncertainty is well known. However, if intrinsic alignments are included the requirements become a factor of three tighter. These results are quite insensitive to the fraction of catastrophic outliers, assuming that this fraction is well known. We show the effect of uncertainties in photometric redshift bias and scatter. Finally we quantify how priors on the intrinsic alignment model would improve dark energy constraints.

Figures (9)

• Figure 1: Dotted line: The best fit to the SDSS data using the HRH* model. Dot-dashed line: The prediction from the linear alignment model roughly normalized to hirataea04, who normalize to SuperCOSMOS. Solid line: The prediction from the linear alignment model if a non-linear matter power spectrum is used in place of the linear theory matter power spectrum. The solid line is closer to the HRH* model and we use this model throughout. The error bars of mandelbaumhisb06 encompass all the models.
• Figure 2: The dot-dashed line shows the linear alignment model. The solid line shows our fiducial model, which uses the non-linear matter power spectrum in the linear alignment model. Data points taken from the analysis of SDSS in Figure 1 of hirataea07. Circles are for blue galaxies and crosses for red galaxies. Note that only $r_p>11.9 h^{-1}$ Mpc ($r_p>4.7 h^{-1}$ Mpc) were used in their most (least) conservative fits (grey shading). Upper L4, the largest sample. Lower L6, the brightest sample. The upper two lines show the linear alignment model predictions multiplied by a factor of ten.
• Figure 3: A selection of shear cross power spectra for our fiducial survey divided into ten tomographic redshift bins. We assume a photometric redshift scatter of $\delta_z = 0.05 (1+z)$ and zero catastrophic outliers. Solid line: lensing shear (GG) term. Dashed line: intrinsic shear (II) term. Dotted line: shear-intrinsic (GI) cross term (absolute values shown). Dot-dashed line: total. Galaxies are divided into tomographic redshift bins with equal numbers of galaxies in each bin. The median redshifts of the tomographic redshift bins 1 to 10 are $(0.30, 0.49, 0.62, 0.73, 0.84, 0.96, 1.1, 1.2, 1.4, 1.9)$ respectively.
• Figure 4: Illustration of the default spatial flexibility we allow in the intrinsic alignment power spectra. Lines are as in the previous figure but the intrinsic alignment power spectra have been multiplied by a function with five bins in k which are interpolated linearly in the log as detailed in the text. We have arbitrarily set the bin values to $B^X_{1 .. (n-1)}=\left(1,\, -1,\, 1,\, -1,\, 1\right)$ to show the freedom.
• Figure 5: Top row: Assuming perfect photometric redshifts ($\delta_z=0$). Bottom row: More realistic photometric redshifts ($\delta_z=0.05$). Left column: Including just the II terms. Middle column: Including just the GI terms. Right column: Including both II and GI terms. Solid lines: figure of merit as a function of number of kbins. Lines from top to bottom within one panel: the number of bins in the redshift direction increases 1, 2, 5. Dotted line: FoM for GG alone. Dashed line: using the linear alignment model with the linear theory matter power spectrum, instead of the non-linear theory matter power spectrum. In every case a free amplitude parameter and unknown power law evolution was marginalized over (allowed to be different for each of GI and II). The default intrinsic alignment model we use for the remaining figures is shown by a circle and our maximally flexible model is marked by a cross.