Constraints on intrinsic alignment contamination of weak lensing surveys using the MegaZ-LRG sample

TL;DR

This study measures position–shape correlations in the MegaZ-LRG photometric sample and combines them with SDSS spectroscopic LRG and Main samples to constrain an intrinsic alignment model across wide redshift and luminosity ranges. It develops a formalism that accounts for photometric redshift scatter and includes contributions from galaxy-galaxy lensing and magnification effects, finding that a nonlinear version of the linear alignment model with a luminosity-dependent amplitude fits the data well. Joint analyses reveal that intrinsic alignments scale roughly linearly with luminosity and show no strong extra redshift evolution beyond the corrected NLA, significantly tightening cosmological parameter biases for tomographic weak lensing surveys. The resulting constraints imply that intrinsic alignments remain subdominant for current surveys, with MegaZ-LRG data markedly improving the precision of IA priors, though future surveys like Euclid may require more aggressive modelling and priors.

Abstract

Correlations between the intrinsic shapes of galaxies and the large-scale galaxy density field provide an important tool to investigate galaxy intrinsic alignments, which constitute a major astrophysical systematic in cosmological weak lensing (cosmic shear) surveys, but also yield insight into the formation and evolution of galaxies. We measure galaxy position-shape correlations in the MegaZ-LRG sample for more than 800,000 luminous red galaxies, making the first such measurement with a photometric redshift sample. In combination with a re-analysis of several spectroscopic SDSS samples, we constrain an intrinsic alignment model for early-type galaxies over long baselines in redshift (z ~ 0.7) and luminosity (4mag). We develop and test the formalism to incorporate photometric redshift scatter in the modelling. For r_p > 6 Mpc/h, the fits to galaxy position-shape correlation functions are consistent with the scaling with r_p and redshift of a revised, nonlinear version of the linear alignment model for all samples. An extra redshift dependence proportional to (1+z)^n is constrained to n=-0.3+/-0.8 (1sigma). To obtain consistent amplitudes for all data, an additional dependence on galaxy luminosity proportional to L^b with b=1.1+0.3-0.2 is required. The normalisation of the intrinsic alignment power spectrum is found to be (0.077 +/- 0.008)/rho_{cr} for galaxies at redshift 0.3 and r band magnitude of -22 (k- and evolution-corrected to z=0). Assuming zero intrinsic alignments for blue galaxies, we assess the bias on cosmological parameters for a tomographic CFHTLS-like lensing survey. Both the resulting mean bias and its uncertainty are smaller than the 1sigma statistical errors when using the constraints from all samples combined. The addition of MegaZ-LRG data reduces the uncertainty in intrinsic alignment bias on cosmological parameters by factors of three to seven. (abridged)

Figures (21)

• Figure 1: Top panel: Redshift distributions of the galaxy samples analysed. Shown are the histograms for the SDSS LRG samples in black (faint, $M_r > -22.3$), blue (medium, $-22.6 < M_r < -22.3$), and purple (bright, $M_r < -22.6$), for the full MegaZ-LRG sample in red, and for the SDSS Main samples in green (L4) and orange (L3). Note that both SDSS LRG and MegaZ-LRG samples are split into two redshift bins each, the SDSS LRG samples at $z=0.27$ and the MegaZ-LRG sample at $z=0.529$. Bottom panel: Distribution of rest-frame absolute magnitudes $M_r$. The colour coding of the histograms is the same as in the top panel. In the case of the SDSS LRG and MegaZ-LRG samples solid lines correspond to the low redshift bin, dotted lines to the high redshift bin, respectively. Note that the MegaZ-LRG histograms rely on photometric redshift estimates, and that they have been downscaled by a factor of 20 to facilitate the comparison with the other samples.
• Figure 2: Binned histogram of spectroscopic redshifts from 2SLAQ and photometric redshift estimates from the MegaZ-LRG catalogue. Note that the shading of the bins is logarithmic. The solid line indicates a one-to-one relation between spectroscopic and photometric redshifts, coinciding with the mean trend to high accuracy. The dotted lines correspond to the $\pm 1\sigma$ scatter.
• Figure 3: Fraction of galaxies in the MegaZ-LRG sample with high-quality shape measurements, as a function of photometric redshift (top left panel), rest-frame absolute $r$ band magnitude $M_r$ (top right panel), $i$ band de Vaucouleurs magnitude $i_{\rm deV}$ which was used as a selection criterion for the MegaZ-LRG catalogue (bottom left panel), and apparent observer-frame $r$ band magnitude used to impose a magnitude limit on the shape catalogue (bottom right panel). The red histograms show the match fraction for the full MegaZ-LRG shape sample, and the blue histograms for shape sample with the additional colour cut that will be discussed in Sect.$\,$\ref{['sec:colorcomparison']}. For reference we have added to each panel the histogram of the full MegaZ-LRG sample with arbitrary normalisation as black dotted lines. Note that the fraction of galaxies with shape information does not depend strongly on redshift and $r$ band magnitude.
• Figure 4: Three-dimensional correlation function models of a sample with the MegaZ-LRG photometric redshift error as a function of comoving line-of-sight separation $\Pi$ and comoving transverse separation $r_p$ at $z_{\rm m} \approx 0.5$. The galaxy bias has been set to 1.9 in all panels. Top panel: Galaxy clustering correlation (gg). Contours are logarithmically spaced between 1 (yellow shading) and $10^{-5}$ (violet shading) with three lines per decade. Centre panel: Galaxy number density-intrinsic shear correlations (gI). Contours are logarithmically spaced between $10^{-3}$ (yellow shading) and $10^{-6}$ (violet shading) with three lines per decade. Bottom panel: Galaxy-galaxy lensing (gG). For ease of direct comparison, the contours are encoded exactly like in the centre panel. Note that the galaxy-galaxy lensing signal is not symmetric around $\Pi=0$, in contrast to the gg and gI terms. Also, it is negative, so that the modulus is plotted. For an illustration of the effect of photometric redshift scatter see Fig.$\,$\ref{['fig:gicorr_photozeffect']}.
• Figure 5: Top panel: Modulus of the angular power spectra of the different signals contributing to galaxy position-shape correlations. Number density-intrinsic correlations (gI) are shown in black, galaxy-galaxy lensing (gG) in red, magnification-shear correlations (mG) in green, and magnification-intrinsic correlations (mI) in blue. Solid curves correspond to the redshift auto-correlations at $z=0.5$, i.e. close to the mean redshift of the low-redshift MegaZ-LRG sample, and dotted curves to the mean redshift of the high-redshift sample at $z=0.59$. Bottom panel: Ratio of the aforementioned signals over the gI correlations, with the same coding of the curves as above. The grey region covers angular scales that do not contribute significantly to the correlation functions. Galaxy-galaxy lensing and possibly mG correlations yield a relevant contribution to number density-shape correlations besides the gI signal.