Controlling weak-lensing shear biases from undetected galaxies in the era of Stage IV Surveys

TL;DR

This paper investigates how undetected faint galaxies contaminate weak-lensing shear measurements in Stage IV surveys, using a Euclid-like setup and a noise-bias-free CNN to isolate blending biases. The authors model two galaxy populations (bright sample galaxies and faint neighbours) with detailed apparent-magnitude, size, ellipticity, and S/N distributions, and simulate PSF-convolved images to quantify multiplicative shear biases. They find baseline biases near $m_i \, oughly\,-8\times10^{-3}$ in the absence of faint galaxies, exceeding Euclid requirements, and demonstrate that calibration simulations must include faint galaxies to $m_{ m AB,f} \,\sim\,27$ (potentially as faint as 29) within about $1.0$ arcsec of each bright galaxy. The study further shows that biases depend not only on mean faint-galaxy density but also on its correlations with the brightness of the bright galaxy, the faint-population magnitude-slope, the radial distribution around the bright galaxy, and faint-galaxy alignments and anisotropies; conversely, many other factors such as faint-galaxy shear coherence and paralleled orientations have negligible impact within explored ranges. These results provide concrete requirements for calibration simulations and highlight the need for deep-field data to constrain faint-galaxy properties (e.g., HUDF) to achieve the stringent Stage IV bias budgets.

Abstract

Gravitational lensing of background galaxies by intervening matter is a powerful probe of the cosmological model. In the era of Stage IV surveys, contamination from galaxies below the detection threshold has emerged as a significant source of bias. Adopting a noise-bias-free machine-learning method to estimate shear, we quantify the impact of faint galaxies for a Euclid-like survey. In our baseline simulations, faint blends induce a multiplicative shear bias of -0.008, well above Euclid's requirement. Similar to previous studies, we find that calibration simulations must include neighbouring galaxies to AB apparent magnitudes as faint as 27.0 (+2.1, -0.9) and within approximately 1.0 (+0.2, -0.2) arcsec of each bright sample galaxy (BSG; the galaxy for which shear is measured). By varying faint galaxy properties, we identify which ones significantly affect shear biases and quantify how well they must be constrained. Crucially, we find that biases not only depend on the mean projected faint-galaxy density and apparent-magnitude distribution across the sample, but also on how these quantities vary with the observed brightness of the BSG. Furthermore, biases are sensitive to radial and tangential alignments and positional anisotropy of faint galaxies relative to BSGs. By contrast, shear coherence between BSGs and faint galaxies, parallel orientation alignments, and variations in the faint galaxy size-magnitude relation have negligible impact within the parameter ranges explored. Our results guide calibration simulations and highlight the critical role of deep observations in measuring the properties of faint galaxies.

Figures (18)

• Figure 1: Mean cumulative number density of galaxies per arcmin$^2$, $\left<N(m_{\mathrm{AB}})\right>$, for the bright (blue) and faint (green) populations as a function of apparent magnitude. The functional form is given in Equation \ref{['eqn:num_cum']} and parameter values in Table \ref{['tab:slopes']}. The linear approximation to the faint galaxy distribution over the range $24.5 < m_{\mathrm{AB}} \leq 27$ is also shown (red dashed), offset to match the green curve at $m_{\mathrm{AB}} = 24.5$ (see Section \ref{['subsec:alphaf']}). The black vertical dotted line shows the division between the bright and faint populations at $m_{\mathrm{AB}}=24.5$.
• Figure 2: Distributions of apparent magnitudes ($m_{\mathrm{AB}}$, left) and effective radii ($r_{\mathrm{e}}$, right) for bright (blue solid) and faint galaxies. Faint galaxy distributions are shown for both the full (green solid) and simplified "linear" (red dashed) models for the apparent magnitude distribution. Parameter values are listed in Table \ref{['tab:slopes']}; see also Figure \ref{['fig:bias_alphamf']}. Bright galaxies are simulated over the range $20 < m_{\mathrm{AB}} < 24.5$, while faint galaxies span $24.5 < m_{\mathrm{AB}} < 29$ (full model) or $24.5 < m_{\mathrm{AB}} < 27$ (simplified model). Histograms use equal bin widths and identical $x$-axis ranges in each panel. Distributions are based on $10^{4}$ BSGs and associated faint galaxies simulated within 3 arcsec of each BSG (see Table \ref{['tab:Nsat']}).
• Figure 3: Signal-to-noise distribution (left) for an independent set of $10^4$ galaxies, where the flux is obtained from (i) noise-free postage stamps (black solid) and (ii) predicted from noisy stamps using CNN$_{\mathrm{snr}}$ (blue dashed). Residuals (right) show predicted minus true $S/N$ for a random subset of $10^3$ galaxies (black dots). The red points show the binned mean residuals with error bars indicating the standard error on the mean, and the light red shaded band indicates the sample standard deviation within each bin. The green dashed line marks zero residuals. Results are shown for zero shear and test set fiducial galaxy parameter values.
• Figure 4: Multiplicative (top) and additive (bottom) biases adopting committees comprising $n_{\mathrm{cnn}}$ subsets of 31 trained CNN$_{e_i}$ models. A selection cut of $S/N \geq 10$, using the CNN$_{\mathrm{snr}}$ predictions, is applied. Black crosses (squares) correspond to $i=1$ ($i=2$), while blue filled circles showing the mean across the two components. Green open circles indicate biases obtained using the "true" $S/N$ with $n_{\mathrm{cnn}}=31$ (offset for clarity). Shaded regions show the top-level Euclid bias requirements (see Section \ref{['sec:ellip_shear']}).
• Figure 5: Images showing 6 by 6 arcsec$^2$ regions of sky centered on the BSG. Each panel displays the PSF-convolved image with zero applied shear, sampled at 0.1 arcsec pixel scale, and scaled so that the central pixel has unit intensity. The images are shown without noise for 10 galaxy pairs (where each galaxy in a pair is the 90$^{\circ}$ rotated version of the other one). Faint neighbour galaxies are illustrated using ellipses that show their intrinsic (pre-PSF convolved) shapes with semi-major and semi-minor axes $a$ and $b$ (solid white; see Section \ref{['sec:gal_psf_models']}), together with the truncation boundary at $4a$ and $4b$ (dashed cyan). Apparent magnitudes are indicated for the BSG (white; top-left corner of each panel) and for each faint neighbour (magenta; at ellipse centres). The green solid square denotes the 1.7 by 1.7 arcsec cut-out region used for shear measurement. Only faint galaxies whose centre lies within the green dotted circle (with radius $\theta_{r}$ arcsec, centred on the centre of the BSG), are simulated in the test sets. Shown for the field number density of faint galaxies to a limiting magnitude $m_{\mathrm{lim}}=29$ (see Table \ref{['tab:Nsat']}).