Prospects for measuring the Doppler magnification dipole with LSST and DESI

TL;DR

This work assesses the feasibility of detecting the Doppler magnification dipole by cross-correlating DESI BGS-like galaxy counts with a convergence field reconstructed from LSST-size galaxy images. Using cosmoDC2 to define DESI-like samples, GalSim and Galight to simulate LSST Year 1–like imaging, and a Doppler-dipole estimator, the authors quantify the total size-noise $\sigma_{\kappa}$ as a combination of intrinsic size dispersion and measurement error. They forecast a robust detectability with total $S/N$ values around $13$ in four redshift bins up to $z\lesssim 0.5$, with peak $S/N$ at small separations ($d\sim 10$–$25\,\mathrm{Mpc}/h$). The results indicate that the Doppler magnification dipole can be measured with high significance in near-future wide-field surveys, offering an independent probe of peculiar velocities and growth while highlighting the importance of intrinsic size scatter and survey overlap. The study also discusses limitations due to image systematics and blending, emphasizing the need for realistic PSF and selection modeling in future analyses.

Abstract

We forecast the detectability of the Doppler magnification dipole with a joint analysis of galaxy spectroscopic redshifts and size measurements. The Doppler magnification arises from an apparent size variation caused by galaxies' peculiar velocities when mapping them from redshift space to real space. This phenomenon is the dominant contribution to the convergence at low redshifts ($\lesssim$ 0.5). A practical observational strategy is to cross-correlate a galaxy number count tracer, e.g. from the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey, with the convergence field reconstructed from galaxy size measurements obtained by the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). To assess the achievable precision of galaxy size measurements, we simulate LSST Y1-quality galaxy images with Galsim and measure them with the Galight profile fitting package. Our investigations, based on galaxy populations from LSST's synthetic galaxy catalogue cosmoDC2, show that the variance due to intrinsic galaxy size variation dominates over size measurement errors as expected, but may be lower than previous studies have suggested. Under our analysis assumptions, the Doppler magnification dipole would be detectable with a signal-to-noise ratio $\geq 10$ in multiple redshift bins between $0.1 \leq z \leq 0.5$ with DESI spectroscopic redshifts and LSST imaging.

Figures (9)

• Figure 1: Distributions of galaxy properties from the BGS-selected cosmoDC2 catalogue. Top: redshift distribution of the sample. Middle: true half-light radii (of the major axis) distribution in four redshift bins. Values above 10 arcsec are excluded from the plot for clarity. Bottom: apparent $r$-band magnitude distribution for the same redshift bins.
• Figure 2: Distribution of $\sigma _{\kappa,\,\mathrm{intrinsic}}$ in bins of $m_r$ and $z$ for the DESI BGS-like simulated sample selected from the LSST cosmoDC2 simulation. The colour scale represents $\sigma _{\kappa,\,\mathrm{intrinsic}}$ within each $(m_r,z)$ bin, ranging from 0 to 1, while the contours represent the number of galaxies selected from the catalogue, plotted in intervals of 200.
• Figure 3: Count-weighted average $\langle \sigma_{\kappa,\,\mathrm{intrinsic}}\rangle$ in finely binned $z$ intervals and the chosen redshift bins. The orange dashed curve shows the values of the computed $\sigma_{\kappa,\,\mathrm{intrinsic}}$ from Figure \ref{['fig:sigmaKappa_mr_z']} averaged over $m_r$. The maroon step function shows the average of $\sigma_{\kappa,\,\mathrm{intrinsic}}$ within the chosen redshift bins, with the square markers at the midpoints of each redshift bin.
• Figure 4: Measurement uncertainty in galaxy half-light radius, $\sigma_{\kappa,\, \mathrm{measured}}$, with varied $r$-band apparent magnitude (top), redshift (middle), and lensed half-light radius (bottom), for a sample of 10,000 galaxies from the cosmoDC2 catalogue selected to match DESI BGS-like criteria. Galaxies with $z\leq0.05$ are excluded from the analysis.
• Figure 5: Predicted Doppler magnification dipole $\xi^{\Delta\kappa}$ for a DESI+LSST-like survey in four redshift bins. The solid curves show the amplitude at different redshifts, with shaded regions representing 1-$\sigma$ uncertainties from the calculated covariance matrix (Equation \ref{['eq:cov']}), computed with the size-noise values $\sigma_{\kappa,\mathrm{total}}$ for each bin from Table \ref{['tab:sigma_kappa']}.