Prospects for measuring the Doppler magnification dipole with LSST and DESI

Technical Summary: Prospects for measuring the Doppler magnification dipole with LSST and DESI

Problem and Motivation
The Doppler magnification effect arises from the peculiar velocities of galaxies, which shift their apparent locations in redshift space, inducing an apparent variation in their flux and angular size. At low redshifts ($z \lesssim 0.5$), this Doppler-induced convergence ($\kappa_v$) dominates over standard gravitational lensing convergence ($\kappa_g$). This phenomenon generates a characteristic dipolar magnification pattern around overdensities: galaxies infalling toward the observer appear demagnified (smaller and fainter), while those receding appear magnified. While the theoretical foundation for this effect has been established (e.g., Bonvin 2008; Bacon et al. 2014), and previous forecasts suggested high signal-to-noise (SNR) detections with future surveys, the effect has not yet been detected. A critical gap remains in quantifying the realistic observational uncertainties, particularly regarding galaxy size measurements, which are necessary to reconstruct the convergence field. This paper addresses the feasibility of detecting the Doppler magnification dipole using a joint analysis of the Dark Energy Spectroscopic Instrument (DESI) and the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST).

Methodology
The authors propose a cross-correlation strategy between a galaxy number count tracer (derived from DESI Bright Galaxy Survey, BGS, spectroscopic redshifts) and a convergence field reconstructed from galaxy size measurements (derived from LSST imaging).

1. Sample Selection: The study utilizes the cosmoDC2 synthetic galaxy catalogue, a realistic simulation based on the Outer Rim $N$-body simulation. A DESI BGS-like sample is selected using magnitude cuts ($r < 19.5$) and color criteria, focusing on the "Bright" sample to ensure high-quality spectroscopic redshifts.
2. Intrinsic Size Variance: The intrinsic scatter in galaxy sizes ($\sigma_{\kappa, \text{intrinsic}}$), which acts as a fundamental noise floor for convergence reconstruction, is calculated directly from the true half-light radii in the cosmoDC2 catalogue. This is binned by redshift and apparent magnitude.
3. Image Simulation and Measurement Errors: To assess measurement uncertainties ($\sigma_{\kappa, \text{measured}}$), the authors simulate LSST Year 1 (Y1) quality images using GalSim. These simulations incorporate realistic Point Spread Functions (PSF), detector noise, and sky background. The galaxies are modeled as single-component Sérsic profiles (fixed index $n=1.5$).
4. Size Recovery: The simulated images are analyzed using the Galight profile fitting package to recover galaxy half-light radii. The measurement error is quantified as the mean squared difference between the recovered and true radii.
5. Forecasting: The total uncertainty ($\sigma_{\kappa, \text{total}}$) is computed by combining intrinsic and measurement errors in quadrature. This uncertainty is propagated into the covariance matrix of the dipole estimator (following Andrianomena et al. 2019) to forecast the Signal-to-Noise Ratio (SNR) for the cross-correlation between number counts and convergence across four redshift bins ($0.1 \le z < 0.5$).

Key Contributions

• Realistic Size Noise Quantification: Unlike previous studies that may have assumed idealized conditions, this work explicitly simulates LSST-like imaging conditions and applies a specific profile fitting pipeline (Galight) to quantify the measurement error contribution to the convergence uncertainty.
• Validation of Intrinsic Dominance: The analysis confirms that, as expected, the variance due to intrinsic galaxy size variation dominates over size measurement errors. However, the authors note that the intrinsic scatter found in cosmoDC2 may be lower than suggested in some previous literature.
• Joint Survey Forecast: The paper provides the first detailed forecast for the Doppler magnification dipole specifically combining DESI spectroscopic data with LSST imaging size measurements, accounting for the specific overlap area and noise characteristics of these surveys.

Results

• Measurement Precision: The simulation results show that the measurement uncertainty in galaxy sizes ($\sigma_{\kappa, \text{measured}}$) is significantly smaller than the intrinsic size dispersion ($\sigma_{\kappa, \text{intrinsic}}$) across all redshift bins. Consequently, the total uncertainty is driven by the intrinsic scatter. The measurement bias ($b_\kappa$) was found to be negligible.
• Dipole Amplitude: The predicted dipole signal ($\xi_{\Delta\kappa}$) is negative across all separations, dropping rapidly at small scales ($d \sim 10\text{--}50$ Mpc/$h$), reaching a broad minimum around $100\text{--}125$ Mpc/$h$, and becoming less negative at larger scales. The amplitude decreases with increasing redshift.
• Detectability (SNR): The forecasts indicate a high detectability of the dipole signal. The total SNR per redshift bin is calculated as:
  • $12.98$ for $0.1 \le z < 0.2$
  • $12.97$ for $0.2 \le z < 0.3$
  • $12.66$ for $0.3 \le z < 0.4$
  • $10.41$ for $0.4 \le z < 0.5$
    The peak SNR per separation bin reaches $\sim 8\text{--}9$ at small scales ($d \sim 10\text{--}25$ Mpc/$h$).
• Variance Decomposition: The covariance analysis reveals that at low redshifts and small separations, the variance is dominated by the size noise term ($\Xi_2$). At larger separations and higher redshifts, cosmic variance ($\Xi_1$) becomes the dominant source of uncertainty. Shot noise ($\Xi_3$) remains negligible across all scales.

Significance and Claims
The paper claims that the Doppler magnification dipole is a robust observable that can be detected with high significance ($\text{SNR} \ge 10$) in multiple redshift bins between $0.1$ and $0.5$ using the combined DESI and LSST datasets. The authors emphasize that this detection is feasible because the measurement errors from LSST-like imaging are sub-dominant to the intrinsic galaxy size scatter.

The study concludes that this joint analysis offers an independent probe of the growth rate of structure and peculiar velocities, complementary to traditional Redshift-Space Distortion (RSD) measurements. The authors note that the dipole estimator's reliance on cross-correlating two different fields (number counts and sizes) from different experiments provides inherent protection against uncorrelated systematics (e.g., PSF modeling errors or seeing variations).

Caveats
The authors explicitly state several limitations:

• The simulations rely on cosmoDC2 size distributions, which are based on semi-analytic models and may not perfectly match real data.
• The image simulations assume isolated galaxies and do not account for blending (overlapping sources), which is expected to affect a significant fraction of galaxies in deep LSST images and could increase measurement uncertainties.
• The analysis assumes a simplified single-component Sérsic profile for all galaxies, whereas real galaxies have complex structures.
• The forecast assumes a specific overlap area ($\sim 5,900$ deg$^2$) which may be smaller in practice, though future surveys like 4MOST could increase this.

Despite these caveats, the paper asserts that under the modeled assumptions, the intrinsic size scatter is the limiting factor, and the resulting SNR is sufficient for a definitive detection of the Doppler magnification dipole.