Correlated residuals in Tully-Fisher and Fundamental Plane relations and their impact on peculiar velocity measurements

Abstract

The Tully-Fisher (TF) and Fundamental Plane (FP) relations are widely used to infer extragalactic distances and peculiar velocities, enabling measurements of large-scale velocity statistics and cosmological parameters. Using the Millennium-TNG hydrodynamical simulation, we assess the accuracy of these methods in the presence of realistic galaxy formation physics. We find that, while the 2-point statistics of velocities are reliably inferred on scales larger than $\sim10\,\hMpc$, significant systematic deviations arise on smaller scales. These deviations originate from spatially correlated residuals in the TF and FP relations, driven by correlations between galaxy structural properties, star-formation history, and the local environment. As a result, TF- and FP-inferred velocity fields exhibit spurious correlations with the galaxy density field that cannot be explained by random scatter alone. We show that extending the TF and FP relations to include additional galaxy properties -- such as star formation rate, gas mass, and stellar mass -- mitigate these environmental correlations, particularly for late-type galaxies. Our results demonstrate that galaxy formation physics induces significant systematics in peculiar velocity measurements on non-linear scales, and that neglecting these effects may bias cosmological analyses.

Figures (9)

• Figure 1: Galaxy sample selection in the MTNG simulation. Left panel: Specific star formation rate (sSFR) as a function of stellar mass for all galaxies at $z=0$, colour-coded by U–K colour. The black dotted line marks the threshold $\mathrm{sSFR}=0.04\mathrm{Gyr}^{-1}$ used to separate star-forming and quiescent galaxies. White contours enclose the 68% and 95% density regions of the distribution. Right panel: Final late-type (LTG) and early-type (ETG) samples after applying an additional cut on the rotational support parameter $\kappa_\mathrm{rot}$. Galaxies are colour-coded by $\kappa_\mathrm{rot}$, highlighting the separation between rotation- and dispersion-dominated systems.
• Figure 2: Tully–Fisher and Fundamental Plane relations in the MTNG simulation. Left: Comparison between true $r$-band absolute magnitudes and those predicted by the non-parametric TF relation for late-type galaxies. Right: Comparison between true logarithmic effective radii and values predicted by the non-parametric FP relation for early-type galaxies. In both panels, the black dashed line indicates the one-to-one relation, while contours enclose 68%, 95%, and 99.7% of the galaxy distribution.
• Figure 3: Radial velocity distributions of the galaxy samples. Blue and red histograms show the inferred line-of-sight peculiar velocities for the LTG (TF) and ETG (FP) samples, respectively. The true velocity distribution of the combined samples measured directly from the simulation is shown in black. The broadening of the inferred distributions reflects the dominant contribution of distance–indicator scatter.
• Figure 4: Velocity clustering statistics inferred from TF and FP distances. Blue and red curves show measurements obtained using TF (LTG) and FP (ETG) samples, respectively, while black curves correspond to clustering measured using the true velocities from the simulation. From top to bottom, the panels display the monopole of the velocity auto-correlation $\xi^{vv}_0$, the dipole of the velocity–galaxy cross-correlation $\xi^{vg}_1$, and the monopole of the velocity–galaxy cross-correlation $\xi^{vg}_0$. Measurements are averaged over three orthogonal lines of sight obtained by rotating the simulation box. The shaded regions indicate the $1\sigma$ scatter expected from purely random distance errors, estimated from 30 realisations per line of sight by adding Gaussian noise to the true velocities with standard deviations std$(\lambda_{\mathrm{TF}}) = 0.062$ (left) and std$(\lambda_{\mathrm{FP}}) = 0.075$ (right).
• Figure 5: Environmental dependence of TF and FP residuals. Mean residuals in log-distance ratio are shown as a function of the galaxy overdensity $1+\delta_g$. The top and bottom panels correspond to TF ($\lambda_\mathrm{TF}$) and FP ($\lambda_\mathrm{FP}$) residuals, respectively. Circles and diamonds denote central and satellite galaxies. Error bars indicate the standard error on the mean in each bin. Shaded bands show the total scatter of the residuals, std$(\lambda_\mathrm{TF}) = 0.062$ and std$(\lambda_\mathrm{FP}) = 0.075$. Histograms indicate the overdensity distributions of the corresponding samples.