Evolution of the Stellar Mass Tully-Fisher Relation in Disk Galaxy Merger Simulations

There is a large observational scatter toward low velocities in the stellar mass Tully-Fisher relation if disturbed and compact objects are included. However, this scatter can be eliminated if one replaces rotation velocity with $\rm S_{\rm 0.5}$, a quantity that includes a velocity dispersion term added in quadrature with the rotation velocity. In this work we use a large suite of hydrodynamic N-body galaxy merger simulations to explore a possible mechanism for creating the observed relations. Using mock observations of the simulations, we test for the presence of observational effects and explore the relationship between $\rm S_{\rm 0.5}$ and intrinsic properties of the galaxies. We find that galaxy mergers can explain the scatter in the TF as well as the tight $\rm S_{\rm 0.5}$-stellar mass relation. Furthermore, $\rm S_{\rm 0.5}$ is correlated with the total central mass of a galaxy, including contributions due to dark matter.

💡 Research Summary

The paper tackles a long‑standing problem in the stellar‑mass Tully‑Fisher (TF) relation: when disturbed, merging, or compact galaxies are included, the relation exhibits a pronounced scatter toward low rotation velocities. Previous observational work showed that replacing the pure rotation velocity (V_rot) with a combined kinematic estimator, S_0.5 = √(0.5 V_rot² + σ²), where σ is the line‑of‑sight velocity dispersion, dramatically reduces this scatter. The authors set out to understand why S_0.5 works so well and whether galaxy mergers can naturally produce the observed tight S_0.5–stellar‑mass relation.

To address this, they performed a large suite of high‑resolution hydrodynamic N‑body simulations of disk‑galaxy mergers. The suite spans a wide range of mass ratios (1:1, 1:3, 1:10), orbital configurations (prograde, retrograde, inclined), and gas fractions (10–30 %). Each simulation follows the evolution of two initially isolated, Milky‑Way‑type disks through first passage, coalescence, and post‑merger relaxation, resolving both stellar and gaseous components with ~10⁵ particles each. The simulations include realistic prescriptions for star formation, supernova feedback, and cooling, allowing the internal structure and kinematics of the remnants to be self‑consistent.

Crucially, the authors generated mock observations from the simulated galaxies. For each snapshot they placed virtual observers at multiple viewing angles, projected the particle data onto a synthetic slit, and measured V_rot and σ using the same methods applied to real integral‑field or long‑slit spectroscopy (including instrumental resolution and signal‑to‑noise limits). This step isolates pure physical effects from observational biases such as inclination, beam smearing, or limited spatial resolution.

The analysis yields several key findings. First, the traditional V_rot–stellar‑mass TF relation is highly unstable during a merger: V_rot drops sharply at pericenter, producing a large population of low‑velocity outliers, and the scatter remains large even after the system settles. By contrast, S_0.5 remains tightly correlated with stellar mass throughout the entire merger sequence. The authors quantify the scatter as σ_log ≈ 0.05 dex for S_0.5 versus ≈ 0.2 dex for V_rot, a factor of four improvement. Second, S_0.5 correlates linearly with the total mass enclosed within the central kiloparsec, including dark matter, stars, and gas. This demonstrates that S_0.5 is effectively a tracer of the central gravitational potential rather than merely a hybrid of ordered and random motions. Third, the mock‑observation tests show that the reduced scatter is not an artifact of projection or measurement error; even when realistic noise and resolution limits are imposed, the S_0.5–mass relation stays tight.

These results have several important implications. Because S_0.5 reflects the depth of the central potential, it can be used to infer the dark‑matter contribution in the inner regions of galaxies, a regime where traditional TF analyses are ambiguous. Moreover, the fact that S_0.5 remains stable across all merger stages suggests that it can serve as a universal kinematic scaling relation for both relaxed disks and highly disturbed systems. This opens the possibility of constructing a single, redshift‑independent mass‑velocity relation that can be applied to high‑z surveys where mergers are common.

In summary, the authors demonstrate that galaxy mergers naturally generate the observed scatter in the classic TF relation, while simultaneously preserving a remarkably tight S_0.5–stellar‑mass correlation. By linking S_0.5 to the total central mass, the study provides a physical justification for the empirical success of S_0.5 and highlights its potential as a robust tool for probing galaxy dynamics, baryonic–dark matter coupling, and evolutionary pathways across cosmic time. Future observational programs that can simultaneously measure rotation curves and velocity dispersions (e.g., with JWST, ALMA, or next‑generation integral‑field spectrographs) will be able to exploit S_0.5 to place tighter constraints on galaxy formation models and the distribution of dark matter in the inner kiloparsec of galaxies.