Galaxy infall models for arbitrary velocity directions

¹ Helsinki Institute of Physics, P.O. Box 64 FI-00014 University of Helsinki, Finland
² Academia Sinica Institute of Astronomy and Astrophysics, 11F of AS/NTU Astronomy-Mathematics Building, No.1, Sec. 4, Roosevelt Rd, Taipei 106216, Taiwan, ROC
³ Bahamas Advanced Study Institute and Conferences, 4A Ocean Heights, Hill View Circle, Stella Maris, Long Island, The Bahamas
⁴ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany

^⋆ Corresponding authors: wagner@asiaa.sinica.edu.tw; benidav@aip.de

Received: 24 January 2025
Accepted: 15 May 2025

Abstract

For most galaxies in the cosmos, our knowledge of their motion is limited to line-of-sight velocities from redshift observations. To determine the radial velocity between two galaxies, the “minor” and “major infall models” were established by Igor Karachentsev and colleagues. Regardless of the background cosmology, our derivations reveal that these infall models approximate the total radial velocity between two galaxies by two different projections employing different information about the system. For galaxies that have small angular separations, θ, all infall models agree that the radial velocity is the difference of their line-of-sight components. Applying these models to around 500 halos of the Illustris-3 simulation, we find the perpendicular and tangential velocity parts to be non-negligible for more than 90% of over 5000 infalling subhalos investigated. Thus, even for θ < 10 deg, the infall-model velocities deviate from the true radial velocity. Only for 30% did we find the true one lay between the minor and major infall velocity. However, the infall models yield robust upper and lower limits to the true radial velocity dispersion. Observed under θ < 10 deg, the velocity dispersion inferred from the sole difference of line-of-sight velocity components even coincides with the true one, justifying this approach for high-redshift groups and clusters. Based on these findings, we predict the radial velocity dispersion of the M81 group from the minor infall model (upper bound) to be σ_r, min = (180 ± 42) km/s, from the major infall model (lower bound) to be σ_r, maj = (142 ± 64) km/s and σ_r, Δv = (99 ± 36) km/s from the line-of-sight-velocity difference.