On a Generalized Mass-Velocity Relation for Disk Galaxies and Galaxy Clusters

We consolidate the BFJ and BTF (MVD) relations into a generalized Scaling Mass Velocity Relation applicable to both pressure-supported galaxy clusters and rotation-supported galaxies. Unlike MOND inspired relations containing a characteristic acceleration scale and its normalization factor, our proposal is dependent on observed dynamic surface mass densities and discrepancies. We perform the same analysis for a sample of HIFLUGCS galaxy clusters (Tian et al, 2021) found in prior work with SPARC galaxies (arXiv: 2101.01537). For this galaxy cluster sample, we find little evidence for a universal acceleration constant as previously recognized for galaxies. We finish with an examination of the virial energies for the combined sample recovering a mass-energy relation consistent with the phenomenology. Introduction Galaxies and clusters exhibit phenomenal correlations (scaling relations) particularly for three fundamental dimensions, mass, length, and time. These are usually simple power laws, but describe specific self-similar properties that the structures tend to follow (Novak, 2012) (Zaritsky, 2008) (Schulz, 2017) (Stone, 2021) (Shenavar, 2021). Scaling relations may be presented as “tight” correlations with low residual scatter between parameters, while others may be significantly dispersed but still retaining general trends and central tendencies. Further, some scaling relations may also be transformed into analytical expressions when simple models are used, which is the approach taken here. It seems with the introduction of dark matter and modified gravity a half-century ago, research directed toward classical dynamical models has been deemphasized. Somewhat disconcerting is that these mainstream models have made little progress even with the capacity to add mass or modify gravity to better match baryon dynamics. Here, we take a step back and model galaxy and clusters with four fundamental components; baryons, Newtonian dynamics, angular momentum all coupled via classical thermodynamics, specifically the virial theorem. Neither ΛCDM or MOdified Newtonian Dynamics (MOND) can offer a simpler explanation for the form and function of the mass-velocity relation proposed herein (Milgrom, 1983). With recent advancements in precision astrometrics, data is now available for a comprehensive analysis for two prominent empirical mass-velocity correlations. First is the Baryonic Tully Fisher Relation (BTFR) specific to rotationally-supported disk galaxies and second is the Baryonic Faber Jackson Relation (BFJR) for velocity dispersion/pressure-dominated systems (Tully, 1977) (Faber, 1976). Our approach, termed the ‘scaling model’ has previously been used to analyze a large sample of SPARC galaxies and now, we apply the exact same model to a sample of 29 HIFLUGCS clusters (Tian, 2021 hereafter T21). We review T21’s modeling methodology used to estimate a Characteristic Acceleration Scale (CAS) for galaxy clusters based on MOND precepts. We interrogate HIFLUGCS galaxy cluster data using the proposed ‘scaling model’ and develop a BFTR zero-point expression that does not involve a predetermined acceleration scale (La Fortune, 2020a) (La Fortune, 2021).