# The two-component virial theorem and the acceleration-discrepancy relation

## TL;DR

This paper revisits the two-component virial theorem (2VT) to explore its consistency with the acceleration-discrepancy relation (ADR) and its implications for dark matter and modified gravity theories.

## Contribution

It demonstrates that the 2VT aligns with the ADR and predicts a constant behavior in low-acceleration regimes, offering a physically meaningful framework for dark matter studies.

## Key findings

- The 2VT is consistent with the observed ADR.
- The 2VT predicts a nearly constant behavior in dwarf spheroidals.
- The paper discusses differences between 2VT and modified gravity theories.

## Abstract

We revisit the "two-component virial theorem" (2VT) in the light of recent theoretical and observational results related to the "dark matter"(DM) problem. This modification of the virial theorem offers a physically meaningful framework to investigate possible dynamical couplings between the baryonic and DM components of extragalactic systems. In particular, we examine the predictions of the 2VT with respect to the "acceleration-discrepancy relation" (ADR). Considering the combined data (composed of systems supported by rotation and by velocity dispersion), we find that: (i) the overall behavior of the 2VT is consistent with the ADR; and (ii) the 2VT predicts a nearly constant behavior in the lower acceleration regime, as suggested in recent data on dwarf spheroidals. We also briefly comment on possible differentiations between the 2VT and some modified gravity theories.