# The Intrinsic Scatter of the Radial Acceleration Relation

## TL;DR

This paper develops a Monte Carlo model to accurately estimate the intrinsic scatter in the stellar radial acceleration relation of galaxies, finding it slightly exceeds LCDM predictions, thus informing galaxy formation theories.

## Contribution

It introduces a new Monte Carlo method to disentangle observational errors from intrinsic scatter in galaxy scaling relations.

## Key findings

- Intrinsic scatter of the stellar RAR is 0.11±0.02 dex.
- Observed scatter of the stellar RAR is 0.17 dex.
- Results are consistent with LCDM predictions, slightly exceeding them.

## Abstract

We present a detailed Monte Carlo model of observational errors in observed galaxy scaling relations to recover the intrinsic (cosmic) scatter driven by galaxy formation and evolution processes. We apply our method to the stellar radial acceleration relation (RAR) which compares the local observed radial acceleration to the local Newtonian radial acceleration computed from the stellar mass distribution. The stellar and baryonic RAR are known to exhibit similar scatter. Lelli+2017 (L17) studied the baryonic RAR using a sample of 153 spiral galaxies and inferred a negligible intrinsic scatter. If true, a small scatter might challenge the LCDM galaxy formation paradigm, possibly favoring a modified Newtonian dynamics interpretation. The intrinsic scatter of the baryonic RAR is predicted by modern LCDM simulations to be ~0.06-0.08 dex, contrasting with the null value reported by L17. We have assembled a catalog of structural properties with over 2500 spiral galaxies from six deep imaging and spectroscopic surveys (called PROBES for the "Photometry and Rotation curve OBservations from Extragalactic Surveys") to quantify the intrinsic scatter of the stellar RAR and other scaling relations. The stellar RAR for our full sample has a median observed scatter of 0.17 dex. We use our Monte Carlo method, which accounts for all major sources of measurement uncertainty, to infer a contribution of 0.12 dex from the observational errors. The intrinsic scatter of the stellar RAR is thus estimated to be 0.11$\pm$0.02 dex, in agreement with, though slightly greater than, current LCDM predictions.