# Analytic expressions for the dark matter-baryon relations

## TL;DR

This paper derives analytic expressions within the CDM framework that accurately explain the observed strong correlations between dark matter and baryons across diverse galaxy types, suggesting these relations are end products of galaxy formation.

## Contribution

It introduces two new analytic expressions based on CDM that successfully model the dark matter-baryon relations observed in galaxies.

## Key findings

- Analytic expressions match observational data well.
- Parameters relate closely to baryon content.
- Supports the idea that relations are end products of galaxy formation.

## Abstract

Recently, some very strong correlations between the distribution of dark matter and baryons (the dark matter-baryon relations) in galaxies with very different morphologies, masses, sizes, and gas fractions have been obtained. Some models have been suggested to explain why the dark matter contribution is fully specified by that of the baryons. In this article, we derive two analytic expressions to explain the observed dark matter-baryon relations based on the cold dark matter (CDM) model. The resultant expressions give excellent agreement with the observational data. The parameters involved in the analytic expressions are closely related to the amount of the baryon content. This model can provide a theoretical understanding of the strong correlations observed. We suggest that the observed relation represents the end product of galaxy formation.