# A model for the infrared-radio correlation of main-sequence galaxies at GHz frequencies and its dependence on redshift and stellar mass

**Authors:** J. Schober, M. T. Sargent, R. S. Klessen, D. R. G. Schleicher  
**arXiv:** [2210.07919](https://arxiv.org/abs/2210.07919)  
**Date:** 2022-10-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2210.07919v1/

## Key points

- The infrared-radio correlation (IRRC) is a useful tool for estimating the star formation rate (SFR) of star-forming galaxies based on radio continuum luminosity.
- Recent observations have shown that the IRRC remains consistent up to z~4 but depends on the stellar mass M_star.
- A phenomenological model for galactic radio emission has been constructed to understand the M_star-dependence of the IRRC and its behavior at higher redshifts.
- The model suggests that an efficiency of 5% for SN-driven turbulence and saturation of the small-scale dynamo provide the best agreement with observed characteristics of the IRRC.
- The mass dependence of the IRRC persists as long as synchrotron emission dominates, but free-free emission and absorption impact the radio spectrum at higher redshifts, leading to an inversion in its M_star dependence at z > 5.
- Future deep radio observations can test this inversion and explore how galaxy orientation affects IR/radio flux ratios in high-z systems.
- Understanding and accounting for factors such as stellar mass and redshift dependence are crucial for accurate SFR calibrations based on radio luminosity.
- The constructed phenomenological model provides insights into underlying physical mechanisms and highlights the importance of future deep radio surveys in refining these models.

## Summary

The infrared-radio correlation (IRRC) of star-forming galaxies is a useful tool for estimating their star formation rate (SFR) based on radio continuum luminosity at MHz-GHz frequencies. However, it is important to determine whether the IRRC remains consistent at high redshifts for future deep radio surveys. Recent observations by Delvecchio et al. (2021) have shown that the 1.4 GHz IRRC correlation of star-forming galaxies is nearly invariant up to z~4, but strongly depends on the stellar mass M_star. This dependence must be taken into account when calibrating SFR based on radio luminosity. To understand the underlying physical cause of the M_star-dependence of the IRRC and its behavior at higher redshifts, a phenomenological model for galactic radio emission has been constructed. This model incorporates magnetic fields generated by a small-scale dynamo, a steady-state cosmic ray population, and observed scaling relations that reduce the number of free parameters. By comparing the model with the characteristics of the IRRC observed by Delvecchio et al., it has been found that an efficiency of 5% for SN-driven turbulence and saturation of the small-scale dynamo once 0.5% of kinetic energy is converted into magnetic energy provide the best agreement. Generally, it has been observed that the mass dependence of the IRRC persists as long as synchrotron emission dominates the galactic radio flux. When extrapolating this reference model to higher redshifts, it has been discovered that free-free emission and absorption significantly impact the radio spectrum leading to an inversion in its M_star dependence at z > 5. Future deep radio observations can test this inversion and also explore how galaxy orientation affects IR/radio flux ratios in high-z systems as predicted by this model. Therefore, understanding and accounting for factors such as stellar mass and redshift dependence are crucial for accurate SFR calibrations based on radio luminosity. The constructed phenomenological model provides insights into physical mechanisms underlying these correlations and their behavior at different redshifts while also highlighting importance of future deep radio surveys in testing and refining these models.