Infrared-Radio Correlation (IRRC) Overview

• IRRC is a fundamental empirical relationship that links dust-reprocessed UV light (infrared emission) from young, massive stars with radio synchrotron emission from cosmic ray electrons.
• It is influenced by galaxy properties such as magnetic field topology, star formation rate surface density, and environmental conditions, which modulate cosmic ray propagation and energy losses.
• Recent studies employ multi-frequency SED models and environmental diagnostics to refine the IRRC as a robust tool for tracing star formation and understanding galaxy evolution.

The Infrared–Radio Correlation (IRRC) is a fundamental empirical relationship between the infrared (IR) and radio continuum emission in galaxies, tightly linking the dust-reprocessed UV light from young, massive stars (observable as IR emission) and the radio synchrotron emission from cosmic ray electrons (CREs) produced by supernovae. Spanning a wide range of galaxy types, masses, environments, and redshifts, the IRRC is both a diagnostic of star formation and a probe of the interplay between cosmic rays, magnetic fields, interstellar medium (ISM) turbulence, and galaxy evolution.

1. Physical Basis and Fundamental Definitions

The IRRC is conventionally parameterized by the logarithmic ratio q defined as

$$q_{IR} = \log_{10}\left(\frac{L_{IR}}{3.75 \times 10^{12}\ \mathrm{W}}\right) - \log_{10}\left(L_{1.4\ \mathrm{GHz}}\ [\mathrm{W\,Hz}^{-1}]\right)$$

where $L_{IR}$ is the total IR (typically integrated 8–1000 μm) luminosity and $L_{1.4\,\mathrm{GHz}}$ is the rest-frame radio luminosity at 1.4 GHz, a canonical frequency for extragalactic surveys (Delvecchio et al., 2020, Delhaize et al., 2017).

For normal star-forming galaxies, this ratio is remarkably constant (e.g., $q_{IR} \approx 2.64$), suggesting a close coupling between star formation, dust heating, and CRE production (Delvecchio et al., 2020). The physical origin of the IRRC rests on the fact that both the IR and radio emissions are ultimately powered by massive stars: IR via dust heating by their UV light, radio via synchrotron emission from CREs accelerated in supernova remnants.

2. Microphysics: Cosmic Ray Propagation and Magnetic Fields

The observed IRRC is critically modulated by CRE propagation, energy losses, and magnetic field configurations. In studied systems such as M31 and M33, the spatial scale on which the synchrotron–IR correlation holds is linked to the CRE diffusion length, $l_{dif}$, which is itself a function of the ratio of ordered to turbulent magnetic field strengths ($B_{ord}/B_{tur}$) (Tabatabaei et al., 2013). CREs diffuse more efficiently in galaxies with higher $B_{ord}/B_{tur}$, enabling propagation over larger distances before energy loss, and correlating radio and IR emission on larger scales.

The diffusion length can be quantified as

$$l_{dif} \propto \left(\frac{B_{ord}}{B_{tur}}\right)B_{ord}^{-1/6}B_{tot}^{-7/8}$$

for synchrotron-loss limited CREs, or

$$l_{dif} \propto \left(\frac{B_{ord}}{B_{tur}}\right)B_{ord}^{-1/6}B_{tot}^{-1/8}t_{conf}^{1/2}$$

when the residence time in the thin disk matters. M31, with higher $B_{ord}/B_{tur}$, exhibits $l_{dif}\sim730\pm90$ pc versus $<400$ pc in M33 (Tabatabaei et al., 2013). This dependence is a direct observational signature of the importance of the galactic magnetic field structure in regulating the IRRC.

Magnetic field strengths themselves are set by a balance between turbulent kinetic and magnetic energy densities (equipartition): $\frac{B^2}{8\pi} = \frac{1}{2}\rho v_{turb}^2$ as shown in analytical models for main-sequence and starburst galaxies (Vollmer et al., 2022, Schober et al., 2022).

3. Environmental, Structural, and Evolutionary Dependencies

3.1. Mass and Surface Density Effects

The IRRC exhibits a strong dependence on stellar mass: more massive galaxies show lower $q_{IR}$, implying a radio enhancement at fixed IR luminosity (Delvecchio et al., 2020, Moloko et al., 8 Sep 2025). This is well described by a parameterization

$$q_{IR}(M_*, z) = (2.646\pm0.024)(1+z)^{-0.023\pm0.008} - (0.148\pm0.013)(\log(M_*/M_\odot) - 10)$$

with almost negligible redshift evolution up to $z\sim4$ once mass is accounted for (Delvecchio et al., 2020). Analytical models attribute this to scaling relations where galaxy radius increases weakly with mass, leading to changes in gas surface density ($\Sigma_g$) and thus CRE loss mechanisms (Schober et al., 2022, Yoon, 24 Aug 2024). Specifically, $q_{IR}$ is anti-correlated with $\Sigma_g$: galaxies with higher $\Sigma_g$ have more efficient CRE confinement, stronger magnetic fields, and therefore excess synchrotron emission resulting in lower $q_{IR}$ values (Yoon, 24 Aug 2024).

3.2. Star Formation and Low-mass Galaxies

In the low star formation surface density regime (e.g., dwarf galaxies), the classical IRRC can break down due to two critical thresholds: (a) a minimum SFR surface density is needed to sustain continuous magnetic field regeneration via the small-scale dynamo, and (b) below a certain SFR density, cosmic ray injection falls below diffusion/escape losses, leading to a “radio faint” regime and increased IRRC scatter (Schleicher et al., 2016). In such cases, the IRRC scaling transitions from $L_s \propto L_{th}^{4/3}$ (steady state) to $L_s \propto L_{th}^{5/3}$ (loss dominated).

3.3. Environmental Effects

Cluster environments induce measurable modulations. Observations at $1 < z < 2$ show cluster galaxies have lower $q$ values (radio excess) than field galaxies, attributed to processes like ram pressure stripping, interactions, or mergers that may either compress magnetic fields or trigger turbulence, enhancing radio continuum emission relative to IR (Samanso et al., 5 May 2025). This radio excess becomes more prominent at lower redshifts where quenching mechanisms are more effective.

3.4. Interactions and Mergers

Galactic interactions and merging systems can significantly perturb the IRRC. In the early interaction phase, tidal shocks heat dust, boosting IR; at later phases, tidal cosmic ray populations (TCRs) injected by merger-induced shocks raise radio synchrotron emission, lowering $q_{IR}$ and steepening the radio spectrum (higher $\alpha$, e.g., from 0.69 to 0.92) (Donevski et al., 2015, Moloko et al., 8 Sep 2025). Merging galaxies exhibit both a lower median $q_{IR}$ and higher dispersion, with non-linear behavior seen in both $L_{TIR}/L_{radio}$ and $L_{TIR}/L_{12\mu m}$ ratios (Moloko et al., 8 Sep 2025).

4. Spectral Energy Distribution and Calibration Systematics

Accurate determination of the IRRC requires careful treatment of the radio spectral energy distribution (SED) and K-corrections. Recent work demonstrates that assuming a single power-law SED (e.g., $\alpha_{NT} \sim 0.7-0.8$) can lead to systematic errors. Observations of highly star-forming galaxies favor a broken power law, with spectral index steepening from $\alpha_1\approx0.51$ below $\sim4.5$ GHz to $\alpha_2\approx0.98$ at higher frequencies (Tisanić et al., 2018). Applying accurate SED and K-correction models is essential, as neglecting SED variation artificially induces apparent trends in q with redshift (Tabatabaei et al., 19 Jun 2025).

Additionally, the observed invariance of the IRRC at $1.5 < z < 3.5$ (in highly star-forming galaxies) upon accounting for SED evolution (Tabatabaei et al., 19 Jun 2025) and in disc-dominated galaxies out to $z\sim1.5$ (Molnar et al., 2017) validates the robustness of the IRRC as a star formation tracer, provided SED effects and AGN contribution are properly managed.

5. Deviations, AGN Contamination, and Nonlinearity

The presence or absence of AGN can affect the interpretation of the IRRC. Residual AGN contamination, particularly from radio-faint or radio-quiet AGNs, is found to introduce only a minor bias to the observed $q_{IR}$, unable to account for the mass dependence or redshift evolution of the IRRC (Peluso et al., 22 Sep 2025, Hansen et al., 9 May 2024). High-sensitivity VLBA observations determine that only $\sim$9% of massive star-forming galaxies on the IRRC host faint AGN, with individual AGN contamination up to $\sim$30% but no systematic shift in the $q_{IR}$ peak (Peluso et al., 22 Sep 2025). This strongly suggests that the mass dependence and other subtle trends are instead intrinsic, driven by ISM conditions.

Some studies report non-linear behavior in the IRRC, with the slope of the $L_{1.4\,\mathrm{GHz}}$–$L_{IR}$ relation being $m\sim1.11$ in low-$z$ galaxies (Molnar et al., 2021). This nonlinearity results in $q$ decreasing with increasing $L_{1.4}$ (radio-brighter galaxies) and is crucial for accurate SFR calibrations from radio luminosity. Apparent redshift evolution of $q$ in flux-limited samples is often due to redshift-dependent selection and non-linearity, not intrinsic evolution (Molnar et al., 2021).

6. Metallicity, Morphology, and Additional Parameters

Systematic lower $q_{IR}$ values are observed in metal-poor galaxies, with the discrepancy growing at longer IR wavelengths (up to –0.61 dex at 160 μm relative to metal-rich galaxies). This is explained by a reduced fraction of obscured SFR (fainter IR dust emission per unit SFR) and a warmer dust SED in low-metallicity environments. The radio emission at 1.4 GHz nonetheless remains a robust tracer of SFR, essentially independent of metallicity (Qiu et al., 2017).

Morphological type exerts further modulation: disc-dominated galaxies show almost no redshift evolution of $q_{IR}$, whereas spheroid-dominated systems, likely hosting residual AGN or enhanced radio emission, display a systematically declining $q_{IR}$ with redshift (Molnar et al., 2017).

7. Theoretical Modeling and Future Directions

Analytical and semi-analytic models, including those built into cosmological galaxy formation scenarios (e.g., SHARK), have been successful in reproducing the observed IRRC and its dependencies. Models emphasize the balance between CRE injection (from SNe), energy losses (synchrotron, IC with the CMB and stellar photons, ionization, adiabatic), turbulence, and magnetic field amplification (small-scale dynamo efficiency) (Schober et al., 2022, Vollmer et al., 2022, Hansen et al., 9 May 2024, Yoon, 24 Aug 2024). A recurring theme is the anti-correlation of $q_{IR}$ with gas surface density and SFR surface density, and the (near-)invariance of $q_{IR}$ with redshift in mass-selected samples (Yoon, 24 Aug 2024).

Going forward, spatially resolved studies (e.g., with ASKAP/WALLABY) reveal that IRRC deviations can diagnose AGN contamination, environmental influences like tidal pre-processing or ram-pressure stripping, and even PAH destruction by shocks (Grundy et al., 2023). Large-area, high-resolution, multifrequency radio and IR surveys, combined with structural and environmental diagnostics, are essential for further disentangling the complex interactions that set the IRRC.

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In summary, the IRRC is a multifaceted diagnostic linking star formation, CRE physics, magnetic fields, and environment. Its apparent simplicity masks rich physical dependencies on magnetic field topology, SFR surface density, environment, stellar mass, metallicity, and interaction stage. While global trends are robust across cosmic time, the underlying physical mechanisms—especially CRE propagation and ISM turbulence—require nuanced modeling for accurate star formation rate estimation, interpretation of deviations, and a fuller understanding of galaxy evolution across the Hubble sequence.