Mid-IR–Radio Correlation (MIRAD)

• MIRAD is an empirical relationship defined by the logarithmic q-parameter that compares mid-infrared and radio flux densities in galaxies.
• It serves as a robust diagnostic for star formation rates and ISM conditions, distinguishing between star-forming systems and AGN through consistent flux ratios.
• Recent applications leverage MIRAD to probe subgalactic structures, differentiate ultra-compact starbursts, and even search for technosignatures, while addressing systematic calibration challenges.

The Mid-IR–Radio Correlation (MIRAD) is a well-established empirical relationship between the mid-infrared (mid-IR) and radio continuum emission of galaxies. Initially recognized in the context of star-forming systems, MIRAD encompasses both integrated galaxy properties and, more recently, subgalactic and pc-scale structures, with broad utility from star-formation diagnostics to AGN identification and even technosignature searches. Fundamentally, the MIRAD measures the flux density or luminosity ratio (often rendered as log (IR/radio)) at specific mid-IR and radio bands, with salient variants utilizing, e.g., 22 μm (WISE), 24 μm (Spitzer), or 12 μm (WISE-W3) for the mid-IR and 1.4 GHz or 5 GHz for the radio regime. The tightness and universality of this correlation in normal systems reflect the shared origin of both mid-IR and radio emission in massive-star formation and ISM processes, while significant deviations signal peculiar ISM conditions, the presence of AGN, or, in the rarest hypotheses, energy-processing by advanced civilizations.

1. Mathematical Formalism and Parameterizations

The MIRAD is most commonly expressed via a logarithmic “q” parameter:

$$q_{\lambda} = \log_{10}\left(\frac{S_{IR,\lambda}}{S_{radio}}\right)$$

where $S_{IR,\lambda}$ is the observed mid-IR flux density (typically at 22 μm, 24 μm, or 12 μm) and $S_{radio}$ is the radio flux density (usually at 1.4 GHz or 5 GHz). This definition is also routinely applied to rest-frame luminosities:

$$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$

For example, the key parameterization at 22 μm and 1.4 GHz is:

$$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$

Analogous definitions for 24 μm or 12 μm (WISE W3) bands are standard in Spitzer and WISE analyses (Garrett, 2015, Huynh et al., 2010, Kozieł-Wierzbowska et al., 2020, Qiu et al., 2017).

The canonical “FIR–radio” $q_{\mathrm{IR}}$ employs integrated 8–1000 μm luminosity:

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

Band-specific and monochromatic definitions are essential for broad applicability across survey data with nonidentical spectral coverage.

2. Empirical Results across Diverse Environments

Measured $q$ values demonstrate remarkable consistency for star-forming systems but show subtleties depending on sample selection, redshift, environment, and ISM conditions:

Sample & Redshift	q Parameter & Mean Value (±σ)	Notable Characteristic
Ĝ (WISE, $\hat{G}$)	$z \lesssim 0.15$	$S_{IR,\lambda}$0
FLS Control	$S_{IR,\lambda}$2	$S_{IR,\lambda}$3
HDFS (Spitzer/MIPS)	up to $S_{IR,\lambda}$5	$S_{IR,\lambda}$6
ROGUE I–WISE	$S_{radio}$0	W3/1.4 GHz
Massive Clusters	$S_{radio}$3	$S_{radio}$4
Metal-poor galaxies	$S_{radio}$7	$S_{radio}$8

The MIRAD thus serves as a baseline against which outliers and population trends are identified.

3. Physical Origins and Theoretical Interpretation

In star-forming galaxies, MIR and radio emission both trace massive, young stellar populations, but via different ISM processes:

• Mid-IR: UV photons from OB stars heat dust, producing strong thermal continuum in the mid- and far-IR; PAH features contribute in the 12–24 μm bands.
• Radio: Supernova remnants from the same massive stars inject cosmic-ray electrons, generating synchrotron emission; H II regions add free–free (thermal) radio flux.

Because these channels are coupled to the high-mass star formation rate (SFR), their emission remains tightly correlated over >5 dex in luminosity (Garrett, 2015). AGN can also inhabit the MIRAD locus, but radio-loud AGN produce excess radio (lower $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$0) and populate a distinct branch (Kozieł-Wierzbowska et al., 2020, Yuan et al., 2018). Ultra-compact starbursts may show MIR “excess” due to free–free absorption, dust temperature effects, or time lag between burst and supernova onset (Petter et al., 2020).

The near-constancy of $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$1 with respect to metallicity (span: $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$2) is notable: $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$3 in low-metallicity and $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$4 in high-metallicity systems (Qiu et al., 2017). Warm dust in metal-poor systems selectively boosts mid-IR, offsetting their lower overall IR/FUV ratio and preserving MIRAD at 24 μm.

4. Observational Methodologies and Survey Implementations

Measurement of MIRAD requires matched mid-IR and radio observations—commonly WISE (12 μm or 22 μm), Spitzer/MIPS (24 μm), and VLA/NVSS or ATCA (1.4 GHz):

• Sample selection: Ranges from all-sky (WISE), color-selected (extreme mid-IR in $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$5, LIRGs/ULIRGs), to redshift-defined cluster samples (Garrett, 2015, Samanso et al., 5 May 2025).
• Flux calibration: Standard zero-points for magnitude-to-flux conversion (e.g., WISE W3: 31.674 Jy) (Kozieł-Wierzbowska et al., 2020). For radio, direct catalog matching with 2–5 mJy completeness for NVSS/FIRST is typical.
• k-corrections: Applied for rest-frame analyses; spectral indices adopted (e.g., radio $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$6 to $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$7).
• Redshifts: Essential for luminosity-based MIRAD; obtained via spectroscopy or multi-band photometry.
• Stacking: Sub-threshold sources are stacked to probe faint populations and measure mean $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$8 at high $$q_{\lambda} = \log_{10}\left(\frac{L_{IR,\lambda}}{L_{radio}}\right)$$9 (Huynh et al., 2010, Samanso et al., 5 May 2025).

Empirically, a dividing line at $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$0 (WISE W3 vs. 1.4 GHz, both in mJy) efficiently discriminates SF and radio-AGN in the ROGUE I–WISE sample, reaching 98%–99.5% classification accuracy (Kozieł-Wierzbowska et al., 2020).

5. Population Trends, Environmental Dependence, and Physical Outliers

While MIRAD is robust in the integrated light of normal disks, systematic departures are observed in specific contexts:

• Cluster environments ($$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$1): At $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$2, cluster galaxies show $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$3 lower by $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$4 dex relative to field analogs, with higher statistical significance at $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$5–$$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$6; no dependence on cluster-centric radius or AGN activity detected (Samanso et al., 5 May 2025). Environmental processes (ram pressure, shocks) may augment radio emission, depressing $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$7.
• Metallicity: Robustness of $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$8 against $$q_{22} = \log_{10}\left(\frac{S_{22\,\mu\mathrm{m}}}{S_{1.4\,\mathrm{GHz}}}\right)$$9 at 24 μm is contrasted with a strong metallicity trend at 70–160 μm, where metal-poor galaxies show much lower $q_{\mathrm{IR}}$0 (Qiu et al., 2017).

A subset of systems emerge as high-$q_{\mathrm{IR}}$1 outliers:

• Young, embedded starbursts: Weak synchrotron emission due to undeveloped cosmic-ray populations; compact or highly dust-embedded nuclei (e.g., NGC 1377, IC 342, NGC 4418) exhibit $q_{\mathrm{IR}}$2 (Garrett, 2015).
• Ultra-compact starbursts: At $q_{\mathrm{IR}}$3, such systems show IR-to-radio SFR exceeding canonical predictions by a factor $q_{\mathrm{IR}}$4, with deviations correlated with SFR surface density or burst age (Petter et al., 2020). Proposed mechanisms include free–free absorption, burst age lag, or compactness-driven dust heating.
• AGN: Radio-loud AGN form a well-separated sequence below the SF branch in MIRAD diagrams; low-excitation (LERG) AGN dominate this locus (Kozieł-Wierzbowska et al., 2020).

6. Applications and Diagnostic Power

The MIRAD offers several powerful applications:

• SFR Diagnostics: Because $q_{\mathrm{IR}}$5 is essentially metallicity-invariant, the 24 μm–radio ratio provides an SFR estimator robust across $q_{\mathrm{IR}}$6 dex in O/H (Qiu et al., 2017). Calibration uncertainties $q_{\mathrm{IR}}$7 dex at fixed IMF dominate.
• AGN/SF Separation: The MIRAD diagram (e.g., $q_{\mathrm{IR}}$8), operating purely on observed fluxes, differentiates SF galaxies and radio-AGN at $q_{\mathrm{IR}}$9 purity and completeness in large surveys without optical spectroscopy (Kozieł-Wierzbowska et al., 2020).
• Technosignatures: $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$0 applied to the $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$1 sample rapidly identifies mid-IR–bright, radio-weak outliers as candidate “waste heat” signatures. For a galaxy-scale Type III civilization, $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$2 is expected (Garrett, 2015).
• Feedback and Compact Starbursts: Deviation from MIRAD in ultra-compact starbursts signals distinct ISM conditions or feedback regimes such as extreme free–free opacity or youth (Petter et al., 2020).
• Jet/Disk Connection: Tight MIR–radio (15 μm–5 GHz) correlations at pc scales imply a universal connection between accretion power and jet base luminosity in radio galaxies (Yuan et al., 2018), supporting the use of MIR as a probe of AGN feedback.

7. Limitations, Systematics, and Future Prospects

Several systematics and caveats attend MIRAD analyses:

• Photometric systematics (e.g., WISE/FIRST beam mismatch, MAG-TO-FLUX conversion, zero-points) introduce scatter at the $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$3 dex level (Kozieł-Wierzbowska et al., 2020).
• Redshift evolution becomes significant at $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$4: PAH features shift out of mid-IR bands, and radio $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$5-corrections become critical (Huynh et al., 2010, Samanso et al., 5 May 2025). Templates derived locally may misestimate SFR in high-$$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$6 ULIRGs/LIRGs.
• Aperture and confusion effects especially at WISE’s $$q_{\mathrm{IR}} = \log_{10}\left(\frac{L_{\mathrm{IR}}/3.75 \times 10^{12}\,{\rm W}}{L_{1.4\,\mathrm{GHz}}\,/\,{\rm W\,Hz}^{-1}}\right)$$7 resolution, limit nuclear/host disentanglement in MIRAD, especially in crowded environments or compact sources.
• Composite systems (mixed SF and AGN) can bridge the dividing loci in MIRAD, necessitating multi-band diagnostics or resolved imaging.
• Breakdown regimes in ultra-compact, Eddington-limited starbursts, or during “cosmic noon” cluster assembly, reflect real ISM differences rather than failure of the formalism—these are regimes of particular interest.

Future high-resolution, multi-frequency surveys (e.g., SKA, JWST/MIRI, FIR missions) will refine MIRAD’s calibration at high redshift and in extreme environments, enabling both more accurate SFR diagnostics and the exploration of non-standard processes.

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References: (Garrett, 2015, Huynh et al., 2010, Kozieł-Wierzbowska et al., 2020, Qiu et al., 2017, Petter et al., 2020, Yuan et al., 2018, Samanso et al., 5 May 2025)