# The far-infrared/radio correlation and radio spectral index of galaxies in the SFR–$M_\ast$ plane up to z~2$^\star$

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Abstract : We study the evolution of the radio spectral index and far-infrared/radio correlation (FRC) across the star-formation rate – stellar masse (i.e. SFR–$M_\ast$) plane up to $z$ ~ 2. We start from a stellar-mass-selected sample of galaxies with reliable SFR and redshift estimates. We then grid the SFR–$M_\ast$ plane in several redshift ranges and measure the infrared luminosity, radio luminosity, radio spectral index, and ultimately the FRC index (i.e. $q_{FIR}$) of each SFR–$M_\ast$–$z$ bin. The infrared luminosities of our SFR–$M_\ast$–$z$ bins are estimated using their stacked far-infrared flux densities inferred from observations obtained with the Herschel Space Observatory. Their radio luminosities and radio spectral indices (i.e. $\alpha$, where $S_ν$ ∝ $ν^{−α}$) are estimated using their stacked 1.4 GHz and 610 MHz flux densities from the Very Large Array and Giant Metre-wave Radio Telescope, respectively. Our far-infrared and radio observations include the most widely studied blank extragalactic fields – GOODS-N, GOODS-S, ECDFS, and COSMOS – covering a total sky area of ~2.0 deg$^2$. Using this methodology, we constrain the radio spectral index and FRC index of star-forming galaxies with $M_\ast$ > 10$^{10}$ $M_⊙$ and 0 <$z$< 2.3. We find that $\alpha_{610 MHz}^{1.4 GHz}$ does not evolve significantly with redshift or with the distance of a galaxy with respect to the main sequence (MS) of the SFR–$M_\ast$ plane (i.e. Δlog (SSFR)$_{MS}$ = log  [SSFR(galaxy) /SSFR$_{MS}$($M_\ast$,$z$) ]). Instead, star-forming galaxies have a radio spectral index consistent with a canonical value of 0.8, which suggests that their radio spectra are dominated by non-thermal optically thin synchrotron emission. We find that the FRC index, q$_{FIR}$,displays a moderate but statistically significant redshift evolution as q$_{FIR}$($z$) = (2.35 ± 0.08) × (1 + $z$)$^{−0.12 ± 0.04}$, consistent with some previous literature. Finally, we find no significant correlation between q$_{FIR}$ and Δlog (SSFR)$_{MS}$, though a weak positive trend, as observed in one of our redshift bins (i.e. Δ [ q$_{FIR}$]/Δ [ Δlog (SSFR)$_{MS}$ ] = 0.22 ± 0.07 at 0.5 <$z$<0.8), cannot be firmly ruled out using our dataset.
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Cited literature [73 references]

https://hal-cea.archives-ouvertes.fr/cea-01290083
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### Citation

B. Magnelli, R. J. Ivison, D. Lutz, I. Valtchanov, D. Farrah, et al.. The far-infrared/radio correlation and radio spectral index of galaxies in the SFR–$M_\ast$ plane up to z~2$^\star$. Astronomy and Astrophysics - A&A, EDP Sciences, 2015, 573, pp.A45. ⟨10.1051/0004-6361/201424937⟩. ⟨cea-01290083⟩

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