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# Probing the timescale of the 1.4 GHz radio emissions as a star formation tracer

R. C. Arango-Toro, L. Ciesla, O. Ilbert, B. Magnelli, E. F. Jiménez-Andrade, V. Buat

► To cite this version:

R. C. Arango-Toro, L. Ciesla, O. Ilbert, B. Magnelli, E. F. Jiménez-Andrade, et al. Probing the timescale of the 1.4 GHz radio emissions as a star formation tracer. Astronomy & Astrophysics, 2023, 675, 10.1051/0004-6361/202345848. insu-04505571

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# Probing the timescale of the 1.4 GHz radio emissions as a star formation tracer

R. C. Arango-Toro<fnref n="1" />, L. Ciesla<fnref n="1" />, O. Ilbert<fnref n="1" />, B. Magnelli<fnref n="2" />, E. F. Jiménez-Andrade<fnref n="3" />, and V. Buat<fnref n="1" />

Received 5 January 2023 / Accepted 14 April 2023

## ABSTRACT

**Context.** Radio used as a tracer of the star formation rate (SFR) presents enormous advantages because it is not affected by dust and radio sources that are located at the subarcsecond level. The interpretation of the low-frequency 1.4 GHz luminosity is hampered by the difficulty of modeling the paths of cosmic rays in the interstellar medium, however, and by their interactions with the magnetic field.

**Aims.** We compare the SFR derived from radio observations and the SFRs derived from spectral energy distribution (SED) modeling. We aim at better understanding the behavior of the SFR radio tracer, with a specific emphasis on the link to star formation histories (SFHs).

**Methods.** The analysis is based on a subsample of 1584 star-forming galaxies extracted from the Cosmic Evolution Survey (COSMOS) with observations of the Very large array project at 3 GHz. We used the SED modeling code investigating galaxy emission, CIGALE, with a nonparametric model for the SFH and fit the data over the wavelength range from the ultraviolet (UV) to the mid-infrared (mid-IR). We interpret the difference between radio and SED-based SFR tracers in the light of recent gradients in the derived SFH. To validate the robustness of the results, we searched for any remaining contribution of active galaxy nuclei and tested the impact of our SFH modeling approach.

**Results.** Approximately 27% of our galaxies present a radio SFR (SFR<sub>radio</sub>) that is at least ten times higher than the instantaneous SFR from SED fitting (SFR<sub>SED</sub>). This trend primarily affects the galaxies whose SFH activity decreased over the last 300 Myr. Both SFR indicators converge toward a consistent value when the SFHs are averaged over a period longer than 150 Myr to derive SFR<sub>SED</sub>.

**Conclusions.** Although the radio at a low frequency of 1.4 GHz is a good tracer of the star formation activity of galaxies with a constant or increasing SFH, our results indicate that this is not the case for quenched galaxies. Our analysis suggests that the star formation time sensitivity of the low radio frequency might be longer than 150 Myr. Interestingly, the discrepancy between the SFR<sub>radio</sub> and SFR<sub>SED</sub> can be used as diagnostic to select post-starburst galaxies.

**Key words.** galaxies: evolution – galaxies: star formation – galaxies: ISM – galaxies: statistics

## 1. Introduction

The star formation activity of galaxies is closely linked to their gas reservoir, feedback processes, and metal production (e.g., Lilly et al. 2013). The star formation rate (SFR) is an essential probe of the instantaneous state of a galaxy. This observable quantity can be estimated from a wide range of wavelengths (e.g., Kennicutt 1998; Kennicutt & Evans 2012).

The various SFR diagnostics have been systematically tested and compared to establish their accuracy (Domínguez Sánchez et al. 2012; Figueira et al. 2022). Most of the SFR diagnostics are related directly or indirectly to the emissivity of the most massive short-lived O and B stars that dominate the ultraviolet (UV) energy density. The UV SFR tracer can be observed from the local Universe (e.g., Boissier et al. 2007) to the most distant galaxies (e.g., Finkelstein et al. 2022) and for millions of galaxies (e.g., Moutard et al. 2020). This tracer is sensitive to short-timescale variations (<100 Myr) of the star formation, although this depends on the assumed star formation history (SFH; Boquien et al. 2019, and reference therein). Dust attenuation cannot be ignored, however. Unobscured galaxies account for less than 20% of the SFR density at $1 < z < 2$

(e.g., Le Floc'h et al. 2005; Magnelli et al. 2013). Because the UV light is reprocessed by dust and emitted in the infrared (IR; from 8 µm to 1000 µm), the combination of the two wavelengths is acknowledged to be one of the most accurate diagnostic of the SFR assuming a constant SFH over 100 Myr (Bell et al. 2005; Buat et al. 2005, 2019; Kennicutt & Evans 2012; Arnouts et al. 2013). Even with a 3.5-m class telescope such as Herschel, the sensitivity is limited to the most active star-forming galaxies (SFGs) at $z > 3$. Moreover, the beam size ranges from 6.8" to 36.3" (Oliver et al. 2012), which limits our ability to locate the associated optical counterpart and might bias the observed flux by blending.

The radio wavelength can be seen as a promising alternative for estimating the SFR. The main advantage is that the radio emission is not affected by dust (Condon 1992). Moreover, radio detection can be located with a positional accuracy at the subarcsecond scale, which makes the identification of the optical counterparts more reliable than in the IR. The small size of the beam allows an efficient use of stacking techniques (Karim et al. 2011; Leslie et al. 2020). The tremendous efforts in the development of radio telescopes (e.g., the Square Kilometer Array) are promising for the future use of the radio as an SFR tracer.

<footnote n="1">¹ Aix-Marseille Univ., CNRS, CNES, LAM, 13000 Marseille, France
e-mail: rafael.arango-toro@lam.fr</footnote>

<footnote n="2">² Université Paris-Saclay, Université Paris-Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France</footnote>

<footnote n="3">³ Instituto de Radioastronomía y Astrofísica, UNAM Campus Morelia, Apartado Postal 3-72, 58090 Morelia, Michoacán, Mexico</footnote>
At high-frequency >10–20 GHz, the thermal emission (free-
free) in the HII region is well understood to explain the radio
emissivity. At this frequency range, the radio traces the star
formation over short timescales (<10 Myr). However, the link
between star formation and radio emission at a lower frequency
(around 1 GHz) is more complex and less well understood
(Condon 1992). The nonthermal emission is created by highly
accelerated electrons that are trapped in the magnetic fields in the
interstellar medium (ISM), which generates synchrotron emis-
sion. The electrons are accelerated during the supernova phase
and travel through the ISM (Tabatabaei et al. 2017). The emis-
sion starts only when the star explodes, which creates a time
lag between the onset of star formation and the radio emission.
Radio emission might occur over long timescales, depending
on the lifetime of the cosmic rays and on the strength of the
magnetic fields. Cosmic rays are subject to several cooling pro-
cesses as they propagate throughout the ISM. The processes are
mainly caused by inverse Compton, bremsstrahlung, and ionisa-
tion losses (e.g., Murphy 2009). The difficulty of understanding
and modeling this radio emission makes its use more uncertain.
Therefore, a standard approach is to use the IR-radio correla-
tion to estimate the SFR (e.g., Helou et al. 1985; Magnelli et al.
2015; Delhaize et al. 2017; Delvecchio et al. 2021). In addi-
tion, the contribution of active galactic nuclei (AGN) in the
radio wavelength domain might bias the result when it is mis-
interpreted as linked to star formation. In the local Universe
(z ≲ 0.3), radio AGNs are preferentially hosted by red and
massive galaxies ($M_{*} \ge 10^{11} M_{\odot}$), which can be identified
and discarded (Smolčić et al. 2008). This criterion is not suffi-
cient to remove high-excitation radio galaxies (HERGs), how-
ever (Best & Heckman 2012; Janssen et al. 2012; Gürkan et al.
2015), which might be hosted by galaxies with a moderate
star formation activity. The difficulty is even more severe at
higher redshift (Williams & Röttgering 2015; Pracy et al. 2016)
because the fraction of HERGs increases in intermediate-mass
galaxies. Therefore, several diagnostics must be implemented
to distinguish radio AGNs sources from star-forming galaxies
(Padovani 2016; Magliocchetti 2022, and references therein).

In this paper, we focus on spectral energy distribution (SED)
modeling techniques to better characterize the radio wave-
length range as a star formation tracer. The past decade has
seen tremendous progress in the SED-fitting techniques, allow-
ing us to extract physical parameters from a wide wavelength
baseline. The first generation of SED-fitting codes was lim-
ited to the exploitation of the stellar light using multi-lambda
images in the visible and near-infrared (NIR), such as Hyperz
(Bolzonella et al. 2000) or Le Phare (Arnouts et al. 2002;
Ilbert et al. 2006) for photometric redshift estimation, or codes
focusing on the physical parameter determination (Walcher et al.
2011, and reference therein). The new generation of codes now
extends to other multi-lambda domains. The IR is a crucial
wavelength domain for assessing the contribution from dust,
which is included in, for instance, CIGALE (Noll et al. 2009;
Boquien et al. 2019) or MAGPHYS (da Cunha et al. 2008). Infor-
mation extracted from narrow spectral features can bring infor-
mation about the physical state of HII regions, such as in BEAGLE
(Chevallard & Charlot 2016). The ability to model more com-
plex star formation histories (SFH) has been a recent progress.
While it was first limited to a simple analytical representation of
the SFH, studies have added the possibility of a recent change
such as a quenching or a burst event (Ciesla et al. 2017, 2021;
Schreiber et al. 2018; Aufort et al. 2020). Even more powerful
techniques have been developed to include a varying SFH with
nonparametric modeling, such as in PROSPECTOR (Leja et al.

2017; Tacchella et al. 2022) or CIGALE (Ciesla et al. 2023). In
this paper, we compare the SFR derived from radio emission
and SED modeling techniques using the multiwavelength data
from the Cosmic Evolution Survey (COSMOS). We aim at better
understanding the sensibility of the radio taken as a tracer of the
SFR, depending on the timescale considered. Our work relies on
the SFH estimated from an SED modeling technique, assuming
a nonparametric modeling of the SFH. The article is organized
as follows. Section 2 describes the data set we employed, which
consists of a seminal galaxy sample from Jiménez-Andrade et al.
(2019). This sample includes several physical parameters, such
as the radio SFR indicator obtained through the IR-radio cor-
relation. In Sect. 3 we present the code investigating galaxy
emission, CIGALE, which has been employed to recover the star-
forming properties from broad- and narrow-band SED modeling,
and this in a wavelength range from the near ultraviolet (NUV)
to the far-infrared (FIR). Section 4 illustrates the results from
the data analysis, and we eventually discuss and conclude in
the last section. We adopt the standard ΛCDM cosmology with
Ω_m = 0.3, Ω_Λ = 0.7 and H_0 = 70 km s⁻<fnref n="1" /> Mpc⁻<fnref n="1" />. We use the ini-
tial mass function (IMF) from Chabrier (2003). The magnitudes
are given the AB system (Oke 1974).

2. Galaxy sample

2.1. VLA COSMOS 3 GHz project

The VLA COSMOS 3 GHz survey<fnref n="1" /> (Smolčić et al. 2017a) counts 348 h of observations using the Karl G. Jansky Very Large Array with a total of 192 individual pointings performed to achieve a uniform rms over the two square degrees of the COSMOS field, where each pointing was imaged individually using a circular restored beam with a full width at half maximum (FWHM) of 0.75 arcsec. The final mosaic was produced using the noise-weighted mean of all the individually imaged pointing, reaching a median rms deviation of 2.3 µJy beam⁻<fnref n="1" />. The final catalog presents a total of 10 830 radio sources down to 5σ.

2.2. Sample of Jiménez-Andrade et al. (2019)

We used the VLA COSMOS 3 GHz subsample of star-forming
galaxies drawn by Jiménez-Andrade et al. (2019), who first ran
PyBDSF (Mohan & Rafferty 2015) to extract the radio sources
from the mosaic to create a catalog with flux and size measure-
ments. Then, this preliminary catalog was cross-matched with
the original catalog from Smolčić et al. (2017a) to select sources
that are detected in both catalogs (this helps to reduce the spuri-
ous fraction in the final sample), where the number of common
sources led to a initial catalog with 9223 galaxies.

2.2.1. Selection of star-forming galaxies

To exclude AGNs from their initial sample, Jiménez-Andrade
et al. (2019) cross-matched the initial catalog of 9223 sources
with the radio source population catalog from Smolčić et al.
(2017a), who presented a sample of purely star-forming galax-
ies by rejecting a AGN if the intrinsic [0.5–8] keV X-ray lumi-
nosity is greater than $L_X = 10^{42}$ erg s⁻<fnref n="1" /> (e.g., Szokoly et al.
2004), the flux throughout the four IRAC bands (3.6, 4.5, 5.8,
and 8 µm) rises monotonically and follows the criterion pro-
posed by Donley et al. (2012), if a AGN component significantly

<footnote n="1">¹ https://cosmos.astro.caltech.edu/news/52</footnote>
improves the fitting of their optical to millimeter SED (see, e.g., da Cunha et al. 2008; Berta et al. 2013; Delvecchio et al. 2014), the observed radio emission $L_{1.4 GHz}$ exceeds the emission expected from the host galaxy SFRIR (estimated via IR SED fitting; Delvecchio et al. 2017), or if the rest-frame NUV minus r+ band ($M_{NUV}-M_R$) is greater than 3.5, which selects quiescent galaxies from the red sequence (Ilbert et al. 2010).

Then Jiménez-Andrade et al. (2019) applied a cut in redshift by considering a distribution between $0.35 < z < 2.25$. They excluded sources whose radio emission was modeled by more than one Gaussian component. This was done to avoid a complex radio morphology and led to a reduced sample of 3184 radio sources. Finally, two more selection criteria were applied by keeping galaxies with distances to the main sequence $\Delta$MS > −0.3, and galaxies with a stellar mass above the mass limit defined for each stellar mass bin ($\log_{10}M_*/M_\odot \approx 10.5$). This was done to guarantee that the sample was complete at stellar masses above these limits. The resulting sample contains 1804 galaxies.

### 2.2.2. Radio-based SFR computation

The 1.4 GHz luminosity $L_{1.4 GHz}$ of our galaxies was derived by Jiménez-Andrade et al. (2019) from the observed flux densities at 3 GHz, $S_{3 GHz}$, as

$$L_{1.4 GHz} = \frac{4\pi D_L^2(z)}{(1+z)^{1-\alpha}} \left(\frac{1.4}{3}\right)^{-\alpha} \frac{S_{3 GHz}}{\text{W Hz}^{-1} \text{m}^{-2}}, \quad (1)$$

with $D_L$ the luminosity distance in meters, and $\alpha$ the spectral index of the synchrotron power law ($S_v \propto v^{-\alpha}$; Condon et al. 1991) of 0.7, which is more adapted for the VLA COSMOS 3 GHz sample (Smolčić et al. 2017b). Then Jiménez-Andrade et al. (2019) derived SFR estimates using the IR-radio calibrations as follows:

$$\frac{\text{SFR}_{\text{radio}}}{M_{\odot} \text{yr}^{-1}} = f_{\text{IMF}} 10^{-24} 10^{g_{\text{IR}}} \frac{L_{1.4 \text{GHz}}}{\text{W Hz}^{-1}}, \quad (2)$$

where $f_{\text{IMF}}$ depends on the initial mass function (IMF; e.g., for a Salpeter IMF $f_{\text{IMF}} = 1.72$), and $q_{\text{IR}}$ in the case of FIR-detected star-forming galaxies only as $q_{\text{IR}} = (2.83 \pm 0.02) \times (1+z)^{-0.15 \pm 0.01}$ (Delhaize et al. 2017). As this calibration is based on the IR-SFR calibration, it relies on the hypothesis of a constant SFR in the last 100 Myr (Kennicutt & Evans 2012).

### 2.3. Optical counterparts and photometric redshifts

We cross-matched the radio-selected sample from Jiménez-Andrade et al. (2019) with the latest photometric catalog released on the COSMOS field (Weaver et al. 2022). We adopted THE FARMER version of the COSMOS2020 photometric catalog. The fluxes were estimated using a profile-fitting tool. This tool is more robust against the blending of nearby sources (Weaver et al. 2022). Moreover, the total flux is directly derived in all the bands, despite variations in the point spread function (PSF). These PSF variations were taken into account in the modeling of the light profile (Lang et al. 2016), while uncertain corrections were required when using aperture fluxes (Laigle et al. 2016).

The sources were cross-matched in position using a maximum radius of 1.5". We recovered 1584 sources. This is fewer sources than the initial 1804 sources from the sample of Jiménez-Andrade et al. (2019). This difference is explained

<table><caption>**Table 1.** Broad- and narrow-band set of filters employed as input data in the CIGALE SED fitting, where $\lambda_{\text{mean}}$ defines the central wavelength of the filters, and MAG$_{AB}$ quantifies the apparent magnitudes for each filter over the 0.25, 0.5, and 0.75 quantiles.</caption><thead><tr><th>Telescope/Camera</th><th>Filter name</th><th>λ<sub>mean</sub><br>[µm]</th><th>MAG<sub>AB</sub><br>25%/50%/75%</th></tr></thead><tbody><tr><td rowspan="2">GALEX</td><td>FUV</td><td>0.154</td><td>24.19/24.83/25.50</td></tr><tr><td>NUV</td><td>0.231</td><td>23.48/24.41/25.01</td></tr><tr><td>CFHT/Megacam</td><td>U</td><td>0.382</td><td>24.20/25.37/26.39</td></tr><tr><td rowspan="8">Subaru/HSC</td><td>g</td><td>0.485</td><td>23.46/24.69/25.80</td></tr><tr><td>r</td><td>0.622</td><td>22.57/23.78/24.93</td></tr><tr><td>i</td><td>0.750</td><td>21.74/22.91/24.18</td></tr><tr><td>z</td><td>0.889</td><td>21.29/22.30/23.51</td></tr><tr><td>Y</td><td>0.976</td><td>21.00/21.93/23.03</td></tr><tr><td>IA427</td><td>0.427</td><td>23.84/25.00/25.94</td></tr><tr><td>IA464</td><td>0.464</td><td>23.51/24.67/25.59</td></tr><tr><td>IA484</td><td>0.484</td><td>23.50/24.68/25.69</td></tr><tr><td rowspan="10">U-VISTA</td><td>IA505</td><td>0.505</td><td>23.30/24.52/25.48</td></tr><tr><td>IA527</td><td>0.527</td><td>23.26/24.49/25.52</td></tr><tr><td>IA574</td><td>0.574</td><td>22.92/24.11/25.12</td></tr><tr><td>IA624</td><td>0.624</td><td>22.65/23.86/24.97</td></tr><tr><td>IA679</td><td>0.679</td><td>22.08/23.34/24.52</td></tr><tr><td>IB709</td><td>0.709</td><td>22.11/23.37/24.59</td></tr><tr><td>IB738</td><td>0.738</td><td>21.95/23.17/24.44</td></tr><tr><td>IB767</td><td>0.767</td><td>21.74/22.93/24.25</td></tr><tr><td>IB827</td><td>0.827</td><td>21.56/22.66/24.00</td></tr><tr><td>NB711</td><td>0.711</td><td>22.00/23.24/24.41</td></tr><tr><td>NB816</td><td>0.816</td><td>21.60/22.72/24.04</td></tr><tr><td rowspan="10">Spitzer/IRAC</td><td>Y</td><td>1.021</td><td>20.92/21.81/22.86</td></tr><tr><td>J</td><td>1.253</td><td>20.51/21.30/22.19</td></tr><tr><td>H</td><td>1.645</td><td>20.09/20.84/21.62</td></tr><tr><td>Ks</td><td>2.153</td><td>19.63/20.30/21.08</td></tr><tr><td>NB118</td><td>1.191</td><td>20.70/21.49/22.35</td></tr><tr><td>CH1</td><td>0.744</td><td>19.49/19.98/20.49</td></tr><tr><td>CH2</td><td>1.011</td><td>19.59/20.02/20.43</td></tr><tr><td>CH3</td><td>1.408</td><td>19.63/20.04/20.41</td></tr><tr><td>CH4</td><td>2.879</td><td>19.75/20.24/20.68</td></tr><tr><td>Spitzer/MIPS</td><td>–</td><td>23.674</td><td>17.43/17.93/18.50</td></tr></tbody></table>

by the large masked areas around bright sources in COSMOS2020, and the difficulty of THE FARMER source extraction method to perform a profile-fitting around the brightest sources (Weaver et al. 2022). The photometry was extracted in the 32 bands listed in Table 1. A threshold for the signal-to-noise ratio (S/N) higher than 3 was applied in the Spitzer/MIPS 24 µm band. We also provide the quantiles of the magnitude distribution in each band to characterize the brightness of our sample.

Finally, we kept the same photometric redshifts as Jiménez-Andrade et al. (2019) in order to be consistent with their radio SFR derivation and AGN removal. These photometric redshifts were derived with the template-fitting code Le Phare
<figure><img src="image_3.png" /><figcaption>Fig. 1. Redshift distribution of the final sample, extracted from the COSMOS VLA 3 GHz survey project, which results from the different selection criteria applied in Jiménez-Andrade et al. (2019). The cross-match with THE FARMER version of the COSMOS2020 (Weaver et al. 2022) for photometric measures leads to a mass-complete sample of 1584 star-forming galaxies over the redshift range 0.35 < z < 2.25. The dashed gray lines indicate the 0.25, 0.5, and the 0.75 quantiles.</figcaption></figure>

(Arnouts et al. 2002; Ilbert et al. 2006) on the COSMOS2015 catalog (Laigle et al. 2016). We compared the photometric redshifts with the spectroscopic sample available in COSMOS that was described in Sect. 2.9 of Weaver et al. (2022). We find a precision of $\sigma_{\Delta z/(1+z_s)} = 0.024$ and an outlier fraction of $\eta = 1\%$. Figure 1 shows the final redshift distribution of our 1584 selected sources, with a mean photometric redshift of $z \approx 1$.

### 3. SED modeling with CIGALE

To model the SED of our galaxy sample, we used the SED modeling code CIGALE<fnref n="2" /> (Boquien et al. 2019). CIGALE can build and fit physical models from X-ray to radio and takes the energy budget between the light that is absorbed in the UV-optical and that is reemitted in IR by dust into account. It uses a Bayesian-like analysis to derive the physical properties of galaxies. Its versatility is characterized by the multiple modules that model the galaxy SFH, the stellar, dust, and nebular emission, the AGN contribution, and the radio emission of galaxies. In particular, the SFH can be handled through analytic, nonparametric, and simulated SFHs (Boquien et al. 2014; Ciesla et al. 2015, 2017). We used the recently added nonparametric SFH module sfhNlevels (Ciesla et al. 2023), Bruzual & Charlot (2003) stellar population models, a Calzetti et al. (2000) attenuation law, and the Dale et al. (2014) dust emission library. To test the robustness of our results in Sect. 5.2, we also considered a classical parametric SFH using a $\tau$-delayed model plus flexibility (Ciesla et al. 2017). For the standard parameterization of the code, we did not include the contribution of an AGN, except for the test presented in Sect. 5.3. Table 2 presents the parameters we used to set up the CIGALE fitting procedure. The accuracy of the physical parameters extracted from SED-fitting benefits from the depth of the imaging data and from the multiwavelength coverage from the FUV (GALEX at 0.15 µm) to mid-IR (Spitzer/MIPS at 24 µm) presented in Table 2.

A probability distribution function was associated with each parameter estimated with CIGALE. The flux uncertainties were handled within the $\chi^2$ estimate. An additional 10% of the flux is included by CIGALE (see Boquien et al. 2019). The final flux uncertainty considered in the $\chi^2$ estimate is given by $err_{tot} = \sqrt{\text{err}_{\text{flux}}^2 + (\text{flux} \times 0.1)^2}$.

#### 3.1. Nonparametric SFH: sfhNlevels module

The CIGALES's nonparametric sfhNlevels module, models the SFH using a given number of bins with a constant SFR. The SFRs of two consecutive bins are compelled by a given prior. We used a continuity prior following a Student-t distribution (Leja et al. 2019). A given number of SFH ($N_{\text{SFH}}$) is computed by randomly selecting the SFR in each bin from the distribution imposed by the prior.

This module includes the computation of a parameter called the SFR gradient, which characterizes the evolution of a galaxy over the SFR-$M_*$ plane. This parameter is defined as an angle (in degrees) and describes the direction of the galaxy evolution in a given time interval $\Delta t = t_2 - t_1$ in which the SFR changes by $\Delta \log_{10} \text{SFR}$ and the mass by $\Delta \log_{10} M_*$,

$$ \nabla \text{SFR}_{\Delta t} = \arctan \left( \frac{\Delta \log_{10} \text{SFR}}{\Delta \log_{10} M_*} \right). \qquad (3) $$

With this definition, galaxies with $\nabla \text{SFR}_{\Delta t} < 0$ present a declining star formation activity, and galaxies with $\nabla \text{SFR}_{\Delta t} > 0$ have an enhanced star formation activity over the last time interval $\Delta t$. This new module of CIGALE and the SFR gradient parameter are presented and tested in Ciesla et al. (2023).

#### 3.2. Mock analysis

To assess the reliability of the parameters derived with CIGALE, we built a mock catalog mimicking the data sample. For each galaxy of the sample, we simulated mock fluxes from the best fit of their observed fluxes: We started with the flux densities obtained by integrating the best-fit template over the same set of filters as the original flux. These mock flux densities were then perturbed by adding a noise that was randomly selected in a Gaussian distribution. The standard deviation $\sigma$ corresponded to the error of the original flux density. By running the code on this synthetic sample, for which all the physical parameters are known, we can compare the exact values of the physical and the retrieved parameters. This test evaluates whether the code can provide constrained values of the physical parameters we wish to study (e.g., Noll et al. 2009; Buat et al. 2014; Ciesla et al. 2015; Boquien et al. 2019). Figure 2 shows the results of the mock analysis for our SFG sample. The stellar mass, SFR, and IR luminosity parameters are well recovered, which is expected because the wavelength coverage of the sample allows us to probe the UV rest frame, NIR rest frame, and a data point to constrain the mid-IR (see, e.g., Buat et al. 2014; Ciesla et al. 2015; Małek et al. 2018). For the purpose of this study, we analyzed the results of the mock analysis of a few SFH parameters as well. For the SFR gradient mentioned is Sect. 3.1, computed over 300 Myr, the true values of the SFR gradient and those derived from CIGALE agree well overall (Fig. 2, bottom right panel). This choice of time interval provides a fair trade between a good indicator of the recent SFH and a well-constrained parameter (see the tests performed in Ciesla et al. 2023).

Finally, we also verified the reliability of the SFR estimates averaged over a number of different time intervals that we used in

<footnote n="2">² https://cigale.lam.fr/</footnote>
<table><caption>**Table 2.** Parameters of the models we used to perform the SED modeling with CIGALE.</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td colspan="2">Star formation history</td></tr><tr><td colspan="2">Non-parametric: sfhNlevels</td></tr><tr><td>Age [Gyr]</td><td>[2.8; 9.8]</td></tr><tr><td>N<sub>SFH</sub></td><td>1000</td></tr><tr><td colspan="2">τ-delayed SFH + flexibility</td></tr><tr><td>Age [Gyr]</td><td>[2.8; 9.9]</td></tr><tr><td>τ<sub>main</sub> [Gyr]</td><td>[0.1; 20]</td></tr><tr><td>Age<sub>trunc</sub> [Myr]</td><td>30, 100, 300, 500</td></tr><tr><td>r<sub>SFR</sub></td><td>[10<sup>-3</sup>; 10<sup>3</sup>]</td></tr><tr><td colspan="2">Dust emission: (Dale et al. 2014)</td></tr><tr><td>α</td><td>1.5, 2.0, 2.5</td></tr><tr><td colspan="2">Dust attenuation: (Calzetti et al. 2000)</td></tr><tr><td>E(B − V)s</td><td>[0, 0.8]</td></tr><tr><td colspan="2">AGN activity: SKIRTOR (Stalevski et al. 2016)</td></tr><tr><td>frac<sub>AGN</sub></td><td>[0, 0.5]</td></tr></tbody></table>

Notes. We refer to Boquien et al. (2019), Ciesla et al. (2017, 2023) for more details about the CIGALE input parameters.

the analysis in the following sections. These estimates are well constrained. The bias and precision are generally in the range 0.2–0.3 dex, as indicated in Fig. 2.

## 4. Results

In this section, we compare the SFR obtained from radio observations by Jiménez-Andrade et al. (2019; SFR<sub>radio</sub>) with the instantaneous SFR obtained from SED fitting (SFR<sub>inst</sub><sub>SED</sub>) with CIGALE. Figure 3 present the ratio SFR<sub>inst</sub><sub>SED</sub>/SFR<sub>radio</sub> as a function of the gradient ∇SFR<sub>300</sub> computed over the last 300 Myr. A positive value of ∇SFR<sub>300</sub> indicates a sustained star formation activity, and a high negative gradient indicates a quenching phase. If both SFR<sub>inst</sub><sub>SED</sub> and SFR<sub>radio</sub> estimators were unbiased and traced the instantaneous SFR, we would expect a distribution centered on 1 (0 in log) in Fig. 3, regardless of the ∇SFR<sub>300</sub>. However, galaxies with values of ∇SFR<sub>300</sub> ≤ 0 are spread over almost four magnitudes, while galaxies with ∇SFR<sub>300</sub> ≥ 0 agree better for the two SFR indicators.

In Fig. 4, galaxies on regions (A) and (B) represent ~19% and ~31% of our radio galaxy sample, respectively. Figure 3 shows that the ratio SFR<sub>inst</sub><sub>SED</sub>/SFR<sub>radio</sub> drops continuously as the gradient decreases below zero. By selecting galaxies at ∇SFR<sub>300</sub> ≤ −20, we find that ~75% of them have an SFR that differs by more than a factor 10 (i.e., log<sub>10</sub> SFR<sub>inst</sub><sub>SED</sub>/SFR<sub>radio</sub> < −1). By contrast, the SFR differs by >10 for only ~25% when we consider galaxies at ∇SFR<sub>300</sub> > 0.

In Fig. 5 we show the mean SFH of 100 randomly selected galaxies in regions (A) and (B). This representation clearly shows that the recent SFH of these two populations evolves differently in recent time. The galaxies in region A (B) increase with time (decrease) of the recent star formation, which is consistent with the definition of the ∇SFR<sub>300</sub> parameter. This trend is present in the last 300 Myr, but is more pronounced in the last 20 Myr. Additionally, the stellar masses are quite different in the two regions, with massive and low specific SFR (sSFR) galaxies in region (A) (with a median of log<sub>10</sub>sSFR = −1.72 and log<sub>10</sub>M* = 11.03, having sSFR in Gyr<sup>−1</sup> and stellar mass in M<sub>☉</sub>), and more active galaxies in region (B) (with a median of log<sub>10</sub>sSFR = 0.2 and log<sub>10</sub>M* = 10.86).

We verified that the χ<sup>2</sup><sub>red</sub> distribution peaks at ≈1, without a particular trend over the SFR ratios or ∇SFR<sub>300</sub>. We conclude that poor-quality fits do not explain the low SFR for a declining SFH.

A possible interpretation is that neither SFR estimator traces the SFR over the same timescale (e.g., Schleicher & Beck 2013). We considered the SFR derived from SED modeling as an instantaneous indicator, SFR<sub>inst</sub><sub>SED</sub>. Using the individual SFH produced with CIGALE, we can artificially construct SFR<sub>SED</sub> indicators that are sensitive over longer timescales. To do this, we averaged the galaxy SFH over different timescales Δt (100, 150, 270, 300, and 500 Myr) and compared them with the SFR<sub>radio</sub>. Hereafter, we note SFR<sub>Δt</sub> the SFH averaged over a time interval Δt. Figure 4 presents the ratio of the SFR<sub>radio</sub> and SFR<sub>Δt</sub> as a function of the SFR gradient ∇SFR<sub>300</sub> for three different timescales 100, 300, and 500 Myr (in addition to the instantaneous SFR<sub>inst</sub><sub>SED</sub>, which is shown in blue). In Fig. 6 we show the distribution of the SFRs ratios for all the different timescales mentioned above. We find that the agreement between the two SFR indicators improves continuously as we consider a longer timescale to integrate the SFH. The bias decreases drastically when a timescale >150 Myr is considered, and the bias falls to below 0.3 dex for the population with ∇SFR<sub>300</sub> ≤ −20 at the timescale of 270 Myr. When we consider a timescale of 270 Myr to estimate SFR<sub>SED</sub>, we find that ~4% of the SFRs differ by a factor >10 when ∇SFR<sub>300</sub> ≤ −20 (to be compared with 75% considering an instantaneous SFR<sub>inst</sub><sub>SED</sub>). We conclude that the radio and SED-fitting SFR tracers converge toward a consistent value if SFR<sub>SED</sub> is averaged over timescales longer than 150 Myr. The SFR<sub>radio</sub> and SFR<sub>SED</sub> of sources with an SFH with flat or positive gradients agree excellently for a timescale of 100 Myr.

To summarize, there is an effect of the SFH on the discrepancy between the two SFR indicators. The galaxies that are most affected by the discrepancy are those with ∇SFR<sub>300</sub> ≤ −20, that is, galaxies in which star formation stops rapidly and the star formation is quenched (Ciesla et al. 2023).

## 5. Additional considerations

In this section, we present an additional analysis to test the robustness of the results presented in Sect. 4. To do this,
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Results of the mock analysis for the SED modeling using the nonparametric SFH model. The input parameters we used to build the mock catalog are shown on the x-axis, and the results from fitting the mock catalogs are shown on the y-axis. From left to right, the upper panels present the instantaneous SFR, the stellar mass $M_*$, and the IR luminosity $L_{IR}$. The middle panels present the time-averaged SFRs for the last 100, 150, and 270 Myr over the SFH, and the bottom panels present the time-averaged SFRs for the last 270 and 500 Myr over the SFH as well as the SFR gradient computed over the last 300 Myr. The one-to-one relation is indicated by the solid black lines. The bias and precision estimated for the parameters are indicated in each panel.</figcaption></figure>

we explore several factors that might explain the discrepancy between the two SFR indicators in galaxies with decreasing star formation activity.

## 5.1. Malmquist bias due to the radio flux selection

Because of the flux selection, we can only select galaxies above a given radio SFR, approximately $10 M_{\odot} \text{yr}^{-1}$. The SFR derived from SED fitting is not limited similarly. As a consequence, the ratio distribution is skewed toward lower values by construction. SFR<sub>Inst</sub> can take low values while SFR<sub>radio</sub> cannot do this because of radio flux selection. Moreover, low values of the gradient $\nabla$SFR<sub>300</sub> correspond to low values of SFR<sub>SED</sub>, as shown in Fig. 3. Therefore, above a given level of uncertainties in SFR<sub>Inst</sub> SED

(especially at low gradient), the Malmquist bias might explain the observed trend.

We used the mock catalog presented in Sect. 3.2 to test this assumption. We reproduce a figure similar to Fig. 3 by studying the ratio of the estimated and true SFR<sub>SED</sub> as a function of the gradient in the simulation. We selected simulated galaxies whose true SFR<sub>Inst</sub> lies above $10 M_{\odot} \text{yr}^{-1}$ to mimic the flux selection of the radio sample. We find that the noise expected in the true SFR<sub>Inst</sub> is not sufficient to create a trend as seen in real data. We do not detect the trend in the simulation for any considered timescale. Moreover, the trend disappears when sufficiently long timescales were considered to estimate SFR<sub>Δt</sub>, while the expected precision on SFR<sub>Inst</sub> remains similar according to the simulation presented in Sect. 3.2. Only a bias of SFR<sub>Inst</sub> toward lower values and a low gradient could explain the trend observed
<figure><img src="image_5.png" /></figure>

**Fig. 3.** Ratio of the SFR<sub>SED</sub><sup>Inst</sup> and SFR<sub>radio</sub> as a function of the SFR gradient over the last 300 Myr (∇SFR<sub>300</sub>). In perfect scenarios in which the two indicators give the same value, we expect a uniform distribution centered at 1 (but 0 in log) over the SFRs ratios along the ∇SFR<sub>300</sub>. The shaded red region shows galaxies with negative values of the ∇SFR<sub>300</sub> (i.e., quenched) and an SFR ratio lower than 0.1, and the shaded region shows galaxies with positive values of the ∇SFR<sub>300</sub> (i.e., starbursting) and an SFR ratio higher than 0.1. The dots are color-coded according to the instantaneous SFR derived from the SED fitting procedure. The mean error bars are shown as black crosses for galaxies inside regions (A) and (B).

in the data. If there is any bias, we expect it in the opposite direc-
tion according to Fig. 2.

5.2. Impact of the assumed SFH

To test whether the results presented in Sect. 4 are sensitive to
the assumed SFH model, we again fit the whole sample with
CIGALE, but used a flexible τ-delayed SFH, as presented in
Ciesla et al. (2017). This SFH has been proposed to disconnect
the SFR and stellar mass estimates through a flexibility in the
recent SFH. It allows for an instantaneous and recent starburst
or for rapid quenching. The time when this happens is a free
parameter, as is the intensity of the burst or quenching. This
parametric SFH provides good estimates of the physical prop-
erties of galaxies, especially in terms of SFR (Ciesla et al. 2017,
2018; Schreiber et al. 2018). The input parameters used to gen-
erate these SFH are provided in Table 2.

As in the previous section, we find a galaxy population in
which the SFR<sub>radio</sub> is higher than the one obtained here with the
SED fitting, SFR<sub>SED</sub><sup>flex</sup>. We define the outlier galaxies such that
their ratio log<sub>10</sub> SFR<sub>SED</sub><sup>flex</sup>/SFR<sub>radio</sub> < -1. We wish to determine
whether the galaxies with divergent SFR tracers are the same
using the SFH delayed scenario or the nonparametric SFH sce-
nario. The result is shown in Fig. 7. The green dots show outliers
in the SFH delayed scenario, and the red dots show outliers in
the two SFHs scenarios<sup>3</sup>. A large fraction (90%) of the galaxies

exhibits a very low SFR<sub>SED</sub><sup>inst</sup> / SFR<sub>radio</sub> ratio regardless of whether the parametric or nonparametric SFH is used to estimate the SED SFR. We conclude that the outliers remain the same regardless of whether we use analytical or nonparametric SFHs, and our results are therefore independent of the choice of SFH model.

5.3. Possible remaining AGN contamination?

As described in Sect. 2.2.1, Jiménez-Andrade et al. (2019) thor-
oughly applied a set of criteria to remove AGNs host galaxies
from their sample of purely star-forming galaxies. However, we
added to this a last test by fitting the galaxies using the AGN
modeling module of CIGALE, skirtor (Stalevski et al. 2016).
This CIGALE module implements a modern clumpy two-phase
torus model to compute the UV-to-IR SED AGN model (see
Yang et al. 2020; Buat et al. 2021, for further information). From
this SED modeling run, we collected the instantaneous SFR as
well the AGN fraction (frac<sub>AGN</sub>), which quantifies the AGN con-
tribution to the total IR luminosity (L<sub>IR</sub>). Figure 8 shows the
ratios of the SFR<sub>SED</sub><sup>Inst</sup>/SFR<sub>radio</sub>, color-coded with frac<sub>AGN</sub>.

As a result, 90% of our galaxy sample have a frac<sub>AGN</sub> lower
than 15% (black dots), which is compatible with no detected
AGN from the UV to IR multiwavelength data (Ciesla et al.
2015). Only 10% of the galaxies have a value higher than 15%
(blue dots) and 2% have a frac<sub>AGN</sub> larger than 30% (yellow dots).
We note that galaxies with a weak to moderate AGN contribu-
tion (>15%) have ratio values that are lower than 0.1 in gen-
eral. However, even when we consider only the sources with
frac<sub>AGN</sub> < 15%, the results described in Sect. 4 are still valid,
and we observe that SFR<sub>SED</sub><sup>Inst</sup> and SFR<sub>radio</sub> diverge in galaxies
with decreasing SFH.

Despite having applied several criteria to remove radio
sources with a significant AGN contribution (see Sect. 2.2.1),
we cannot rule out a remaining low level of AGN contamination
in the radio emission. We note that further AGNs classification
would require a spectroscopic follow-up to establish additional
criteria (e.g., Baldwin et al. 1981; Best & Heckman 2012).

5.4. Insights from other star formation tracers

We confirmed the robustness of our results by adding two other
star formation tracers that are available in the COSMOS field:
the IR luminosity and the Hα emission lines. Here, the IR lumi-
nosity is not an output of our CIGALE run, but comes from inde-
pendent IR SED fits of COSMOS galaxies. These two additional
tracers are sensitive at different timescales.

As presented in Sect. 4, the SFRs derived from the radio are
orders of magnitude higher than those derived from SED fitting
for galaxies with a declining SFH. One possible interpretation is
that the radio traces the SFR over a longer timescale (>100 Myr),
while SED fitting is considered to provide an instantaneous SFR.
Because Hα traces the SFR over short timescales (<10 Myr,
Kennicutt & Evans 2012), the SFR derived from Hα should
follow the instantaneous SFR from SED fitting more closely.
The spectroscopic compilation established by Saito et al. (2020)
includes public Hα emission line measurements, mainly from
3D-HST (Momcheva et al. 2016) and the zCOSMOS catalog of
emission lines presented in Silverman et al. (2009), but extended
to the final zCOSMOS-Bright spectroscopic sample. As in
Saito et al. (2020), emission lines were corrected for dust attenu-
ation derived using the SED fitting. Then, the Hα intrinsic lumi-
nosity was converted into SFR following Kennicutt & Evans
(2012). Because of the small size of the spectroscopic sample
with Hα measured, we find only 29 matches to the radio sources.

<footnote n="3">³ We cannot produce a figure similar to Fig. 7 using directly SFR<sub>SED</sub><sup>flex</sup> rather than SFR<sub>SED</sub> in the nonparametric SFH scenario because the ∇SFR<sub>Δt</sub> parameter is not available as output of CIGALE for a flexible SFH.</footnote>
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Ratios of the SFR<sub>SED</sub> and the SFR<sub>radio</sub> as a function of the SFR gradient over the last 300 Myr (∇SFR<sub>300</sub>). Galaxies with ∇SFR<sub>300</sub> < 0 present a recent quenching, and galaxies with ∇SFR<sub>300</sub> > 0 present a recent starburst. Blue dots show instantaneous values of the SFR<sub>SED</sub>, and the orange, purple, and brown circles show an SFR<sub>SED</sub> that was averaged for the last 100, 300, and 500 Myr, respectively. Black dots show the mean trend and the dispersion of SFR ratio along the ∇SFR<sub>300</sub> inside a fixed bin size of 10°. The color-codes are the same as in Fig. 6.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Mean normalized SFHs (SFR(t)/∫SFR(t)dt) over 100 randomly selected galaxies for regions A and B in Fig. 3.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Ratio of the SFR<sub>Inst</sub> and the SFR<sub>radio</sub> as a function of the SFR gradient over the last 300 Myr (∇SFR<sub>300</sub>). Black dots represent galaxies that agree in both SFRs indicators, green dots show outliers in the SFH delayed scenario, and red dots show outliers for the two SFH models. 90% of the outliers would be selected as outliers with the flexible or nonparametric SFHs.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Distribution (in logarithmic scale) of the ratio of the radio and SED SFRs. Each color corresponds to an SFR<sub>SED</sub> obtained by averaging the SFH over different timescales from 100 Myr up to 500 Myr. The inset presents the same statistics, but selects only galaxies with a declining SFH (∇SFR<sub>300</sub> ≤ -20). The bias and the dispersion are indicated for each timescale.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Ratio of the SFR<sub>Inst</sub> and the radio SFR as a function of the SFR gradient over the last 300 Myr, as in Fig. 3. The color-code represents the AGN fraction.</figcaption></figure>

We find a good agreement between the SFR derived from Hα and radio (see the blue dots in Fig. 9). However, we find no source detected in Hα within the region showing a declining SFH. This

result is consistent with low SFR values in the ∇SFR<sub>300</sub> < 0 part of the sample, as expected from the SED fitting. However, a robust conclusion would require a larger spectroscopic sample.
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Ratio of the SFR<sub>radio</sub> and SFR from other tracers as a function of the SFR gradient over the last 300 Myr (∇SFR<sub>300</sub>). We use tree different SFR indicators: SFR<sub>IR</sub>, shown with black circles, SFR<sub>Hα</sub>, shown with blue stars, and SFR<sup>Inst</sup><sub>SED</sub>, shown with red circles. The galaxies marked with red circles are not detected in *Herschel*.</figcaption></figure>

Another interpretation of the results discussed in Sect. 4 is that the *q*<sub>IR</sub> parameter used in Sect. 2.2.2 to convert the radio luminosity into SFR depends on the stellar mass or sSFR (Gürkan et al. 2018). Delvecchio et al. (2021) reported that *q*<sub>IR</sub> decreases with stellar mass. However, we estimate that this would not explain more than a 0.3 dex overestimate for the SFR<sub>radio</sub> for massive galaxies, which is not sufficient to correct the difference seen at low ∇SFR<sub>300</sub>. We can directly test the validity of the *q*<sub>IR</sub> factor with our sample. We used the super-deblended FIR catalog from Jin et al. (2018) including MIPS (Le Floc’h et al. 2009), as well as Herschel data from the PEP survey (Lutz et al. 2011) at 100 and 160 µm, and the HerMES survey (Oliver et al. 2012) at 250, 350, and 500 µm. The fit over the full wavelength range was performed with Le Phare (Arnouts et al. 2002; Ilbert et al. 2006) in exactly the same way as described in Ilbert et al. (2015), using a combination of Dale & Helou (2002) and Bruzual & Charlot (2003) templates. The IR luminosity was based on the integral of the SED from 8 to 1000 µm. Figure 9 shows the comparison between SFR<sub>IR</sub> and SFR<sub>radio</sub>. We find an excellent agreement, even in the regime of declining SFH. Because the far-IR is sensitive over a long timescale (~100 million yr; Kennicutt & Evans 2012), as a consequence of old stars heating the dust, we conclude that this agreement between radio and IR tracers is expected. Moreover, we find that the population without any *Herschel* counterpart is located well within the region with a declining SFH, as expected. The existence of this population indicates that the radio tracer might be sensitive over a longer timescale than the far-IR tracer for a significant population of galaxies.

**6. Conclusions and perspectives**

We used a mass-complete subsample of star-forming galaxies drawn from the VLA 3 GHz project that was described in Jiménez-Andrade et al. (2019) to investigate the difference between the SFR derived from radio observations and the SFR derived from UV-to-IR SED modeling. We used the SED modeling code CIGALE that includes the new non-parametric SFH models (Ciesla et al. 2023).

The results of our analysis can be summarized as follows:

- The radio SFR of approximately 30% of our galaxies is ten times higher than the instantaneous SED SFR. This trend primarily affects the galaxies with a declining SFH activity over the last 300 Myr, that is, that are about to quench.

- By averaging the SFH over different timescales, we found that the two SFR indicators converge toward a consistent value when the SFHs obtained from the best fits are averaged over a period longer than 150 Myr to derive SFR<sub>SED</sub>.

- From a set of tests, we showed that these results are independent of the choice of SFH model and are not due to persistent AGN contamination.

- For the sources detected with *Herschel*, the SFR derived from FIR and radio agree well even for a declining SFH. We conclude that the *q*<sub>IR</sub> dependence on stellar mass does not explain our result and that 1.4 GHz traces star formation over a similar or longer timescale than the IR.

These results, and in particular, the discrepancies between the SFRs indicators, suggest that the SFRs obtained via radio observations at 1.4 GHz rest frame trace a longer timescale than the SFR derived from the SED template fitting, which we considered here as an instantaneous SFR indicator. As presented in Fig. 6, the SFH derived from SED-fitting needs to be integrated on a period longer than 150–300 Myr to agree with the radio SFR. On shorter timescales, the discrepancy between the two estimators primarily affects galaxies with a declining SFH. This can be problematic when the SFR in rapidly quenched galaxies is to be measured. On the other hand, this divergence of SFR<sup>Inst</sup><sub>SED</sub> and SFR<sub>radio</sub> for a sample free from AGN contamination might be a good criterion for isolating post-starburst galaxies.

Two mechanisms might explain the different timescale of the radio tracer and the SFR derived via SED template fitting. First, there is a time delay between the beginning of star formation and supernova explosions of up to 30 Myr, assuming that stars more massive than 8 M<sub>☉</sub> explode as SNe. The radio emission therefore necessarily lags emission in the UV or IR. Second, the radio emission is due to the synchrotron emission of CRe accelerated by SN and trapped in magnetic fields (e.g., Murphy 2009). Therefore, this radio emission might occur over long timescales, related to the timescale during which CRe travel through the ISM. The cooling timescale due to synchrotron emission for CRe emitting at 1 GHz might be about 30–100 Myr (Condon 1992; Murphy 2009). These two factors might explain that the radio wavelength still traces the star formation up to 100 Myr after quenching. Still, our results show that this timescale can exceed 150 Myr for the specific population with low sSFR that might undergo quenching.

On the other hand, the turbulence of the galactic magnetic fields can be triggered by gravitational instabilities during mergers (e.g., Drzazga et al. 2011; Rajpurohit et al. 2022) and can generate an excess of synchrotron radiation compared to undisturbed magnetic fields via scattering process and confinement of CRe (Lisenfeld & Völk 2010; Heesen et al. 2014; Reichherzer et al. 2021). A morphological study of our galaxy sample might help us to understand the discrepancy between the SFR indicators studied in this work. One of the most favored candidates for developing this perspective would be the imagery data from the James Webb Space Telescope (JWST; Gardner et al. 2006; Snyder et al. 2019; Sailer 2021).

We conclude that the use of 1.4 GHz as a star formation tracer still needs some investigation, especially for galaxy populations with a declining SFH. A better understanding of how the
radio wavelength traces the star formation is becoming crucial, with the Square Kilometre Array (SKA)<fnref n="4" /> being able to measure and study the radio continuum of millions of radio sources, even in the very deep universe (Murphy 2009; Jarvis et al. 2015).

**Acknowledgements.** We thank the referee for his/her comments which helped improve the paper. We also thank Alessandro Boselli, David Elbaz, and Vernesa Smolčić for insightful ideas and discussions. This project has received financial support from the CNRS through the MITI interdisciplinary programs. We warmly acknowledge the contributions of the entire COSMOS collaboration consisting of more than 100 scientists. The HST-COSMOS program was supported through NASA grant HST-GO-09822. More information on the COSMOS survey is available at https://cosmos.astro.caltech.edu. This research is also partly supported by the Centre National d'Etudes Spatiales (CNES). O.I. acknowledges the funding of the French Agence Nationale de la Recherche for the project iMAGE (grant ANR-22-CE31-0007).

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