# ViCTORIA project: The LOFAR view of environmental effects in Virgo cluster star-forming galaxies

H. W. Edler, I. D. Roberts, A. Boselli, F. de Gasperin, V. Heesen, M.

Brüggen, A. Ignesti, L. Gajović

► To cite this version:

H. W. Edler, I. D. Roberts, A. Boselli, F. de Gasperin, V. Heesen, et al. ViCTORIA project: The LOFAR view of environmental effects in Virgo cluster star-forming galaxies. Astronomy & Astrophysics - A&A, 2024, 683, 10.1051/0004-6361/202348301. insu-04726541

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# ViCTORIA project: The LOFAR view of environmental effects in Virgo cluster star-forming galaxies

H. W. Edler<fnref n="1" />, I. D. Roberts<fnref n="2" />, A. Boselli<fnref n="3" />,*, F. de Gasperin<fnref n="1" />,<fnref n="4" />, V. Heesen<fnref n="1" />, M. Brüggen<fnref n="1" />, A. Ignesti<fnref n="5" />, and L. Gajović<fnref n="1" />

Received 17 October 2023 / Accepted 21 December 2023

## ABSTRACT

**Context.** Environmental effects such as ram pressure stripping (RPS) shape the evolution of galaxies in dense regions.

**Aims.** We used the nearby Virgo cluster as a laboratory to study the environmental effects on the nonthermal components of star-forming galaxies.

**Methods.** We constructed a sample of 17 RPS galaxies in the Virgo cluster and a statistical control sample of 119 nearby galaxies from the *Herschel* Reference Survey. All objects in these samples were detected in LOFAR 144 MHz observations and come with $H\alpha$ and/or far-UV star formation rate (SFR) estimates.

**Results.** We derived the radio–SFR relations, confirming a clearly super-linear slope of ≈1.4. We found that Virgo cluster RPS galaxies have radio luminosities that are a factor of 2–3 larger than galaxies in our control sample. We also investigated the total mass-spectral index relation, where we found a relation for the Virgo cluster RPS galaxies that is shifted to steeper spectral index values by 0.17 ± 0.06. Analyzing the spatially resolved ratio between the observed and the expected radio emission based on the hybrid near-UV + 100 µm SFR surface density, we generally observed excess radio emission all across the disk with the exception of a few leading-edge radio-deficient regions.

**Conclusions.** The radio excess and the spectral steepening for the RPS sample could be explained by an increased magnetic field strength if the disk-wide radio enhancement is due to projection effects. For the galaxies that show the strongest radio excesses (NGC 4330, NGC 4396 and NGC 4522), a rapid decline in the SFR ($t_{\text{quench}} \le 100$ Myr) could be an alternative explanation. We disfavor shock acceleration of electrons as a cause for the radio excess since it cannot easily explain the spectral steepening and radio morphology.

**Key words.** stars: formation – galaxies: clusters: individual: Virgo cluster – galaxies: interactions – radio continuum: galaxies – radio continuum: general

## 1. Introduction

Galaxies that inhabit dense environments such as galaxy clusters show a lower cold gas content (e.g., Catinella et al. 2013; Boselli et al. 2014a) and a reduced star-forming (SF) activity (e.g., Kennicutt 1983; Boselli et al. 2014b, 2016a) compared to those located in poorer environments. It is thought that those differences are caused by environmental processes, that is, perturbations due to interactions with other galaxies or the intra-cluster medium (ICM). The process that is often thought to be the dominant perturbation affecting galaxies in massive (>10¹<fnref n="4" /> $M_\odot$), low-redshift clusters is ram pressure stripping (RPS; see Cortese et al. 2021; Boselli et al. 2022, for recent reviews). RPS is the removal of the interstellar medium (ISM) of a galaxy moving at a high velocity $v$ relative to the ICM. The ram pressure scales as $P \propto \rho v^2$ where $\rho$ is the ICM density. Consequently, it is most effective in massive clusters where the galaxy velocities and the ICM densities are high.

Ram pressure stripping impacts the diffuse atomic phase of the ISM due to the advection of the loosely bound neutral hydrogen (H1), which can give rise to tails that can be traced by 21 cm line observations (e.g., Chung et al. 2007). This can also explain the truncated radial H1 profiles (e.g., Chung et al. 2009) and the statistical H1 deficiency (e.g., Boselli & Gavazzi 2006) of galaxies in clusters. The subsequent ionization of the stripped H1 due to interactions with the ICM creates tails of ionized gas that are most commonly observed in the $H\alpha$ line (e.g., Gavazzi et al. 2001, 2018a; Yagi et al. 2010; Boselli et al. 2016b); as those recently observed during the GAs Stripping Phenomena (GASP) in galaxies with MUSE (Poggianti et al. 2017) program and the Virgo Environmental Survey Tracing Ionized Gas Emission (VESTIGE; Boselli et al. 2018a). In some cases, RPS may also affect the dense molecular gas, which is fueling star formation, either indirectly by displacing the atomic gas or directly by displacing the molecular gas from the stellar disk (e.g., Cramer et al. 2020; Watts et al. 2023); this in turn reduces the star formation rate (SFR). The timescale on which the star formation is quenched may depend on a number of

<footnote n="1">¹ Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
e-mail: henrik.edler@hs.uni-hamburg.de</footnote>

<footnote n="2">² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands</footnote>

<footnote n="3">³ Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France</footnote>

<footnote n="4">⁴ INAF – Istituto di Radioastronomia, Via P. Gobetti 101, Bologna, Italy</footnote>

<footnote n="5">⁵ INAF – Astronomical Observatory of Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy</footnote>

<footnote>* Scientific associate at INAF – Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy.</footnote>
parameters such as galaxy mass, orientation, and velocity with
respect to the ICM as well as the ICM density and dynam-
ical state. Observational evidence points to quenching times
of ≤1 Gyr (e.g., Boselli et al. 2006, 2016a; Ciesla et al. 2016;
Fossati et al. 2018).

Current RPS events in star-forming galaxies show tails in
the atomic or ionized hydrogen distribution, as well as in the
radio continuum (e.g., Gavazzi 1978; Gavazzi et al. 1995). The
radio continuum emission of star-forming galaxies is caused
by cosmic-ray electrons (CRe) that were shock-accelerated in
supernovae gyrating in weak magnetic fields (i.e., synchrotron
radiation). Thus, it is a tracer of the SFR (Condon 1992;
Gürkan et al. 2018; Heesen et al. 2019, 2022). The CRe are
transported by diffusion processes in the galactic magnetic fields,
but may also be subject to advection through ram pressure,
creating asymmetric or tailed radio continuum profiles. The
advance of sensitive radio surveys, such as those undertaken with
the LOw-Frequency ARray (LOFAR; van Haarlem et al. 2013),
allowed the identification of >100 ongoing RPS events in the
past few years (Roberts et al. 2021a,b, 2022; Ignesti et al. 2022a,
2023; Edler et al. 2023).

Observations in the radio continuum are well suited to iden-
tify RPS events and trace the galaxy SFR. They also allow us
to probe the nonthermal phase of the ISM, that is, the CRe and
the magnetic fields via their synchrotron emission. Indeed, this
nonthermal component is thought to be of importance for the
evolution of RPS events by magnetically binding low- and high-
density regions in the ISM (Kenney et al. 2015) or by magneti-
cally stabilizing the stripped gas against mixing and disruption
(e.g., Ruszkowski et al. 2014; Tonnesen & Stone 2014). The
radio emission of RPS galaxies often appears to be in excess of
what is expected given their SFR inferred from observations at
other wavelengths (e.g., Gavazzi et al. 1991; Murphy et al. 2009;
Vollmer et al. 2010; Chen et al. 2020; Ignesti et al. 2022a,b).
Several explanations for the radio excess of cluster SF galaxies
have been discussed in the literature: Gavazzi & Boselli (1999)
proposed that the ram pressure leads to a compression of the
magnetic field and, consequently, it increases synchrotron
luminosity. Völk & Xu (1994) and Murphy et al. (2009) favored
a scenario where the higher radio luminosity is not simply
caused by compression, but instead due to shocks driven into
the ISM by collisions with fragments of cold gas present in the
ICM. Diffusive shock acceleration can then accelerate CRe in the
ISM, which should result in a flatter radio spectral index. A third
explanation of the radio excess was brought up more recently in
Ignesti et al. (2022a,b) based on the analysis of so-called jelly-
fish galaxies which are the most extreme examples of galaxies
undergoing strong RPS events. The strong radio excess com-
pared to the Hα emission was interpreted as the consequence
of a rapid quenching of the star-forming activity due to RPS.
While the Hα emission is a nearly instantaneous SF tracer, with
a typical delay of only a few million years, the radio-emitting
CRe have a typical lifetime >100 Myr. Thus, if the star forma-
tion is quenched on timescales shorter than the CRe lifetime, we
observe an apparent excess of radio emission simply due to the
different timescales probed by Hα and the radio observations.
As a consequence, the spectral index of those objects should be
rather steep owing to spectral aging.

This work is part of the Virgo Cluster multi-Telescope
Observations in Radio of Interacting galaxies and AGN (ViC-
TORIA) project, a broadband radio imaging campaign of the
Virgo cluster (de Gasperin et al., in prep.). In Edler et al. (2023),
we recently published a 144 MHz survey of the Virgo cluster
region using the LOFAR high-band antenna system as the first

data release of ViCTORIA. The survey led to the radio detection
of 112 cluster members, with 19 objects that show signs of RPS
in their radio morphology. We use this dataset to study the RPS
phenomenon in the Virgo cluster.

In this work, we assume a flat ΛCDM cosmology with
Ω_m = 0.3 and H₀ = 70 km s⁻¹ Mpc⁻¹. At the distance of M 87,
for which we adopted a value of 16.5 Mpc (Mei et al. 2007;
Cantiello et al. 2018), one arcsecond corresponds to 80 pc. This
paper is arranged as follows: In Sect. 2, we report the data used
for this work and our samples. In Sect. 3, we present a statistical
study of the radio and star-forming properties and in Sect. 4, we
carried out a spatially resolved analysis of the LOFAR maps and
compared them to the expected radio emission based on the SFR
surface density. Finally, our conclusions are outlined in Sect. 6.

## 2. Data and sample

This paper builds primarily on the LOFAR HBA Virgo Cluster
Survey (Edler et al. 2023) published as part of the ViCTORIA-
project. This 144 MHz survey covers a 132 deg² field around the
Virgo cluster and is to date the deepest blind radio continuum
survey of this particular region.

### 2.1. RPS sample

For our LOFAR study of star-forming galaxies in the Virgo clus-
ter, we composed a sample of objects detected in Edler et al.
(2023) that show signs of RPS in the radio continuum. As crite-
ria, we require an asymmetric radio morphology in combination
with an undisturbed optical appearance. The latter is to exclude
cases where the dominant perturbing mechanism is tidal interac-
tion. If the available literature clearly shows that an object suffers
both from tidal interactions and RPS, we include it in our sample.
This is the case for NGC 4254 (Vollmer et al. 2005a), NGC 4438
(Vollmer et al. 2005b) and NGC 4654 (Vollmer 2003). The Virgo
cluster has been the target of several multifrequency surveys and
dedicated studies of individual objects. Out of the 19 galaxies
with evident tails in radio continuum, 15 were already identified
as suffering a RPS event in these detailed studies, as summarized
in Boselli et al. (2022). They show tails of stripped atomic or
ionized gas, have truncated gaseous and star-forming disks, and
have been identified as suffering a RPS event from tuned models
and hydrodynamic simulations. Four of the objects are for the
first time reported to be RPS candidates based on our LOFAR
data: IC 800 shows a radio tail to the northeast, in agreement with
being on a radial orbit toward the cluster center, and is strongly
H I deficient. IC 3258 is a dwarf galaxy with a radio tail that is
also in agreement with a highly radial orbit. NGC 4607 shows a
mild asymmetry with an extension of the radio contours toward
the northeast and a strong gradient in the opposite direction, it
is also highly deficient in neutral hydrogen. Lastly, NGC 4634
shows a radio tail toward the west and is slightly deficient in H I,
a star-forming object is coincident with the radio tail (Stein et al.
2018). Preliminary images from the ViCTORIA MeerKAT Sur-
vey confirm the morphological peculiarities found in LOFAR
for all four objects. For four other galaxies in our RPS sample
(IC 3105, IC 3476, NGC 4302, and NGC 4424), the impact of
RPS was previously observed at other wavelengths (Chung et al.
2007; Boselli et al. 2021, 2022) but not in the radio continuum.

Since our analysis focuses on the star-forming proper-
ties, radio emission due to active galactic nuclei (AGN) is a
strong contamination. Thus, we investigate the possible con-
tribution of AGN-emission for the galaxies that show signs of
<table><caption>**Table 1.** LOFAR sample of ram-pressure-stripped galaxies in the Virgo cluster.</caption><thead><tr><th>VCC<br>(1)</th><th>NGC<br>(2)</th><th>IC<br>(3)</th><th>Morphology<br>(4)</th><th>log M<sub>★</sub><br>[log M<sub>☉</sub>]<br>(5)</th><th>H I-def.<br>(6)</th><th>Δv<sub>rad,M 87</sub><br>[km s<sup>-1</sup>]<br>(7)</th><th>Literature<br>(8)</th><th>Comment<br>(9)</th></tr></thead><tbody><tr><td>241</td><td></td><td>3105</td><td>SW tail</td><td>7.89</td><td>0.41</td><td>-1439</td><td>B22</td><td>New radio tail, Hα tail</td></tr><tr><td>307</td><td>4254</td><td></td><td>N tail</td><td>10.39</td><td>0.06</td><td>1124</td><td>V05, H07, V12b, B18a, M09</td><td>RPS + tidal interaction</td></tr><tr><td>497</td><td>4302</td><td></td><td>Light N tail</td><td>10.44</td><td>0.50</td><td>-153</td><td>C07, V13, W12</td><td>New radio tail, H I tail</td></tr><tr><td>630</td><td>4330</td><td></td><td>S tail</td><td>9.52</td><td>0.92</td><td>321</td><td>C07, M09, V12a, V12b, V13, F18</td><td>H I tail, Hα tail</td></tr><tr><td>664</td><td></td><td>3258</td><td>W tail</td><td>8.20</td><td>0.57</td><td>-1713</td><td></td><td>New candidate</td></tr><tr><td>865</td><td>4396</td><td></td><td>NW tail</td><td>9.25</td><td>0.20</td><td>-1398</td><td>C07, V07, V10, M09</td><td>H I tail</td></tr><tr><td>873</td><td>4402</td><td></td><td>NW tail</td><td>10.04</td><td>0.83</td><td>-1049</td><td>CR05, V07, M09, V10, V12b</td><td>H I tail, stripped dust</td></tr><tr><td>979</td><td>4424</td><td></td><td>Small S tail</td><td>10.17</td><td>0.98</td><td>-842</td><td>C07, V13, B18b</td><td>H I tail, Hα tail/outflow, radio deficient</td></tr><tr><td>1401</td><td>4501</td><td></td><td>NE tail</td><td>10.98</td><td>0.58</td><td>999</td><td>W07, V07, V10, V12b</td><td></td></tr><tr><td>1450</td><td></td><td>3476</td><td>Long W tail</td><td>9.02</td><td>0.66</td><td>-1112</td><td>B21</td><td>New radio tail, Hα tail, M87 side-lobes</td></tr><tr><td>1516</td><td>4522</td><td></td><td>Long NW tail</td><td>9.38</td><td>0.68</td><td>1037</td><td>V04, M09, V12b</td><td></td></tr><tr><td>1532</td><td></td><td>800</td><td>NE tail</td><td>9.07</td><td>1.00</td><td>1051</td><td></td><td>New candidate</td></tr><tr><td>1615</td><td>4548</td><td></td><td>N-S asymmetry</td><td>10.74</td><td>0.94</td><td>-802</td><td>V99, W07</td><td>Old stripping event</td></tr><tr><td>1690</td><td>4569</td><td></td><td>SW tail, outflows</td><td>10.66</td><td>1.05</td><td>-1503</td><td>M09, V12b, B16</td><td>Hα tail</td></tr><tr><td>1868</td><td>4607</td><td></td><td>Asymmetry</td><td>9.60</td><td>1.20</td><td>973</td><td></td><td>New candidate</td></tr><tr><td>1932</td><td>4634</td><td></td><td>SW tail</td><td>9.57</td><td>0.45</td><td>-1163</td><td>S18</td><td>New candidate, star-forming object in the tail (S18)</td></tr><tr><td>1987</td><td>4654</td><td></td><td>Asymmetry</td><td>10.14</td><td>-0.05</td><td>-240</td><td>V03, V07, C07, W07, V10</td><td>H I tail, RPS and tidal interaction</td></tr></tbody></table>

**Notes.** Columns 1–3 list the identifiers of the galaxies in the VCC, NGC and IC. Column 4 comments on the LOFAR morphology of the sources and Cols. 5–7 show the stellar mass (from Boselli et al. 2015), H I deficiency and the radial velocity relative to M 87 (taken from HyperLeda https://leda.univ-lyon1.fr/). In Cols. 8 and 9, we list the relevant literature and additional comments.

**References.** V99 – Vollmer et al. (1999); V03 – Vollmer (2003); V04 – Vollmer et al. (2004) CR05 – Crowl et al. (2005); V05 – Vollmer et al. (2005a); C07 – Chung et al. (2007); H07 – Haynes et al. (2007); W07 – Weżgowiec et al. (2007); V07 – Vollmer et al. (2007); M09 – Murphy et al. (2009); V10 – Vollmer et al. (2010), V12a – Vollmer et al. (2012a); V12b – Vollmer et al. (2012b), W12 – Weżgowiec et al. (2012); V13 – Vollmer et al. (2013); B16 – Boselli et al. (2016b); B18a – Boselli et al. (2018b); B18b – Boselli et al. (2018c); S18 – Stein et al. (2018); B21 – Boselli et al. (2021); B22 – Boselli et al. (2022).

ram pressure stripping in the radio continuum. Three of those objects, NGC 4388, NGC 4438 and NGC 4501 are Seyfert galaxies. The first two have a radio morphology that is clearly dominated by nuclear emission (Hummel & Saikia 1991). However, in NGC 4501, the nuclear point-source accounts for only 1% of the total radio emission. The other galaxies mostly host H II-nuclei in the BPT (Baldwin, Phillips & Terlevich; Baldwin et al. 1981) and WHAN ($W_{H\alpha}$ versus N II/Hα; Cid Fernandes et al. 2011) diagrams according to Gavazzi et al. (2018b). Exceptions are NGC 4302, NGC 4548 and NGC 4569 and which have a nuclear WHAN classification as AGN and an inconclusive nuclear BPT classification. NGC 4607 is also classified as AGN in the WHAN diagram and as LINER (Low Ionization Nuclear Emission-line Region; Heckman 1980) or transition object in the BPT, but has an integrated classification as an H II galaxy. Of those, only NGC 4569 shows a compact nuclear source in the LOFAR maps. While a minor contribution of an AGN cannot be ruled out for this object, this central source is dominantly fueled by nuclear star formation giving rise to prominent outflows (Boselli et al. 2016b). Thus, the only AGN we remove from our sample are NGC 4388 and NGC 4438.

We are left with a sample of 17 RPS galaxies which are listed in Table 1. The H I-deficiency parameter (Haynes et al. 1984) reported in this table is the logarithm of the ratio between the observed H I mass and a reference mass for isolated galaxies that is based on the diameter and Hubble type. We follow the H I-deficiency values reported in Boselli et al. (2014c) and Köppen et al. (2018), which are based on the similar calibrations of Boselli & Gavazzi (2009) and Gavazzi et al. (2013).

The 20"-resolution LOFAR contours on top of the optical images of the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey data release 10 (Dey et al. 2019) are displayed in Fig. 1. They range from galaxies with clear and prominent 144 MHz tails, such as NGC 4330, NGC 4396, NGC 4522, or IGC 3476 to objects with only mild asymmetry, such as NGC 4548 and NGC 4607. With the availability of high-sensitivity images of the nearby Virgo cluster, we start probing the regime of dwarf galaxies with radio continuum tails by detecting lower mass systems, down to a stellar mass of $M_{\star} = 7.8 \times 10^7 M_{\odot}$. Previous studies of more distant clusters and groups are limited to objects with masses $M_{\star} \ge 10^9 M_{\odot}$ (Roberts et al. 2021a,b, 2022; Ignesti et al. 2022a).

A number of galaxies that were reported in the literature to suffer from RPS (Boselli et al. 2022) are not part of our LOFAR RPS sample. Of those, IC 3412, IC 3418, NGC 4506 and UGC 7636 have not been detected by LOFAR with a detection limit of $4\sigma$. Others, mostly galaxies which have tails in H I, are radio-detected but show a symmetric radio morphology. Those objects are NGC 4294, NGC 4299, NGC 4469, NGC 4470 NGC 4491 and NGC 4523 (Chung et al. 2007; Boselli et al. 2023a). For these objects, we speculate that they experience rather mild ram pressure, which mostly affects the outskirts of the ISM, such that a tail in radio continuum is below our sensitivity threshold. Alternatively, the peculiar H I morphology of these objects could be due to other process than RPS. In the case of NGC 4470, the nondetection of a continuum tail is due to local dynamic range limitations in the LOFAR map, indeed preliminary images of our VICTORIA MeerKAT survey reveal
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Radio continuum emission in galaxies with a radio morphology indicative of RPS. We show LOFAR radio continuum intensity contours at 144 MHz overlaid on top of optical images from the DESI Legacy Survey. Contour-levels increase in increments of powers of two and pink arrows indicate the direction and angular distance (in units of degree) to the center of the Virgo cluster. The white circle in the bottom left corresponds to the synthesized beam size of 20".</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Fig. 1. continued.</figcaption></figure>

a prominent tail at 1.3 GHz. For NGC 4523, a continuum counterpart to the H I tail which we reported in Boselli et al. (2023a) is also observed in the preliminary MeerKAT maps, although at low significance.

## 2.2. LOFAR-HRS sample

To assess how the nonthermal properties of galaxies in the Virgo cluster are shaped by their local surroundings, we compiled a comparison sample of nearby galaxies with high-quality star formation tracer data available. For this, the Herschel Reference Survey (HRS; Boselli et al. 2010), which also contains all but two of the galaxies in our RPS sample, is well suited. This survey consists of a statistically complete, K-band limited sample of 323 nearby (15–25 Mpc distance) galaxies. Around a quarter of those galaxies reside in the Virgo subclusters around either M 87 or M 49, another quarter is located in other substructures of the Virgo cluster or its outskirts. The remaining objects are in less dense environments such as groups and pairs or are isolated galaxies. This allowed us to compare the properties of galaxies in the Virgo cluster with those that are inhabiting poorer surroundings.

We constructed a sample of the 144 MHz LOFAR-detected star-forming galaxies in the HRS. For this, we used data of the LOFAR HBA Virgo Cluster Survey (Edler et al. 2023), which covers the majority of the galaxies in the Virgo cluster. In addition, all the HRS galaxies at declinations of $\delta > 30^\circ$ are covered by the second data release of the LOFAR Two-meter Sky Survey (LoTSS-DR2; Shimwell et al. 2022). Further galaxies were observed by more recent, previously unpublished observations of LoTSS, processed by the LOFAR Surveys Key

Science Project<fnref n="1" />. All LOFAR HBA observations were taken with identical observational settings and processed using the ddf-pipeline algorithm (Tasse et al. 2021). For the Virgo cluster observations, additional preprocessing was necessary due to the close proximity to the extremely luminous radio galaxy M 87 (Virgo A), those steps are described in Edler et al. (2023).

For the HRS galaxies in the footprint of the LOFAR HBA Virgo Cluster Survey, we used the 144 MHz measurements reported in Edler et al. (2023) based on the 20"-resolution LOFAR-maps. In this paper, all HRS galaxies within the survey area were considered. We extended this sample also to the HRS galaxies covered by LoTSS-DR2 as well as to those which are within $1.97^\circ$ angular distance of unpublished LoTSS-observations processed before August 2023. We manually inspected all HRS galaxies in the LoTSS 20"-maps and, if they were visible in the radio images, we measured the flux density in a region encompassing the $3\sigma$-contours as it was done in Edler et al. (2022) for the Virgo objects. For observations outside of LoTSS-DR2, we used the pointing closest to the galaxy of interest and we took into account a field-dependent factor to align the flux density scale with the one of the 6 C-survey (Hales et al. 1988) and NRAO VLA Sky Survey (NVSS; Condon et al. 1998). This factor was calculated as described in Shimwell et al. (2022). We consider all galaxies with an integrated signal-to-noise ratio above four as radio-detected. While we use the 10% systematic uncertainty of the flux density scale for LoTSS-DR2 as reported in Shimwell et al. (2022), a larger uncertainty of 20% is assumed for the other LOFAR maps due

<footnote n="1">¹ https://lofar-surveys.org/</footnote>
<figure><img src="image_4.png" /><figcaption>Fig. 2. LOFAR coverage of the HRS. The galaxies are either in the LOFAR HBA Virgo Cluster Survey (blue), in LoTSS-DR2 (orange) or covered in further LoTSS observations (green). Gray crosses are not covered by LoTSS, and colored but partially transparent points are covered but not detected. Dashed regions mark structures of galaxies other than the Virgo cluster.</figcaption></figure>

to the reduced overlap and statistics, the higher uncertainty of the primary beam model for low declinations, and the presence of bright sources such as M87 (for sources in the Virgo field, Edler et al. 2023). In Fig. 2, we show the sky distribution of the HRS galaxies and their coverage by the different LOFAR projects. In total, out of the 261 late-type galaxies in the statistically complete sample of the HRS (excluding ellipticals and lenticulars), 193 are in the footprint of our LOFAR observations. Of those, 141 galaxies are detected, 76 are in the LOFAR Virgo field, 44 are from LoTSS-DR2, and 21 are in LoTSS-fields outside of the LoTSS-DR2 footprint.

Since we are interested in radio emission as a tracer of the SFR, we need to exclude objects where a significant fraction of the radio emission is due to an active galactic nucleus (AGN). By excluding elliptical and lenticular galaxies, we remove most objects with strong AGN contamination. In Gavazzi et al. (2018b), nuclear spectroscopy-based BPT and WHAN classifications for the HRS galaxies were presented. Eleven of the LOFAR-detected objects were classified as either strong or weak AGN in the WHAN diagram and as Seyfert galaxy in the BPT diagram. Visually inspecting the radio maps of those revealed that for six of them the nuclear point-like sources contribute >15% to the flux density. These objects (NGC 3227, NGC 4313, NGC 4419, NGC 4586) were removed from our sample. All galaxies in the RPS sample described in Sect. 2.1 except for IC 3105 and IC 3258, which are fainter than the limiting K-band magnitude of 12, are also part of the HRS. Those two objects are also part of our analysis but were excluded from any fitting since they do not meet the selection criteria of the HRS. In the following, we refer to the objects in our LOFAR-HRS sample minus the objects in our RPS sample for simplicity as the non-RPS sample.

In Appendix A, we display the 144 MHz measurements of the 137 LOFAR-detected star-forming galaxies used in this work. The spectral luminosity $L_{144}$ at 144 MHz is calculated from the measured flux densities $S$ according to $L_{144} = 4\pi d^2S$; since our sample only consists of nearby galaxies at $v < 1750$ km s$^{-1}$, we neglected $k$-correction. We employed distances $d$ following the HRS (Boselli et al. 2010), with the difference that we set the distance to objects in the Virgo cluster to 16.5 Mpc instead of 17 Mpc to be consistent with what is assumed in the NGVS (Ferrarese et al. 2012) and VESTIGE (Boselli et al. 2018a).

### 2.2.1. Star formation tracers

The integrated radio luminosities serve as a tracer of the SFR of the individual galaxies in the sample. A key advantage of radio-inferred SFR is that it is not affected by dust attenuation (Condon 1992; Murphy et al. 2011). Thus, no extinction-correction is required. While at low radio frequencies, the radio emission is almost free from the Bremsstrahlung contribution of thermal electrons, the synchrotron lifetime of CRe in a magnetic field $B$ (Beck & Krause 2005):

$$t_{\text{syn}} = 88 \text{ Myr} \left( \frac{B}{10 \mu\text{G}} \right)^{-3/2} \left( \frac{v}{144 \text{ MHz}} \right)^{-1/2} \quad (1)$$

is longer compared to CRe probed at higher frequencies. So an underlying assumption of SFRs derived from low frequency observations is that the SFR is constant on timescales of ≈100 Myr.

To compare the radio luminosity to further tracers of the star-forming activity, we consider SFRs based on far-UV (FUV) and Hα. The SFRs obtained from Hα and FUV were reported in Boselli et al. (2015) for the HRS star-forming galaxies based on the Salpeter initial mass function (IMF) and the calibration of Kennicutt (1998). We converted the SFR to a Chabrier IMF (Chabrier 2003) by applying a factor of 0.63 to the SFRs (Madau & Dickinson 2014). The SFRs also need to be corrected for dust attenuation. For the UV-based SFR, Boselli et al. (2015) employed a correction based on the 24 µm emission. For the Hα-inferred SFR, two approaches were compared in Boselli et al. (2015) – a correction based on the Balmer-decrement using spectroscopic data (Boselli et al. 2013) and a method relying on the 24 µm dust emission. The authors found that the correction with the Balmer decrement $C(H\beta)$ as defined in Lequeux et al. (1981) is only accurate if the fractional uncertainty is $\sigma[C(H\beta)] < 0.1$; on the other hand, the correction using the 24 µm emission can be biased for systems with a particularly low specific SFR due to the contribution of the old stellar population to the dust heating (Cortese et al. 2008; Boselli et al. 2015). Thus, we used the values corrected with the Balmer-decrement if $\sigma[C(H\beta)] < 0.1$, and with the 24 µm emission otherwise.

No uncertainty estimates are available for the SFRs published in Boselli et al. (2015). In the following, we assume a systematic uncertainty of 15% for the GALEX UV measurements (Gil de Paz et al. 2007) and the Hα photometry with the San Pedro Martir telescopes (Boselli et al. 2015, 2023b). We neglect the photometric uncertainty of the Spitzer 24 µm measurements used for a dust correction as they have a uncertainty of only 2% (Engelbracht et al. 2007). Those estimates are only a rough first-order approximation of the true uncertainties, which also would require us to take into account the complex and hardly quantifiable dependencies on the dust and N II line corrections and the SFR conversion (for discussions of those, see e.g.,
<figure><img src="image_5.png" /><figcaption>Fig. 3. SFR (mean of Hα and UV-based values) as a function of the stellar mass for galaxies in the RPS sample (orange diamonds), galaxies in the Virgo cluster region (within 10° from M87, green circles) and galaxies outside of the cluster (blue circles). For comparison, we show the star-forming main sequence for Virgo cluster galaxies with normal H1 content (Boselli et al. 2023b, gray line).</figcaption></figure>

Boselli et al. 2015, 2016a, 2023b). We ensured that the SFRs are based on the same distances as the radio luminosities by rescaling the SFRs by $(d/d_{HRS})^2$.

Another common SFR-tracer is the infrared-emission which traces the dust heated by the young stellar population. As already mentioned, in systems with low specific SFR, older stellar populations also contribute to the dust heating. Low specific SFR systems are systematically more common in our sample which includes relatively quenched galaxies in the Virgo cluster (Boselli et al. 2016a). For this reason, we do not consider SFRs based purely on the infrared emission.

### 2.2.2. Sample properties

The stellar masses of our sample were obtained from Cortese et al. (2012) who used the Chabrier IMF and span a large regime, ranging from $3.0 \times 10^8 M_{\odot}$ to $1.3 \times 10^{11} M_{\odot}$. The two additional RPS galaxies outside of the HRS, IC 3105 and IC 3258, are of even lower mass with $M_{\star} = 7.8 \times 10^7 M_{\odot}$ and $M_{\star} = 8.3 \times 10^7 M_{\odot}$, respectively. In Fig. 3, the mean of the Hα and UV-based SFR is shown as a function of the stellar mass. We also display the star-forming main sequence relation for Virgo cluster galaxies with normal H1 content (Boselli et al. 2023b). As RPS generally reduces the SFR, RPS galaxies are expected to mostly lie below this relation. In some cases, RPS galaxies can show a high specific SFR due to a temporary enhancement of SFR (Bothun & Dressler 1986; Vulcani et al. 2018; Roberts & Parker 2020). Since our sample is limited to 144 MHz detected objects, we are biased toward high-SFR objects, in particular at the low-mass end of the distribution.

## 3. Statistical analysis

### 3.1. Radio-SFR relation

The availability of radio and other SFR tracers for our data allows us to investigate the radio-SFR relation for our samples. Particularly at low radio frequencies, this radio-SFR relation is known to deviate from the linear scenario (Heesen et al. 2022).

Thus, we fit a power-law relation of the form:

$$ \left( \frac{L_{144}}{\text{W Hz}^{-1}} \right) = N_0 \left( \frac{\text{SFR}}{M_{\odot} \text{yr}^{-1}} \right)^{\beta} \qquad (2) $$

Fitting was performed in log-log space, where the expression assumes a linear form. We used the orthogonal method of the bivariate errors and intrinsic scatter (BCES) regression algorithm (Akritas & Bershady 1996; Nemmen et al. 2012) for the minimization.

We fit Eq. (2) for the Hα and UV inferred SFRs and for the HRS galaxies in the RPS sample and those not in the RPS sample independently. The scatter $\sigma_{\text{raw}}$ of the data points around the fit is calculated as:

$$ \sigma_{\text{raw}}^2 = (n-2)^{-1} \sum_i (\log L_{144,i} - \beta \log \text{SFR}_i - \log N_0)^2, \qquad (3) $$

where n is the sample size. The best-fitting parameters are reported in Table 2 and we display the fit results together with the data points in Fig. 4.

For both SFR tracers, the relation for the radio continuum luminosity derived for the RPS sample is a factor of 2–3 above the one found for the non-RPS galaxies. This is expected given the reports of enhanced radio-to-SFR ratios for RPS galaxies in the literature (Murphy et al. 2009; Vollmer et al. 2010, 2013; Roberts et al. 2021a; Ignesti et al. 2022a). In Fig. 4, we also display the relations derived from LOFAR observations of SF-galaxies in other works: Heesen et al. (2022) analyzed a sample of 45 nearby galaxies, Gürkan et al. (2018) studied a sample of >2000 SF-galaxies across a wide range of redshifts and Roberts et al. (2021a) published a relation for a sample of 95 jellyfish galaxies in low-redshift clusters. We discuss the differences between these relations and our findings in Sect. 5.1.

### 3.2. Mass dependency and radio excess

The resulting power-law fits for our samples are super-linear with $\beta \approx 1.4$. This super-linearity is thought to originate from a mass-dependence in the calorimetric efficiency $\eta = \eta(M)$, which is the ratio of CRe energy that is radiated withing galaxy. In larger galaxies with a higher mass M, CRe have longer escape times $t_{\text{esc}}$ in relation to their lifetime $t_{\text{syn}}$, thus, they lose a greater fraction of their energy inside the galaxy before escaping into regions with low magnetic field strengths.

We used the following parametrization to enforce a linear radio-SFR relation while taking into account a mass-dependent calorimetric efficiency (see e.g., Heesen et al. 2022):

$$ L_{144} = N_0 \left( \frac{\text{SFR}}{M_{\odot} \text{yr}^{-1}} \right) \left( \frac{M_{\star}}{10^{10} M_{\odot}} \right)^{\gamma} \qquad (4) $$

Here, $\gamma$ describes the dependency on the stellar mass $M_{\star}$. We repeated the fitting for the RPS and non-RPS galaxies for both SFR-tracers. The best-fitting model-parameters are reported in Table 2, and the data points and fits are shown in Fig. 5. For the galaxies that do not show a RPS-morphology, we can reproduce the systematic increase of $L_{144}/\text{SFR}$ as a function of mass, finding a positive mass-exponent of $\gamma \approx 2$.

Again, the population of RPS galaxies has a clear radio excess with 12/14 galaxies above the relation for non-RPS galaxies. However, for them, the mass-dependency is less clear. This could be either due to an increased scatter in $L_{144}/\text{SFR}$ for this population, indirectly connected to the ram pressure stripping, or due to the small sample size.
<table><caption>**Table 2.** Best-fitting parameters for different parametrizations of the radio–SFR relation.</caption><thead><tr><th>Tracer</th><th>Sample</th><th>N<sub>0</sub> [10<sup>21</sup>]</th><th>β</th><th>γ</th><th>σ<sub>raw</sub></th><th>n</th></tr></thead><tbody><tr><td>Hα</td><td>RPS</td><td>15.8 ± 2.1</td><td>1.21 ± 0.11</td><td>–</td><td>0.28</td><td>14</td></tr><tr><td>Hα</td><td>Others</td><td>8.5 ± 0.67</td><td>1.39 ± 0.06</td><td>–</td><td>0.28</td><td>103</td></tr><tr><td>UV</td><td>RPS</td><td>20.0 ± 2.6</td><td>1.27 ± 0.11</td><td>–</td><td>0.23</td><td>14</td></tr><tr><td>UV</td><td>Others</td><td>10.8 ± 0.8</td><td>1.42 ± 0.06</td><td>–</td><td>0.24</td><td>102</td></tr><tr><td>Hα</td><td>RPS</td><td>13.7 ± 2.5</td><td>–</td><td>0.08 ± 0.13</td><td>0.29</td><td>14</td></tr><tr><td>Hα</td><td>Others</td><td>7.2 ± 0.6</td><td>–</td><td>0.23 ± 0.05</td><td>0.27</td><td>103</td></tr><tr><td>UV</td><td>RPS</td><td>16.0 ± 2.5</td><td>–</td><td>0.08 ± 0.12</td><td>0.26</td><td>14</td></tr><tr><td>UV</td><td>Others</td><td>7.8 ± 0.5</td><td>–</td><td>0.21 ± 0.04</td><td>0.25</td><td>102</td></tr><tr><td>Hα</td><td>RPS</td><td>14.1 ± 3.6</td><td>1.05 ± 0.25</td><td>0.05 ± 0.21</td><td>0.29</td><td>14</td></tr><tr><td>Hα</td><td>Others</td><td>8.3 ± 0.7</td><td>1.22 ± 0.06</td><td>0.12 ± 0.06</td><td>0.26</td><td>103</td></tr><tr><td>UV</td><td>RPS</td><td>20.3 ± 5.2</td><td>1.26 ± 0.23</td><td>0.09 ± 0.19</td><td>0.25</td><td>14</td></tr><tr><td>UV</td><td>Others</td><td>9.9 ± 0.8</td><td>1.28 ± 0.06</td><td>0.08 ± 0.05</td><td>0.24</td><td>102</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Radio–SFR relations. Top panel: Hα-inferred SFRs against radio luminosity for galaxies in the RPS sample (orange data points) and other galaxies in the LOFAR HRS sample (blue data points). The orange and blue lines represent the best-fitting power-law fits and the corresponding 1σ uncertainty bands for those samples. The green, purple and brown lines are fits taken from the literature. Bottom panel: same as above but for the UV-based SFRs.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Radio–SFR relations taking into account the stellar mass. Top panel: ratio of L<sub>144</sub> to SFR<sub>Hα</sub> as a function of M<sub>⋆</sub>. The orange data points mark the galaxies in the RPS sample, the blue ones the galaxies outside the RPS sample. The orange and blue lines are the corresponding fits. Bottom panel: same but for the UV-inferred SFR.</figcaption></figure>

We further investigated a relation with an additional free parameter, which is a power-law in both mass and SFR (see Gürkan et al. 2018):

$$ \left( \frac{L_{144}}{\text{W Hz}^{-1}} \right) = N_0 \left( \frac{\text{SFR}}{M_{\odot} \text{yr}^{-1}} \right)^{\beta} \left( \frac{M_{\star}}{10^{10} M_{\odot}} \right)^{\gamma}. \qquad (5) $$

The best-fitting results for this parametrization are displayed in Table 2. For the non-RPS galaxies, we found a mass-exponent

of γ ≈ 0.1 and an SFR-exponent of β ≈ 1.25. Those results can be compared to the ones from Gürkan et al. (2018), who found a flatter relation with SFR (β = 0.77) but a steeper exponent in mass (γ = 0.44).

To quantify the radio excess (or deficit) compared to the best fit of Eq. (5) for the non-RPS sample, we calculated the distance of the RPS-galaxies to the best-fitting plane in log space
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Distance of the RPS galaxies to the best-fitting $L_{144}$–SFR–$M_*$ plane for the non-RPS galaxies in log space. The galaxies are sorted by the mean of the SFR$_{UV}$- and SFR$_{H\alpha}$-based log distances.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Total mass against the spectral index for the RPS sample (orange markers and labels) and the other galaxies in the sample (blue markers). For clarity, uncertainties are only displayed for the RPS sample, they are of comparable size ($\sigma_{\alpha} \sim 0.1$) for the other galaxies. Downward pointing arrows correspond to $4\sigma$ upper limits. The orange and blue line show the corresponding best-fitting relations, and the red dashed line shows the fit from Heesen et al. (2022).</figcaption></figure>

according to:

$$d_{3D} = \frac{\log\left(\frac{L_{144}}{\text{W Hz}^{-1}}\right) - \beta \log\left(\frac{\text{SFR}}{M_{\odot} \text{yr}^{-1}}\right) - \gamma \log\left(\frac{M_{\star}}{10^{10} M_{\odot}}\right)}{\sqrt{\beta^2 + \gamma^2 + 1}} \quad (6)$$

We display those distances in Fig. 6. In general, there is a good agreement between the distances based on the UV and Hα-inferred SFR. The only object with a strong radio-deficit is the peculiar galaxy NGC 4424, which is thought to be a merger remnant and shows outflows of ionized gas (Boselli et al. 2018c). Similarly, the galaxies with a clear RPS morphology in radio show the strongest radio excesses, those are NGC 4522, NGC 4330, NGC 4396, NGC 4402 and NGC 4634. Qualitatively, there appears to be a connection between the asymmetry of the radio emission and the strength of the radio excess. The only exception being IC 3476, which shows a strong tail but only a mild excess of ≈10%. Possibly, the radio emission of this source is underestimated due to masked background sources and side-lobes of M 87 which unfortunately cover parts of the tail of this source.

### 3.3. Spectral properties

To probe if the spectral properties of the galaxies in the ram-pressure stripped sample differ from the ones of unperturbed galaxies, we determined the integrated spectral index $\alpha$<fnref n="2" /> for all objects which have radio-measurements also at 1.4 GHz available in the literature. The spectral index $\alpha$ between two frequencies $v_1, v_2$ with flux density measurements $S_1, S_2$ is calculated as: $\alpha = \ln(S_1/S_2)/\ln(v_1/v_2)$. We estimated the corresponding uncertainties following Gaussian propagation of uncertainty. The 1.4 GHz flux densities or upper limits were collected from Murphy et al. (2009), Chung et al. (2009; remeasured in cases where the maps were provided by the authors), Vollmer et al. (2010) and Boselli et al. (2015). For the two RPS objects which are not in the HRS, we derived the $4\sigma$ upper limits from the NVSS (Condon et al. 1998). To allow for comparison with the work of Heesen et al. (2022), we estimated the total masses of the galaxies in our sample. For this, we employed the dynamical data derived from Hα (Gómez-López et al. 2019) or Hα (Boselli et al. 2014c) observations according to $M_{tot} = r_{SF}v_{rot}^2/G$, where G is the gravitational constant, $v_{rot}$ the rotation velocity

and $r_{SF}$ the size of the star-forming disk, estimated from D24 or D25 as described in Gómez-López et al. (2019).

In Fig. 7, we display the total mass-spectral index distribution of the 114 galaxies with available 1.4 GHz measurements, for the 26 objects without detection, we provide an upper limit. We also show the best-fitting log-linear relation of the form $\alpha = A \log(M_{tot}/M_{\odot}) + B$. For the galaxies outside of our RPS sample, we find $A = -0.13 \pm 0.02$ and $B = 0.83 \pm 0.20$, in excellent agreement with the parameters derived by Heesen et al. (2022; $A = -0.13$ and $B = 0.81$). However, for the RPS sample, we find evidence that the relation is shifted toward steeper spectral index values with $A = -0.06 \pm 0.05$ and $B = 0.09 \pm 0.52$. Evaluated at $M_{tot} = 3 \times 10^{10} M_{\odot}$, the relations differ by $\Delta\alpha = 0.17 \pm 0.06$. We cross checked that this finding is not simply caused by a systematic underestimation in the dynamical estimates of $M_{tot}$ due to truncated gas disks in RPS galaxies by repeating the fit using $M_*$, where we found $\Delta\alpha = 0.13 \pm 0.07$ at $M_* = 4 \times 10^9 M_{\odot}$.

A strong outlier from the relation is NGC 4548 with a particularly steep spectral index of $\alpha = -1.3 \pm 0.1$ measured from the VIVA (Chung et al. 2009) map with low image fidelity. However, the $4\sigma$ upper limit from the NVSS map (Condon et al. 1998) agrees with a steep spectrum $\alpha \le -1.0$. Our finding with a best-fitting relation for the RPS galaxies that is shifted to lower values of $\alpha$ holds when repeating the analysis without NGC 4548 ($\Delta\alpha = 0.13 \pm 0.04$ at $M_{tot} = 3 \times 10^{10} M_{\odot}$).

We also investigated if there is a correlation between the spectral index and the log-distance from the best-fitting $L_{144}$–SFR–$M_*$ plane for the RPS sample. We found a slightly positive Pearson’s correlation coefficient of 0.30 using SFR$_{UV}$ and 0.377 SFR$_{H\alpha}$, however, both are not significant (p-value > 0.23), the slightly positive relation is due to the low luminosity steep spectrum source NGC 4548.

### 4. Spatially resolved radio–SFR analysis

In Sect. 3.2, we showed that the radio emission of our Virgo RPS sample is enhanced up to a factor of 3 compared to the Hα and UV-inferred SFR. The localization of this excess allows to constrain the origin of the surplus radio emission. So could a leading-edge enhancement point toward compression of the

<footnote n="2">² Defined as $S \propto v^{\alpha}$.</footnote>
magnetic field lines or to ram-pressure driven shocks as additional source of CRe. To investigate this, we created maps of the ratio between the observed radio surface brightness $B_{\text{obs}}$ and the expected radio surface brightness $B_{\text{model}}$ based on the SFR-surface density $\Sigma_{\text{SFR}}$. A similar analysis was carried in Murphy et al. (2009) for six of the galaxies in our sample using 1.4 GHz VLA observations and Spitzer far-infrared emission as SFR-tracer. For our analysis, we derived the SFR-surface density from GALEX NUV (Martin et al. 2005) following the calibration of Leroy et al. (2019). We employed a dust-correction based on Herschel 100 µm measurements obtained from the HRS (Cortese et al. 2014) and HeVICS (Davies et al. 2010) according to Kennicutt & Evans (2012). Foreground and background sources in the $\Sigma_{\text{SFR}}$ and LOFAR maps were manually masked and the maps were grided to the same pixel layout. We convolved the $\Sigma_{\text{SFR}}$-maps to match the resolution of our LOFAR maps (either 9'' × 9'' or 20'' × 20'') using the convolve method implemented in astropy (Astropy Collaboration 2022). We obtained the model for the radio emission using Eq. (4) and our best-fitting parameters ($N_0 = 7.7 \times 10^{21}$ and $\gamma = 0.21$) for the non-RPS sample to convert $\Sigma_{\text{SFR}}$ to the radio surface brightness $B$:

$$ \frac{B_{\text{model}}}{\text{Jy beam}^{-1}} = \frac{N_0}{4\pi \times 10^{-26}} \left( \frac{\Sigma_{\text{SFR}}}{M_{\odot} \text{yr}^{-1} \text{kpc}^2} \right) \times \left( \frac{M_{\star}}{10^{10} M_{\odot}} \right)^{\gamma} \left( \frac{A_{\text{beam}}}{\text{kpc}^2} \right)^{-1} \left( \frac{d}{m} \right)^{-2} . \quad (7) $$

Since the CRe have lifetimes of ~100 Myr and are subject to CR transport, the synchrotron emission of an undisturbed galaxy should be a smoothed version of SFR-surface density (e.g., Heesen et al. 2023a), this can be expressed in terms of the CRe-transport length $l_{\text{CRe}}$. The shape of the smoothing kernel used to model the CR transport depends on the transport process. We assume as a benchmark the case of pure diffusion modeled by a Gaussian kernel. The width $\sigma$ of the Gaussian kernel used for the smoothing is related to $l_{\text{CRe}}$ according to $\sigma = (2\ln2)^{-0.5}l_{\text{CRe}}$.

Since CRe diffuse away from the star-forming regions into regions with low or no star-forming activity, the resolved $B-\Sigma_{\text{SFR}}$-relation is sublinear, opposite to the global radio-SFR-relation. Taking into account CRe diffusion with an appropriate choice of $l_{\text{CRe}}$, the relation can be linearized (Murphy et al. 2009; Berkhuijsen et al. 2013; Heesen et al. 2023a). To linearize this relation, we fit the convolution kernel size $\sigma$. For each $\sigma$, we determined the slope $a$ of the relation by fitting the pixels that are above a signal-to-noise ratio of 5 in both maps. Due to their low surface brightness, we instead required a S/N of 3 for IC 800 and IC 3105 and 4 for NGC 4548. The optimal $\sigma$ is found once the slope reaches unity. We carried out the smoothing procedure based on maps at 9'' resolution (for sources with sufficient surface brightness) and at 20'' resolution. The resulting transport lengths are listed in Table 3, there is decent agreement between the values derived at different resolutions. Two notable outliers with a large transport length are NGC 4254 and NGC 4548 with $l_{\text{CRe}} > 5$ kpc. Those values are larger than the values $\le 3.8$ found for field galaxies at 144 MHz in Heesen et al. (2023b). This is likely due to the significant contribution of RPS (and in the case of NGC 4254, also the tidal perturbation, Vollmer et al. 2005a) to the CRe-transport, a scenario also suggested by Ignesti et al. (2022b).

We then convolved the maps of the model surface brightness using a Gaussian kernel with the corresponding width $\sigma$. In Fig. 8, we display the log-ratio $R = \log_{10}(B_{\text{obs}}/B_{\text{model}})$ between the observed and the modeled radio emission for all pixels with a signal-to-noise ratio above 3 (above 2 in the case of IC 3105). We also mark the $5\sigma$ contours of the SFR-surface density and

<table><caption>**Table 3.** CRe transport length and spectral indices of the RPS sample.</caption><thead><tr><th>Name</th><th><i>l</i><sup>9''</sup><sub>CRe</sub><br>[kpc]</th><th><i>l</i><sup>20''</sup><sub>CRe</sub><br>[kpc]</th><th><i>α</i><sup>1.4 GHz</sup><sub>144 MHz</sub></th></tr></thead><tbody><tr><td>IC 3105</td><td>—</td><td>2.3</td><td>&lt;−0.36 <sup>(a)</sup></td></tr><tr><td>NGC 4254</td><td>5.2</td><td>5.4</td><td>−0.77 ± 0.10 <sup>(b)</sup></td></tr><tr><td>NGC 4302</td><td>4.4</td><td>3.9</td><td>−0.77 ± 0.10 <sup>(c)</sup></td></tr><tr><td>NGC 4330</td><td>1.9</td><td>1.1</td><td>−0.63 ± 0.11 <sup>(c)</sup></td></tr><tr><td>IC 3258</td><td>—</td><td>1.8</td><td>&lt;−0.74 <sup>(a)</sup></td></tr><tr><td>NGC 4396</td><td>2.3</td><td>1.3</td><td>−0.79 ± 0.10 <sup>(c)</sup></td></tr><tr><td>NGC 4402</td><td>1.4</td><td>1.6</td><td>−0.81 ± 0.10 <sup>(c)</sup></td></tr><tr><td>NGC 4424</td><td>1.9</td><td>1.4</td><td>−0.67 ± 0.11 <sup>(c)</sup></td></tr><tr><td>NGC 4501</td><td>1.3</td><td>0.9</td><td>−0.75 ± 0.10 <sup>(c)</sup></td></tr><tr><td>IC 3476</td><td>1.7</td><td>1.8</td><td>−0.81 ± 0.1 <sup>(a)</sup></td></tr><tr><td>NGC 4522</td><td>1.0</td><td>1.6</td><td>−0.48 ± 0.10 <sup>(b)</sup></td></tr><tr><td>IC 800</td><td>—</td><td>2.2</td><td>&lt;−0.76 <sup>(a)</sup></td></tr><tr><td>NGC 4548</td><td>—</td><td>5.5</td><td>−1.32 ± 0.10 <sup>(d)</sup></td></tr><tr><td>NGC 4569</td><td>2.5</td><td>2.0</td><td>−0.55 ± 0.10 <sup>(b)</sup></td></tr><tr><td>NGC 4607</td><td>1.6</td><td>1.5</td><td>−0.70 ± 0.10 <sup>(d)</sup></td></tr><tr><td>NGC 4634</td><td>2.0</td><td>1.8</td><td>−0.66 ± 0.10 <sup>(e)</sup></td></tr><tr><td>NGC 4654</td><td>3.0</td><td>3.0</td><td>−0.87 ± 0.10 <sup>(d)</sup></td></tr></tbody></table>

**Notes.** The 1.4 GHz flux densities for the spectral index estimation are taken from: <sup>(a)</sup>NVSS (4σ upper limits Condon et al. 1998); <sup>(b)</sup>Murphy et al. (2009), <sup>(c)</sup>Vollmer et al. (2010); <sup>(d)</sup>measured from the maps provided by Chung et al. (2009) and <sup>(e)</sup>Boselli et al. (2015).

radio surface brightness. For sufficiently bright sources, we used the 9''-resolution maps to derive the ratios, otherwise the 20''-resolution ones. For the former, we present the 20'' maps, which are more sensitive to the faint tails, in Appendix B.

In general, the radio excess is a global phenomenon and all galaxies but NGC 4424, NGC 4548 and IC 3258 show enhanced radio emission across the disk. As expected, the excess is strongest at the trailing edge or in the tail, where all objects show some form of enhanced radio emission or radio contours that extend asymmetrically beyond the SFR contours at the trailing edge. This is most pronounced in NGC 4330, NGC 4522, NGC 4634 and IC 3476, while NGC 4548 shows only a mild enhancement in parts of the trailing half of the disk. The reason for the excess radio emission in the tails is the advection of CRe from the disk due to RPS to regions with low star-forming activity (e.g., Murphy et al. 2009; Ignesti et al. 2022a). At the same time, many galaxies show a deficit of radio emission at the leading edge (i.e., $\Sigma_{\text{SFR}}$ contours that extend beyond the radio contours). Examples for this are NGC 4330, NGC 4396, NGC 4402, NGC 4522, NGC 4548 and IC 3476 (see also Murphy et al. 2009). For these objects, the leading-edge deficit is followed by a region with an radio excess, this is most pronounced in NGC 4330. However, the leading-edge deficit is not omnipresent. Most notably, in NGC 4501, we instead observe an enhancement of radio emission at the leading edge without a preceding deficit region. This is likely connected to a local compression of magnetic fields (Vollmer et al. 2008).

# 5. Discussion

## 5.1. Radio-SFR relations

In Fig. 4, our best-fitting radio SFR relations are displayed. As expected, our result for the noninteracting galaxies is in good agreement with Heesen et al. (2022), who worked on galaxies
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Logarithmic ratio between the observed and modeled radio emission. The color scale is symmetric and increases in increments of 0.1 dex, red colors indicate a local radio excess, blue colors a radio deficit and gray areas are masked background sources. Magenta and green lines are the 5σ contours of $B_{\text{obs}}$ and $\Sigma_{\text{SFR}}$, respectively. The black arrow indicates the approximate orbit of the galaxy as inferred from the direction of the tail. The circles in the bottom left correspond to the angular resolution of the radio data, which is 9", except for IC 3105, IC 3258, NGC 4424, IC 800 and NGC 4654 where we used maps at 20" resolution.</figcaption></figure>
which are nearby and are not members of a cluster. Comparison of our relation for the non-RPS objects with the work of Gürkan et al. (2018) shows that their relation is shifted toward higher radio luminosity, in particular toward the low SFRs. These authors also used LOFAR data, but their sample extends to significantly larger redshifts and has a mean stellar mass that is 2.5 times higher than in our work. We argue that the mass-dependency can mitigate the discrepancy between the various relations, taking into account the mean stellar mass of the samples can account for a discrepancy of ≈0.1 dex in Fig. 4. Roberts et al. (2021a) on the other hand studied a sample of 95 jellyfish galaxies in low-redshift clusters and found a relation even above our RPS sample. In agreement with the picture that RPS increases the radio-SFR ratio, this relation is closest to the ones for our RPS sample. Indeed, the fact that the relation of Roberts et al. (2021a) is offset to higher radio luminosities compared to our relations for the RPS sample could be explained by the more efficient RPS for the objects in the Roberts et al. (2021a) sample, since they are mostly in clusters that are more massive than Virgo. It was also previously reported that Coma and A1367, more massive nearby clusters, show a greater radio excess compared to Virgo (see Boselli & Gavazzi 2006, and references therein).

That galaxies suffering from RPS do not follow the radio-SFR relation of normal star-forming galaxies but show a higher radio luminosity is well established now due to observations in nearby galaxy clusters. In our RPS sample, this radio excess is widespread (~14/17 objects) and ranges from 0.1 to 0.5 dex (Murphy et al. 2009), in line with previous radio continuum studies of the cluster (e.g., Niklas et al. 1995; Murphy et al. 2009).

## 5.2. Spectral index of RPS galaxies

We additionally report for the first time tentative evidence for a spectral index-mass relation for RPS galaxies that is shifted to steeper spectral index values compared to normal star-forming galaxies (Fig. 7). While the significance of this result is currently limited by the availability of uniform, high-fidelity continuum data at 1.4 GHz, it is noteworthy that also other studies reported steep spectral indices for a number of objects suffering from RPS (Chen et al. 2020; Müller et al. 2021; Ignesti et al. 2022b). The spectral steepening is indicative of a CRe population that is of higher radiative age.

Little is known about the spectral indices of RPS galaxies, with studies mostly limited to a few or individual object (Vollmer et al. 2013; Chen et al. 2020; Müller et al. 2021; Ignesti et al. 2022b; Lal et al. 2022; Roberts et al. 2022). A multitude of effects that could explain the enhanced radio luminosity of RPS galaxies are also able to influence the spectral properties of this population. Particle (re-)acceleration due to ISM-ICM shocks could introduce an additional source of CRe (Murphy et al. 2009) with an injection spectral index that may differ from acceleration at supernova shocks associated with star-forming activity. In front of a galaxy moving at a velocity greater than the speed of sound $c_s$ through the ICM, a bow shock is expected to form (Stevens et al. 1999). In principle, particle acceleration may occur at this bow shock, or at reverse shocks launched into the ISM.

Due to the high speed of sound ($c_s \sim 500 \text{ km s}^{-1}$, e.g., Simionescu et al. 2017) in the ICM, the bow shock acceleration would take place in the regime of low Mach numbers $M$. That

means that the injection spectral index of the bow shock (Drury 1983):

$$ \alpha_{\text{inj}}(\mathcal{M}) = -\frac{\mathcal{M}^2 + 1}{\mathcal{M}^2 - 1} + 0.5 \qquad (8) $$

would be steeper than the $\alpha \sim -0.5$ in high Mach-number SN explosions. Thus, additional acceleration of CRe at the bow shock could in principle explain both a spectral steepening and an increased radio luminosity. However, one also needs to consider the expected radio morphology of this scenario. The distance between the galaxy and the bow shock depends primarily on the Mach number and the size of the galaxy. Assuming an ideal gas with an adiabatic index of 5/3, the standoff distance of the bow shock is given by Farris & Russell (1994):

$$ \Delta_{\text{BS}} = 0.2 R_c \frac{\mathcal{M}^2 + 3}{\mathcal{M}^2 - 1}, \qquad (9) $$

where $R_c$ is the curvature radius at the leading point of the galaxy.

As an example, for a galaxy with a curvature radius at the leading point of $R_c = 5 \text{ kpc}$ and $\mathcal{M} = 2$, the standoff distance of the shock would be $\Delta_{\text{BS}} \approx 2.3 \text{ kpc}$ and increase further toward lower Mach numbers. For larger curvature radii, the standoff distance would increase and vice versa. While the exact distance depends on the size of the galaxy and also on the angle between the disk and the velocity vector, in most cases, in particular for low-Mach number galaxies or face-on stripping, we expect a standoff distance $\Delta_{\text{BS}} > 1 \text{ kpc}$ that is larger than the resolution of our LOFAR data at the distance of the Virgo cluster (720 pc $\times$ 450 pc). Thus, we should observe radio emission in advance of the leading edges of the galaxies, which is not the case, with the only exceptions being NGC 4607 and NGC 4634. Conversely, these regions are oftentimes deficient in radio emission, as already reported by Murphy et al. (2009). Thus, we do not consider the acceleration of CRe at a bow shock as a scenario to explain the radio properties of RPS galaxies.

As alternative to the acceleration at the bow shock, CRe could instead be accelerated at reverse shocks launched into the ISM. However, due to the lower temperature of the ISM and the correspondingly slow speed of sound, these shocks would then again be in the high Mach-number regime resulting in $\alpha_{\text{inj}} \sim -0.5$, such that they would not lead to a steepening of the synchrotron spectrum. Therefore, we disregard the acceleration due to ISM-ICM shocks as mechanism that can explain steeper radio spectral indices for RPS galaxies.

Another scenario is that of an enhanced magnetic field strength due to compression of the ISM magnetic field (Boselli & Gavazzi 2006) or the magnetic draping mechanism (Dursi & Pfrommer 2008; Pfrommer & Dursi 2010). This effect would cause a steepening of the synchrotron spectrum, since the loss time $t_{\text{sync}}$ would decrease compared to the escape time $t_{\text{esc}}$, meaning that more spectral aging can occur before the CRe escape the galaxy. In this scenario, the enhancement of the radio emission should also be localized at the leading edge, where the magnetic field compression takes place. This mechanism is supported by the detection of asymmetric polarized ridges in some of the Virgo cluster RPS galaxies (e.g., Vollmer et al. 2008; Pfrommer & Dursi 2010). If the magnetic fields are enhanced due to leading-edge compression of the ISM, the corresponding gas compression could possibly introduce relevant ionization capture losses for low-energy electrons. Those compete with the fast radiative losses at high electron energy due to the accelerated radiative aging in shaping the observed synchrotron spectral index.
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 9. Scenario (1) – quenched star formation model. Top panel: log ratio of the 144 MHz to FUV emission (blue) and Hα emission (orange) for a quenching time of 50 Myr (solid lines), 100 Myr (dashed lines), and 200 Myr (dotted lines) as a function of the time since the onset of SFR quenching. The ratios are relative to t = 0. Bottom panel: evolution of the 144 MHz to 1.4 GHz spectral index for the two models.</figcaption></figure>

As third scenario, Ignesti et al. (2022b) suggested a rapid quenching of the SFR due to the environmental interaction as explanation for the radio excess. This would translate to a strong reduction of SFR<sub>Hα</sub> after a delay of only few Myr but would only affect L<sub>144</sub> at later times due to the lifetime of the massive O-B stars and the cosmic rays that contribute to the 144 MHz synchrotron emission. The availability of UV data presents us with the opportunity to constrain the quenching scenario, since it probes time scales in between the Hα and 144 MHz continuum emission (Kennicutt & Evans 2012; Leroy et al. 2012). This scenario would also lead to a steeper radio spectrum for the RPS galaxies due to the declining injection of fresh CRe, resulting in an increased average radiative age of the CRe.

### 5.3. Model scenarios

In the following, we analyze the phenomenology of simple homogeneous models for the third and second scenario mentioned above. We consider the following version of the momentum-space Fokker-Planck-equation (ignoring diffusion and reacceleration processes) to describe the evolution of the electron spectrum N(E, t) as a function of time t and energy E:

$$ \frac{\partial N(E, t)}{\partial t} = \frac{\partial}{\partial E} [N(E, t)b(E)] - \frac{N(E, t)}{t_{\text{esc}}} + Q(E, t). \quad (10) $$

Here, t<sub>esc</sub> is the CRe escape time and b(E) describes the energy losses. For the former, we employ a value of 50 Myr (see e.g., Dörner et al. 2023). In the case of isotropic diffusive escape, the escape time is t<sub>esc</sub> = L<sub>CRe</sub><sup>2</sup>/4D with the CRe scale height L<sub>CRe</sub> and the diffusion coefficient D. Using the value of D = 2.1 × 10<sup>28</sup> cm<sup>2</sup> s<sup>-1</sup> found by Heesen et al. (2023a), the escape time of 50 Myr corresponds to a scale height of L<sub>CRe</sub> ≈ 4 kpc. Assuming equipartition, the radio continuum scale height is L<sub>rc</sub> = L<sub>CRe</sub>/2 ≈ 2 kpc, which is in good agreement with LOFAR measurements (Heald et al. 2022).

In the case of synchrotron and inverse Compton losses, the energy-loss term b(E) = b<sub>0</sub>E<sup>2</sup> with:

$$ b_0 = 3.2 \times 10^{-6} (B^2/2\mu_0 + u_{\text{rad}}) \text{m}^3 \text{MeV}^{-2} \text{Myr}^{-1}, \quad (11) $$

where we assume a photon field of energy density u<sub>rad</sub> = 6 × 10<sup>5</sup> eV m<sup>-3</sup> and synchrotron radiation in a magnetic field B = 10 µG (Sarazin 1999). For the source term Q(E, t) = qE<sup>-δ</sup> we consider the injection of electrons with a power-law shock-acceleration spectrum with an exponent of δ = -2 and a normalization factor q. The full model and numerical solution of Eq. (10) and the calculation of the radio, FUV and Hα emission are described in Appendix C.

We start from the equilibrium state electron spectrum, which corresponds to a spectral index of α = -0.77. We then consider two scenarios: (1) the RPS causes a quenching of the SFR, modeled by an exponential decay of the source term Q(E) with an e-folding time scale of t<sub>quench</sub> by a factor exp(-t/t<sub>quench</sub>); and (2) compression of the ISM magnetic field enhances the magnetic field of a galaxy by a factor of f<sub>B</sub>.

For scenario (1), the exponential SFR history is of course a simplification valid only for the recent star-forming history (~few 100 Myr). However, this parametrization with only one free parameter allows us to describe the basic effects of a declining SFR due to RPS. In Fig. 9, we show the time evolution of the observed radio-FUV and radio-Hα ratio (normalized to 1 at t = 0) and the radio spectral index for this scenario with quenching time scales of 50, 100 and 200 Myr. In the model with t<sub>quench</sub> = 50 Myr, we can reproduce the observed enhancement of ~0.4 dex in the radio-Hα ratio and a significant steepening of the radio spectral index of Δα ≈ 0.2, in agreement with our tentative evidence of steeper spectral indices for RPS galaxies. Higher values of t<sub>quench</sub> cause a less severe steepening and radio excess. A property of this model is that, due to the longer life time of the stars responsible for the FUV emission, the radio-FUV ratio should be less enhanced compared to the radio-Hα ratio. Indeed for three of the objects with the highest radio excesses (NGC 4330, NGC 4501, and NGC 4522) we find that the distance to the best-fitting relation is stronger relative to SFR<sub>Hα</sub> and weaker relative to SFR<sub>FUV</sub> (see Fig. 6). These objects may experience more violent quenching due to a higher velocity and their moderate mass. However, for the remaining objects, no trend can be identified and we also find no significant difference in the SFR<sub>UV</sub>/SFR<sub>Hα</sub> ratios for the RPS and non-RPS sample. For the quenching scenario (1) to fully explain the radio excess and the steep radio spectra of RPS galaxies, violent quenching of the star-formation activity with t<sub>quench</sub> ≤ 100 Myr would need to be a widespread phenomenon and should also imprint in a systematic excess of UV to Hα emission, which we only observe for NGC 4330, NGC 4501 and NGC 4522. Spectral energy density fitting of Virgo cluster galaxies yields similarly short quenching time scales for NGC 4330 and NGC 4522 (Boselli et al. 2016a). Less violent quenching would still yield some contribution to the radio excess and spectral steepening, but cannot fully explain the observations.
In scenario (2), we model the effect of an increase of the magnetic field strength by a factor of $f_B$. This boosts the synchrotron emission and also steepens the spectral index. In the limit $t_{syn} \gg t_{esc}$, the electron spectrum is escape-dominated and the corresponding radio slope approaches $\alpha = (\delta - 1)/2 = -0.5$. In the opposite case of high magnetic field strength ($t_{esc} \gg t_{syn}$), it is loss-dominated and the radio slope is close to $\alpha = \delta/2 = -1$. For the initial state with $B = 10$ µG, the spectral index is $\alpha = -0.77$. The blue line in Fig. 10 shows the change in radio emission and spectral index for different values of $f_B$. An increase of the magnetic field by $f_B = 1.5$ steepens the spectral index to $\alpha = -0.84$ and increases the synchrotron emission by 0.17 dex, for $f_B = 2$, we find a spectral index of $\alpha = -0.88$ with a radio enhancement of 0.27 dex. To explain the galaxies with the strongest excesses of $\ge 0.4$ dex, we would require an increase in the magnetic field strength by $f_B > 4$ (corresponding to a factor of 16 in energy). The quoted values represent the equilibrium states, but we note that during the ramp-up phase of the magnetic field, the radio emission will be higher and the spectral index may be steeper while the “surplus” electrons (compared to the new equilibrium state) are being depleted. Also, less drastic increases of the magnetic field can be required to explain the enhanced radio emission if the electron distribution is strongly dominated by other processes than synchrotron radiation, for example in the case of strong Bremsstrahlung and ionization losses (see e.g., Basu et al. 2015). If we extend our model by ionization and Bremsstrahlung losses with a gas number density of $N_{gas} = 10^6 m^{-3}$ (orange line in Fig. 10), we still find a significant steepening ($\alpha = -0.64$ to $\alpha = -0.73$) and increased radio emission (by 0.3 dex) in the case $f_B = 2$. The main effect of ionization losses is that for the same magnetic field strength, the observed radio spectrum is flattened toward low frequencies (thus also explaining why the spectral indices in the model without ionization losses are mostly steeper than the observed ones). If the increasing magnetic field is due to adiabatic compression, the magnetic field enhancement would be accompanied by gas compression $n_{gas} \propto B^{3/2}$ (Ostriker 2006). This would result in stronger ionization losses that, depending on the initial density, may reduce or even prevent the spectral steepening (green dotted line in Fig. 10). To model the relative importance of gas and magnetic field compression and cosmic ray transport, refined simulations are required.

An important open question in scenario (2) is the nature of physical mechanism that is able to increase the magnetic field in RPS galaxies. With simulations, Farber et al. (2022) were able to reproduce a magnetic field enhancement due to compression in the range $f_B \le 3$, however, Tonnesen & Stone (2014) found that increase to only last a short time (~25 Myr). An alternative to the adiabatic compression of the ISM magnetic fields is the magnetic draping mechanism, where the galaxy sweeps up ICM magnetic field lines at the leading edge (Dursi & Pfrommer 2008). It was proposed to explain the asymmetric polarized radio emission for a number of Virgo cluster galaxies (Pfrommer & Dursi 2010). The main difficulty of both mechanisms is that they generate a magnetic field enhancement localized at the leading edge. This is only clearly the case in NGC 4501, where the leading edge radio excess (see Fig. 8) corresponds well with the asymmetric polarized radio emission (e.g., Vollmer et al. 2007, 2008). Many other galaxies in the RPS sample (e.g., NGC 4330, NGC 4396, NGC 4402, NGC 4522, IC 3476) even show a deficit of radio continuum emission in that region, likely due to the fast advection of CRe or locally efficient ionization losses, amplified by the ISM compression. The compression or magnetic draping scenario can also not easily explain the enhanced radio emis-

<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Scenario (2) – compression model. The effect of increasing the initial 10 µG magnetic field on the radio excess and synchrotron spectrum (blue continuous line). Diamond symbols mark the fractional increase of the magnetic field in increments of 0.25, integer values are highlighted. The orange dashed line shows the same model when including ionization and Bremsstrahlung losses. The green dotted line shows the same model when also increasing the gas density as $n_{gas} \propto B^{3/2}$.</figcaption></figure>

sion across the disk that is observed for most galaxies. However, the limited angular resolution of our maps, the varying alignment between the galaxy disks and the velocity vector combined with projection effects (the line of sight velocity relative to M87 is commonly ~1000 km s⁻¹, indicating significant radial stripping, see Table 1) complicate the identification of such local signatures. Tuned simulations may be required to investigate if the observed disk-wide radio enhancement can be generated by magnetic field enhancement and projection effects alone.

## 6. Conclusion

In this paper, we analyzed a sample of 17 Virgo cluster galaxies with a radio morphology indicative of RPS. This sample contains galaxies with masses as low as $7.8 \times 10^7 M_{\odot}$. Our LOFAR observations allowed the identification of four new RPS candidates (NGC 4607, NGC 4634, IC 800, IC 3258) and four new objects with radio continuum tails (NGC 4302, NGC 4424, IC 3105, IC 3476) in the cluster. We compare them to a statistical sample of 120 nearby star-forming galaxies in the HRS. Using 144 MHz observations of the LOFAR HBA Virgo Cluster Survey and LoTSS together with the multiwavelength data of the HRS, our findings are:

- The galaxies in the statistical sample without signs of environmental perturbation in LOFAR follow a super-linear radio-SFR relation with a slope of 1.39±0.06 and 1.42±0.06 compared to Hα and FUV-based SFRs, in good agreement with previous low-frequency studies of nearby galaxies.

- Considering the stellar mass as additional parameter in the radio-SFR relation results in fits with comparable scatter (≥0.25 dex), supporting a mass-dependent calorimetric efficiency of star-forming galaxies.

- We find a clear radio excess for the RPS sample, with radio luminosities that are a factor of 2–3 higher compared to the radio-SFR relation for normal star-forming galaxies. Qualitatively, we find the strongest radio excess in galaxies with pronounced radio tails.

- We derived a radio spectral index-total mass relation of the non-RPS galaxies that is in excellent agreement with the
literature. For the RPS sample, we find a relation that is shifted toward lower spectral index values by $\Delta\alpha \approx 0.15$.

- We model the expected radio emission based on a pure diffusion scenario and hybrid NUV+100 µm SFR surface densities. Comparing the observed to the expected emission, we find that the radio excess is of global nature and mostly extends across the disks. In a number of cases, we can confirm leading-edge radio-deficit regions as a signature of RPS. Only for NGC 4501 we find a leading-edge radio enhancement.

- The radio excess and spectral steepening can be explained by variations in SF history only for NGC 4330, NGC 4396 and NGC 4522 which show the highest radio excesses, which are also accompanied by FUV excesses. This explanation would require rapid quenching with e-folding times $\le 100$ Myr.

- Alternatively, an increased magnetic field due to RPS is also able to generate both enhanced radio emission and a steeper synchrotron spectrum. A doubling of the magnetic field strength can explain a moderate enhancement of the radio luminosity ($\le 0.27$ dex) and steepening ($\Delta\alpha \approx 0.1$). To explain the highest radio excesses with magnetic field increase only, a strong enhancement of more than a factor of four would be required.

This study allowed us for the first time to test different models for the radio excess, with the emerging picture that there are multiple realistic channels which can contribute to anomalous radio continuum properties of RPS galaxies. In extreme RPS galaxies, a rapid quenching of the star-forming activity may be a relevant mechanism to explain excess radio emission, however, for the broad population of objects suffering form RPS, magnetic field enhancement likely dominates. In the near future, our Virgo Cluster multi-Telescope Observations on Radio of Interacting galaxies and AGN (ViCTORIA) project will allow to further constrain the nonthermal physical mechanisms at play in RPS galaxies with deep, polarized L-band observations by MeerKAT and ultra-low frequency measurements with the LOFAR Low-Band Antenna. Crucially, with the homogeneous multifrequency data, we will be able to definitely confirm or reject the claim presented in this paper that RPS galaxies in the Virgo cluster show steeper radio spectral indices than normal SF galaxies. Further, we will be able to perform high-fidelity spatially resolved studies of the spectral index and to probe the magnetic field structure using polarization information.

**Acknowledgements.** H.E. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 427771150. M.B. acknowledges funding by the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy - EXC 2121 "Quantum Universe" - 390833306. F.d.G. acknowledges support from the ERC Consolidator Grant ULU 101086378. A.I. acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 833824, PI: Poggianti) and the INAF founding program "Ricerca Fondamentale 2022" (PI: A. Ignesti). LOFAR (van Haarlem et al. 2013) is the Low Frequency Array designed and constructed by ASTRON. It has observing, data processing, and data storage facilities in several countries, which are owned by various parties (each with their own funding sources), and that are collectively operated by the ILT foundation under a joint scientific policy. The ILT resources have benefited from the following recent major funding sources: CNRS-INSU, Observatoire de Paris and Université d'Orléans, France; BMBF, MIWF-NRW, MPG, Germany; Science Foundation Ireland (SFI), Department of Business, Enterprise and Innovation (DBEI), Ireland; NWO, The Netherlands; The Science and Technology Facilities Council, UK; Ministry of Science and Higher Education, Poland; The Istituto Nazionale di Astrofisica (INAF), Italy. This research made use of the Dutch national e-infrastructure with support of the SURF Cooperative (e-infra 180169) and the

LOFAR e-infra group. The Jülich LOFAR Long Term Archive and the German LOFAR network are both coordinated and operated by the Jülich Supercomputing Centre (JSC), and computing resources on the supercomputer JUWELS at JSC were provided by the Gauss Centre for Supercomputing e.V. (grant CHTB00) through the John von Neumann Institute for Computing (NIC). This research made use of the University of Hertfordshire high-performance computing facility and the LOFAR-UK computing facility located at the University of Hertfordshire and supported by STFC [ST/P000096/1], and of the Italian LOFAR IT computing infrastructure supported and operated by INAF, and by the Physics Department of Turin university (under an agreement with Consorzio Interuniversitario per la Fisica Spaziale) at the C3S Supercomputing Centre, Italy.

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Appendix A: LOFAR data

<table><caption>Table A.1. LOFAR data.</caption><thead><tr><th>Name<br>(1)</th><th>S<sub>144</sub><br>[Jy]<br>(2)</th><th>d<br>[Mpc]<br>(3)</th><th>L<sub>144</sub><br>[W Hz<sup>-1</sup>]<br>(4)</th><th>α<sup>1400</sup><sub>144</sub><br>(5)</th></tr></thead><tbody><tr><td>HRS 2</td><td>(1.5±0.3)e-2</td><td>18.44</td><td>(6.1±1.3)e+20</td><td>-0.47 ± 0.11<sup>a</sup></td></tr><tr><td>IC 610</td><td>(2.0±0.4)e-2</td><td>16.71</td><td>(6.5±1.3)e+20</td><td>-0.58 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 3254</td><td>(3.4±0.5)e-2</td><td>19.37</td><td>(1.5±0.2)e+21</td><td>&lt; -1.25<sup>a</sup></td></tr><tr><td>NGC 3277</td><td>(1.8±0.3)e-2</td><td>20.21</td><td>(8.8±1.4)e+20</td><td>-0.58 ± 0.09<sup>a</sup></td></tr><tr><td>HRS 10</td><td>(8.2±1.3)e-3</td><td>21.66</td><td>(4.6±0.8)e+20</td><td>-0.56 ± 0.13<sup>a</sup></td></tr><tr><td>NGC 3287</td><td>(2.8±0.6)e-2</td><td>18.93</td><td>(1.2±0.2)e+21</td><td>-0.39 ± 0.10<sup>a</sup></td></tr><tr><td>HRS 12</td><td>(3.4±0.8)e-3</td><td>19.89</td><td>(1.6±0.4)e+20</td><td>&lt; -0.27<sup>a</sup></td></tr><tr><td>NGC 3294</td><td>(2.3±0.3)e-1</td><td>22.47</td><td>(1.4±0.2)e+22</td><td>-0.70 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3338</td><td>(7.1±1.4)e-2</td><td>18.57</td><td>(2.9±0.6)e+21</td><td>-0.40 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3346</td><td>(3.0±0.6)e-2</td><td>18.0</td><td>(1.2±0.2)e+21</td><td>-0.34 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3380</td><td>(1.1±0.2)e-2</td><td>22.91</td><td>(7.1±1.2)e+20</td><td>-0.68 ± 0.12<sup>a</sup></td></tr><tr><td>NGC 3381</td><td>(2.9±0.4)e-2</td><td>23.29</td><td>(1.9±0.3)e+21</td><td>-0.70 ± 0.09<sup>a</sup></td></tr><tr><td>NGC 3395</td><td>(3.9±0.6)e-1</td><td>23.1</td><td>(2.5±0.4)e+22</td><td>-0.64 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3424</td><td>(3.0±0.4)e-1</td><td>21.44</td><td>(1.6±0.2)e+22</td><td>-0.75 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3430</td><td>(1.4±0.2)e-1</td><td>22.64</td><td>(8.7±1.3)e+21</td><td>-0.68 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3437</td><td>(2.6±0.5)e-1</td><td>18.24</td><td>(1.0±0.2)e+22</td><td>-0.59 ± 0.10<sup>a</sup></td></tr><tr><td>HRS 26</td><td>(4.8±0.8)e-3</td><td>22.41</td><td>(2.9±0.5)e+20</td><td>&lt; -0.42<sup>a</sup></td></tr><tr><td>NGC 3442</td><td>(4.6±0.7)e-2</td><td>24.77</td><td>(3.4±0.5)e+21</td><td>-0.56 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3451</td><td>(3.0±0.6)e-2</td><td>19.03</td><td>(1.3±0.3)e+21</td><td>-0.43 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3448</td><td>(1.9±0.3)e-1</td><td>19.63</td><td>(8.6±1.3)e+21</td><td>-0.54 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3504</td><td>(8.8±1.3)e-1</td><td>21.94</td><td>(5.1±0.8)e+22</td><td>-0.51 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3512</td><td>(3.8±0.6)e-2</td><td>19.61</td><td>(1.7±0.3)e+21</td><td>-0.56 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3596</td><td>(5.8±1.2)e-2</td><td>17.04</td><td>(2.0±0.4)e+21</td><td>-0.51 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3629</td><td>(2.1±0.4)e-2</td><td>21.53</td><td>(1.2±0.2)e+21</td><td>-0.46 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3631</td><td>(4.3±0.6)e-1</td><td>16.5</td><td>(1.4±0.2)e+22</td><td>-0.72 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3655</td><td>(1.6±0.3)e-1</td><td>21.43</td><td>(8.6±1.7)e+21</td><td>-0.43 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3657</td><td>(9.1±1.4)e-3</td><td>17.2</td><td>(3.2±0.5)e+20</td><td>-0.39 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3666</td><td>(5.1±1.0)e-2</td><td>15.14</td><td>(1.4±0.3)e+21</td><td>-0.45 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3684</td><td>(6.4±1.6)e-2</td><td>16.54</td><td>(2.1±0.5)e+21</td><td>-0.64 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 3683</td><td>(4.9±0.7)e-1</td><td>24.4</td><td>(3.5±0.5)e+22</td><td>-0.69 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3686</td><td>(8.7±1.8)e-2</td><td>16.51</td><td>(2.8±0.6)e+21</td><td>-0.74 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3729</td><td>(6.8±1.0)e-2</td><td>15.14</td><td>(1.9±0.3)e+21</td><td>-0.51 ± 0.08<sup>a</sup></td></tr><tr><td>HRS 61</td><td>(4.3±0.7)e-3</td><td>17.39</td><td>(1.6±0.3)e+20</td><td>&lt; -0.37<sup>a</sup></td></tr><tr><td>NGC 3755</td><td>(3.2±0.5)e-2</td><td>22.44</td><td>(2.0±0.3)e+21</td><td>-0.57 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3756</td><td>(2.8±0.4)e-2</td><td>18.41</td><td>(1.1±0.2)e+21</td><td>-0.81 ± 0.09<sup>a</sup></td></tr><tr><td>NGC 3795</td><td>(3.7±0.6)e-3</td><td>17.33</td><td>(1.3±0.2)e+20</td><td>&lt; -0.31<sup>a</sup></td></tr><tr><td>NGC 3794</td><td>(1.0±0.2)e-2</td><td>19.76</td><td>(4.8±0.8)e+20</td><td>&lt; -0.74<sup>a</sup></td></tr><tr><td>NGC 3813</td><td>(3.4±0.5)e-1</td><td>20.97</td><td>(1.8±0.3)e+22</td><td>-0.57 ± 0.08<sup>a</sup></td></tr><tr><td>HRS 67</td><td>(6.2±1.0)e-3</td><td>20.51</td><td>(3.1±0.5)e+20</td><td>-0.34 ± 0.11<sup>a</sup></td></tr><tr><td>HRS 68</td><td>(1.1±0.2)e-2</td><td>20.17</td><td>(5.6±0.8)e+20</td><td>-0.49 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 3898</td><td>(3.9±0.6)e-2</td><td>16.73</td><td>(1.3±0.2)e+21</td><td>-0.78 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3953</td><td>(2.4±0.4)e-1</td><td>15.0</td><td>(6.4±1.0)e+21</td><td>-0.75 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 3982</td><td>(2.5±0.4)e-1</td><td>15.83</td><td>(7.6±1.1)e+21</td><td>-0.61 ± 0.08<sup>a</sup></td></tr><tr><td>HRS 76</td><td>(4.7±0.8)e-3</td><td>15.27</td><td>(1.3±0.2)e+20</td><td>-0.18 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 4100</td><td>(2.1±0.3)e-1</td><td>15.31</td><td>(6.0±0.9)e+21</td><td>-0.60 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 4178</td><td>(5.6±1.2)e-2</td><td>16.5</td><td>(1.8±0.4)e+21</td><td>-0.38 ± 0.10<sup>a</sup></td></tr><tr><td>IC 3061</td><td>(1.2±0.3)e-2</td><td>16.5</td><td>(3.8±0.9)e+20</td><td>&lt; -0.80<sup>a</sup></td></tr><tr><td>NGC 4207</td><td>(3.4±0.7)e-2</td><td>16.5</td><td>(1.1±0.2)e+21</td><td>-0.25 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4212</td><td>(1.3±0.3)e-1</td><td>16.5</td><td>(4.1±0.8)e+21</td><td>-0.72 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4216</td><td>(6.4±1.3)e-2</td><td>16.5</td><td>(2.1±0.4)e+21</td><td>-0.72 ± 0.10<sup>b</sup></td></tr><tr><td>NGC 4222</td><td>(1.3±0.3)e-2</td><td>16.5</td><td>(4.4±1.0)e+20</td><td>-0.58 ± 0.12<sup>a</sup></td></tr><tr><td>NGC 4237</td><td>(2.3±0.5)e-2</td><td>16.5</td><td>(7.5±1.7)e+20</td><td>-0.58 ± 0.11<sup>a</sup></td></tr><tr><td>IC 3105<sup>†</sup></td><td>(4.0±1.1)e-3</td><td>16.5</td><td>(1.3±0.4)e+20</td><td>&lt; -0.36<sup>c</sup></td></tr><tr><td>NGC 4254<sup>†</sup></td><td>(2.5±0.5)e+0</td><td>16.5</td><td>(8.3±1.7)e+22</td><td>-0.77 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4289</td><td>(1.5±0.4)e-2</td><td>16.5</td><td>(4.8±1.2)e+20</td><td>-0.53 ± 0.12<sup>b</sup></td></tr><tr><td>NGC 4294</td><td>(8.6±1.7)e-2</td><td>16.5</td><td>(2.8±0.6)e+21</td><td>-0.51 ± 0.10<sup>b</sup></td></tr></tbody></table>

<table><caption>Table A.1. continued.</caption><thead><tr><th>Name<br>(1)</th><th>S<sub>144</sub><br>[Jy]<br>(2)</th><th>d<br>[Mpc]<br>(3)</th><th>L<sub>144</sub><br>[W Hz<sup>-1</sup>]<br>(4)</th><th>α<sup>1400</sup><sub>144</sub><br>(5)</th></tr></thead><tbody><tr><td>NGC 4298</td><td>(1.3±0.3)e-1</td><td>16.5</td><td>(4.2±0.8)e+21</td><td>-0.88 ± 0.10<sup>d</sup></td></tr><tr><td>NGC 4302<sup>†</sup></td><td>(2.5±0.5)e-1</td><td>16.5</td><td>(8.0±1.6)e+21</td><td>-0.77 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4303</td><td>(2.0±0.4)e+0</td><td>16.5</td><td>(6.5±1.3)e+22</td><td>-0.67 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4307</td><td>(9.5±2.1)e-3</td><td>23.0</td><td>(6.0±1.4)e+20</td><td>-0.57 ± 0.14<sup>a</sup></td></tr><tr><td>NGC 4312</td><td>(3.6±0.7)e-2</td><td>16.5</td><td>(1.2±0.2)e+21</td><td>-0.50 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4316</td><td>(2.1±0.4)e-2</td><td>23.0</td><td>(1.3±0.3)e+21</td><td>-0.54 ± 0.10<sup>c</sup></td></tr><tr><td>NGC 4321</td><td>(1.5±0.3)e+0</td><td>16.5</td><td>(4.9±1.0)e+22</td><td>-0.74 ± 0.10<sup>d</sup></td></tr><tr><td>NGC 4330<sup>†</sup></td><td>(5.6±1.1)e-2</td><td>16.5</td><td>(1.8±0.4)e+21</td><td>-0.63 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 4343</td><td>(4.2±0.9)e-2</td><td>23.0</td><td>(2.7±0.5)e+21</td><td>-1.01 ± 0.11<sup>b</sup></td></tr><tr><td>IC 3258<sup>†</sup></td><td>(9.8±2.1)e-3</td><td>16.5</td><td>(3.2±0.7)e+20</td><td>&lt; -0.74<sup>a</sup></td></tr><tr><td>NGC 4351</td><td>(2.0±0.4)e-2</td><td>16.5</td><td>(6.5±1.3)e+20</td><td>&lt; -1.03<sup>a</sup></td></tr><tr><td>IC 3268</td><td>(8.0±1.9)e-3</td><td>23.0</td><td>(5.1±1.2)e+20</td><td>-0.26 ± 0.12<sup>a</sup></td></tr><tr><td>NGC 4359</td><td>(1.1±0.2)e-2</td><td>17.9</td><td>(4.2±0.7)e+20</td><td>&lt; -0.77<sup>a</sup></td></tr><tr><td>NGC 4370</td><td>(1.1±0.2)e-2</td><td>23.0</td><td>(6.8±1.5)e+20</td><td>&lt; -0.77<sup>a</sup></td></tr><tr><td>NGC 4376</td><td>(5.0±1.4)e-3</td><td>23.0</td><td>(3.1±0.9)e+20</td><td>&lt; -0.43<sup>b</sup></td></tr><tr><td>NGC 4380</td><td>(2.0±0.4)e-2</td><td>23.0</td><td>(1.2±0.3)e+21</td><td>&lt; -0.68<sup>a</sup></td></tr><tr><td>NGC 4383</td><td>(1.2±0.2)e-1</td><td>16.5</td><td>(3.9±0.8)e+21</td><td>-0.45 ± 0.10<sup>a</sup></td></tr><tr><td>VCC 827</td><td>(5.1±1.1)e-2</td><td>23.0</td><td>(3.2±0.7)e+21</td><td>-0.59 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4390</td><td>(1.8±0.4)e-2</td><td>23.0</td><td>(1.1±0.2)e+21</td><td>&lt; -0.98<sup>d</sup></td></tr><tr><td>IC 3322</td><td>(1.9±0.4)e-2</td><td>23.0</td><td>(1.2±0.3)e+21</td><td>-0.79 ± 0.12<sup>d</sup></td></tr><tr><td>NGC 4396<sup>†</sup></td><td>(9.6±1.9)e-2</td><td>16.5</td><td>(3.1±0.6)e+21</td><td>-0.79 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4402<sup>†</sup></td><td>(4.3±0.9)e-1</td><td>16.5</td><td>(1.4±0.3)e+22</td><td>-0.81 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4413</td><td>(8.8±1.9)e-3</td><td>16.5</td><td>(2.9±0.6)e+20</td><td>&lt; -0.68<sup>a</sup></td></tr><tr><td>NGC 4412</td><td>(4.0±0.9)e-2</td><td>16.5</td><td>(1.3±0.3)e+21</td><td>-0.44 ± 0.11<sup>d</sup></td></tr><tr><td>NGC 4416</td><td>(1.8±0.4)e-2</td><td>16.5</td><td>(6.0±1.3)e+20</td><td>-0.57 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 4424<sup>†</sup></td><td>(3.0±0.6)e-2</td><td>23.0</td><td>(1.9±0.4)e+21</td><td>-0.67 ± 0.11<sup>a</sup></td></tr><tr><td>NGC 4430</td><td>(2.5±0.5)e-2</td><td>23.0</td><td>(1.6±0.3)e+21</td><td>-0.57 ± 0.10<sup>b</sup></td></tr><tr><td>VCC 1091</td><td>(6.1±1.4)e-3</td><td>23.0</td><td>(3.9±0.9)e+20</td><td>-0.25 ± 0.12<sup>a</sup></td></tr><tr><td>NGC 4450</td><td>(4.3±0.9)e-2</td><td>16.5</td><td>(1.4±0.3)e+21</td><td>-0.71 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4451</td><td>(2.1±0.4)e-2</td><td>23.0</td><td>(1.3±0.3)e+21</td><td>-0.52 ± 0.10<sup>b</sup></td></tr><tr><td>IC 3392</td><td>(8.2±1.8)e-3</td><td>16.5</td><td>(2.7±0.6)e+20</td><td>-0.44 ± 0.13<sup>a</sup></td></tr><tr><td>NGC 4457</td><td>(8.0±1.7)e-2</td><td>16.5</td><td>(2.6±0.5)e+21</td><td>-0.45 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4470</td><td>(2.1±0.4)e-2</td><td>16.5</td><td>(7.0±1.4)e+20</td><td>-0.14 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4480</td><td>(2.2±0.5)e-2</td><td>16.5</td><td>(7.1±1.6)e+20</td><td>-0.86 ± 0.13<sup>a</sup></td></tr><tr><td>NGC 4491</td><td>(7.5±2.0)e-3</td><td>16.5</td><td>(2.4±0.7)e+20</td><td>&lt; -0.61<sup>a</sup></td></tr><tr><td>NGC 4505</td><td>(2.7±0.6)e-2</td><td>16.5</td><td>(8.7±2.0)e+20</td><td>&lt; -1.15<sup>d</sup></td></tr><tr><td>IC 797</td><td>(1.1±0.2)e-2</td><td>16.5</td><td>(3.6±0.8)e+20</td><td>&lt; -0.78<sup>a</sup></td></tr><tr><td>NGC 4501<sup>†</sup></td><td>(1.8±0.4)e+0</td><td>16.5</td><td>(6.0±1.2)e+22</td><td>-0.75 ± 0.10<sup>a</sup></td></tr><tr><td>IC 3476<sup>†</sup></td><td>(5.0±1.0)e-2</td><td>16.5</td><td>(1.6±0.3)e+21</td><td>-0.81 ± 0.10<sup>c</sup></td></tr><tr><td>NGC 4519</td><td>(6.4±1.3)e-2</td><td>16.5</td><td>(2.1±0.4)e+21</td><td>-0.83 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4522<sup>†</sup></td><td>(8.1±1.6)e-2</td><td>16.5</td><td>(2.6±0.5)e+21</td><td>-0.48 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4525</td><td>(2.1±0.4)e-3</td><td>16.77</td><td>(7.2±1.4)e+19</td><td>&lt; -0.07<sup>d</sup></td></tr><tr><td>IC 800<sup>†</sup></td><td>(1.1±0.2)e-2</td><td>16.5</td><td>(3.5±0.8)e+20</td><td>&lt; -0.76<sup>b</sup></td></tr><tr><td>NGC 4532</td><td>(5.0±1.0)e-1</td><td>16.5</td><td>(1.6±0.3)e+22</td><td>-0.63 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4535</td><td>(6.4±1.3)e-1</td><td>16.5</td><td>(2.1±0.4)e+22</td><td>-0.96 ± 0.10<sup>a</sup></td></tr><tr><td>IC 3521</td><td>(2.6±0.5)e-2</td><td>16.5</td><td>(8.3±1.7)e+20</td><td>-0.84 ± 0.12<sup>b</sup></td></tr><tr><td>NGC 4540</td><td>(1.4±0.3)e-2</td><td>16.5</td><td>(4.5±1.0)e+20</td><td>-0.64 ± 0.12<sup>a</sup></td></tr><tr><td>NGC 4548<sup>†</sup></td><td>(1.1±0.2)e-1</td><td>16.5</td><td>(3.7±0.8)e+21</td><td>-1.32 ± 0.10<sup>b</sup></td></tr><tr><td>NGC 4565</td><td>(8.6±1.7)e-1</td><td>17.61</td><td>(3.2±0.6)e+22</td><td>-0.80 ± 0.10<sup>b</sup></td></tr><tr><td>NGC 4567</td><td>(7.1±1.4)e-2</td><td>16.5</td><td>(2.3±0.5)e+21</td><td>-0.76 ± 0.10<sup>c</sup></td></tr><tr><td>NGC 4568</td><td>(5.8±1.2)e-1</td><td>16.5</td><td>(1.9±0.4)e+22</td><td>-0.60 ± 0.10<sup>c</sup></td></tr><tr><td>NGC 4569<sup>†</sup></td><td>(5.5±1.1)e-1</td><td>16.5</td><td>(1.8±0.4)e+22</td><td>-0.55 ± 0.10<sup>c</sup></td></tr><tr><td>NGC 4579</td><td>(6.5±1.3)e-1</td><td>16.5</td><td>(2.1±0.4)e+22</td><td>-0.59 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4580</td><td>(1.2±0.3)e-2</td><td>16.5</td><td>(3.8±0.9)e+20</td><td>&lt; -0.79<sup>b</sup></td></tr><tr><td>NGC 4595</td><td>(9.6±2.2)e-3</td><td>16.5</td><td>(3.1±0.7)e+20</td><td>-0.31 ± 0.12<sup>b</sup></td></tr><tr><td>NGC 4606</td><td>(8.9±2.1)e-3</td><td>16.5</td><td>(2.9±0.7)e+20</td><td>&lt; -0.68<sup>a</sup></td></tr><tr><td>NGC 4607<sup>†</sup></td><td>(9.8±2.0)e-2</td><td>16.5</td><td>(3.2±0.6)e+21</td><td>-0.70 ± 0.10<sup>a</sup></td></tr></tbody></table>
<table><caption>Table A.1. continued.</caption><thead><tr><th>Name<br>(1)</th><th>S<sub>144</sub><br>[Jy]<br>(2)</th><th>d<br>[Mpc]<br>(3)</th><th>L<sub>144</sub><br>[W Hz<sup>-1</sup>]<br>(4)</th><th>α<sup>1400</sup><sub>144</sub><br>(5)</th></tr></thead><tbody><tr><td>NGC 4630</td><td>(2.4±0.5)e-2</td><td>16.5</td><td>(7.9±1.7)e+20</td><td>-0.28 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4634<sup>†</sup></td><td>(1.5±0.3)e-1</td><td>16.5</td><td>(5.0±1.0)e+21</td><td>-0.66 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4639</td><td>(3.7±0.8)e-2</td><td>16.5</td><td>(1.2±0.3)e+21</td><td>-0.68 ± 0.10<sup>b</sup></td></tr><tr><td>NGC 4647</td><td>(3.0±0.6)e-1</td><td>16.5</td><td>(9.8±2.0)e+21</td><td>-0.92 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4654<sup>†</sup></td><td>(8.5±1.7)e-1</td><td>16.5</td><td>(2.8±0.6)e+22</td><td>-0.87 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4689</td><td>(1.4±0.3)e-1</td><td>16.5</td><td>(4.6±0.9)e+21</td><td>-1.15 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4725</td><td>(1.8±0.3)e-1</td><td>17.27</td><td>(6.4±1.0)e+21</td><td>-0.79 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 4747</td><td>(1.6±0.3)e-2</td><td>16.84</td><td>(5.4±0.9)e+20</td><td>-0.33 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 4746</td><td>(1.8±0.4)e-1</td><td>16.5</td><td>(5.9±1.2)e+21</td><td>-0.52 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 4758</td><td>(6.7±1.5)e-3</td><td>16.5</td><td>(2.2±0.5)e+20</td><td>-0.34 ± 0.13<sup>a</sup></td></tr><tr><td>NGC 4779</td><td>(2.6±0.5)e-2</td><td>16.5</td><td>(8.4±1.8)e+20</td><td>-0.49 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 5014</td><td>(3.2±0.5)e-2</td><td>16.23</td><td>(10.0±1.5)e+20</td><td>-0.44 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 5145</td><td>(1.3±0.2)e-1</td><td>17.5</td><td>(4.7±0.7)e+21</td><td>-0.58 ± 0.08<sup>a</sup></td></tr><tr><td>IC 902</td><td>(2.1±0.3)e-2</td><td>22.97</td><td>(1.3±0.2)e+21</td><td>-0.46 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 5248</td><td>(5.4±1.1)e-1</td><td>16.46</td><td>(1.8±0.4)e+22</td><td>-0.58 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 5301</td><td>(7.2±1.1)e-2</td><td>21.54</td><td>(4.0±0.6)e+21</td><td>-0.63 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 5303</td><td>(7.4±1.1)e-2</td><td>20.27</td><td>(3.6±0.5)e+21</td><td>-0.46 ± 0.08<sup>a</sup></td></tr><tr><td>HRS 300</td><td>(3.0±0.6)e-3</td><td>19.34</td><td>(1.4±0.3)e+20</td><td>&lt; -0.22<sup>a</sup></td></tr><tr><td>NGC 5372</td><td>(5.2±0.8)e-2</td><td>24.53</td><td>(3.7±0.6)e+21</td><td>-0.51 ± 0.08<sup>a</sup></td></tr><tr><td>NGC 5486</td><td>(9.5±1.5)e-3</td><td>19.76</td><td>(4.4±0.7)e+20</td><td>&lt; -0.71<sup>a</sup></td></tr><tr><td>HRS 315</td><td>(3.2±0.7)e-3</td><td>20.57</td><td>(1.6±0.4)e+20</td><td>&lt; -0.24<sup>a</sup></td></tr><tr><td>NGC 5645</td><td>(4.1±0.9)e-2</td><td>19.57</td><td>(1.9±0.4)e+21</td><td>-0.44 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 5669</td><td>(2.6±0.5)e-2</td><td>19.54</td><td>(1.2±0.2)e+21</td><td>-0.38 ± 0.10<sup>a</sup></td></tr><tr><td>NGC 5692</td><td>(3.0±0.6)e-2</td><td>22.59</td><td>(1.8±0.4)e+21</td><td>-0.68 ± 0.10<sup>a</sup></td></tr></tbody></table>

**Notes.** Column (1) lists the galaxy names, objects that are marked with a dagger symbol are in the RPS sample. Column (2) shows the LOFAR flux density measured at 20" resolution, column (3) the distance (taken from Boselli et al. 2010 for objects outside the Virgo cluster, otherwise assumed to be 16.5 Mpc), column (4) the 144 MHz luminosity and column (5) the spectral index between 144 MHz and 1.4 GHz. The 1.4 GHz flux densities (or upper limits) are taken from a Boselli et al. (2015); b measured from the maps of Chung et al. (2009); c Murphy et al. (2009) and d Vollmer et al. (2010).
Appendix B: Radio-SFR maps

<figure><img src="image_14.png" /><figcaption>**Fig. B.1.** Logarithmic ratio between the observed and modeled radio emission. The figure is identical to Fig. 8, except that we only show the images based on the 20'' radio maps that were not displayed previously.</figcaption></figure>
## Appendix C: Synchrotron emission model

To numerically solve Eq. 10, we used the Chang-Cooper discretization scheme (Chang & Cooper 1970) implemented in the pychangcooper<fnref n="3" /> library. We extended this code to include an escape term $N(E, t)/t_{esc}$, a time-dependent injection term $Q(E, t) = qE^{-2} \exp(-t/t_{quench})$ and the relevant loss processes, that is Synchrotron radiation, inverse Compton scattering, ionization and Bremsstrahlung. Those are described by (Longair 2010):

$$b(E) = b_0 E^2 + N_{\text{gas}} \left( b_1 \left( 3 \log \frac{E}{m_e c^2} + 19.8 \right) + b_2 E \right), \quad (C.1)$$

with $b_0 = 3.2 \times 10^{-6} (B^2/2\mu_0 + u_{\text{rad}}) m^3 \text{MeV}^{-2} \text{Myr}^{-1}$, $b_1 = 2.4 \times 10^{-7} \text{MeV m}^3 \text{Myr}^{-1}$, and $b_2 = 1.2 \times 10^{-8} \text{m}^3 \text{Myr}^{-1}$. Here, $m_e$ is the electron rest mass, $c$ the speed of light and $N_{\text{gas}}$ the gas density. For the latter, we assumed that only the H I content contributes and approximate a typical mean density $N_{\text{gas}} = 4.4 \times 10^5 \text{m}^{-3}$ assuming the H I mass of NGC 4396 $M_{H1} = 8.6 \times 10^8 M_{\odot}$ (Chung et al. 2009) is distributed in a cylinder with a radius of 5 kpc and a height of 1 kpc.

We split the energy domain into 100 logarithmically spaced points ranging from 1 MeV to 100 GeV. The time domain was discretized in steps of 0.1 Myr. For the initial electron spectrum, we used the source term $Q(E)$ for constant injection and let the spectrum evolve for $t \gg t_{esc}$ until it reached a steady state. This spectrum was then either subject to a time-dependent decrease of the source term on a scale $t_{quench}$ or to an increase of the magnetic field by a factor of $f_B$ and evolved in time.

The flux density of the corresponding synchrotron emission at a frequency $\nu$ and after a time $t$ is given by (e.g., Kardashev 1962; Pacholczyk 1970; Harwood et al. 2013):

$$S(v, B, t) = S_0 B \int_0^\pi d\delta \sin(\delta)^2 \int dE F(x) N(E, B, t), \quad (C.2)$$

where $\delta$ is the pitch angle, $S_0$ a normalization constant and $F(x)$ the following integral of the Bessel function of order 5/3:

$$F(x) = x \int_x^\infty K_{5/3}(z) dz. \quad (C.3)$$

The variable $x = \nu/\nu_c$ is the ratio of the frequency $\nu$ and the critical frequency $\nu_c$, which is given by:

$$\nu_c = \frac{3E^2 eB \sin(\delta)}{4\pi m_e^3 c^4}. \quad (C.4)$$

Here, $e$ is the electron charge.

For the electron spectrum an the corresponding synchrotron emission, we included a 10 Myr delay between the star formation and the CRe injection due to the lifetime of the massive O and B stars. The FUV and H$\alpha$ emission is also delayed compared to the star formation, although less severely. We defined $I_{\text{burst}}(t)$ as the time-dependent intensity after an instantaneous burst of star formation, where we used the distribution provided in Leroy et al. (2012). To take into account the contribution of the prior SFR history to the intensity $I(t)$, we used the convolution:

$$I(t) = \int \text{SFR}(\tau) I_{\text{burst}}(t - \tau) d\tau. \quad (C.5)$$

In the scenario of reducing SFR due to RPS, the SFR is given by:

$$\text{SFR}(t) = \begin{cases} \text{SFR}_0, & \text{if } t \le 0 \\ \text{SFR}_0 e^{-t/t_{\text{quench}}}, & \text{otherwise.} \end{cases} \quad (C.6)$$

<footnote n="3">³ https://github.com/grburgess/pychangcooper</footnote>