# Walk on the Low Side: LOFAR explores the low-frequency radio emission of
GASP jellyfish galaxies

Alessandro Ignesti INAF-Padova Astronomical Observatory, Vicolo
dell’Osservatorio 5, I-35122 Padova, Italy  Benedetta Vulcani INAF-Padova
Astronomical Observatory, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
Bianca M. Poggianti INAF-Padova Astronomical Observatory, Vicolo
dell’Osservatorio 5, I-35122 Padova, Italy  Alessia Moretti INAF-Padova
Astronomical Observatory, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
Timothy Shimwell ASTRON, the Netherlands Institute for Radio Astronomy,
Postbus 2, 7990 AA Dwingeloo, The Netherlands  Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA Leiden, The Netherlands  Andrea Botteon
Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The
Netherlands  Reinout J. van Weeren Leiden Observatory, Leiden University, PO
Box 9513, 2300 RA Leiden, The Netherlands  Ian D. Roberts Leiden Observatory,
Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands  Jacopo Fritz
Instituto de Radioastronomía y Astrofísica, UNAM, Campus Morelia, A.P. 3-72,
C.P. 58089, Mexico  Neven Tomičić INAF-Padova Astronomical Observatory, Vicolo
dell’Osservatorio 5, I-35122 Padova, Italy  Giorgia Peluso INAF-Padova
Astronomical Observatory, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
Dipartimento di Fisica e Astronomia ”G. Galilei”, Universit‘a di Padova,
Vicolo dell’Osservatorio 3, 35122 Padova, Italy  Rosita Paladino INAF,
Istituto di Radioastronomia di Bologna, via Piero Gobetti 101, 40129 Bologna,
Italy  Myriam Gitti Dipartimento di Fisica e Astronomia, Università di
Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy  INAF, Istituto di
Radioastronomia di Bologna, via Piero Gobetti 101, 40129 Bologna, Italy  Ancla
Müller Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical
Institute, Universitätsst 150, 44801 Bochum, Germany  Sean McGee School of
Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United
Kingdom  Marco Gullieuszik INAF-Padova Astronomical Observatory, Vicolo
dell’Osservatorio 5, I-35122 Padova, Italy

###### Abstract

Jellyfish galaxies, characterized by long filaments of stripped interstellar
medium extending from their disks, are the prime laboratories to study the
outcomes of ram pressure stripping. At radio wavelengths, they often show
unilateral emission extending beyond the stellar disk, and an excess of radio
luminosity with respect to that expected from their current star formation
rate. We present new 144 MHz images provided by the LOFAR Two-metre Sky Survey
for a sample of six galaxies from the GASP survey. These galaxies are
characterized by a high global luminosity at 144 MHz ($6-27\times 10^{22}$ W
Hz-1), in excess compared to their ongoing star formation rate. The comparison
of radio and H$\alpha$ images smoothed with a Gaussian beam corresponding to
$\sim$10 kpc reveals a sub-linear spatial correlation between the two
emissions with an average slope $k=0.50$. In their stellar disk we measure
$k=0.77$, which is close to the radio-to-star formation linear relation. We
speculate that, as a consequence of the ram pressure, in these jellyfish
galaxies the cosmic rays transport is more efficient than in normal galaxies.
Radio tails typically have higher radio-to-H$\alpha$ ratios than the disks,
thus we suggest that the radio emission is boosted by the electrons stripped
from the disks. In all galaxies, the star formation rate has decreased by a
factor $\leq 10$ within the last $\sim 10^{8}$ yr. The observed radio emission
is consistent with the past star formation, so we propose that this recent
decline may be the cause of their radio luminosity-to-star formation rate
excess.

Radio astronomy(1338) – Extragalactic radio sources(508) – Late-type
galaxies(907)

##  1 Introduction

Star formation plays a key role in galaxy evolution, and understanding the
physical effects that impact the properties and the distribution of star
formation and/or inter-stellar medium (ISM) are one of the main focusses of
modern, extra-galactic research. Amongst the processes able to alter the gas
content of a galaxy, and hence quench its star formation, ram pressure
stripping (RPS) is considered to be the most efficient mechanism in removing
the ISM from galaxies in galaxy clusters (Boselli & Gavazzi, 2006; Boselli et
al., 2021). The most extreme examples of galaxies undergoing strong RPS are
the so-called jellyfish galaxies (Fumagalli et al., 2014; Smith et al., 2010;
Ebeling et al., 2014; Poggianti et al., 2017a). In the optical/UV band, these
objects show extraplanar, unilateral debris extending beyond their stellar
disks, and striking tails of ionised gas. Jellyfish galaxies mostly reside in
galaxy clusters and are a transitional phase between infalling star-forming
spirals and quenched cluster galaxies, hence they provide a unique opportunity
to understand the impact of gas removal processes on galaxy evolution.
Moreover, in jellyfish galaxies we can study the physics of the interplay
between stripped, cold ($<10^{4}$ K) ISM and the surrounding, hot ($\sim
10^{7}$ K) intracluster medium (ICM), hence obtain insights into the more
general astrophysical case of the interplay between cold clouds and hot winds.

A number of jellyfish galaxies are also found to show extraplanar, nonthermal
radio emission (e.g., Gavazzi, 1978; Gavazzi & Jaffe, 1986; Gavazzi et al.,
1995; Gavazzi & Boselli, 1999; Vollmer et al., 2013; Poggianti et al., 2019a;
Ignesti et al., 2020; Chen et al., 2020; Müller et al., 2021; Roberts et al.,
2021b, a; Ignesti et al., 2022; Roberts et al., 2022; Luber et al., 2022). In
general, radio continuum emission in spiral galaxies is composed of the
thermal emission from the $\sim 10^{4}$ K plasma in the HII regions produced
via thermal bremsstrahlung, and the non-thermal synchrotron emission of the
relativistic cosmic rays electrons (CRe), which are accelerated by supernovae
shocks reaching energies of a few GeV (e.g. Condon, 1992, for a review). Given
the connection between supernovae and CRe and the fact that galaxies are
generally optically-thin to radio wavelengths, the continuum radio emission is
a reliable proxy to evaluate their star formation rate (SFR) (e.g., Kennicutt
& Evans, 2012).

At GeV energies, CRe energy losses are dominated by synchrotron emission in
the galactic magnetic fields with typical values of 10-30 $\mu$G (e.g., Beck &
Krause, 2005, and references therein), which results in nonthermal radio
emission in the 100 MHz-10 GHz band, and Inverse Compton scattering with the
galactic and stellar radiation field (e.g., Pacholczyk, 1970; Longair, 2011).
The CRe synchrotron lifetime, $t_{\text{syn}}$, determined by the synchrotron
and, in a lesser extent, by the Inverse Compton losses can be expressed as:

$\frac{t_{\text{syn}}}{\text{Myr}}\simeq
34.2\left(\frac{\nu}{\text{GHz}}\right)^{-0.5}\left(\frac{B}{10\text{
}\mu\text{G}}\right)^{-1.5}\left(1+\frac{U_{\text{Rad}}}{U_{\text{B}}}\right)^{-1}\text{,}$
(1)

where $\nu$ is the emission frequency, $B$ is the magnetic field intensity,
and $U_{\text{Rad}}/U_{\text{B}}$ is the ratio between the radiation field and
magnetic field energy densities (Heesen et al., 2016). In the densest region
of the galaxies additional losses can also occur via bremsstrahlung and, for
CRe with energy $\lesssim$1 GeV (i.e., those responsible for the radio
emission below $\sim 200$ MHz in a 10 $\mu$G magnetic field), via ionization
captures (e.g., Murphy, 2009; Basu et al., 2015). Therefore, the CRe radiative
time depends on the combination of the aforementioned physical effects, and on
the CR energy, the magnetic and radiation fields intensity, and the local ISM
density (for a detailed discussion, see Murphy, 2009; Lacki & Thompson, 2010;
Basu et al., 2015). So CRe emitting at different frequencies have different
radiative time, with the CRe emitting in the 100-1000 MHz band being in the
order of $10^{7-8}$ yr (e.g., Basu et al., 2015; Heesen et al., 2019). Within
this timescale, CRe can move within the galaxies resulting in extended radio
emission. The CRe transport can take place either via diffusion along and
across magnetic field lines, streaming, or advection. The dominant mechanism
has been observed to vary in the different galactic environments (e.g.,
Heesen, 2021, for a recent review). In the stellar disk, the transport is
generally dominated by diffusion. Outside of the stellar disk, such as in the
galactic radio halos, it is generally dominated by advection/streaming where,
in the case of normal spiral galaxies, the CRe speed should be of the order of
the Alfvén speed ($V=B/\sqrt{4\pi\rho}$, with $B$ magnetic field intensity,
and $\rho$ medium mass density). In the case of jellyfish galaxies’ tails, the
CRe transport mechanism is advection by the ram pressure wind (Murphy et al.,
2009; Vollmer et al., 2013). The CRe velocity should, therefore, be similar to
the velocity of the stripped clouds which, depending on the galactic velocity
and the distance from the disk, can be of the order of several hundreds of
kilometers per second (Tonnesen & Bryan, 2021). Hence the radio tail length,
in absence of CRe re-acceleration/injection within the tail, should depend on
the advection speed and the cooling time-scale (e.g., Chen et al., 2020;
Müller et al., 2021), resulting in a dependence of the radio tail’s length on
the observed frequency and, specifically, in longer radio tails at lower
frequencies (Ignesti et al., 2022).

High resolution observations have revealed radio-deficit regions on the
leading edge of jellyfish galaxies (Murphy et al., 2009). Nevertheless, these
systems, as well as spiral galaxies in clusters, have been reported to show a
global excess of radio emission with respect to their current star formation
rate when compared to similar objects outside of clusters (e.g., Gavazzi &
Jaffe, 1986; Niklas et al., 1995; Gavazzi & Boselli, 1999; Boselli & Gavazzi,
2006; Murphy et al., 2009; Vollmer et al., 2010, 2013; Chen et al., 2020;
Roberts et al., 2021b). This evidence has been generally explained as either
being due to the compression, and resulting amplification, of the magnetic
field frozen within the ISM during RPS (e.g., Boselli & Gavazzi, 2006; Boselli
et al., 2021; Farber et al., 2022), or as a consequence of the interactions
between the CRe and the ICM-driven ‘shocklets’. Recently, Ignesti et al.
(2022) suggested that, instead, it could be due to a fast decline of the SFR
within the CRe radiative time which can leave a population of old CRe which
dominates the global, nonthermal radio emission, and naturally causes a
discrepancy between the radio luminosity and the present SFR.

Observing nonthermal radio emission extending beyond their disk proves that
jellyfish galaxies host large-scale, extraplanar magnetic fields. Previous
works constrained such magnetic fields around $\sim 10-20$ $\mu$G in the
stellar disks and $\sim 4-6$ $\mu$G in the tails of two jellyfish galaxies
(JO206 and JW100, see Müller et al., 2021; Ignesti et al., 2022). Such fields
can affect the geometry of tails (e.g., Tonnesen & Stone, 2014; Ruszkowski et
al., 2014; Ramos-Martínez et al., 2018), as well as the evolution of the
stripped gas. Indeed, simulations of cold gas clouds subjected to a hot wind
found that magnetic fields can have a significant impact on the dynamics of
wind-cloud interactions by suppressing fluid instabilities and, thus,
extending the lifetime of the gas and the star-forming clouds in the stripped
gas (e.g., Berlok & Pfrommer, 2019; Cottle et al., 2020; Sparre et al., 2020).
This physical scenario is similar to jellyfish galaxies moving in the hot
($kT\simeq 3-8$ keV) ICM, thus it suggests that magnetic fields could be
crucial to preserve the cold ($kT<0.1$ keV), stripped ISM clouds in the hot,
hostile environment by damping the thermal conduction between the two gasses.
These cold clouds could further cool down to temperatures that allow new star
formation episodes tracked by both the CO and H$\alpha$ emission (e.g.,
Poggianti et al., 2019a; Moretti et al., 2020). The effect of the magnetic
fields can potentially last for hundreds of Myr, thus permitting to the
stripped ISM to survive in form of cold clouds in the ICM (e.g., Ge et al.,
2021).

The scale length of jellyfish galaxies’ magnetic fields is also thought to be
increased by their interaction with the ICM. A galaxy moving in a magnetised
medium, such as the ICM (e.g. Carilli & Taylor, 2002), can sweep up the
surrounding magnetic field. This process, which is known as ‘magnetic draping’
(e.g. Dursi & Pfrommer, 2008; Pfrommer & Dursi, 2010) can produce a magnetic
sheath that surrounds the ISM and extends into the galaxy’s wake along the
tail of the jellyfish galaxy. In this scenario, as a consequence of the
injection of relativistic electrons by supernovae into an ordered magnetic
field, jellyfish tails should show, in the absence of depolarization effects,
highly-polarized synchrotron emission (Sparre et al., 2020). Indeed, deep Very
Large Array observations recently provided the first detection of these
aligned magnetic fields in the tail of the jellyfish galaxy JO206 (Müller et
al., 2021).

Galaxy | $z$ | log $M_{*}$ | Cluster | $z_{\text{cluster}}$ | Beam | RMS | $S_{\text{Rad}}$ | $L_{\text{Rad}}$ | SFR
---|---|---|---|---|---|---|---|---|---
|  | [$M_{\odot}$] |  |  | [arcsec2] | [$\mu$Jy beam-1] | [mJy] | [1022 W Hz-1] | [$M_{\odot}$ yr-1]
JW39 | 0.0663 | 11.21 | A1668 | 0.0634 | 10.7$\times$6.6 | 183 | 19.2$\pm$3.2 | 22.8$\pm$3.8 | 3.6$\pm$0.7
J085 | 0.0355 | 10.67 | A2589 | 0.0422 | 11.5$\times$5.2 | 109 | 56.4$\pm$9.6 | 27.0$\pm$4.6 | 6.0$\pm$1.0
JO60 | 0.0622 | 10.40 | A1991 | 0.0586 | 10.8$\times$5.5 | 145 | 14.7$\pm$2.2 | 12.0$\pm$1.8 | 4.5$\pm$0.9
JW100 | 0.0619 | 11.47 | A2626 | 0.0551 | 8.8$\times$6.4 | 94 | 13.8$\pm$2.0 | 10.2$\pm$1.5 | 4.0$\pm$0.8
JO49 | 0.0451 | 10.68 | A168 | 0.0452 | 13.3$\times$6.0 | 299 | 10.7$\pm$2.3 | 5.6$\pm$1.2 | 1.4$\pm$0.3
JO206 | 0.0511 | 9.52 | IIZW108 | 0.0489 | 11.9$\times$5.4 | 298 | 18.8$\pm$3.7 | 10.6$\pm$2.3 | 5.0$\pm$1.0
Table 1: Properties of the GASP-LOFAR sample. From left to right: GASP name;
galaxy redshift; stellar mass from Vulcani et al. (2018a); Host cluster name
and redshift (Gullieuszik et al., 2020); resolution and RMS of the 144 MHz
images reported in Figure 1; integrated radio flux density and luminosity at
144 MHz; total SFR from Vulcani et al. (2018a). The integrated radio flux
densities were measured within the last contour reported in Figure 1. We
report, from top to bottom, an alternative name for each galaxy: IC 4141, UGC
12582, 2MASX J14535156+1839064, IC 5337, 2MASX J01144386+0017100, WINGS
J211347.41+022834.9 (source http://cdsportal.u-strasbg.fr/).

In this work we explore the nonthermal side of jellyfish galaxies by analyzing
the low-frequency radio emission of a sub-sample of objects from the GASP
survey (GAs Stripping Phenomena in galaxies with
MUSE111https://web.oapd.inaf.it/gasp/, Poggianti et al., 2017a). The GASP
sample consists of 114 galaxies in different environments and characterized by
a range of stellar masses from $10^{9}$ to $3.2\times 10^{11}$ M⊙ with
redshift $0.04<z<0.07$. The GASP project aims to investigate the process of
gas removal in cluster galaxies by means of multi-wavelength studies. In this
context, low-frequency ($<200$ MHz) observations represent an unique probe. On
one hand, at these frequencies the radio emission is usually dominated by the
nonthermal component (e.g., Condon, 1992; Tabatabaei et al., 2016). Hence low-
frequency observations are a solid proxy of the star formation (e.g., Gürkan
et al., 2018; Heesen et al., 2019). On the other hand, low-frequency ($\sim
100$ MHz) observations probe low-energy particles that, due to their lower
emissivity, have typical life-times of a factor $\sim 3$ longer than the high-
energy particles traced by high-frequency ($>$1 GHz) radio emission (e.g.,
Pacholczyk, 1970). This entails that low-frequency observations probe the
oldest electrons moving along the extraplanar magnetic fields and provide us
the most comprehensive view of this phenomenon. For these reasons, we studied
a sample of GASP galaxies with the LOw Frequency ARray (LOFAR, van Haarlem et
al., 2013), that, up to date, provides the highest sensitivity and resolution
at these frequencies. Previous studies of jellyfish galaxies with LOFAR are
presented in Ignesti et al. (2020); Roberts et al. (2021b, a, 2022); Ignesti
et al. (2022). In the latter, a multi-frequency analysis of the GASP galaxy
JW100 unveiled a connection between the star formation history and the
nonthermal synchrotron emission.

We pursue these studies by extending them on a sample of 6 GASP galaxies in
the northern sky. We present the new LOFAR data and a series of diagnostic
diagrams that we designed to characterize the local connection between the
radio emission, the SFR, and the properties of the stripped gas. In this paper
we use a Chabrier (2003) initial mass function (IMF) and the standard
concordance cosmology parameters $H_{0}=70\,\rm km\,s^{-1}\,Mpc^{-1}$,
${\Omega}_{M}=0.3$ and ${\Omega}_{\Lambda}=0.7$. At the galaxies redshift it
results in $1^{\prime\prime}\simeq 0.9-1.1$ kpc. We define the synchrotron
spectrum as $S\propto\nu^{\alpha}$, where $S$ is the flux density at the
frequency $\nu$, and $\alpha$ is the spectral index.

##  2 Data analysis

###  2.1 The GASP-LOFAR sample

We considered a sub-sample of 6 cluster galaxies from the GASP survey (Table
1). This selection was necessarily driven by the declination of the targets.
Indeed, LOFAR can effectively observe at high sensitivity only the northern
sky where only 13 out of 114 GASP galaxies are located (Poggianti et al., in
preparation). In this work we present 6 of those galaxies observed which have
been observed by LoTSS. For two galaxies of our sample, JW100 and JO49, the
LOFAR images have been already presented in Ignesti et al. (2020, 2022) and
Roberts et al. (2021b) respectively.

The galaxies of the GASP-LOFAR sample are characterized by extraplanar
H$\alpha$ emission produced by warm filaments of stripped ISM (Poggianti et
al., 2019b). We observe galaxies where the H$\alpha$ emission, in projection,
is mostly contained within the disk, as well as examples of truncated disks,
long tails, or unwinding arms. The sample includes both galaxies at an early
and an advanced stage of stripping. According to the SFR-stellar mass relation
(Vulcani et al., 2018b), half of the sample (JW100, JW39 and JO49) shows a
deficiency in SFR that indicates an advanced stage of stripping. Finally, the
sample also presents a high incidence of AGN with 5 out of 6 galaxies showing
nuclear activity according to the Baldwin, Phillips & Terlevich diagnostic
diagrams (BPT, Baldwin et al., 1981): JW39, JO85, JO49 (Peluso et al., 2022)
host LINER-like nuclei, while JW100 and JO206 have a Seyfert nucleus
(Poggianti et al., 2017b; Radovich et al., 2019).

###  2.2 Data preparation

####  2.2.1 LOFAR

The 120-168 MHz images presented in this work are provided by the LOFAR Two-
metre Sky Survey (LoTSS, Shimwell et al., 2017, 2019, 2022). For details on
the observation strategy and calibration of the LoTSS data we refer to
Shimwell et al. (2022). Following the LoTSS procedure, the datasets were
calibrated by using the direction-dependent calibration and imaging pipeline
ddf-pipeline222https://github.com/mhardcastle/ddf-pipeline v. 2.2. This
pipeline was developed by the LOFAR Surveys Key Science Project and it
corrects for ionospheric and beam model errors in the data. The latest version
of the pipeline is described in Tasse et al. (2021). The entire data
processing procedure makes use of prefactor (van Weeren et al., 2016; Williams
et al., 2016; de Gasperin et al., 2019), killMS (Tasse, 2014; Smirnov & Tasse,
2015) and DDFacet (Tasse et al., 2018). The observations presented here have
been further processed to improve the calibration in a smaller region of the
LOFAR field-of-view containing the target of interest, employing the
”extraction and self-calibration” procedure described in van Weeren et al.
(2021). We then produced the final images of the galaxies at a central
frequency of the observation, 144 MHz, by using WSClean v2.10.1 (Offringa et
al., 2014) and using a ROBUST=-0.5 (Briggs, 1995). The imaging was carried out
on the HOTCAT cluster (Taffoni et al., 2020; Bertocco et al., 2020). The Root
Mean Square (RMS) map noise of each map was measured in source-free regions of
the sky and it is reported in Table 1.

In order to explore the low-brightness, extraplanar emission, in this work we
considered the radio surface brightness above the $2\times$RMS level similarly
to Roberts et al. (2021b). Our choice is justified by the absence of large-
scale artifacts at a similar level of brightness near the galaxies. This
assured us that the $2\times$RMS level structures observed extending from the
galaxies in the direction of the H$\alpha$ tails are not calibration or
imaging artifacts. For JW100, due to the proximity with the bright Kite radio
source (see Ignesti et al., 2020, 2022), to not include possible artifacts we
preferred to conservatively cut the radio emission at the $3\times$RMS level.
In the following analysis of the radio emission we adopted a calibration error
of $20\%$, according to what is done in LoTSS (Shimwell et al., 2019, 2022).
In our calculation we neglect the contribution of the thermal radio emission
because, at these frequencies, it corresponds to the $2-5\%$ of the total
radio emission (e.g., Tabatabaei et al., 2017; Ignesti et al., 2022) and it
cannot be differentiated from the nonthermal emission with these data alone.

####  2.2.2 MUSE

We make use of the previous results obtained by the GASP team from the Multi
Unit Spectroscopic Explorer (MUSE) optical observations of the sample. The
MUSE observations, data reduction and the methods of analysis are described in
Poggianti et al. (2017a). Briefly, data were reduced with the most recent
available version of the MUSE pipeline and data cubes were averaged filtered
in the spatial direction with a 5 × 5 pixel kernel ($\sim$1 arcsec2). Data
cubes were corrected for extinction due to the dust in the Milky Way, using
the value estimated at the galaxy position (Schlafly & Finkbeiner, 2011) and
assuming the extinction law from Cardelli et al. (1989). Emission-only data
cubes were obtained by subtracting the stellar-only component of each spectrum
derived with our spectrophotometric code SINOPSIS (SImulatiNg OPtical Spectra
wIth Stellar population models, Fritz et al., 2017,
333https://www.irya.unam.mx/gente/j.fritz/JFhp/SINOPSIS.html). This code
searches the combination of Single Stellar Population (SSP) model spectra that
best fits the equivalent widths of the main lines in absorption and emission
and the continuum at various wavelengths and provides spatially resolved
estimates of a number of stellar population properties, such as stellar masses
and star formation histories. In particular, it provides information on the
average SFR in twelve age bins. These bins can be combined into larger bins in
such a way that the differences between the spectral characteristics of the
stellar populations are maximal (Fritz et al., 2017).

Emission-line fluxes and errors were derived using the IDL software KUBEVIZ
(Fossati et al., 2016). Only spaxels with signal-to-noise ratio S/N(H$\alpha$)
$>$ 3 were considered as reliable. H$\alpha$ luminosities were corrected both
for stellar absorption and for dust extinction. The latter was estimated from
the Balmer decrement assuming an intrinsic value H$\alpha$/H$\beta$=2.86 and
the Cardelli et al. (1989) extinction law. SFRs were computed from the dust-
and absorption-corrected H$\alpha$ luminosities (Vulcani et al., 2018a),
following the Kennicutt (1998) relation:

$\text{SFR}=4.6\times 10^{-42}\left(\frac{L_{H\alpha}}{\text{erg
s${}^{-1}$}}\right)\text{ $M_{\odot}$ yr${}^{-1}$}.$ (2)

In order to characterize the ionization mechanism of warm gas emitting in
H$\alpha$, we consider both the BPT diagnostic diagrams presented in Radovich
et al. (2019); Poggianti et al. (2019b); Peluso et al. (2022) (using the NII
lines for every galaxy with the only exception of JW100, for which we use the
SII lines because the nitrogen line was contaminated by a sky line).

##  3 Results

###  3.1 The new LOFAR images

Figure 1: MUSE H$\alpha$ images with the contours of the stellar continuum
(gold dashed) and the LOFAR 144 MHz continuum emission (silver-filled
contours). The radio continuum levels start from 2$\times$RMS level (except
JW100 for which they start from 3$\times$RMS level) and progress by a factor
2.

Figure 2: MUSE H$\alpha$ images smoothed to the resolution of the
corresponding LOFAR images (see Table 1) with the contours of the stellar
continuum (gold dashed) and the LOFAR 144 MHz continuum emission (silver-
filled contours). The radio continuum levels start from 2$\times$RMS level
(except JW100 for which they start from 3$\times$RMS level) and progress by a
factor 2.

In order to investigate the connection between the stripped ISM and nonthermal
radio emission, in Figure 1 we show the contours of the radio emission at 144
MHz of each galaxy (silver, filled) on top of their emission-only, dust-
corrected H$\alpha$ emission. In Figure 2 we present the same contours on top
of the H$\alpha$ maps that have been smoothed with a gaussian beam to match
the resolution of the LOFAR images. In both figures we show also the contours
of the stellar disk (gold dashed, from Gullieuszik et al., 2020). The
resolution and RMS noise level of each image is reported in Table 1. We note
that the emission to the north of JW100 (central-left panel in Figure 1) is
not related to the galaxy but it is instead part of the Kite radio source (see
Ignesti et al., 2020, 2022).

The new LOFAR images reveal that in the stellar disk of these galaxies, with
the only exception of JO85, the radio emission is truncated with respect to
the stellar emission (i.e., the radio emission is less extended than the
stellar one, leaving radio-devoid regions at the outer edges of the stellar
disk). In principle, this truncation may be the result of the stripping of the
ISM magnetic fields and the CRe, together with the ISM, or low-frequency flux
losses occurring in the high-density, star forming regions of the disk due to
the ionization captures. The former scenario should be characterized by lack
of both radio and H$\alpha$ emission at the disk edges as result of the ISM
stripping, whereas in the latter we should observe H$\alpha$ emission without
radio counterpart and a local flattening of the radio spectral index at low
frequencies due to the loss of the low-energy CRe (e.g., Lacki, 2013; Basu et
al., 2015; Heesen et al., 2022). In Figure 1 and 2 we observe galaxies with
signatures of stripping of both the thermal and nonthermal ISM (e.g., the
northern edge of JW39), whereas evidence of ionization losses have been
observed at the disk edges of JW100 in form of flat-spectrum emission between
144 MHz and 1.4 GHz (Ignesti et al., 2022). Interestingly, in JO206 we observe
both truncated radio and H$\alpha$ emission in the northern half of the disk,
and H$\alpha$ without radio in the southern half. This suggests that the two
processes, stripping and ionization captures, can coexist.

In general, the peak of the radio emission is close to the galactic centre. We
evaluated the presence of radio-loud AGN by computing the radio-loudness
parameter $\mathcal{R}:=(L_{\text{1.4 GHz}}/\text{W
Hz}^{-1})/(L_{\text{H}\alpha}/L_{\odot})$, where $L_{\text{1.4 GHz}}$,
$L_{\text{H}\alpha}$ and $L_{\odot}$ are the radio at 1.4 GHz, H$\alpha$, and
solar luminosities, respectively (e.g., Kozieł-Wierzbowska et al., 2017). To
compute $\mathcal{R}$ we use $L_{\text{1.4 GHz}}$ measured in the NRAO VLA Sky
Survey (Condon et al., 1998), and $L_{\text{H}\alpha}$ estimated from the MUSE
observations by selecting the spaxels classified as LINER or Seyfert in the
BPT diagrams within a circular region centered on the galactic centre. A
radio-loud AGN shows, typically, $\text{log}\mathcal{R}>15.8$, whereas in our
sample we measure $13.1<\text{log}\mathcal{R}<14$, thus we conclude that the
GASP-LOFAR sample does not contain radio-loud AGN. Nevertheless, we cannot
rule out a contamination in the central emission due to low-power radio
emission associated with AGN processes such as AGN driven wind, free-free
emission from photo-ionized gas, low-power jets, or the black hole accretion
(e.g., White et al., 2017; Panessa et al., 2019).

The distribution of the radio emission with respect to the H$\alpha$ emission
in the stellar disks is more diverse. Figure 1 shows galaxies in which radio
and H$\alpha$ emission are similarly truncated with respect to the stellar
disk (JW39 and JO49), or where radio emission appears to be more truncated
than H$\alpha$ (JW100 and JO206), or where only radio is truncated whilst
H$\alpha$ closely follows the stellar disk (JO60). JW39, JO49 and JO206 show
radio-devoid regions located on their leading edge, that become more evident
in the smoothed images (Figure 2). A similar feature has been observed also in
the Virgo galaxies, and they have been interpreted as result of the ram
pressure winds stripping the gaseous ISM (Murphy et al., 2009). At odds with
the other galaxies, JO85 shows no radio-devoid regions within its stellar
disk, although they are present on its eastern edge. This sample shows a
higher incidence of truncated disks at radio than H$\alpha$ emission which
might suggest that the nonthermal ISM components are more affected by the RPS
than the warm plasma which, in turn, is more affected than the cold, star-
forming gas because the ram pressure acceleration is inversely proportional to
the gas column density (e.g., Tonnesen & Bryan, 2021). We suggest that the
combination of this stripping ‘hierarchy’ and ionization captures in the high-
density gas can explain the different morphology of jellyfish galaxies at the
different wavelength, and it will be further discussed in Section 4.

JW39, JO60 and JW100 show unilateral, extraplanar radio emission extending for
up to $\sim 40$ arcsec in the direction of the stripped H$\alpha$ tail. JW39
shows also radio-devoid edges in the opposite direction. As observed in Murphy
et al. (2009), the combination of these two features suggests that the
relativistic, radio-emitting plasma could have been stripped from the disk
into the tail. This provides very strong evidence that this emission is
affected by the RPS. To a lesser extent, the radio emission appears to be
aligned with the stripping direction in JO49. The extraplanar emission in
JO206 appears to be composed of several, barely-resolved patches along the
stripped H$\alpha$ tail, though, the detection is less certain. JO85 shows
radio emission extending outside the stellar disk toward West, which may
appear at odds with the fact that it is moving toward south-west (Bellhouse et
al., 2021).

###  3.2 The radio luminosity-star formation rate relation

Cluster galaxies, and especially jellyfish galaxies, generally present an
excess of radio emission with respect to their current SFR (e.g., Gavazzi &
Boselli, 1999; Roberts et al., 2021b). In order to test if the GASP-LOFAR
galaxies follow this trend, we compare their radio luminosity at 144 MHz,
including both the disk and the extraplanar emission, with their integrated
SFR, measured in their disks and tails from the H$\alpha$ emission. The
integrated flux density of each galaxy, $S_{\text{Rad}}$, is evaluated within
the lowest radio contour presented in Figure 1. In order to evaluate the
contribution of the extraplanar radio emission, we include the emission within
the contours in Figure 1 that coincides with the H$\alpha$ tails. The
corresponding error is the quadrature sum of the RMS contribution in the area
used for the integrated intensity measure and the calibration error. We then
compute the corresponding luminosity at 144 MHz, $L_{\text{Rad}}=4\pi
D_{L}^{2}S_{\text{Rad}}[(1+z)^{\alpha-1}]$, where $D_{L}$ is the luminosity
distances of the hosting clusters (see Table 1)444 Due to the missing
information on the spectral index of the galaxies, we prefer to neglect the
$k$-correction. However, given the low redshift of the sample, its
contribution is negligible.. The resulting radio luminosity at 144 MHz are in
the range $L_{\text{Rad}}=6-27\times 10^{22}$ W Hz-1. The integrated SFRs,
including disks and tails, based on the H$\alpha$ emission (Table 1) are taken
directly from Vulcani et al. (2018a).

The values of $L_{\text{Rad}}$ and the integrated SFR are reported in Table 1
and Figure 3. In the latter, we also show the values reported for 95 other
LoTSS jellyfish galaxies from Roberts et al. (2021b), and the corresponding
best-fitting $L_{\text{Rad}}$-SFR relation at 144 MHz (red line). For
reference, we show the empirical, global $L_{\text{Rad}}$-SFR relation
computed at 144 MHz presented in Gürkan et al. (2018) (blue line):

$\text{log }L_{\text{Rad}}=1.07\pm 0.08\times\text{log SFR}+22.07\pm
0.02\text{.}$ (3)

where $L_{\text{Rad}}$ and SFR are in units of W Hz-1 and $M_{\odot}$ yr-1,
respectively. This relation was fitted on a sub-sample of $15,088$ star-
forming galaxies with redshift $0<z<0.6$ from the seventh release of the Sloan
Digital Sky Survey. The optical spectroscopic informations were provided by
the $H$-ATLAS survey (Eales et al., 2010).

Figure 3: Radio luminosity at 144 MHz vs. SFR of the GASP-LOFAR (gold) and
LoTSS (silver) samples. We report the empirical relations between
$L_{\text{Rad}}$ and SFR presented in Gürkan et al. (2018) (blue) and Roberts
et al. (2021b) (red), the latter is fitted on the LoTSS sample. The shaded
regions show the dispersion at 1$\sigma$ around the corresponding best-fit
relations.

The comparison with the previous studies highlights that the galaxies of the
GASP-LOFAR sample generally occupy the poorly-sampled high SFR area. They show
enhanced radio emission compared to the aforementioned relations (blue and red
lines). They fall outside of the $1\sigma$ scatter of the Gürkan et al. (2018)
relation (blue-shaded area) but, with the only exception of JO85 and JW39,
within the larger scatter of the LoTSS Jellyfish’s relation (red-shaded area).
In the following, we further explore the origin of this radio excess by
studying the connection between radio, H$\alpha$ emission and SFR.

###  3.3 Point-to-point diagnostic diagrams

The difference in resolution between the LOFAR and MUSE images does not permit
a reliable comparison between the different maps on a pixel-by-pixel basis.
Therefore, we used the point-to-point analysis555The point-to-point analysis
was carried out with the Point-to-point TRend Extractor (PT-REX, see Ignesti,
2022, for further details) to compare the two emissions over larger regions.
For each galaxy, we sample the radio emission with a grid composed by
rectangular cells large at least as the beam of each LOFAR image (Table 1).
Each cell covers a region with an average radio surface brightness above the
levels discussed in Section 2.2.1. Then, we use those cells to simultaneously
measure:

  1. 1.

Integrated radio flux density, $S_{\text{Rad}}$, with the corresponding
errors. From this quantity we derive the radio surface brightness,
$I_{\text{Rad}}$, (by dividing $S_{\text{Rad}}$ for the area of each cell) and
luminosity, $L_{\text{Rad}}$, as done in Section 3.2 for the total values;

  2. 2.

Integrated, dust-corrected, emission-only H$\alpha$ flux density measured in
the smoothed H$\alpha$ maps (Figure 2). The uncertainties are defined as
described in Section 2.2.2. We compute the H$\alpha$ surface brightness,
$I_{\text{H}\alpha}$, in each cell. Then, by using only the spaxels defined as
star forming or composite in the BPT diagrams, we estimate the corresponding
current SFR according to Equation 2, SFRHα;

  3. 3.

Sum of the time-averaged SFR during the last $2\times 10^{8}$
(SFR${}_{\text{recent}}$) yr prior to observations as reconstructed with the
SINOPSIS code in each spaxel (see Section 2.2.2). This time bin approximately
represents the maximum radiative time of the CRe emitting at 144 MHz (e.g.,
Basu et al., 2015; Heesen et al., 2019).

The aforementioned quantities are combined in a series of diagnostic plots
shown in Figure 4. For each galaxy, we show the sampling grid on top of the
radio emission and stellar disk contours (top panel). We assign a number to
each cell of the grid to ease locating the regions in the corresponding
diagnostic plots. For reference, we indicate the position of the galactic
centre with a black cross. The diagnostic plots include the radio vs.
H$\alpha$ surface brightness (central panel, see Section 3.3.1), and the radio
luminosity vs. star formation rate (SFR${}_{\text{recent}}$ and SFRHα) (bottom
panel, see Section 3.3.2).

In order to test if the grids provide a reliable picture of each galaxy, we
tested the total radio vs. H$\alpha$ surface brightness correlation with the
Monte Carlo point-to-point analysis (see Appendix A), finding that the general
results did not depend on the choice of the grid. This indicates that the
grids are fine enough to reliably sample the relevant spatial variations
(i.e., $\sim 10$ kpc at the galaxies’ redshift), and, thus, that diagnostic
plots are solid. However, we are aware that the point-point analysis is
intrinsically biased by the arbitrary choice of the sampling grid, in the
sense that the position of each point on the plots necessarily depends on the
geometry of the grids. For this reason, in the followings we focus on the
general results of the point-to-point analysis, instead of the individual
features of each galaxy.

Figure 4:  Diagnostic plots for JW39 (left) and JO85 (right). Top: Sampling
grid on top of the radio (grey) and the stellar disk (orange) contours. The
star forming cells are reported in magenta. The numbers map the points in the
other panels. The black cross shows the galactic centre; Centre:
$I_{\text{Rad}}$ vs. $I_{\text{H$\alpha$}}$ measured from the maps in Figure 2
with the best-fit (continuous, blue for the total and orange for the disk-
only) and the SFR-based (dashed, from Equation 4) relations. Bottom:
$L_{\text{Rad}}$ vs. SFR (SFR${}_{\text{recent}}$, gold, and SFRHα, red), with
the trend expected from Equation 3 (blue line); The shaded regions show the
1$\sigma$ confidence interval of the best-fit relations.

Figure 4 (continued): Diagnostic plots for JO60 (left) and JW100 (right).

Figure 4 (continued): Diagnostic plots for JO49 (left) and JO206 (right).

####  3.3.1 Radio vs. H$\alpha$ surface brightness

The comparison of the two surface brightness values can provide insights into
the ISM microphysics and the connection between the different phases
responsible for the two different types of emission. In the central panels of
Figure 4 we compare $I_{\text{Rad}}$ and $I_{\text{H$\alpha$}}$ computed for
each cell. We identify the disk cells as those that share $>10\%$ of their
surface with the stellar disk mask shown in the top panel (gold contour), and
indicate them with an orange contour. In this way we can infer the differences
in the $I_{\text{Rad}}-I_{\text{H$\alpha$}}$ spatial correlation between the
total galaxy and the stellar disk-only. This corresponds to analyze how the
spatial correlation between thermal and nonthermal ISM evolves from the
stellar disk to the extraplanar regions. We report the errors on
$I_{\text{Rad}}$ and $I_{\text{H$\alpha$}}$ derived from the respective fluxes
(although the errors on $I_{\text{H$\alpha$}}$ are almost negligible and are
smaller than the marker size). In order to test the presence of possible
spatial correlations, both for the total galaxy and the stellar disk only, we
estimate the Spearman and Pearson correlation coefficients and fit a power-law
$I_{\text{Rad}}\propto I_{\text{H$\alpha$}}^{k}$ (blue for the total galaxy
and in orange for the disk) by using the bivariate correlated errors and
intrinsic scatter method (BCES, Akritas & Bershady, 1996). For reference, we
plot also the global $I_{\text{Rad}}-I_{\text{H$\alpha$}}$ relation (green-
dashed line) derived by combining Equations 2 and 3, and by converting the
luminosity into surface brightness:

$\frac{I_{\text{Rad}}}{\text{Jy arcsec}^{2}}\simeq 5.4\times
10^{-10}\frac{I_{\text{H$\alpha$}}}{\text{erg
s}^{-1}\text{cm}^{-2}\text{arcsec}^{-2}}.$ (4)

Equation 4 describes the global radio-to-H$\alpha$ ratio expected when both
the emissions are powered by the total SFR. The resulting slopes $k$, for both
the total and disk-only distributions are reported in the legend of each
panel, and they are summarized in Figure 5.

Figure 5: Slopes $k$ of the $I_{\text{Rad}}$-$I_{\text{H}\alpha}$ relations
for each galaxy (Figure 4). The vertical lines indicate the mean value of each
distribution and the $k=1$ level (dashed grey line).

We find that, for every galaxy, the points lie above the global, linear
correlation expected based on the standard SFR calibrations (Equation 4,
dashed green line), which is expected from the global excess of radio emission
of these galaxies (Figure 3). This study reveals that a sub-linear spatial
correlation holds between $I_{\text{Rad}}$ and $I_{\text{H$\alpha$}}$ in the
form $I_{\text{Rad}}\propto I_{\text{H$\alpha$}}^{k}$ with an average
$k=0.50$. In the stellar disks, the average slope steepens to $k=0.77$. The
gap between the total and the disk-only slopes is more striking for those
galaxies with the most evident radio tails, that are JW39, JO60, JW100, and
JO206. Indeed in their corresponding plots we observe two distinct
distributions, the disk cells which follow a steep, almost linear correlation,
and those in the tail which show a flat trend with constant values of
$I_{\text{Rad}}$ that flattens the total slopes. The implications of this
result are discussed in Section 4.1. As a caveat, we note that the selection
of the disk cells, and hence the resulting slope, ultimately depends on our
arbitrary choice of the overlap threshold ($>10\%$), that was chosen
empirically. Due to the low number of cells used for the fit, increasing this
threshold reduces the number of disk’s cells and, thereby, the goodness of the
fit. However, the main conclusion, that is the steepening of the slopes in the
disk with respect to the total, does not change.

####  3.3.2 Radio luminosity vs. star formation rate

In the bottom panels of Figure 4 we compare $L_{\text{Rad}}$ with
SFR${}_{\text{recent}}$ (gold points) and SFRHα (red points), which trace the
SFR in the last 2$\times 10^{8}$ and $\sim 10^{7}$ yr, respectively. This
comparison permits us to test how much the radio excess depends on the fact
that radio and H$\alpha$ emissions trace the SFR on different timescales
(Kennicutt & Evans, 2012). For reference, we show also the global trend
predicted by Equation 3 (blue line). As we are interested only in the star
forming regions, we first select in the MUSE H$\alpha$ emission maps only
those spaxels classified as star forming or composite in the BPT diagrams.
Then we arbitrarily define as ’star-forming’, (magenta boxes in the top panels
in Figure 4) those cells in which $\geq 50\%$ of the total H$\alpha$ flux
computed in spaxels with a BPT classification comes from those classified as
star-forming and composite, and we ultimately use only the star-forming cells
for this analysis.

For every galaxy, the SFRHα points are located above the expected
$L_{\text{Rad}}-$SFR ratio, which is in agreement with their integrated radio
luminosity excess (Figure 3). However, the SFR${}_{\text{recent}}$, which are
generally higher than the SFRHα, are in better agreement with the expected
ratio. This is observed both in the disks and the tails, which entails that
this result does not depend on the threshold adopted to select the star
forming cells. Increasing the threshold would only exclude those cells with
less star-forming spaxels, which are usually located in the tails (Poggianti
et al., 2019b). We also observe that the cells adjacent to the AGN show radio-
to-SFR ratios that are in line with the rest of the galaxy, further suggesting
that the contamination from the AGN radio emission is limited (see Section
3.1). This result is going to be further discussed in Section 4.2.

##  4 Discussion

###  4.1 Implications of the $I_{\text{Rad}}$-$I_{\text{H$\alpha$}}$ spatial
correlation

The jellyfish galaxies in the GASP-LOFAR sample show sub-linear
$I_{\text{Rad}}$-$I_{\text{H$\alpha$}}$ spatial correlations, which are at
odds with the linear, global one expected based on the standard SFR-
calibrators (Equation 4). Moreover, all the points are located above this
relation, which indicates that the radio-to-H$\alpha$ excess is ubiquitous in
these galaxies. These results suggest that the nonthermal radio emission does
not depend solely on the local, ongoing star formation. The galaxies with the
most extended extraplanar emission (JW39, JO60, JW100 and JO206) show
different trends in the total’s and disk’s slope, with the slopes measured in
their disks being systematically steeper than those derived by using the whole
galaxy (Figure 5). Moreover, the more distant, faintest regions have, on
average, a constant $I_{\text{Rad}}$ and higher ratios of radio-to-H$\alpha$
emission with respect to Equation 4 than those in the disk.

The existence of sub-linear spatial correlations between the resolved
nonthermal radio emission and the ISM star-formation tracers in spiral
galaxies has been previously reported in literature (e.g., Hoernes et al.,
1998; Berkhuijsen et al., 2013; Heesen et al., 2019). In general, the
correlation slope can depend on the observed radio frequency, where the lower
the frequency, the flatter the correlation, or on the radio spectral index,
where the steeper the spectral index, the flatter the slope (Heesen et al.,
2019). Those pieces of evidence suggest that CRe diffusion plays a role in
defining these spatial correlations and, more specifically, that the
flattening of the slope is a consequence of the CRe transport away from the
star forming regions. This would entail that old CRe, which can be traced by
low-frequency observations, should be the main responsible for the spatial
correlations flattening because they have been transported over large scales
during their radiative time. In this framework, the sub-linear spatial
correlations observed in the disks of GASP-LOFAR sample (Figure 5) could be
explained by a combination of radio emission dominated by the old, steep-
spectrum CRe, which is consistent with the steep-spectrum nonthermal radio
emission observed in JO206 and JW100 (Müller et al., 2021; Ignesti et al.,
2022), and an efficient CRe transport.

For JW39 and JW100 the disks’ slopes are consistent with the linearity, that
is the trend expected from Equation 4. This may suggests that the smoothing
scale ($\sim 10$ kpc) is similar to the CRe transport scale, and, hence, the
slopes resembles the standard SFR-calibrators. Therefore, the spatial
correlation slopes observed in the disks of JW39 and JW100 are consistent with
the idea that the CRe transport scale in these galaxies is larger than
observed in spiral galaxies’ disks ($\sim 1-5$ kpc). We investigate this
result by comparing the spatial scales, $L$, of the two principal CRe
transport processes in these systems, that are diffusion and advection. In the
case of CRe diffusion, the spatial scale is:

$L=\sqrt{4D\tau}\simeq
1.1\times\sqrt{\frac{D}{10^{28}\text{cm}^{2}\text{s}^{-1}}\frac{\tau}{\text{10
Myr}}}\text{ kpc,}$ (5)

where $\tau$ is a time scale, and $D$ is the diffusion coefficient, which
depends on the CRe energy and the local magnetic field power spectrum, and can
vary between $10^{27}$ and $10^{29}$ cm2 s-1 (Strong et al., 2007). For the
CRe advection, the typical spatial scales is:

$L=V\cdot\tau\simeq\frac{V}{\text{100 km s}^{-1}}\frac{\tau}{\text{10
Myr}}\text{ kpc,}$ (6)

where $V$ is the CRe velocity. Equation 5 shows that to reach $L=10$ kpc, for
a typical $D=1\times 10^{28}$ cm2 s-1, the time scale is of the order of
$\sim$900 Myr, which is longer than the typical CRe radiative time in galactic
disks. Covering these spatial scales in $\leq 10^{8}$ yr requires a diffusion
coefficient $D\geq 9\times 10^{28}$ cm2 s-1, which is slightly higher than
observed in spiral galaxies (e.g., Strong et al., 2007; Tabatabaei et al.,
2013; Heesen et al., 2019). On the other hand, these scales would be
consistent with the CRe advection (Equation 6), as a typical velocity of 100
km s-1 would be able to cover 10 kpc in $\sim 10$ Myr, which is more
reasonable for low-energy electrons emitting at 144 MHz. Therefore, our
results might hint that CRe transport in the disks of these jellyfish
galaxies, JW39 and JW100, is either dominated by advection, due to the ram
pressure which is stripping the nonthermal ISM (see Section 3.1), or that the
CRe diffusion might be more efficient than in normal galaxies. The diffusion
coefficient $D$ depends on the local magnetic field configuration and
turbulence spectrum (Strong et al., 2007), thus it may be possible that the
RPS, by affecting the ISM microphysics, may induce higher values of $D$ and,
hence, a more efficient CRe diffusion (Equation 5) than the one observed in
normal spiral galaxies. However, we note that, for the rest of the sample, the
spatial correlations in their stellar disks are not consistent with the
linearity (Figure 5). We argue that this might be due to projection effects
that mix the disk and the extraplanar emissions, which, on the basis of what
we observe for JW39, JO60, JW100, and JO206, follows a flat, almost uniform,
distribution. Thus this blend may result in a flattening of the disks’ slopes.
Another possible explanation could be a discrepancy between the sampling
resolution and the transport scale that was not solved by the smoothing.

Concerning the extraplanar emission, observing a sub-linear
$I_{\text{Rad}}-I_{\text{H$\alpha$}}$ relation might shed some light on the
physics of the stripped ISM. Previous studies reported that jellyfish galaxies
commonly show a steepening of the radio spectral index in the extraplanar
emission (Vollmer et al., 2004; Müller et al., 2021; Ignesti et al., 2022;
Roberts et al., 2022) that indicates that the CRe in these regions were
originally accelerated in the disk and subsequently swept in the tail by the
ram pressure wind. In the case of the radio tails observed in GASP-LOFAR
sample, which show projected lenghts of $\sim 40$ kpc, Equation 6 indicates
that a ram pressure wind speed $V\geq 400$ km s-1 would be required to
transport the CRe in $\leq 10^{8}$ yr. For comparison, for magnetic field
intensities $B\leq 10$ $\mu$G (Ignesti et al., 2022), and CRe energy losses
dominated by synchrotron (i.e., $U_{\text{Rad}}/U_{\text{B}}\simeq 0$),
Equation 1 yields $t_{\text{syn}}\geq 9\times 10^{7}$ yr for CRe emitting at
144 MHz in the tails. Concerning the wind speed, albeit the total velocity of
these galaxies is still unknown, the line-of-sight velocities for JW39, JO60,
JW100, and JO206 are 820, 1000, 1950, and 632 km s-1, respectively
(Gullieuszik et al., 2020). Therefore, the observed radio tails lengths are
consistent with a pure advection scenario. Our results provide complementary
pieces of evidence for this scenario. Observing that the extraplanar regions
locate the farthest from the trend defined by Equation 4 can be naturally
explained by the presence of additional electrons coming from the disk that
flatten the spatial correlation slope by boosting the local radio emission in
the extraplanar regions with the faintest H$\alpha$ emission.

###  4.2 The echoes of the past star formation

Figure 6: Integrated radio luminosity at 144 MHz vs. SFR. For each galaxy, the
SFRHα from Vulcani et al. (2018a) (red points) and SFR${}_{\text{recent}}$
(gold points, see Section 3.3), with the corresponding errors, are connected
by the dashed lines. We show also the best-fit $L_{\text{Rad}}-$SFR relations
from Gürkan et al. (2018) (blue line) and Roberts et al. (2021b) (red line).
The shaded regions show the dispersion at 1$\sigma$ around the corresponding
best-fit relations.

The GASP-LOFAR galaxies, analogously to cluster galaxies, show an excess of
radio emission with respect to the ongoing SFR (Figure 3). As highlighted by
the $L_{\text{Rad}}$-SFR plots (Section 3.3.2), this excess does not appear to
be localized on the leading edge of the galaxies (as observed in Murphy et
al., 2009), but it is ubiquitous over the galaxies. Historically, this radio
excess has been explained as the results of ISM compression, or due to the
contribution of the CRe re-accelerated by the ICM winds (e.g., Gavazzi et al.,
1995; Boselli & Gavazzi, 2006; Murphy et al., 2009). In Ignesti et al. (2022)
we presented an alternative view based on the multi-frequency analysis of
JW100. By comparing the excess of SFR between the radio and H$\alpha$
estimates with the average SFR inferred by the stellar population synthesis,
we found the radio excess in its stellar disk to be consistent with a decline
of the SFR happening within the time-scale of the radio emission (i.e.,
$10^{7-8}$ yr). This scenario was further supported by the fact that the
nonthermal emission in both the disk and the tail of JW100 showed evidence of
spectral steepening above 1.4 GHz, thus indicating that the radio emission is
dominated by old CRe.

In this work we further explore the hypothesis of a connection between the
radio luminosity excess and the SFR decline. In the $L_{\text{Rad}}$ vs. SFR
point-to-point plots (Section 3.3.2) we observe that the
SFR${}_{\text{recent}}$, which is generally higher than the SFRHα, is close to
the expected ratio (blue line in Figure 4, bottom plots), especially for the
central regions. In the extraplanar regions the excess seems to persist, which
would be consistent with the idea of a local radio emission boost provided by
the CRe advected from the disk by the ram pressure winds. In Figure 6 we
present the integrated $L_{\text{Rad}}$ and SFRHα for the GASP sample (red
points, see Table 1) and the corresponding integrated SFR${}_{\text{recent}}$
(gold points). For every galaxy SFR${}_{\text{recent}}>$SFRHα, which indicates
that the SFR in these galaxies declined in the last $2\times 10^{8}$ yr. The
extent of the SFR decline varies within the sample, ranging from a factor
$\sim 10$ in JW100 to $\sim 2$ in JO85.

Overall, we observe that SFR${}_{\text{recent}}$ is in better agreement than
SFRHα with the global, empirical relations (blue and red lines, from Gürkan et
al., 2018; Roberts et al., 2021b). Specifically, we measure a decrease of the
root-mean-square deviations from 0.5 to 0.4 and from 0.4 to 0.3 for the Gürkan
et al. (2018) and Roberts et al. (2021b) relations, respectively, as more
galaxies fit within the $1\sigma$ scatter (Figure 6). At odds with the other
galaxies, the total radio emission of JW100 appears to be more in agreement
with the current SFR rather than the past one, whereas in the stellar disk the
radio emission is well explained by the past star formation (Ignesti et al.,
2022).

The result shown in Figure 6 supports the idea that the current radio emission
is related to the past, higher SFR, (or, in other words, that the radio
emission is dominated by old CRe) and thus, that the jellyfish galaxies’ radio
excess is a consequence of the fast evolution of the star formation activity
induced by the RPS in these galaxies. Qualitatively, a past phase of higher
SFR would entail a higher CRe injection, thus a higher radio emission. When
the SFR declines, the CRe injection should decline correspondingly. But if the
decline time-scale is fast ($\sim 10^{7}$ yr) , such as in the case of those
galaxies heavily processed by RPS, and shorter than CRe radiative time, its
effect on the total radio emission (especially at lower frequencies) goes
unseen because the bulk of the radio emission is produced by the old CRe
injected previously. On the contrary, tracers which probe the most recent SFR
(e.g., H$\alpha$) are affected by the SFR decline (e.g., Cleland & McGee,
2021, for a study of the SFR evolution with multiple tracers). Thus the result
is that the radio emission appears in excess with respect to the current SFR.

Observations at higher frequency will be able to conclusively test this
scenario. Observing signatures of a old, steep-spectrum CRe population (i.e.,
spectral steepening at frequencies above 1 GHz) would confirm that the radio
emission is dominated by the older CRe injected during a past phase of higher
SFR. Indeed, evidence of steep-spectrum emission at high frequencies have
already been reported for JW100, which shows an integrated, nonthermal
spectral index $\alpha=-0.92\pm 0.15$ and $-2.43\pm 0.37$ in the $1.4-3.2$ and
$3.2-5.5$ GHz bands, respectively, in the disk, and $\alpha<-0.85$ between 1.4
and 3.2 GHz in the tail (Ignesti et al., 2022), and for JO206, which shows
$\alpha\simeq-1$ in the disk and $\alpha\simeq-2$ in the tail between 1.4 and
2.7 GHz (Müller et al., 2021). Moreover, by comparing the detection levels of
JO206’s radio tail in the new LOFAR data and in the maps presented in Müller
et al. (2021), we can now roughly constrain the spectral index between 144 MHz
and 2.7 GHz to $\alpha=-1.1$, which further indicates that the synchrotron
spectrum is curved, i.e. that the CRe population is old. In order to
conclusively test this scenario, the study of spectral index in the GASP-LOFAR
sample will be the object of future works. This scenario should also imply
that the radio excess broadly depends on the observed radio frequency.
Observations at higher frequencies trace CRe with higher energy and shorter
radiative times, hence more similar to the other tracers and more sensible to
the SFR decline. On the contrary, observations at lower frequencies, such as
the ones that are going to be provided by the LOFAR LBA Sky Survey (de
Gasperin et al., 2021), should observe an higher radio excess because they
trace CRe with the longer radiative times. This scenario can be further
explored also by detailed numerical simulations of these galaxies to trace the
CRe evolution by taking into account the different transport process and the
different energy loss mechanism in a multi-phase ISM.

Our conclusions do not rule out that the other processes proposed previously
in literature (such as magnetic field amplification due to ISM compression, or
CRe re-acceleration, see Section 1) could further contribute in producing the
jellyfish galaxies’ radio luminosity excess. However, we note that the results
in Figure 4 challenge the scenario of radio excess due to ISM compression
(Boselli & Gavazzi, 2006). In the $I_{\text{Rad}}$ vs. $I_{\text{H}\alpha}$
plots we observe that the radio excess is not limited to the regions in the
compressed zone (i.e., where the contours of the radio emission are more
dense) and, on the contrary, in some cases we observe that these regions,
which should be the most compressed by RPS, are the closest to the expected
radio-H$\alpha$ ratio. This could result from multiple effects in action. It
could be that in those regions, due to the increased density of the compressed
ISM, the low-energy electrons emitting at 144 MHz are more affected by the
ionization captures (e.g., Basu et al., 2015), thus balancing the synchrotron
emissivity enhancement due to RPS. It could be that those regions, as a
consequence of the ISM compression, are harbouring an intense phase of ongoing
star formation that dominates the local radio emission and, therefore, they
are less affected by the echoes of the past star formation. Furthermore, we
note that, due to the radio images resolution, the sampling cells located on
the leading edges of some of these galaxies include both radio-rich and
-deficient star-forming regions (Figure 2). This blend may result into a
seemingly regular radio-to-SFR ratio.

##  5 Summary and conclusions

We presented a study of the extended, nonthermal radio emission at 144 MHz for
a sample of six jellyfish galaxies from the GASP sample. The GASP-LOFAR sample
shows high radio luminosities ($6-27\times 10^{22}$ W Hz-1), and a series of
recurring patterns in the radio and H$\alpha$ morphology, such as truncated
radio emission with respect to the stellar disk and extraplanar components.
These results highlight that the nonthermal ISM components, that are CRe and
magnetic fields, are heavily influenced by the RPS similarly to the warm,
ionized ISM. We observe an excess of radio luminosity in the GASP-LOFAR sample
with respect to their current SFR. This is in agreement with the previous
studies of jellyfish galaxies, and cluster galaxies in general. We devise a
series of diagnostic plots to frame the connection between ISM stripping, star
formation history, and radio emission. We found that a sub-linear relations
holds between the radio and H$\alpha$ surface brightness
($I_{\text{Rad}}\propto I_{\text{H}\alpha}^{k}$) with an average slope
$k=0.50$, whereas in the stellar disks we measure $k=0.77$. The extraplanar
regions have, in general, higher relative deviance from the expected radio
luminosity-SFR relation than those in the disk. We argue that this is due to
the presence of CRe coming from the disk that boost the local radio emission.

We observe that for JW39 and JW100 the $I_{\text{Rad}}-I_{\text{H}\alpha}$
correlation in their stellar disks is consistent with being linear, which
would agree with the trend expected from the SFR calibrators. We speculate
that it is because the smoothing scale is consistent with the CRe transport
scale. In this case, a spatial scale of $\sim 10$ kpc would entail that the
CRe transport in their stellar disks is more efficient than observed in normal
spiral galaxies. We speculate that this large spatial scale could be explained
either by a CRe transport dominated by advection rather than diffusion, or a
diffusion efficiency higher than usual induced by RPS.

From the comparison between the radio luminosity and the recent SFR evolution,
both local and integrated, it emerges that the SFR of these galaxies declined
in the last $10^{8}$ yr, and that the radio luminosity can be explained better
by the past, higher SFR than by the ongoing one traced by the H$\alpha$
emission. The implications are twofold. On the one hand, our work shows that
the combined radio-H$\alpha$ studies can constrain the SFR history. On the
other hand, the radio luminosity excess could emerge when the timescale of the
SFR decline is shorter than the CRe radiative time, leaving a population of
old CRe that produces the bulk of the radio emission. The CRe advection by ram
pressure outside of the disk would then be the responsible of the extraplanar
radio emission. This connection between star formation history and radio
luminosity might hint that, in general, the integrated radio luminosity excess
of cluster galaxies could be signature of a (fast) SFR decline. This work is
among the few studies comparing the resolved properties of H$\alpha$ and low
frequency radio emission, and is surely focused on a peculiar class of
objects. However, the intimate connection between the recent, instead of the
ongoing, star formation and the radio emission could be a general property of
cluster galaxies that have a similar star formation histories. Future studies
on larger samples of galaxies, including those not evidently affected by the
ram-pressure, will help clarifying the possible caveats in using the low-
frequency radio emission as a tracer for the ongoing SFR.

The results presented here call now for follow-up observations at higher
frequencies. By combining these new pieces of information with detailed
spectral index maps it will be possible to study the CRe lifecycle within
these galaxies. Moreover, our findings provide a benchmark for numerical
simulations of RPS, or more in general of cloud-crushing scenarios. The fact
that, thanks to LOFAR, we are discovering more and more jellyfish galaxies
with extraplanar, nonthermal radio emission indicates that large-scale
magnetic fields are common in these systems, and that their evolution is
intimately connected with the evolution of the stripped gas.

## Acknowledgments

We thank the Referee for the constructive report that improved the
presentation of this work. This work is the fruit of the collaboration between
GASP and the LOFAR Survey Key Project team (“MoU: Exploring the low-frequency
side of jellyfish galaxies with LOFAR”, PI A. Ignesti). We acknowledge the
INAF founding program ’Ricerca Fondamentale 2022’ (PI A. Ignesti). A.I., B.V.,
R.P., M.G. acknowledge the Italian PRIN-Miur 2017 (PI A. Cimatti). This
project has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (grant
agreement No. 833824). R.J.vW and A.B. acknowledges support from the VIDI
research programme with project number 639.042.729, which is financed by the
Netherlands Organisation for Scientific Research (NWO). I.D.R. acknowledges
support from the ERC Starting Grant Cluster Web 804208. S.L.M. acknowledges
support from the Science and Technology Facilities Council through grant
number ST/N021702/1. J.F. acknowledges financial support from the UNAM- DGAPA-
PAPIIT IN111620 grant, México. We acknowledge funding from the INAF main-
stream funding programme (PI B. Vulcani).

Based on observations collected at the European Organization for Astronomical
Research in the Southern Hemisphere under ESO programme 196.B-0578. 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. This research
made use of Astropy, a community-developed core Python package for Astronomy
(Astropy Collaboration et al., 2013, 2018), and APLpy, an open-source plotting
package for Python (Robitaille & Bressert, 2012). A.I. thanks the music of
Black Sabbath for providing inspiration during the preparation of the draft.

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##  Appendix A Monte Carlo point-to-point analysis

We tested the reliability of the grids adopted in the point-to-point analysis
(Figure 4) by performing a Monte Carlo point-to-point analysis (MCptp, for
further details see Ignesti, 2022). For each galaxy, we replied 100 different
sampling of the radio emission with randomly-generated grids (each grids with
the same cell size and thresholds of the ones shown in Figure 4) and measured
the slope $k$ of the corresponding $I_{\text{Rad}}-I_{\text{H$\alpha$}}$
correlation. Then, by bootstrapping a value of $k$ from the best-fit of each
cycle, we composed a distribution of 100 slopes for each galaxy. In Figure 7
we report the final distributions and the mean and standard deviation of the
slope $k$ for each galaxy. The values reported in Figure 4 fall within these
distributions. This supports that the results presented in Section 3 are not
biased by the choice of the grids.

Figure 7: Results of MCptp with 100 iterations for each galaxy of the GASP-
LOFAR sample. For each galaxy, the mean and the standard deviation of the
distribution is reported in the respective label.