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Low-frequency Radio Continuum Imaging and SED Modeling of 11 LIRGs: Radio-only and FUV to Radio Bands

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Abstract

We present a detailed analysis of 11 local luminous infrared galaxies from ultraviolet through far-infrared to radio (∼70 MHz to ∼15 GHz) bands. We derive the astrophysical properties through spectral energy distribution (SED) modeling using the Code Investigating GALaxy Emission (CIGALE) and UltraNest codes. The radio SEDs include our new observations at 325 and 610 MHz from the GMRT and the measurements from public archives. Our main results are (1) radio SEDs show turnovers and bends, (2) the synchrotron spectral index of the fitted radio spectra ranges between −0.5 and −1.7, and (3) the infrared luminosity, dust mass, dust temperature, stellar mass, star formation rates (SFRs), and active galactic nuclei (AGN) fraction obtained from CIGALE fall within the range exhibited by galaxies of the same class. The ratio of 60 μ m infrared and 1.4 GHz radio luminosity, the 1.4 GHz thermal fraction, and emission measure range between 2.1 and 2.9, 0.1% and 10%, 0.02 and 269.5 × 10 ⁶ cm ⁻⁶ pc, respectively. We conclude that the turnovers seen in the radio SEDs are due to free–free absorption; this is supported by the low AGN fraction derived from the CIGALE analysis. The decomposed 1.4 GHz thermal and nonthermal radio luminosities allowed us to compute the SFR using scaling relations. A positive correlation is observed between the SFR IR obtained 10 Myr ago (compared to 100 Myr ago) and 1.4 GHz radio (total and nonthermal) because similar synchrotron lifetimes are expected for typical magnetic field strengths observed in these galaxies (≈50 μ G).
Low-frequency Radio Continuum Imaging and SED Modeling of 11 LIRGs: Radio-only
and FUV to Radio Bands
Subhrata Dey
1
, Arti Goyal
1
, Katarzyna Małek
2
, Timothy J. Galvin
3,4
, Nicholas Seymour
3
, Tanio Díaz Santos
5
,
Julia Piotrowska
1
, and Vassilis Charmandaris
5,6,7
1
Astronomical Observatory of the Jagiellonian University, Orla 171, 30-244 Kraków, Poland; sdey@oa.uj.edu.pl
2
National Centre for Nuclear Research, ul. Pasteura 7, 02-093 Warsaw, Poland
3
International Centre for Radio Astronomy Research, Curtin University, Bentley, WA 6102, Australia
4
CSIRO Space & Astronomy, PO Box 1130, Bentley WA 6102, Australia
5
Institute of Astrophysics, Foundation for Research and Technology-Hellas, GR-71110, Heraklion, Greece
6
Department of Physics, University of Crete, Heraklion, 71003, Greece
7
European University Cyprus, Diogenes Street, Engomi, 1516 Nicosia, Cyprus
Received 2022 March 1; revised 2022 July 13; accepted 2022 July 15; published 2022 October 21
Abstract
We present a detailed analysis of 11 local luminous infrared galaxies from ultraviolet through far-infrared to radio
(70 MHz to 15 GHz)bands. We derive the astrophysical properties through spectral energy distribution (SED)
modeling using the Code Investigating GALaxy Emission (CIGALE)and UltraNest codes. The radio SEDs include
our new observations at 325 and 610 MHz from the GMRT and the measurements from public archives. Our main
results are (1)radio SEDs show turnovers and bends, (2)the synchrotron spectral index of the tted radio spectra
ranges between 0.5 and 1.7, and (3)the infrared luminosity, dust mass, dust temperature, stellar mass, star
formation rates (SFRs), and active galactic nuclei (AGN)fraction obtained from CIGALE fall within the range
exhibited by galaxies of the same class. The ratio of 60 μm infrared and 1.4 GHz radio luminosity, the 1.4 GHz
thermal fraction, and emission measure range between 2.1 and 2.9, 0.1% and 10%, 0.02 and 269.5 ×10
6
cm
6
pc,
respectively. We conclude that the turnovers seen in the radio SEDs are due to freefree absorption; this is supported
by the low AGN fraction derived from the CIGALE analysis. The decomposed 1.4 GHz thermal and nonthermal
radio luminosities allowed us to compute the SFR using scaling relations. A positive correlation is observed between
the SFR
IR
obtained 10 Myr ago (compared to 100 Myr ago)and 1.4 GHz radio (total and nonthermal)because
similar synchrotron lifetimes are expected for typical magnetic eld strengths observed in these galaxies (50 μG).
Unied Astronomy Thesaurus concepts: Radio continuum emission (1340);Luminous infrared galaxies (946);
Spectral energy distribution (2129);Interstellar medium (847);Galaxy photometry (611)
Supporting material: gure set
1. Introduction
Characterized by a prodigious amount of emission at infrared
(IR)wave bands, luminous and ultraluminous infrared galaxies
((U)LIRGs)dominate the IR sky. LIRGs and ULIRGs have IR
luminosity in the wavelength range 8 μm<λ<1000 μm, L
IR
,
>10
11
L
e
and >10
12
L
e
, respectively, where L
e
is the
solar luminosity (Helou et al. 1988). As the name suggests,
these galaxies bridge the gap between underlying astrophysical
processes contributing to emission in normal star-forming
galaxies and the active galactic nuclei (AGN)activity (for a
review see Sanders & Mirabel 1996; Pérez-Torres et al. 2021).
Their spectral energy distribution (SED), although dominated
by emission at IR wave bands, ranges from radio to UV/X-rays
frequencies (Yun et al. 2001; Pereira-Santaella et al. 2011),
containing imprints of different astrophysical processes such as
star formation, stellar evolution, chemical enrichment, pro-
cesses in the interstellar medium, and the AGN (e.g.,
Conroy 2013). Therefore, a detailed and broadband SED
modeling provides not only important constraints on astro-
physical properties shaping SEDs, but also the evolutionary
history of a galaxy, providing insights into the cosmic
evolution of the galaxy population (Lonsdale et al. 2006).
As the radio waves remain unaffected by dust, the study of the
radio continuum offers a promising approach to studying the
astrophysical properties of galaxies. The q
IR
parameter, dened
as the ratio of IR (60100 μm)to radio (1.4 GHz)luminosities,
shows a surprisingly tight correlation for normal galaxies
because emission at these wave bands is ascribed to a common
origin and interpreted as calorimetric models (Helou et al. 1988;
Condon 1992; Yun et al. 2001; Murphy 2009). In this frame-
work, the galaxies are optically thick to UV radiation from young
massive stars that are absorbed by the dust in the interstellar
medium and reradiated in the far-infrared (FIR)regime. Later,
these stars explode to form type II supernovae and accelerate
cosmic-ray electron (CRe)that produces radio emission via a
synchrotron process before escaping the galaxy (Voelk 1989).
Helou et al. (1985)suggested that galaxies can be optically thin
to both UV photons and cosmic rays, but coupling between gas
and magnetic eld should exist to maintain the radio-IR
correlation (see also Lacki et al. 2010; Tabatabaei et al. 2013).
Furthermore, a secondary component of the radio continuum
emission due to freefree interactions between charged particles,
i.e., freefree radiation, is also produced by ionization of gas in H
II regions. In general, synchrotron emission is characterized by a
power-law (PL)emission spectrum, f
ν
ν
α
(α;0.8)dom-
inating the 110 GHz frequency range, whereas freefree
emission has an almost at spectrum with ux proportional
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 https://doi.org/10.3847/1538-4357/ac82f2
© 2022. The Author(s). Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further
distribution of this work must maintain attribution to the author(s)and the title
of the work, journal citation and DOI.
1
to ν
0.1
, dominating in the frequency range 10 GHz
(Condon 1992). The radio spectra of galaxies bend (or atten)
at lower frequencies <1GHz due to absorption processes such as
freefree absorption (FFA), synchrotron self-absorption (SSA),
or the TsytovitchRazin effect (Israel & Mahoney 1990;
Condon 1992; Clemens et al. 2010; Marvil et al. 2015).
Therefore, the exact shape of the radio spectra between the
megahertz and gigahertz range depends on either the quantity
and distribution of ionized (thermal)gas in galaxies (Vardoulaki
et al. 2015; Clemens et al. 2008;Chyżyetal.2018; Galvin et al.
2018)or the presence of AGN (Clemens et al. 2010).Typically,
the thermal fraction, TF, dened as the ratio of thermal to total
emission, ranges between 0.1% and 10% at 1.4 GHz for normal
star-forming galaxies and LIRGs (see Galvin et al. 2018).
Therefore, constraining the radio spectrum to low frequencies is
essential to understanding the absorption models for these
galaxies.
Multiwavelength SED modeling, from UV to IR, provides
information about the light emitted by stars, either directly or
through reprocessing by the gas (emission and absorption
features in the SED)and dust in the interstellar medium, while
radio SED probes the nonthermal and thermal processes in
galaxies (for a review see Walcher et al. 2011; Tabatabaei et al.
2017; Pérez-Torres et al. 2021). Therefore, different regimes of
the broad SED provide critical insight into the nature, origin of
emission, and factors that establish the energy balance. The
astrophysical properties of galaxies using the Code Investigat-
ing GALaxy Emission (CIGALE)model set for main-sequence
(normal)star-forming galaxies (Ciesla et al. 2017; Vika et al.
2017; Pearson et al. 2018; Riccio et al. 2021; Shirley et al.
2021), LIRGs, and ULIRGs have been characterized (Małek
et al. 2017,2018; Paspaliaris et al. 2021). As these galaxies can
host AGNs, the CIGALE code includes the AGN component in
the modeling. In particular, the AGN fraction (dened as the
ratio of IR luminosity due to AGN and a sum of IR luminosity
due to AGN and starburst), stellar mass (M
å
), star formation
rate (SFR
IR
), and dust luminosity (L
IR
), dust temperature (T
dust
)
have been obtained. The most signicant nding of these
studies is that LIRGs are characterized by a relatively higher
SFR
IR
,L
IR
,T
dust
, and AGN fraction compared to normal star-
forming galaxies and lower than those obtained by ULIRGs
(Małek et al. 2017). On the other hand, detailed radio SED
analysis of a large sample of galaxies is rare, primarily due to
the lack of wide-area multifrequency radio surveys and targeted
follow-up of suitable samples.
With this motivation, we performed a SED modeling of radio-
only and far-ultraviolet (FUV)to radio bands of a sample of 11
LIRGs, including our new measurements at 325 and 610 MHz
frequencies using the Giant Metrewave Radio Telescope
(GMRT; Swarup 1990),
8
operated by the National Center for
Radio AstronomyTata Institute of Fundamental Research,
India. In this paper, we report the results of detailed radio SED
modeling covering 80 MHz to 15 GHz and CIGALE SED
modeling covering gigahertz band radio frequencies up to UV
frequencies. As the CIGALE modeling cannot capture the
complex shapes of low-frequency radio spectra exhibited by
LIRGs and ULIRGs (e.g., Clemens et al. 2008,2010; Galvin
et al. 2018), we therefore include >1.4 GHz band radio uxes
to cover the ve decades of the spectral range. Furthermore, an
essential aspect of CIGALE modeling is that it works on the
energy balance between UV and IR, which is ultimately related
to the radio luminosity; hence, including radio uxes in
CIGALE modeling is essential for better constraining the
model parameter space (in particular, the L
dust
).
One of the primary goals of this paper is to compare the
astrophysical properties resulting from SED modeling at radio-
only and FUV to radio bands. The shapes of SEDs reect the
radiation laws and their parameters (such as PL energy index or
emissivity)and the physical processes affecting those para-
meters, such as cooling or heating mechanisms in the medium.
Moreover, integrated SEDs provide total energetics from
different frequency regimes, and comparing those offers key
information on the nature of emission and general factors that
determine their energy balance principle. Furthermore, our
radio SED modeling allowed us to decompose the nonthermal
and thermal emission components and estimate the SFR using
the basic nonthermal and thermal radio SFR calibration
presented in Murphy et al. (2011)and compare them with the
SFR
IR
estimated from CIGALE SED modeling.
We perform detailed SED modeling of a sample of 11 nearby
LIRGs (median redshift equal to 0.0181), focusing separately on
radio-only and FUV-radio spectral bands. This paper is
organized as follows. Sample selection is given in Section 2
while Section 3describes data collection and analysis. Section 4
gives details of the radio-only and panchromatic (FUV to radio)
SED modeling procedures. Section 5provides the results of
model tting, i.e., characterization of the astrophysical proper-
ties of our sample. A discussion of the results obtained is given
in Section 6while the conclusion is given in Section 7.
2. Sample Selection
In this study, we have assembled a sample of 10 LIRGs with
the selection criteria log
10
(L
IR
)>10.75 L
e
from the 1.425 GHz
Atlas of the IRAS Bright Galaxy Sample catalog (Condon et al.
1996)and one galaxy, NGC3508 from the 1.49GHz Atlas of
the IRAS Bright Galaxy Sample (Condon et al. 1990)of with
ux densities greater than 5.24 Jy at 60 μm. These galaxies were
selected based on the availability of 150 MHz data in the original
release of the TIFR GMRT Sky Survey (TGSS)Data Release
(DR)4, covering 1sr of the sky, using the GMRT (for a basic
description of the survey see Sirothia 2014).WenotethatIntema
et al. (2017)presented the entire TGSS data in their alternate
data release (TGSS ADR1). Although, we selected our sample
from the original TGSS DR4 release, which had slightly better
sensitivity for extended emission (rms error 79 mJy beam
1
)
as compared to TGSS ADR1 (Intema et al. 2017),weuse
TGSS ADR1 integrated uxes for radio SED tting as its
reduction and calibration methodology is fully described. The
basic properties of the LIRG sample are listed in Table 1.
3. Multiwavelength Data Sets: Radio to FUV
3.1. Radio Data and AIPS Analysis
To construct the integrated radio SED for modeling, we use
data in the 70 MHz to 15 GHz frequency range. These include
our continuum observations at 325 and 610 MHz conducted
using the GMRT (ID: 23_051, PI: Arti Goyal)and the publicly
available archival data sets at 4.8, 8.4, and 14.5 GHz from the
Karl G. Jansky Very Large Array (VLA
9
)operated by the
National Radio Astronomical Observatory, USA.
8
http://www.gmrt.ncra.tifr.res.in/
9
https://public.nrao.edu/telescopes/vla/
2
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
3.1.1. New GMRT Data at 325 and 610 MHz
We carried out radio continuum imaging of our sample using
the GMRT at 325 and 610 MHz. The primary and phase
calibrators used in our observations are provided in Table A1.
We observed each target with 32 MHz bandwidth divided into
256 spectral channels. We observed standard ux calibrators at
the beginning and end of the observation to calibrate the antenna
gains. Phase calibrators were selected from the NRAO VLA
calibrator manual list and were within 20°. Phase calibrators
were observed every 30 minutes for a typical duration of 45
minutes to correct for antenna gain drifts, atmospheric and
ionospheric gain, and phase variations. Each source was
observed for a total duration of 32 minutes, in two scans
consisting of 16 minutes each to enable better UVcoverage.
3.1.2. Archival VLA Data at 1.4, 4.8, 8.4, and 14.9 GHz
We analyzed the archival VLA data for galaxies wherever
possible. Most galaxies in our sample were observed for a few
minutes of integration time with different array congurations
and different central frequencies. The data set with the largest
on-source integration time was reduced when several observa-
tions were available with the same conguration and central
frequency.
3.1.3. AIPS Analysis
The interferometric observations from both the GMRT and the
VLA were analyzed using NRAO AIPS.
10
Data reduction was
carried out in a standard fashion. The ux density scale of
Baars et al. (1977)was used to obtain the ux densities of the
primary (ux)calibrator, the secondary (phase)calibrator, and
the target source. Antennas and baselines affected with strong
radio frequency interference, nonworking antennas, were
edited out after visual inspection. For the GMRT data sets,
bandpass calibration was determined using the phase calibrator
and the spectral channels were collapsed to generate the
continuum database. Usually, spectral channels below 10 and
above 200 were discarded before collapsing the data. Images
were produced using task IMAGR on the channel collapsed
data. To correct for distortions in the imaging, the large eld of
view with non-coplanar baselines (GMRT at frequencies <1
GHz), polyhedron imaging was employed where the eld of
view was divided into smaller elds (facets). These were 5 ×5
facets that covered the entire eld of view up to the half power
beamwidth. Usually, 35 rounds of phase-based self-calibra-
tion were performed iteratively by choosing point sources in
the eld such that the ux density is >3σwith one synthesized
beam. The nal images were made with full UV coverage and
robust weighting of 0 to weight the UV data (Briggs 1995).
Facets were combined using the task FLATN. The same steps
were followed for the VLA observations except that the data
were obtained in two intermediate frequency (IF)channels
calibrated for antenna gains before averaging them together for
imaging. We did not apply any bandpass calibration since the
data were obtained in a single spectral channel of 50 MHz
bandwidth (BW). The nal images were corrected for the
reduction in sensitivity due to the shape of the antenna beam
using task PBCOR with the specied parameters for the
GMRT
11
and the VLA.
12
Integrated ux densities (and uncertainty)were obtained
using the task TVSTAT in AIPS for the GMRT and VLA images.
We note that the synthesized beam sizes range from
0638. Assuming a typical resolution of 5, the linear
scale is 0.54 kpc at the galaxy distance (z=0.0070.048).
Therefore, it is reasonable to state that we obtain emissions
from extended regions in most galaxies. Furthermore, we note
in GMRT observations, all the proposed galaxies are detected
at 610 MHz observations while LIRGs NGC 6000, IR 16164-
0746, and ESO 453-G005 could not be detected at 325 MHz
because the data could not be calibrated by a weak phase
calibrator.
3.1.4. Radio Fluxes from the Literature
We searched for ux measurements at other frequencies along
with the observations described above. In particular, we obtained
measurements at the central frequencies of 74 MHz from the VLA
Low-Frequency Sky Survey (VLSSr; Cohen et al. 2007),
74231 MHz GaLactic, and Extragalactic MWA Survey
(GLEAM; Wayth et al. 2015), 150 MHz TGSS ADR, 843 MHz
Sydney University Molonglo Sky Survey (SUMSS; Mauch et al.
2003,2013), 3.0 GHz VLA Sky Survey (VLASS; Lacy et al.
2020; Gordon et al. 2021)within the positional uncertainties
provided by the survey parameters. For LIRGs ESO 440-IG080
and ESO 500-G034, we also included 10.0 GHz ux densities
from the Australia Telescope Compact Array, published in Hill
et al. (2001). For NGC 5135, we included 2.3 GHz measurements
from the S-band Polarization All-Sky Survey (Meyers et al. 2017),
and 6.7 GHz measurements from the Effelsburg telescope
(Impellizzeri et al. 2008).Inaddition,wealsoincluded1.4GHz
NRAO VLA Sky Survey (NVSS; Condon et al. 1998)ux for the
galaxy IR 18293-3413. The GLEAM survey frequency bands are
72103 MHz, 103134 MHz, 139170 MHz, 170200 MHz, and
200231 MHz where each band is divided into 7.68 MHz
subchannels for imaging purposes (Hurley-Walker et al. 2017).
The survey provides ux measurements into sub-bands of
7.68 MHz BW (each band has a frequency resolution of
Table 1
Basic Information on Our Sample of LIRGs
Name R.A.(J2000)Decl.(J2000)zlog
10
(L
IR
)
(hms)(°
¢
)(L
e
)
(1)(2)(3)(4)(5)
ESO 500-G034 10 24 31.4 23 33 10 0.0122 10.77
NGC 3508 11 02 59.7 16 17 22 0.0128 10.65
ESO 440-IG058 12 06 51.9 31 56 54 0.0232 11.18
ESO 507-G070 13 02 52.3 23 55 18 0.0217 11.34
NGC 5135 13 25 44.0 29 50 01 0.0136 11.12
IC 4280 13 32 53.4 24 12 26 0.0162 10.85
NGC 6000 15 49 49.6 29 23 13 0.0070 10.92
IR 16164-0746 16 19 11.8 07 54 03 0.0271 11.29
ESO 453-G005 16 47 31.1 29 21 22 0.0209 11.69
IR 18293-3413 18 32 41.1 34 11 27 0.0181 11.62
ESO 593-IG008 19 14 31.1 21 19 09 0.0485 11.77
Note. Columns: (1)source name, (2)R.A., (3)decl., (4)spectroscopic redshift
from the NASA/IPAC Extragalactic Database (NED);(https://ned.ipac.caltech.
edu/)(5)absolute FIR luminosity from Table 1 of Condon et al. (1996), except
for NGC 3508, which is taken from Table 1 of Condon et al. (1990).
10
The National Radio Astronomy Observatory is a facility of the National
Science Foundation operated under a cooperative agreement by Associated
Universities, Inc.
11
http://www.ncra.tifr.res.in:8081/~ngk/primarybeam/beam.html
12
http://www.aips.nrao.edu/cgi-bin/ZXHLP2.PL?PBCOR
3
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
30.72 MHz), which are not independent of each other; therefore,
we averaged the uxes within each band for spectral modeling.
Table A2 summarizes the GMRT and VLA data sets
analyzed by us, while Figure A1 provides total intensity radio
maps overlaid on Digital Sky Survey (DSS)2-R-band images
in Appendix A. For radio SED modeling, we further upscaled
the errors to account for variations in uncalibrated system
temperature. In particular, we added in quadrature to the ux
density errors an additional 10% for 150 MHz TGSS ADR1
(Intema et al. 2017), 5% for 325 and 610 MHz GMRT
(Żywucka et al. 2014; Mhlahlo & Jamrozy 2021), 3% for 1.4,
4.8, 8.4, and 14.9 GHz VLA (Perley & Butler 2017), 3% for
NVSS (Condon et al. 1998), 10% for VLASS (Lacy et al.
2020), 10% for GLEAM (Mhlahlo & Jamrozy 2021), 5% for
SUMSS (Mauch et al. 2003; Galvin et al. 2018), 15% for
Effelsberg measurements (Impellizzeri et al. 2008), 10% for S-
PASS (Meyers et al. 2017), and 5% for ATCA (Galvin et al.
2018)measurements, respectively, as calibration error (see
Equation (1)of Żywucka et al. 2014). As can be seen from
Table A2 that the synthesized beam sizes for our continuum
images range between a few arcseconds and 10×a few
arcseconds. Because we analyzed data sets taken mostly at the
B, C, and D array congurations of the VLA, it is unlikely that
our galaxies are missing ux due to the lack of short UV
spacing data. To establish this, we compared the 1.4 GHz
uxes from Table A2 with the NVSS uxes, obtained at a
resolution of 45. The two measurements are comparable
within the measurement uncertainties. Table A3 provides the
list of ux measurements used for the radio SED tting.
3.2. UV, Optical, and IR Fluxes
We collected photometric measurements from several
instruments from both ground and space-based facilities for
SED modeling using CIGALE. Specically, we obtained the
uxes from the literature by cross-matching the optical
positions of our galaxies to public databases such as NED
(NASA/IPAC 2019), SIMBAD (Wenger et al. 2000), VizieR
(Ochsenbein et al. 2000, and NASA/IPAC Infrared Science
Archive (IRSA)
13
using a matching radius of 515. This
matching radius was chosen to ensure that there exists a
counterpart, depending on the instruments resolution. Speci-
cally, the UV and optical data were collected from the NED
and VizieR Photometry viewer, while the IR data were
obtained from the IRSA database.
About 2030 bands of UV-IR broadband photometry are
available for these sources. They include measurements from
Galaxy Evolution Explorer (GALEX), Optical/UV monitor of
XMM-Newton telescope (XMM-OM), Swift ultraviolet/opti-
cal telescope, SkyMapper Southern Sky Survey (SMSS), Sloan
Digital Sky Survey (SDSS)DR 16, the Two-Micron All-Sky
Survey (2MASS), the Wide-eld Infrared Survey Explorer
(WISE), Spitzer space telescope, AKARI, and Herschel Space
Observatory. Table B1 lists the instrumentscharacteristics. In
the case of the availability of multiple ux measurements at a
given wavelength, we chose the one that contained the entire
galaxy. Moreover, ve galaxies in our sample, namely, ESO
440-IG058, ESO 507-G070, ESO 593-IG008, IR 16164-0746,
and IR 18293-3413 are either interacting, merging, or post-
merging types; for these, the uxes used in modeling include
emission from the companion, too. Table B2 provides the
integrated uxes along with the integration area per band for
each source used for SED modeling. For galaxies ESO 440-
IG058 and NGC 5135, the IRAC apertures were optimized on a
source-by-source basis to cover individual components when
measuring galaxies in merger systems and to contain all the
integrated ux in the case of isolated galaxies (J. M. Mazzarella
et al. 2022, in preparation).
4. SED Modeling
4.1. Radio SED
Integrated radio SEDs are modeled with physically motivated
scenarios in which the radio continuum originates from either
single or two emission regions characterized by the same or
different populations of CRe and optical depths. Most of our
adopted models are presented in Galvin et al. (2018).All
modeling was performed in the observersframe with a reference
frequency, ν
0
=1.4 GHz. We consider the following models.
4.1.1. Single PL
A single PL model with emission characterized by
synchrotron processes, following the form
SA ,1
0
⎜⎟
()
n
n
=
n
a
where Aand αare the normalization and the spectral index,
respectively, treated as free parameters.
4.1.2. Synchrotron and FreeFree Emission (SFG NC)
A radio continuum is a sum of optically thin (no curvature)
synchrotron and freefree emission processes, following the
form
SA B ,2
00
0.1
⎜⎟ ⎜⎟
()
n
n
n
n
=+
n
a-
where Aand Bare the nonthermal and thermal normalization
components, respectively, treated as free parameters. The free
parameter, α, is the synchrotron spectral index.
4.1.3. Synchrotron and FreeFree Emission with FFA (C)
A radio continuum is a sum of optically thick synchrotron
and freefree emission processes where the synchrotron
emission can be suppressed due to FFA. If the frequency of
this turnover due to FFA is parametrized by ν
t,1
, then the
optical depth, τ, can be dened as t,1 2.1
(
)nn -. This model has
the following form:
SeBA1,3
tt,1
0.1
,1
2
⎜⎟ ⎜⎟
() ()
n
n
n
n
=- +
nt
a
-
+
where Aand Bare the nonthermal and thermal normalization
components and treated as free parameters. The free para-
meters, ν
t,1
and αare the turnover frequency and the
synchrotron spectral index, respectively. To reduce the
degeneracy of the model, we replace the term ν
0
with the
turnover frequency parameter for each component. A key point
here is that the models assume that the synchrotron emission is
completely commingled within the extended plasma, which
causes the FFA (a plasma will exhibit FFA regardless of the
13
https://irsa.ipac.caltech.edu/
4
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
physical origin of the radio photoni.e., it does not matter
what causes a radio photon to be there; it will get absorbed by
the plasma).
4.1.4. Multiple FFA Components
Multiple (two)components with emission and absorption
represent two star-forming regions with different orientations or
compositions. The radio continuum could be complex in these
cases, as these regions are integrated by large synthesized beams
for unresolved galaxies. We distinguish ve scenarios in the
multiple components framework, which are described below: (a)
radio continuum originating from two different relativistic
electron populations, characterized by synchrotron spectral
indices, αand α
2
in two distinct star-forming regions without
FFA turnovers, labeled as SFG NC2, following the form
SA B
CD 4
00
0.1
0
2
0
0.1
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
()
n
n
n
n
n
n
n
n
=+
++
n
a
a
-
-
where Aand Care the nonthermal normalization components,
respectively, while Band Dare the thermal normalization
components, respectively. A,B,C,D,α, and α
2
are treated as
free parameters.
(b)Radio continuum characterized by the same (single)
relativistic electron population, α, in two distinct star-forming
regions having different optical depths, τ
1
and τ
2
, respectively,
labeled as C2 1SA:
SeBA
eDC
1
1,5
tt
tt
,1
0.1
,1
2
,2
0.1
,2
2
1
2
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
()
() ()
n
n
n
n
n
n
n
n
=- +
+- +
nt
a
t
a
-
+
-
+
where Aand Care the nonthermal normalization components,
respectively, while Band Dare the thermal normalization
components, respectively. A,B,C,D,α,τ
1
, and τ
2
are treated
as free parameters.
(c)Radio continuum characterized by the same (single)
relativistic electron population, α, in two distinct star-forming
regions, one without a turnover (optically thin)while the other
characterized by optical depth, τ
2
(optically thick), respec-
tively, labeled as C2 1SAN:
SBA
eDC1,6
tt
0
2.1
0
0.1
0
2
,2
0.1
,2
2
2
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟ ⎜⎟
() ()
n
n
n
n
n
n
n
n
n
n
=+
+- +
n
a
t
a
-+
-
+
where Aand Care the nonthermal normalization components,
respectively, while B and D are the thermal normalization
components, respectively. A,B,C,D,α, and τ
2
are treated as
free parameters. This model is most suited to explain the high-
frequency kinks, elaborated in Condon & Yin (1990)and
Clemens et al. (2010).
(d)Radio continuum characterized by the two different
relativistic electron populations, αand α
2
, in two distinct
star-forming regions, one without a turnover while the other
characterized by optical depth, τ
2
, respectively, labeled as C2
1SAN2:
SBA
eDC1,7
tt
0
2.1
0
0.1
0
2
,2
0.1 2
,2
2
2
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟ ⎜⎟
() ()
n
n
n
n
n
n
n
n
n
n
=+
+- +
n
a
t
a
-+
-
+
where Aand Care the nonthermal normalization components,
respectively, while Band Dare the thermal normalization
components, respectively. A,B,C,D,α,α
2
, and τ
2
are treated
as free parameters.
(e)Radio continuum characterized by the two different
relativistic electron populations, αand α
2
, in two distinct star-
forming regions, characterized by optical depths, τ
1
and τ
2
,
respectively, labeled as C2.
SeBA
eDC
1
1,8
tt
tt
,1
0.1
,1
2
,2
0.1
,2
2
1
2
2
⎜⎟ ⎜⎟
⎜⎟ ⎜⎟
()
() ()
n
n
n
n
n
n
n
n
=- +
+- +
nt
a
t
a
-
+
-
+
where Aand Care the nonthermal normalization components,
respectively, while Band Dare the thermal normalization
components, respectively. A,B,C,D,α,α
2
,τ
1
and τ
2
are
treated as free parameters.
Models labeled as SFG NC2, C2 1SAN2, and C2 are
motivated by a galaxy merger scenario where two distinct
systems with distinct electron populations drive a new burst of
star formation. For tting the models and model comparison,
we applied the Bayesian inference package called UltraNest
(Buchner 2021). UltraNest works on the principle of the Monte
Carlo technique called nested sampling (Skilling 2004). The
advantage of nested sampling is that it allows Bayesian
inference on arbitrary user-dened likelihood and provides
posterior probability distributions on model parameters and
marginal likelihood (evidence)Z. The likelihood function used
in UltraNest is given as
Df
ln 1
2ln 2 , 9
n
n
n
n
2
2
2
() (())() ()å
qq
sps=- -+
where D
n
and σ
n
are the vectors at ndifferent frequencies
containing ux densities and uncertainties. f(θ)represents the
model tted with the data and the parameter vector θ. For
model tting, we assume independent ux measurements with
normally distributed errors, which is a prerequisite for the
likelihood function used by the UltraNest. Within the Bayesian
framework, the posterior distribution of any model parameter
requires a prior distribution along with a likelihood function,
which gives the condence interval on the derived parameter.
In our analysis, we consider a uniform prior distribution of
model parameters. We constrain the priors for the normal-
ization parameters, A,B,C, and Das positive, spectral index
parameters αand α
2
in the range 0.2 and 1.8, and turnover
frequencies are between 1 MHz and 50 GHz (see, for details,
Galvin et al. 2018).
5
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
The evidence value is used to predict the most preferred
model by calculating the Bayes odds ratio as follows:
e,10
12 ()
D= -
where 1
and 2
are the evidence values for models M
1
and
M
2
, respectively. The strongest evidence supporting M
1
over
M
2
is when 150
D
>while for 150>
D
>20 and 20>
D
>3, respectively, it is either strong or positive evidence. For
D
<3, the models are considered indistinguishable. Table 2
summarizes the natural logarithm of the Bayes odds ratio
between each model and the most preferred model (Kass &
Raftery 1995). This means that for a given model, log
e
(1)=0.0
indicates the most preferred model. The least preferred model
will have the most negative value in this representation. For
each source, we provide the natural logarithm of the Bayes
odds ratio for the most preferred model in boldface.
The best-t radio SEDs are presented in Figure 1while
Table 4gives the corresponding model parameters, along with
the 1σuncertainties corresponding to the 16th and 84th
percentiles of the posterior distribution of the parameter. Our
radio-only modeling separates the thermal and nonthermal
components from the total emission. Using the best-t model,
we estimated total thermal(nonthermal)emission by setting the
normalization of the nonthermal(thermal)component(s)to
zero. Table 5gives the total, thermal, and nonthermal uxes at
1.4 GHz, derived from the radio-only SED modeling, along
with the 1σuncertainties corresponding to the 16th and 84th
percentiles of the posterior distribution of the parameter. To
assess the degeneracy caused by the number of free parameters
in the best-t model, we give corner plots for all our galaxies in
Appendix (Figure A2). The complete gure set (11 images)is
available in the online journal. In Figure A2, the corner plot
illustrates the one- and two- dimensional projections of the
posterior probability distribution of parameters. Most of our
corner plots show poorly constrained thermal components,
most likely due to weaker thermal emission in the frequency
range covered by our data. In Table 5, we also provide the
1.4 GHz thermal fraction (TF
1.4
). The TF at a given frequency
is the ratio of thermal radio emission to total radio emission
(synchrotron and freefree emission). NGC 3508 shows an
excellent t to the single power-law (PL)shape. Three other
galaxies, NGC 6000, IR 16164-0746, and ESO 453-G005, are
tted with a single-component model without a turnover (SFG
NC). The galaxies ESO 440-IG058, NGC 5135, IC 4280, and
ESO 593-IG008 are tted with the single-component model
with low-frequency turnover (C). For galaxies ESO 500-G034
is best tted with a multiple component model characterized by
a single relativistic electron population in two different star-
forming regions (one region with no turnover at low
frequencies and the other characterized by a turnover (C2
1SAN). For galaxies ESO 507-G070 and IR 18293-3413, the
best-t model turned out to be multiple components, one
characterized by different relativistic electron populations in
two different star-forming regions (one region with no turnover
at low frequencies and the other characterized by a turnover
(C2 1SAN2). None of our galaxies ts with models described
by a single relativistic electron population in two different star-
forming regions with different optical depths (C2 1SA)and a
multiple component model representing two different electron
populations in the two distinct star-forming galaxies with
different optical depths (C2).
4.2. UV to Radio SED Modeling with CIGALE
We estimate the astrophysical properties of our galaxies
using the SED tting technique with the CIGALE version
2020.0
14
(Noll et al. 2009; Boquien et al. 2019). The CIGALE
modeling works on the energy balance principle, i.e., the
energy emitted by dust in the mid and FIR corresponds to the
energy absorbed by dust in the UV to optical range (Efstathiou
& Rowan-Robinson 2003). Moreover, it uses a Bayesian-like
approach to model the SED and obtains the model parameters
efciently. CIGALE is parallelized and modular, which makes
it user-friendly and efcient, as it does not solve the
computationally demanding radiative transfer equation
(Boquien et al. 2019). It provides the best-t model for the
SED by selecting a suitable set of parameters. For this, a large
grid of models is tted to the data. The grid dimension is set by
the number of input parameters used to dene the different
galaxy components, such as stellar emission spectra, star
formation history (SFH), AGN emission, dust attenuation,
nebular emission, and the slope of the radio synchrotron
spectrum.
The interpretation of the observed SED is based on a
comparison of all the modeled SEDs obtained from the xed
grid of parameters used for the modeling. First, each model is
scaled and normalized to the data by minimizing χ
2
. Then the
Table 2
An Overview of the Natural Log of the Bayes Odds Ratio from the UltraNest Fitting of Each Model to Each Source
Name PL SFG C SFG C2 C2 C2 C2
NC NC2 1SA 1SAN 1SAN2
ESO 500-G034 68.1 67.5 6.3 76.3 1.2 0 1.5 4.2
NGC 3508 0 3.5 7.2 8.7 19.3 4.6 2.8 7.1
ESO 440-IG058 17.2 14.9 0 25.7 3.9 9.1 6.8 2.3
ESO 507-G070 74.2 69.9 159.1 21.8 235.1 1.9 0 453.1
NGC 5135 6.5 3.7 0 11.8 13.0 2.9 35.4 6.8
IC 4280 3.2 6.1 0 12.4 8.8 1.6 4.4 0.7
NGC 6000 3.4 0 21.4 6.1 11.2 1.6 3.1 408.8
IR 16164-0746 3.4 0 1.2 1.3 4.1 0.9 0.8 3.0
ESO 453-G005 2.9 0 0.6 3.5 4.9 2.1 2.3 1.5
IR 18293-3413 88.7 86.8 90.4 99.5 4.3 5.1 0 5.1
ESO 593-IG008 3.0 5.9 0 7.5 4.3 6.8 3.8 2.1
Note. In boldface, we present the most preferred model with the highest evidence value (see Equation (10)).
14
https://cigale.lam.fr/
6
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
probability that a given model matches the data is quantied by
the likelihood taken as e2
2
c-. These likelihoods can then be
used as weights to estimate the physical parameters (the
likelihood-weighted means of the physical parameters)and the
related uncertainties (the likelihood-weighted standard devia-
tion of the physical parameters). Finally, models with low
probability are discarded, leaving only the best models to
determine the physical parameters. Due to this process, the
calculated uncertainties are symmetric (see also, Section 4.3 of
Boquien et al. 2019). This method of choosing the best-t
model also takes care of the degeneracies in the model
parameters, as only one parameter value (one with the highest
probability in the probability distribution function (PDF)) can
result in the best-t SED.
Next, we provide a brief account of the selected models used
in our study. The rst step toward obtaining the SED model
Figure 1. Radio SED for our sample of LIRGs. Galaxy name and the best-t radio SED model name are provided at the top and inside each panel. The solid black line
represents the best-t model, while the gray shaded region represents the 1σuncertainties sampled by the UltraNest package. The dotteddashed magenta and dotted
blue lines show the decomposed synchrotron and freefree components. The pink and blue shaded regions represent the 1σuncertainties in the synchrotron and free
free components, respectively. For galaxies tted with two-component models, the freefree and synchrotron components correspond to the sum of individual free
free and synchrotron components. The ux density measurements obtained with GMRT (365 and 610 MHz)are shown by the lled red star symbol, while the archival
VLA data that were reduced and analyzed by us (1.4, 4.8, 8.4, and 14.9 GHz)are shown by the lled cyan triangle. The lled green square indicates the TGSS ADR1
150 MHz uxes, and the open circle represents the ux density measurements taken from the literature (GLEAM, SUMSS, NVSS, VLASS, ATCA, and Effelsberg
telescope)(see Section 3.1, Table A2).
7
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
requires building the stellar emission, which consists of
selecting the single stellar population model (in our case;
Bruzual & Charlot 2003), assuming a Salpeter (1955)initial
mass function. Next, to model the SFH, we adopted a delayed
SFR with an additional burst prole (in accordance with Małek
et al. 2018). This form of SFH provides good estimates of the
SFRM
å
relation compared to observations (Ciesla et al. 2015).
The SFH is dened as
tttt
tttt
SFR SFR : if .
SFR SFR , :if . 11
delayed 0
delayed burst 0
() ()
() () ()µ<
+
where t
0
is the age since the onset of the second episode (burst)
of star formation.
To model starlight attenuation by dust, we chose the
extinction law of Calzetti et al. (2000), and to model dust
emission, we selected The Heterogeneous Evolution Model for
Interstellar Solids (THEMIS; Jones et al. 2017)model.
THEMIS successfully explains the observed FUV to near-IR
extinction and the shape of the IR to millimeter dust thermal
emission. Furthermore, it predicts the observed relationship
between the E(BV)color excess and the inferred submilli-
meter opacity derived from Planck observation (for information
see Jones et al. 2017; Nersesian et al. 2019). To incorporate the
AGN component in the SED, we selected the SKIRTOR
module (Stalevski et al. 2012,2016). SKIRTOR is based on the
3D radiative transfer code SKIRT (Baes et al. 2011). It includes
obscuration by dusty torus and obscuration by dust settled
along with the polar directions. Since our galaxies have a rich
amount of radio data, we used 1.4 and 4.8 GHz uxes to model
the nonthermal synchrotron emission taking into account the
PL of the synchrotron spectrum and the ratio of the FIR/radio
correlation in the CIGALE tting.
Table 3gives the set parameters used to build the SEDs of
our galaxies. We adopted parameters similar to those used in
Małek et al. (2017)and Paspaliaris et al. (2021)and modied
them accordingly to suit the galaxies in the current sample. The
SED tting was performed with a very careful adjustment of
the tting parameters, module by module. We performed a
PDF analysis method to calculate the likelihood function (χ
2
)
for all possible combinations of parameters (see Section 4.3 of
Boquien et al. 2019). We generate the marginalized PDF for
every parameter and assess the suitability of the SED model by
visual inspection. An example of this method is given in
Figure 2for the galaxy IC 4280 for dust mass. Figure 3
provides the CIGALE t for our LIRGs. We note that some of
the photometric data and the best model vary, and for them, the
residuals exceed 20%30%. We want to stress that those
residuals are often related to strong emission lines, visible for
the nebular model. Moreover, this kind of catalog, which
includes data from different surveys and instruments, some-
times performed more than 1020 yr ago (GALEX, XMM-
OM), reduced with different reduction procedures, can result in
heterogeneous photometric coverage of the spectra. In the SED
tting procedure, all measurements are treated with the same
weight, and it can happen that the residuals of some of them are
not as small as we would expect. The most signicant residuals
can be found for the g
¢
and
r¢
bands for our galaxies. As ts for
the UV part of the spectra look very good, we can assume that
the young stellar population was tted with very good
precision. The same observation can be made for i
¢
,
, and
Table 3
List of Input Parameters for CIGALE Modeling
Parameters Values
Delayed SFH +Additional Burst (Ciesla et al. 2015)
e-folding time of the main
stellar population
model [Myr]
τ
main
30015,000 by a bin of 300
e-folding time of the late
starburst population
model [Myr]
τ
burst
501000 by a bin of 50
Mass fraction of the late burst
population
f
burst
0.05, 0.1, 0.3, 0.6, 0.9
Age of the main stellar
population in the
galaxy [Myr]
age 1000, 2000, 3000, 4500, 5000,
6500, 10,000, 12,000
Age of the late burst [Myr]age
burst
10.0, 40.0, 80.0, 110, 150, 170
Stellar Synthesis Population (Bruzual & Charlot 2003)
Initial mass function IMF (Salpeter 1955)
Metallicity Z0.02
Separation age 1 Myr
Dust Attenuation Laws (Calzetti et al. 2000)
Color excess of young stars E(BV)0.12 by a bin of 0.2
Reduction factor
(iii)
f
att
0.3, 0.44, 0.6,0.7
Dust Grain Model; THEMIS (Jones et al. 2017)
Fraction of small hydro-
carbon solids
q
hac
0.02, 0.06, 0.1,0.17, 0.24
Minimum radiation eld U
min
1, 5, 10, 15, 20, 30
PL index of the radiation α2
Fraction illuminated from
U
min
to U
max
γ0.02,0.06,0.1,0.15,0.2
Active Nucleus Model; Skirtor (Stalevski et al. 2012,2016)
Optical depth at 9.7 μmτ
9.7
3.0, 7.0
Torus density radial
parameter
pl 1.0
Torus density angular
parameter
q 1.0
Angle between the equatorial
plan and edge of the
torus [deg]
oa 40
Ratio of outer to the inner
radius
R20
Fraction of total dust mass
inside clumps [%]
Mcl 97
Inclination (viewing
angle)[deg]
i30(type 1),70(type 2)
AGN fraction 0.00.4 by a bin of 0.05
Extinction law of polar dust SMC
E(BV)of polar dust 0.010.7 by a bin of 0.5
Temperature of the polar dust K 100
Emissivity index of the
polar dust
1.6
Synchrotron Emission
FIR/radio parameter
a
q
IR
2.32.9 by a bin of 0.1
PL slope (ux
frequency synch
a)
α
synch
1.8 to 0.2 by a bin of 0.1
Note.
a
Computed as Llog10 IR 8 1000 m()m--Llog10 1.4 GHz where L
1.4 GHz
is the radio
luminosity at 1.4 GHz.
8
The Astrophysical Journal, 938:152 (31pp), 2022 October 20 Dey et al.
near-IR measurements, which assume a good estimation of the
stellar mass and properties of older stellar populations.
Another issue we want to address here is effect of different
aperture sizes taken for ux measurements at different
wavelengths for the SED modeling. Indeed, the apertures do
not match for