11institutetext: European Space Agency (ESA), European Space Research and
Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, the Netherlands
11email<EMAIL_ADDRESS>22institutetext: Department of
Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The
Netherlands 33institutetext: Department of Physics, University of Warwick,
Gibbet Hill Road, CV4 7AL Coventry, United Kingdom 44institutetext: Inter-
University Institute for Data Intensive Astronomy, Department of Astronomy,
University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa
55institutetext: South African Astronomical Observatory, P.O. Box 9, 7935
Observatory, South Africa 66institutetext: Oxford Astrophysics, Denys
Wilkinson Building, Keble Road, Oxford, OX1 3RH, United Kingdom

# Multi-wavelength observations of the Luminous Fast Blue Optical Transient AT
2023fhn

Up to $\sim$200 days post-explosion

A. A. Chrimes, ESA Research Fellow1122 D. L. Coppejans 33 P. G. Jonker 22 A.
J. Levan, 2233 P. J. Groot,, 224455 A. Mummery 66 E. R. Stanway 33

(Received September 15, 1996; accepted March 16, 1997)

###### Abstract

Context. Luminous Fast Blue Optical Transients (LFBOTs) are a class of
extragalactic transients notable for their rapid rise and fade times, blue
colour and accompanying luminous X-ray and radio emission. Only a handful have
been studied in detail since the prototypical example AT 2018cow. Their
origins are currently unknown, but ongoing observations of previous and new
events are placing ever stronger constraints on their progenitors.

Aims. We aim to put further constraints on the LFBOT AT 2023fhn, and LFBOTs as
a class, using information from the multi-wavelength transient light-curve,
its host galaxy and local environment.

Methods. Our primary results are obtained by fitting galaxy models to the
spectral energy distribution of AT 2023fhn’s host and local environment, and
by modelling the radio light-curve of AT 2023fhn as due to synchrotron self-
absorbed emission from an expanding blast-wave in the circumstellar medium.

Results. We find that the neither the host galaxy nor circumstellar
environment of AT 2023fhn are unusual compared with previous LFBOTs, but that
AT 2023fhn has a much lower X-ray to ultraviolet luminosity ratio than
previous events.

Conclusions. We argue that the variety in ultraviolet-optical to X-ray
luminosity ratios among LFBOTs is likely due to viewing angle differences, and
that the diffuse, yet young local environment of AT 2023fhn - combined with a
similar circumstellar medium to previous events - favours a progenitor system
containing a massive star with strong winds. Plausible progenitor models in
this interpretation therefore include black hole/Wolf-Rayet mergers or failed
supernovae.

###### Key Words.:

Supernovae: individual: AT 2023fhn – Supernovae: general – Stars: black holes
– Black hole physics – Stars: winds, outflows – Stars: circumstellar matter

##  1 Introduction

Luminous Fast Blue Optical Transients (LFBOTs) are a rare class of rapidly-
evolving, hot, multi-wavelength extragalactic transients. The prototypical
example, AT 2018cow (‘the Cow’, Prentice et al., 2018), is the nearest and
best-studied event of this class so far. Its characteristic early-time
features include a peak optical absolute magnitude of $\sim$–20 with a rapid
rise and decay timescale of $\sim$5 days, constraining the 56Ni mass in the
ejecta to $<$$0.004$ M⊙, and ruling out standard core-collapse or
thermonuclear supernova models (Perley et al., 2019; Margutti et al., 2019).
The optical-ultraviolet (UV) emission is well fit by a hot black-body and
power-law component, where the black-body temperature was $\sim 3\times
10^{4}$ K initially, falling to $\sim 1.5\times 10^{4}$ K over two weeks
(Prentice et al., 2018; Perley et al., 2019). The optical spectra were largely
featureless, with broad hydrogen absorption features (indicative of a high
outflow velocity) appearing and disappearing between 2–8 days, and narrow He
lines appearing after $\sim$20 days. At other wavelengths, AT 2018cow was
X-ray and radio bright (Rivera Sandoval et al., 2018; Margutti et al., 2019;
Ho et al., 2019; Nayana & Chandra, 2021). The X-ray emission was well in
excess of power-law extrapolations from the radio (e.g. Ho et al., 2019) and
was also highly variable after a break in the light-curve, which declined as
$L\propto t^{-2}$ after $\sim$20 days (Migliori et al., 2024). The broadband
X-ray spectrum, and X-ray variability, cannot be explained by an external
shock origin, and the synchrotron self-absorbed radio emission - consisting of
a slow rise and rapid decay - was instead smoothly evolving, indicating a
distinct physical origin from the highly variable X-rays. An interpretation is
that a central engine powers the X-ray emission, while an expanding blast wave
produces the radio emission (e.g. Ho et al., 2019; Margutti et al., 2019). The
slow radio variability timescale set the size of the emission region at 5–6
days at $<3\times 10^{15}$ cm, while the X-ray variability gave a length scale
$\sim$five times smaller (Ho et al., 2019). Therefore, the X-rays appear to
originate from a central engine or internal shock, while the radio emission is
generated externally. A claim of quasi-periodic oscillations in the X-rays can
interpreted as evidence for a $<850M_{\odot}$ central engine (Pasham et al.,
2021), while a separate claim of $\sim$250s quasi-periodicity instead implies
an intermediate mass (103-105 M⊙) black hole (Zhang et al., 2022). Synchrotron
modelling of the sub-millimetre and radio data revealed a mildly-relativistic
expansion velocity ($\sim$0.1$c$) into a wind-like extended circumstellar
medium (CSM) with a high density of $\sim$105 cm-3 (Margutti et al., 2019; Ho
et al., 2019). For Wolf-Rayet-like wind speeds of $\sim$1000 km s-1, this
implies a mass-loss rate $\dot{M}=10^{-4}$-$10^{-3}$ $M_{\odot}$ yr-1
(Margutti et al., 2019).

Since AT 2018cow, several more LFBOTs have been discovered. Confirmed events
include AT 2018lug/ZTF 18abvkwla (‘the Koala’, Ho et al., 2020), CSS161010
(Coppejans et al., 2020), AT 2020xnd/ZTF 20 acigmel (‘the Camel’, Perley et
al., 2021; Bright et al., 2022; Ho et al., 2022), AT 2020mrf (Yao et al.,
2022), AT 2022tsd (‘the Tasmanian Devil’, Matthews et al., 2023) and AT
2023fhn (‘the Finch’, Chrimes et al., 2024). Despite variety (e.g. in peak
luminosity), they share the same key features of hot, largely featureless
spectra at early times, optical luminosities rivalling gamma-ray burst (GRB)
afterglows and superluminous supernovae, plus bright X-ray and radio emission.
They are estimated to occur at $<$0.1% of the local core-collapse supernova
rate (Ho et al., 2023d).

Recent developments have provided further insight into the origin of LFBOTs.
Polarimetry of AT 2018cow demonstrated the emission region to be highly
aspherical, indicative of an accretion disc (Maund et al., 2023).
Unexpectedly, AT 2018cow was found to be UV (Sun et al., 2022; Chen et al.,
2023; Sun et al., 2023; Inkenhaag et al., 2023) and X-ray (Migliori et al.,
2024) bright at late times, several years post-explosion. This emission has
been interpreted as from a black hole accretion disc. Estimates for the black
hole mass range from $\sim$10–100 M⊙ (super-Eddington accretion) to
$\sim$103–104 M⊙ (sub-Eddington, from X-ray observations, Migliori et al.,
2024) and $\sim$1000 M⊙ (UV observations, Inkenhaag et al., 2023). Magnetar
central engine models struggle to produce both the early and late UV emission
(Chen et al., 2023). Further evidence for a black hole accretion scenario
comes from minute-long optical flares, up to several months post-explosion,
from AT 2022tsd (Ho et al., 2023c). An interpretation is that the central
engine is undergoing highly variable, short-lived bursts of accretion.

Several models have been put forward to explain LFBOTs. Tidal disruptions of
compact, hydrogen-poor stars (such as white dwarfs) around intermediate mass
black holes (IMBHs) can plausibly explain the optical rise and fall timescale,
spectral features and X-ray variability timescale (Perley et al., 2019; Kuin
et al., 2019). However, the dense CSM inferred from radio observations is hard
to explain in such a scenario (e.g. Margutti et al., 2019). Other
possibilities include failed supernovae, in which a black hole is formed and
the emission is powered by accretion onto the natal black hole rather than
radioactive decay in the ejecta (Perley et al., 2019; Quataert et al., 2019),
choked jets (e.g. Gottlieb et al., 2022; Soker, 2022), highly aspherical
supernovae (‘ellipsars’, DuPont et al., 2022), and the mergers of compact
objects and/or massive stars (Lyutikov & Toonen, 2019; Uno & Maeda, 2020;
Schrøder et al., 2020), such as black holes and Wolf-Rayet stars (Metzger,
2022). A dense outflow from the progenitor may result in dust echoes (Metzger
& Perley, 2023). CSM shock interaction models have also been put forward (e.g.
Fox & Smith, 2019; Xiang et al., 2021; Pellegrino et al., 2022; Khatami &
Kasen, 2023), but the X-ray variability, broadband spectral evolution, late-
time UV/X-ray emission from AT 2018cow and giant optical flares from AT
2022tsd all indicate the presence of a central engine.

In this paper, we present multi-wavelength radio, optical, UV, and X-ray
observations of the LFBOT AT 2023fhn up to $\sim$200 days post-explosion. We
place AT 2023fhn in the context of other LFBOTs so far, in terms of its host
galaxy, optical/UV/X-ray light-curve, and radio emission, with the event
energetics and blast wave properties inferred from synchrotron modelling of
the radio observations. Throughout, we use a flat $\Lambda$CDM cosmology with
$\Omega_{\rm m}$=0.3 and $H_{0}$=70 kms-1Mpc-1. All magnitudes are reported in
the AB system (Oke & Gunn, 1982).

##  2 Observations and data reduction

###  2.1 X-ray

We obtained four epochs of Chandra X-ray Observatory (CXO) ACIS-S observations
of AT 2023fhn up to $\sim$200 days post-explosion. The epochs consist of 1, 2,
6 and 14 observations, respectively (full details are provided in Table 1).
The data are reduced, and transient fluxes measured, with standard CIAO
(v4.13, caldb v4.9.3, Fruscione et al., 2006) procedures. The images are
reprocessed and filtered to the energy range 0.5-7.0 keV. wavdetect is used to
find point sources, and srcflux used to measure the flux (or upper limits) at
the location of AT 2023fhn. We merged the datasets in each of the four epochs
(with merge$\\_$obs) to increase the signal-to-noise ratio. The mean (mid-
point, exposure-time weighted) observation times of these epochs are 15.0,
28.9, 64.5 and 210.9 days (since JD–2460045, or 12:00 UT on 10-Apr-2023). The
total exposure times per epoch are $\sim$30, 60, 83 and 193 ks respectively.
Finally, the fluxes are de-absorbed by assuming a photon index $\Gamma=2$
(e.g. Rivera Sandoval et al., 2018), and a Galactic neutral hydrogen column
density of $N_{\rm H}=2.78\times 10^{20}$ cm-2 (Dickey & Lockman, 1990).

Table 1: All CXO observations of AT 2023fhn from programme 24500143 (PI: Chrimes). ObsID, exposure start times (since JD-2460045) and data mode are listed. All observations are made with ACIS-S. The fluxes FX are unabsorbed and measured in the energy range 0.5-7.0 keV. Individual observations in each of the four epochs are merged as indicated. Uncertainties are given at 1$\sigma$, upper limits at 2$\sigma$. ObsID | Start date | texp | Data mode | FX
---|---|---|---|---
| JD-2460045 | ks |  | erg s-1 cm-2
26624 | 14.78957 | 29.68 | FAINT | (7.6${}^{+2.2}_{-1.8}$)$\times 10^{-15}$
26625 | 27.98310 | 29.68 | FAINT | $\left.\begin{array}[]{l}\\\ \end{array}\right\\}\hskip 2.84544pt$(4.5${}^{+4.7}_{-2.9}$)$\times 10^{-16}$
27833 | 29.47145 | 29.67 | FAINT
26626 | 61.80356 | 16.88 | VFAINT | $\left.\begin{array}[]{l}\\\ \\\ \\\ \\\ \\\ \end{array}\right\\}\hskip 2.84544pt<8.2\times 10^{-16}$
27895 | 62.33516 | 10.94 | VFAINT
27835 | 65.12251 | 13.89 | FAINT
27905 | 65.45429 | 13.89 | FAINT
27906 | 65.79704 | 13.89 | FAINT
27907 | 66.13969 | 13.89 | FAINT
26627 | 198.66317 | 10.74 | VFAINT | $\left.\begin{array}[]{l}\\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \\\ \end{array}\right\\}\hskip 2.84544pt<3.5\times 10^{-16}$
28997 | 198.96634 | 10.74 | VFAINT
28998 | 199.27127 | 11.12 | VFAINT
27837 | 205.89744 | 13.4 | VFAINT
29031 | 206.23509 | 13.3 | VFAINT
29032 | 206.57170 | 13.5 | VFAINT
29034 | 207.96147 | 10.93 | VFAINT
29033 | 208.26639 | 14.39 | VFAINT
27838 | 215.80840 | 16.85 | VFAINT
29054 | 216.19957 | 17.84 | VFAINT
29056 | 216.60163 | 14.39 | VFAINT
28991 | 218.76822 | 9.94 | VFAINT
28999 | 219.12318 | 18.69 | VFAINT
29055 | 219.54352 | 16.85 | VFAINT

###  2.2 UV-optical

A second epoch of HST imaging was obtained on 23/24 October 2023 (the first
was on 17 May 2023, Chrimes et al., 2024), using the WCF3 instrument and six
filters ($F225W,F336W,F555W,F763M,F814W,F845M$). Full details are given in
Table 2. The data are reduced with drizzlepac (Hoffmann et al., 2021), re-
drizzling the charge-transfer-efficiency-corrected $\\_$flc input images with
North oriented up and a final pixel scale of 0.025 arcsec pixel-1
(pixfrac=0.8). Image stamps around the location of AT 2023fhn in epochs 1 and
2 are shown in Figure 1. Visible in the bottom left is the presumed satellite
of the larger spiral to the south (see Figure 3). Both galaxies lie at a
common redshift of $\sim$0.24 (Ho et al., 2023b; Chrimes et al., 2024).

Table 2: All HST data for AT 2023fhn, from program 17238 (PI: Chrimes). Filter, exposure start times (JD-, where is 12:00 UT on 10-APR-2023) and exposure durations texp are given. All observations are with WFC3 in the UVIS channel. Filter | Start date | texp
---|---|---
| JD–2460045 | s
F555W | 36.87666 | 1092
F814W | 36.89272 | 1092
F555W | 196.42824 | 990
F814W | 196.44313 | 1092
F225W | 196.49431 | 1068
F336W | 196.51027 | 1068
F845M | 196.56034 | 990
F763M | 196.57515 | 1068

###  2.3 Radio

We obtained radio observations with the Karl G. Jansky Very Large Array (VLA)
between 22 Apr 2023 and 16 December 2024 (programme SC240143, PI: Chrimes).
Details of the observations are listed in Table 3. The observations were taken
in standard phase-referencing mode using 3C286 as a flux density and bandpass
calibrator, with ICRF J101447.0+230116, FIRST J101644.3+203747, FIRST
J101353.4+244916 and ICRF J095649.8+251516 as complex gain calibrators. The
observations were calibrated using the VLA Calibration Pipeline versions
2023.1.0.124 and 2022.2.0.64 in CASA 6.5.4 and 6.4.1 respectively, with
additional manual flagging. The images were created using the tclean task in
CASA with Briggs weighting with a robust parameter of 1. In the observations
where the source was not detected we quote the upper limit on the flux density
as three times the local RMS. The one exception to this is during the last
epoch (see Table 3) where the synthesized beam (resolution element) was large
and included other sources. In this case we quoted the upper limit as the flux
density at the source location. For the observations where we detected the
target, we fitted the flux density using the imfit task within CASA and
constrained the fit to the synthesized beam.

The observations up to $\sim$12 days post JD-2460045 are already published
(Chrimes et al., 2024) and all produced non-detections. In the $\sim$87–95 day
and $\sim 138$ day epochs we have sufficient data points for fitting a
synchrotron self-absorbed spectrum. The KU band (15 GHz) data point at 138
days has sufficient signal-to-noise to split into 3 (centred on 13, 15 and 17
GHz), as listed in Table 3, increasing the points at $\sim$138 days to 7 (with
6 detections). We fit a self-absorbed synchrotron model to the $\sim$87-95 and
$\sim$138 day epochs in Section 4.4.

Table 3: AT 2023fhn flux densities from our VLA programme (SC240143, PI: Chrimes). Observation start times are listed with respect to JD–2460045 (12:00 on 10-Apr-2023). The quoted uncertainties do not include the systematic uncertainty of 5% on the absolute flux calibration at these frequencies. Upper limits are given as 3 times the local RMS. aThe resolution of the last three observations was lower (as the VLA was in D configuration at the time), so we could not remove contaminating sources at the target location and have consequently listed the upper limit as the flux density at the source location. Start date | Freq. | Bandwidth | texp | Flux Density
---|---|---|---|---
JD–2460045 | GHz | GHz | min. | $\mu\rm{Jy/beam}$
11.80740 | 1.52 | 1.024 | 38 |  $<$130
11.78309 | 3.00 | 2.048 | 32 |  $<$35
11.76507 | 6.00 | 4.096 | 23 |  $<$18
11.74688 | 10.00 | 4.096 | 23 |  $<$18
11.72090 | 15.08 | 6.144 | 35 |  $<$11
11.69229 | 22.00 | 8.192 | 35 |  $<$17
11.66552 | 33.00 | 8.192 | 33 |  $<$25
87.59185 | 1.52 | 1.024 | 39 |  $<$45
87.56657 | 3.00 | 2.048 | 33 | 110$\pm$8
87.54257 | 6.00 | 4.096 | 32 | 128$\pm$5
95.58690 | 10.00 | 4.096 | 31 | 105$\pm$7
95.56438 | 15.00 | 6.144 | 30 | 71$\pm$7
95.52738 | 22.00 | 8.192 | 47 | 60$\pm$10
137.17440 | 1.52 | 1.024 | 39 |  $<$58
137.14178 | 3.00 | 2.048 | 44 | 110$\pm$10
137.10567 | 6.00 | 4.096 | 50 | 221$\pm$5
138.16972 | 10.00 | 4.096 | 42 | 197$\pm$6
138.13664 | 13.00 | 2.050 | 42 | 180$\pm$10
138.13664 | 15.00 | 2.050 | 42 | 160$\pm$10
138.13664 | 16.96 | 2.050 | 42 | 140$\pm$20
249.95139 | 6.00 | 4.096 | 35 |  $<$311a
249.90997 | 10.00 | 4.096 | 57 |  $<$181a
249.86861 | 15.08 | 6.144 | 57 |  $<$125a
Figure 1: F555W and F814W HST/WFC3 image stamps at the location of AT 2023fhn
in the first epoch (May 2023, left) and the second epoch (October 2023,
centre). The right-hand panels show difference images (epoch 1 - epoch 2).
North is up, East is left, and the stamps are 2.5 arcsec on each side.

##  3 Environmental analysis

###  3.1 Local environment

The second epoch of HST imaging presented in this paper allows us to examine
the environment directly underlying the transient after it has faded. As noted
by Chrimes et al. (2024), there is diffuse emission in the vicinity of the
transient. To characterise this faint underlying population, we place 0.2
arcsec (and 0.4 arcsec) apertures at the location of AT 2023fhn in all six
epoch 2 images. The images are aligned with $x$-$y$ shifts using 5 common
point sources in every image, with respect to the location of AT 2023fhn in
the epoch 1 F555W image. The rms of these relative astrometric alignments is
$\sim$5–10 mas, better than the absolute astrometry of the images (which have
been aligned with the Gaia DR3 reference frame), and much smaller than the
aperture size. We perform photometry with photutils, estimating the background
with either the median image background (with medianbackground) or an annulus
(1.5 to 4 times the aperture radius, with pixels values clipped at 3$\sigma$).
The appropriate encircled energy corrections for each filter and aperture are
applied. Magnitudes are then calculated using the photplam and photflam header
keywords111https://hst-docs.stsci.edu/wfc3dhb/chapter-9-wfc3-data-
analysis/9-1-photometry, and are listed in Table 4. The only detections are in
F555W and F814W. To investigate the nature of these detections, we place eight
0.4 arcsec apertures at equal spacing around the location of AT 2023fhn in a
circle of radius 20 pixels (0.5 arcsec). With the F555W filter and median
background subtraction, we have significant detections in 5/8 apertures, with
a mean magnitude of 25.9$\pm$0.6 in these apertures - consistent with the
measurement at the precise location of AT 2023fhn. This demonstrates that the
emission in this area is from an extended, diffuse background, rather than any
significant contribution by residual light from AT 2023fhn. This can also be
seen in Table 4, where the magnitudes calculated with annulus background
subtraction are fainter, since the local background is elevated. Larger
apertures also give brighter magnitudes, despite encircled energy correction
(unlike point sources in the field). We similarly disfavour any significant
contribution from a compact cluster at this specific location, which would
appear as a point source in the image given the physical scale at this
redshift of $\sim$100 pc pixel-1. However, the presence of a globular cluster
(which would favour an IMBH interpretation, e.g., Lützgendorf et al., 2013)
cannot be ruled out, as even the brightest globular clusters would be far
below detection limits at this distance and limiting magnitude (Chrimes et
al., 2024). Shifting the circle of apertures 5 arcsec to the north, well away
from the galaxies, we find non-detections in all eight apertures with a
3$\sigma$ upper limit of 26.7. We therefore conclude that there is extended,
diffuse emission from an underlying stellar population at the location of AT
2023fhn.

We now estimate the age and dust extinction of this underlying population.
First, we correct for the (low) Galactic extinction of $E(B-V)$=0.0254
(Schlafly & Finkbeiner,
2011)222https://irsa.ipac.caltech.edu/applications/DUST/ using the filter
effective wavelengths (Rodrigo et al., 2012; Rodrigo & Solano, 2020) and the
Python extinction package (Barbary, 2016) with a Fitzpatrick (1999) extinction
law and $R_{\rm V}=3.1$. To estimate the age and local (intrinsic) extinction,
we fit the Galactic-extinction corrected $F225W,F336W,F555W$ and $F814W$
photometry to BPASS (Binary Population and Spectral Synthesis v2.1, Eldridge
et al., 2017; Stanway & Eldridge, 2018) single-age spectral templates. These
are constructed by assuming that a stellar population of 106M⊙ is formed
instantaneously, and left to evolve with no further star formation. We use
these simple stellar populations since the limited data available to model
solely the local environment of AT 2023fhn precludes a more complex procedure,
including, for example, the star-formation history (however, see the next
section). A fixed metallicity of half-Solar is adopted ($Z=0.01$ by mass
fraction). We therefore simply fit for the age of the population, the
luminosity (i.e. mass) of the stellar population is then allowed to freely
vary to minimise $\chi^{2}$. Four data points are used ($F225W,F336W,F555W$
and $F814W$) where the upper limits are treated as data points with zero flux
and an uncertainty equal to the flux of the 1$\sigma$ upper limit. We
therefore have 2 fit parameters and 4 data points for 2 degrees of freedom.
Fitting is performed by multiplying the (de-redshifted) filter response curves
(Rodrigo et al., 2012; Rodrigo & Solano, 2020) with the BPASS spectra to
extract fluxes and hence magnitudes from the spectra. These are compared with
the absolute magnitudes in each filter, after correction for a range of
intrinsic extinction values from $A_{\rm V}$=0.0 to 1.0. The intrinsic
extinction correction uses the rest-frame effective wavelength of each filter.
The $F763M$ and $F845M$ filters are not used in this fit since the upper
limits are shallower than the $F555W$ and $F814W$ detections, and so provide
no additional constraints.

The results are shown in Figure 2. The top panel shows the best-fit single-age
BPASS spectrum. The lower panel shows log${}_{10}(\chi^{2})$ across the
parameter space (indicated by the shading). Each pixel represents a unique
combination of $A_{\rm V}$ and a BPASS simple stellar population at a given
age. The 68% and 90% confidence intervals are indicated by white contours
(where the $\Delta\chi^{2}$ intervals are from Avni, 1976).

We also measure the local surface brightness in epoch 2 (in a 0.5 arcsec
radius around AT 2023fhn’s position), giving 25.1 mag arcsec-2 in $F555W$ and
24.65 mag arcsec-2 in $F814W$. This compares well with the 25.2 mag arcsec-2
and 24.6 mag arcsec-2 values from the transient-subtracted images in Epoch 1
(see Chrimes et al., 2024). The $F336W$ surface brightness is 25.76 mag
arcsec-2, which after Galactic extinction correction is 25.27 mag arcsec-2.
The rest-frame central wavelength of $F336W$ is $\sim$2700Å. This allows for a
better comparison with the UV ($u^{\prime}$) surface brightness distribution
for supernova environments, as reported by Kelly & Kirshner (2012) than made
by Chrimes et al. (2024) with $F555W$. The Galactic extinction-corrected
$F336W$ surface brightness is in the faintest $\sim$10% for local supernova
values; this is therefore faint but not unprecedented. We note that supernovae
type IIb are the most likely supernova sub-class to explode in young, but low
surface brightness environments, and are also found at the highest host-
normalised offsets on average (Kelly & Kirshner, 2012).

Table 4: HST magnitudes $m$, and their uncertainties $\delta m$, for the second epoch of AT 2023fhn imaging at $\sim 200$ days (Table 2). In all six filters, two photometry methods are listed - aperture photometry with median background estimation, and aperture photometry with annulus background estimation. Two aperture sizes (and hence enclosed energy corrections) are given in each case. Filter | Method | Bkg. | Aper. | m |  $\delta$m
---|---|---|---|---|---
F225W | photutils | Median | 0.2′′ | ¿26.1 | -
F225W | photutils | Annulus | 0.2′′ | ¿26.1 | -
F225W | photutils | Median | 0.4′′ | ¿25.4 | -
F225W | photutils | Annulus | 0.4′′ | ¿25.5 | -
F336W | photutils | Median | 0.2′′ | ¿26.6 | -
F336W | photutils | Annulus | 0.2′′ | ¿26.6 | -
F336W | photutils | Median | 0.4′′ | ¿25.9 | -
F336W | photutils | Annulus | 0.4′′ | ¿25.9 | -
F555W | photutils | Median | 0.2′′ | 26.9 | 0.2
F555W | photutils | Annulus | 0.2′′ | 27.1 | 0.3
F555W | photutils | Median | 0.4′′ | 25.8 | 0.2
F555W | photutils | Annulus | 0.4′′ | 25.6 | 0.1
F763M | photutils | Median | 0.2′′ | ¿26.0 | -
F763M | photutils | Annulus | 0.2′′ | ¿26.0 | -
F763M | photutils | Median | 0.4′′ | ¿25.3 | -
F763M | photutils | Annulus | 0.4′′ | 25.0 | 0.3
F814W | photutils | Median | 0.2′′ | 26.4 | 0.2
F814W | photutils | Annulus | 0.2′′ | 26.5 | 0.3
F814W | photutils | Median | 0.4′′ | 25.3 | 0.2
F814W | photutils | Annulus | 0.4′′ | 25.2 | 0.2
F845M | photutils | Median | 0.2′′ | ¿25.6 | -
F845M | photutils | Annulus | 0.2′′ | ¿25.6 | -
F845M | photutils | Median | 0.4′′ | ¿24.9 | -
F845M | photutils | Annulus | 0.4′′ | ¿24.9 | -

Figure 2: Epoch 2 HST photometry at the location of AT 2023fhn, corrected for
Galactic extinction, and fit to BPASS single age spectral models while
allowing the (intrinsic) extinction to vary. Upper panel: the best fit single-
age BPASS spectrum, with local extinction applied. Wavelengths are observer
frame. Lower panel: the colourmap corresponds to the fit log10($\chi^{2}$) as
a function of extinction and age. We find a best fitting combination of
age=$16^{+4}_{-6}$ Myr and A${}_{\rm V}=0.1^{+0.6}_{-0.1}$ (uncertainties at
68% confidence, Avni, 1976). The 68% and 90% confidence regions are indicated
by white contour lines.

###  3.2 Global host properties

We next consider how the overall host galaxy properties compare with the local
environment of AT 2023fhn, and how they compare with the hosts of other
LFBOTs. To do this, we perform spectral energy distribution (SED) fitting of
the integrated light of the host. By host, we refer to the spiral and
satellite galaxy together, since their proximity likely results in
interactions (e.g. tidal) and therefore the two galaxies can be considered as
one interacting system. Furthermore, the two galaxies are not spatially
resolved in ground-based imaging (e.g. PanSTARRS), which we used to add
photometric points to the SED.

We attempt to collect as close to 100% of the galaxy light from HST photometry
as possible. We measure the Petrosian radius $R_{\rm petro}$ (Petrosian, 1976)
of the spiral galaxy with the statmorph package (Rodriguez-Gomez et al., 2019,
$\eta=0.2$) and adopt 1.5$R_{\rm petro}$ as a radius that encloses $\sim$100%
of the flux (e.g. Conselice, 2003). We account for the projected ellipticity
and orientation of the galaxy using the ellip and theta outputs. A pixel mask
is produced using these parameters as measured from the $F555W$ image, and
applied to the other HST images, as shown in Figure 3. The flux within the
mask is summed, and background subtraction (as for the local environment
measurements above) uses the sigma-clipped median background, scaled for the
number of pixels in the mask. Repeating the procedure for the satellite galaxy
produces a 1.5$R_{\rm petro}$ pixel mask that lies entirely within the
spiral’s mask. We therefore use spiral pixel mask alone as it captures
$\sim$100% of the flux from both galaxies.

To supplement the HST data we add host photometry from archival catalogues.
For additional optical points we use PanSTARRS data release 2 (Chambers et
al., 2016). We use the catalogued Kron magnitudes (Kron, 1980, in $g$, $r$,
$i$, $z$ and $y$), which capture $\sim$90% of the light of extended sources,
and increase the fluxes by a further 10% to approximate the $\sim$100% flux
value
333https://outerspace.stsci.edu/display/PANSTARRS/PS1+Kron+photometry+of+extended+sources.
The Kron radii for the spiral (4.41, 4.62, 4.36, 3.33 and 2.89 arcsec in
$g,r,i,z,y$ respectively) extend past the position of the satellite in
$g,r,i$, so the system can be considered blended. Effective wavelengths for
these filters are from Tonry et al. (2012). We also add far-UV and near-UV
photometry from GALEX (Martin et al., 2003), plus W1, W2 and W3 detections
from WISE. The spiral and satellite cannot be separated at the spatial
resolution of these surveys, and neither galaxy is detected in 2MASS. The full
list of photometry used to performed SED fitting is provided in Table 5.

To perform SED fitting we use prospector (Leja et al., 2017; Johnson et al.,
2021), which makes use of FSPS (Flexible Stellar Population Synthesis Conroy
et al., 2009; Conroy & Gunn, 2010) and Python-FSPS (Johnson et al., 2023). For
the Markov Chain Monte Carlo (MCMC) implementation we use emcee (Foreman-
Mackey et al., 2013). We again use BPASS (Binary Population and Spectral
Synthesis v2.1, Eldridge et al., 2017; Stanway & Eldridge, 2018) for the
spectral models. Before being passed to prospector, the input photometry is
corrected for Galactic extinction (as described in Section 3.1). We fit four
parameters: the stellar mass $M_{\star}$, intrinsic extinction $A_{\rm V}$,
population age $t_{\rm age}$ and the timescale for an exponentially declining
star-formation history $\tau$. The redshift is fixed at $z=0.238$, and the
luminosity distance at $D_{\rm L}=1192$ Mpc.

We run the MCMC with 128 walkers and 512 iterations; the full list of MCMC
set-up parameters and joint posterior distributions (in the form of a corner
plot) are provided in Appendix A. The maximum a posterior (MAP) spectrum is
shown in Figure 4, with the associated properties from the posterior
distribution listed in Table 6. Thus far, the metallicity $Z$ has been fixed
at half-Solar, based on the approximate mass of $10^{10}$ M⊙ and the mass-
metallicity relation (Tremonti et al., 2004; Gallazzi et al., 2005). A similar
table containing the results when metallicity is allowed to vary is also
provided in Appendix A. In this case, the mass and SFR are similar, such that
fixing $Z$ at a more realistic value does not change our results in a
qualitative sense. In the delayed-$\tau$ model, the current star-formation
rate (SFR) is proportional to $(t/\tau)e^{(-t/\tau)}$. The absolute value is
obtained by normalisation with respect to the mass formed, yielding a SFR of
$\sim$4 M⊙ yr-1. The galaxy pair is therefore dominated by a fairly typical
star-forming spiral, but is perhaps notable for the likely presence of tidal
interactions between the spiral and its satellite. In Figure 5 we plot its
mass versus SFR, comparing with the host galaxies of previous LFBOTs. The
galaxy has a high SFR and mass for LFBOT hosts, lying slightly above average
in terms of specific star formation rate (sSFR), but well below the sSFR of
the host of ZTF 18abvkwla.

Figure 3: HST imaging of the galaxy hosting AT 2023fhn in the six epoch 2 filters. Pixels within 1.5 Rpetro of the spiral galaxy centroid are selected as associated with the host, and given an orange-purple colourmap (see text for details). This region fully encompasses the satellite galaxy. The location of AT 2023fhn is marked with a $+$ sign. The image cutouts are 13 arcsec on each side. North is up and east is left. Table 5: Host galaxy photometry used for SED fitting. All magnitudes are in the AB system, and before Galactic extinction correction. The filter effective wavelengths and Galactic extinction at that wavelength - assuming E(B-V)=0.0254, R${}_{\rm V}=3.1$ and a Fitzpatrick (1999) extinction law - are also listed. We increase the PanSTARRS fluxes by 10% over the values below, as described in the text. Filter | Source | m | err |  $\lambda_{\rm eff}$ [Å] | A($\lambda$)
---|---|---|---|---|---
FUV | GALEX | 20.93 | 0.31 | 1548.85 | 0.20
NUV | GALEX | 20.74 | 0.25 | 2303.37 | 0.22
F225W | HST | 20.60 | 0.05 | 2358.70 | 0.20
F336W | HST | 20.40 | 0.03 | 3359.11 | 0.13
$g$ | PS | 19.70 | 0.01 | 4810.00 | 0.09
F555W | HST | 19.34 | 0.01 | 5235.33 | 0.08
$r$ | PS | 19.17 | 0.01 | 6170.00 | 0.07
$i$ | PS | 18.93 | 0.01 | 7520.00 | 0.05
F763M | HST | 18.93 | 0.01 | 7602.85 | 0.05
F814W | HST | 18.84 | 0.01 | 7954.84 | 0.04
F845M | HST | 18.68 | 0.01 | 8430.20 | 0.04
$z$ | PS | 19.02 | 0.02 | 8660.00 | 0.04
$y$ | PS | 19.00 | 0.04 | 9620.00 | 0.03
W1 | WISE | 18.91 | 0.07 | 33526.00 | 0.00
W2 | WISE | 18.82 | 0.13 | 46028.00 | 0.00
W3 | WISE | 16.92 | 0.38 | 115608.00 | 0.00
Figure 4: Host galaxy photometry and best-fit spectrum from prospector. The model spectrum is red-shifted into the observer frame. A light blue shaded region encloses the 90% confidence interval on the posterior flux distribution at each wavelength. The photometry is from GALEX, PanSTARRS, WISE and HST/WFC3 as listed in Table 5, and is corrected for Galactic extinction with the Python module extinction at the filter effective wavelengths. The corresponding galaxy properties are listed in Table 6.  Table 6: Host galaxy properties derived from prospector SED fitting. The median values from the marginalised posterior distributions are quoted, with uncertainties bounding the 68% confidence interval on each parameter. Host property | Value
---|---
$M_{\star}$ / M⊙ | $(0.93\pm 0.04)\times 10^{10}$
SFR / M⊙ yr-1 | 4.0${}^{+0.9}_{-0.7}$
$A_{{\rm V}}$ | 0.15$\pm 0.07$
$t_{{\rm age}}$/Gyr | 0.95${}^{+0.11}_{-0.09}$
$\tau$/Gyr | 0.26${}^{+0.06}_{-0.04}$
Figure 5: Stellar mass versus SFR for LFBOT host galaxies, including AT
2023fhn. Other LFBOT host data are from Perley et al. (2019, AT 2018cow), Ho
et al. (2020, ZTF 18abvkwla), Coppejans et al. (2020, CSS161010) and Perley et
al. (2021, ZTF 20acigmel). Lines of constant specific star formation rate
(sSFR/yr-1) are drawn in grey. The core-collapse supernova host galaxy sample
of Schulze et al. (2021) is plotted as transparent cyan points.

##  4 Transient emission

###  4.1 UV-optical

We now compare the UV-optical constraints on AT 2023fhn’s light-curve with
previous LFBOTs. All times used in Section 4 are in the rest-frames of the
LFBOTs. Comparison data are corrected for Galactic extinction of $E(B-V)$=0.08
(AT 2018cow, Prentice et al., 2018) and $E(B-V)$=0.07 (ZTF 20acigmel, Perley
et al., 2021), their UV light-curves (in absolute magnitude) are compared with
AT 2023fhn in Figure 6. We fit the light-curve of AT 2018cow in 2 phases,
early ($<200$ d) and late-time, with a fit of the form $M=a\log(t)^{b}+c$. For
the fit to AT 2018cow, we assume that the late-time UV is dominated by
residual transient emission (Sun et al., 2022, 2023; Chen et al., 2023;
Inkenhaag et al., 2023). We shift the AT 2018cow best-fit up in absolute
magnitude such that it lies between the early-time ATLAS $c$-band and FORS2
$u$-band AT 2023fhn detections (Ho et al., 2023b). The extrapolated curve
passes below the late-time HST F225W and F336W upper limits reported in this
work. Another LFBOT with good UV photometric coverage is ZTF 20acigmel, but
here we consider only the early, pre-break phase due to a lack of late-time
constraints. ZTF 20acigmel starts brighter than AT 2018cow and fades faster,
whereas AT 2023fhn is the most luminous LFBOT yet at UV-optical wavelengths. A
final addition to Figure 6 are bands of constant UV absolute magnitude,
corresponding to late-time emission from black holes of different masses in
the tidal disruption event model of Mummery et al. (2024). This model yielded
a black hole mass of $\sim$103 M⊙ for AT 2018cow. Assuming similar evolution,
the HST F336W point source upper limit for AT 2023fhn tentatively constrains
the accreting black hole mass in a TDE interpretation to $\lesssim 10^{5}$ M⊙.

Figure 6: The UV data points for AT 2023fhn, compared with the UV light-curves
of AT 2018cow (Early $u$-band and late-time F222W and F336W, Prentice et al.,
2018; Perley et al., 2019; Inkenhaag et al., 2023) and ZTF 20acigmel (Perley
et al., 2021). A light-curve fit to the AT 2018cow data is increased in
luminosity to intercept the sole early-time AT 2023fhn UV point, the
subsequent F336W limit at $\sim$112 rest-frame days lies just above the
expected UV magnitude at this epoch, assuming identical evolution to the Cow.
A similar fit is made for the early-time ZTF 20acigmel points. Cyan horizontal
bands show the expected UV absolute magnitudes at late times for accretion
discs around intermediate mass black holes of different masses, following a
tidal disruption event (Mummery et al., 2024).

###  4.2 X-ray

Figure 7 shows our X-ray observations of AT 2023fhn, and the X-ray light-
curves of other LFBOTs. The AT 2018cow broken power-law and late-time plateau
fit of Migliori et al. (2024) is also shown. AT 2023fhn is the faintest LFBOT
in X-rays at early times. Assuming a shallow decay initially, similar to AT
2022tsd, ZTF 20acigmel and AT 2018cow, the break time can be - at the latest -
similar to AT 2018cow and ZTF 20acigmel. There appears to be a correlation
between break time and X-ray luminosity, with brighter LFBOTs transitioning to
a steeper decay at later times. Assuming instead that epochs 1 and 2 are on
the same phase of the light-curve, the decay index $n=2.1^{+0.7}_{-0.9}$
(where $L\propto t^{-n}$). Expectations for the X-ray decay rate are $t^{-1}$
(shock power), $t^{-2}$ (magnetar central engine) and $t^{-5/3}$ (fallback,
i.e. a TDE). Overall, the detections and upper-limits are consistent with AT
2023fhn behaving like a fainter version of previous LFBOTs in the X-ray band,
and demonstrates that they can exhibit several orders of magnitude of variety
in their X-ray luminosity.

Figure 7: The X-ray light-curve of AT 2023fhn compared with other LFBOTs. All
data are in the $\sim$0.5-10 keV range, are unabsorbed and from Rivera
Sandoval et al. (2018, AT 2018cow); Kuin et al. (2019, AT 2018cow); Migliori
et al. (2024, AT 2018cow), Coppejans et al. (2020, CSS161010), Bright et al.
(2022, ZTF 20acigmel); Ho et al. (2022, ZTF 20acigmel), Yao et al. (2022, AT
2020mrf) and Matthews et al. (2023, AT 2022tsd). Given the marginal nature of
the second AT 2023fhn measurement, we also plot the 2$\sigma$ upper limit at
this epoch. A broken-power law and late-time plateau interpretation of AT
2018cow’s light-curve is shown by the solid black line (Migliori et al.,
2024).

###  4.3 UV/X-ray ratio

Motivated by the fact that AT 2023fhn appears to be the brightest LFBOT yet at
UV-optical wavelengths, and the faintest in terms of X-ray luminosity, in
Figure 8 we show the ratio of X-ray to UV luminosity for the 3 LFBOTs with
such constraints. The data points for AT 2023fhn take the X-ray detections at
12 and 23 rest-frame days, and the corresponding point on the shifted AT
2018cow light-curve in Figure 6. The uncertainties shown are exclusively from
the X-ray observations. For AT 2018cow, we take the ratio of the X-ray fit of
Migliori et al. (2024) in Figure 7, and our fit to the UV light-curve fit in
Figure 6. Finally, for ZTF 20acigmel we take the ratio of the X-ray luminosity
with the UV light-curve fit at the same time. LFBOTs therefore exhibit at
least $\sim 3$ orders of magnitude in their X-ray/UV luminosity ratio, even at
similar times in their evolution. This is plausibly a viewing angle effect. A
qualitative prediction of tidal disruption models is a trade-off between UV-
optical and X-ray luminosity as a function of viewing angle, where on-axis
angles (which may also be aligned with a beamed outflow) would see a higher
X-ray luminosity (Dai et al., 2018; Hayasaki & Jonker, 2021). Differences in
LX/LUV are also expected for different black hole masses and spins, due to
varying accretion disc formation rates (which in turn affects the delay
betweeen peak X-ray and UV/optical emission, Jonker et al., 2020). However, a
scenario in which the peak X-ray emission is delayed due to a delay in forming
the inner accretion disc is hard to reconcile with the energetics and
(variability) timescales of LFBOT emission, which demands energy input from a
central engine and therefore active accretion (e.g. Ho et al., 2019; Margutti
et al., 2019). Alternatively, the range of $L_{\rm x}$/$L_{\rm UV}$ could
reflect differences in the circumstellar media, which we investigate in the
following Section.

Figure 8: The ratio of X-ray to UV luminosity for LFBOTs AT 2023fhn, AT
2018cow and ZTF 20acigmel. The AT 2023fhn points use the dashed orange line in
Figure 6 and the two Chandra X-ray detections (errorbars reflect the X-ray
uncertainties only). The black curve is the ratio of the Migliori et al.
(2024) X-ray light-curve fit (see the solid black line, Figure 7) and a broken
power-law fit to the UV observations (the solid black line in Figure 6). The
small $k$-corrections are neglected in this comparison. The evolution past 200
days (drawn as a dashed line) is highly uncertain due to the sole X-ray
detection. The ZTFacigmel data are from Ho et al. (2022); Bright et al.
(2022), where we have taken the ratio of X-ray points and the power-law fit to
the ZTFacigmel UV-light-curve in Figure 6. The uncertainties on these points
again solely reflect the X-ray measurement uncertainties.

###  4.4 Radio

Assuming that the radio emission is synchrotron-dominated with self-absorption
- as we will see, the radio SED of AT 2023fhn is consistent with this - and
that the peak of the SED occurs at the synchtrotron self-absorption (SSA)
frequency, we can estimate several shock parameters, and properties of the
circumstellar medium. We follow the synchrotron self-absorption model of
Chevalier (1998) (see also Soderberg et al., 2005). Adopting this framework
for AT 2023fhn is reasonable since this best fits other LFBOTs studied so far
(based on the brightness temperature, which precludes thermal emission, and
the spectral shape, e.g. Margutti et al., 2019; Coppejans et al., 2020; Ho et
al., 2020; Nayana & Chandra, 2021; Ho et al., 2022; Yao et al., 2022; Bright
et al., 2022).

We fit the radio spectrum at $\sim$90 and $\sim$138 days ($\sim$70 and
$\sim$110 rest-frame days) following Chevalier (1998); Granot & Sari (2002);
Chevalier & Fransson (2006). At a given time $t$ the radio SED has the form,

$F(\nu)=F_{\rm pk}\left[\left(\frac{\nu}{\nu_{\rm
pk}}\right)^{-s\beta_{1}}+\left(\frac{\nu}{\nu_{\rm
pk}}\right)^{-s\beta_{2}}\right]^{-\frac{1}{s}},$ (1)

where $F(\nu)$ is the flux density, $F_{\rm pk}$ is the flux at the peak
(break) frequency $\nu_{\rm pk}$ where the optically thick and thin power laws
intersect, $s$ is a smoothing factor and $\beta_{1}$ and $\beta_{2}$ are
spectral indices in the optically thick and thin regimes, respectively. In our
case the cooling frequency $\nu_{\rm c}$ lies at higher frequencies than
probed by our observations ($\sim$400-800 GHz), where $\nu_{\rm c}$ is given
by $18\pi m_{e}ce)/(t^{2}\sigma_{t}^{2}B^{3})$ (DeMarchi et al., 2022). We
therefore expect $F(\nu)\propto\nu^{-(p-1)/2}$ in the optically thin regime,
where $p$ is the power law index of the electron energy distribution in the
shock (i.e. the number $N$ of electrons with Lorentz factor $\gamma_{\rm e}$
goes as $N(\gamma_{\rm e})\propto\gamma_{\rm e}^{-p}$).

Using the scipy curve_fit function, and working with rest-frame times and
central frequencies throughout this section, we fit equation 1 to the $\sim$90
day and $\sim$138 day (observer frame) data. At 90 days we have 6 data points
(5 detections, 1 upper limit, we combine the 87 and 95 day data for this
epoch), and at 138 days we have 7 data points (6 detections, 1 upper limit).
There are 5 parameters to fit: $F_{\rm pk}$, $\nu_{\rm pk}$, $\beta_{1}$,
$\beta_{2}$ and $s$. The best-fit values for these parameters and their
uncertainties are listed in Table 7. The optically-thin spectral index of
-0.59 (138 days) yields an electron energy spectral index of $\sim$2.2, which
is relatively shallow - 2.5 is expected from theory, while values closer to
$\sim$3 are often measured in gamma-ray bursts, tidal disruption events and
supernovae (e.g. Chevalier & Fransson, 2006; Cendes et al., 2023). Values from
other LFBOTs are also in the range $\sim$2–3 (Margutti et al., 2019; Ho et
al., 2020; Coppejans et al., 2020; Yao et al., 2022; Bright et al., 2022).

The peak flux Fpk and (rest-frame) frequency at the peak flux $\nu_{\rm pk}$
(at the intersection of the power-laws, rather than the fitted peak) allow us
to estimate the radius of the shock, circumstellar density at that radius, and
the CSM surface density parameter $A_{\star}\propto\dot{M}/v_{w}$ (see
DeMarchi et al., 2022, for a detailed description of the modelling
assumptions). Following the formulism of Chevalier (1998) (see also Chevalier
& Fransson 2006; DeMarchi et al. 2022; Bright et al. 2022), we first have the
shock radius $R_{\rm p}$, given by,

$R_{\rm p}=4\times 10^{14}\left(\frac{\epsilon_{\rm e}}{\epsilon_{\rm
B}}\right)^{\frac{-1}{19}}\left(\frac{f}{0.5}\right)^{\frac{-1}{19}}\left(\frac{F_{\rm
pk}}{{\rm(1+z)\,mJy}}\right)^{\frac{9}{19}}\left(\frac{D_{\theta}}{{\rm
Mpc}}\right)^{\frac{18}{19}}\left(\frac{\nu_{\rm pk}}{5\leavevmode\nobreak\
{\rm GHz}}\right)^{-1}{\rm cm},$ (2)

where Dθ is the angular diameter distance, and $\epsilon_{e}$ and
$\epsilon_{B}$ are the fraction of the shock energy in electrons and in the
magnetic field, respectively. The average shock velocity can then be
calculated as $R_{\rm p}/t_{\rm obs}=\Gamma\beta c$, where $\beta=v/c$,
$\Gamma$ is the Lorentz factor and $t_{\rm obs}$ is the rest-frame observation
time. Next we have, for the internal magnetic field $B$,

$B=1.1\left(\frac{\epsilon_{\rm e}}{\epsilon_{\rm
B}}\right)^{\frac{-4}{19}}\left(\frac{f}{0.5}\right)^{\frac{-4}{19}}\left(\frac{F_{\rm
pk}}{{\rm(1+z)\,mJy}}\right)^{\frac{-2}{19}}\left(\frac{D_{\theta}}{{\rm
Mpc}}\right)^{\frac{-4}{19}}\left(\frac{\nu_{\rm pk}}{5\leavevmode\nobreak\
{\rm GHz}}\right){\rm G}$ (3)

and for the wind density (the mass loss rate $\dot{M}$ over the wind
velocity),

$\frac{\dot{M}}{v_{\rm w}}\left(\frac{1000\leavevmode\nobreak\ {\rm
kms^{-1}}}{10^{-4}\leavevmode\nobreak\ M_{\odot}yr^{-1}}\right)=2.5\times
10^{-5}\left(\frac{1}{\epsilon_{\rm B}}\right)\left(\frac{\epsilon_{\rm
e}}{\epsilon_{\rm
B}}\right)^{\frac{-8}{19}}\left(\frac{f}{0.5}\right)^{\frac{-8}{19}}\times\\\
\left(\frac{F_{\rm
pk}}{{\rm(1+z)\,Jy}}\right)^{\frac{-4}{19}}\left(\frac{D_{\theta}}{{\rm
Mpc}}\right)^{\frac{-8}{19}}\left(\frac{\nu_{\rm pk}}{5\leavevmode\nobreak\
{\rm GHz}}\right)^{2}\left(\frac{t_{\rm pk}}{{\rm days}}\right)^{2}$ (4)

Under the assumption that the CSM is dominated by fully ionised hydrogen, the
electron number density can be related to $\dot{M}/v_{w}$ by
$n_{e}=\dot{M}/(4\pi m_{p}r^{2}v_{w})$ \- where $m_{p}$ is the proton mass -
so that,

$n_{\rm e}=1.02418\left(\frac{1}{\epsilon_{\rm
B}}\right)\left(\frac{\epsilon_{\rm e}}{\epsilon_{\rm
B}}\right)^{\frac{-6}{19}}\left(\frac{f}{0.5}\right)^{\frac{-6}{19}}\times\\\
\left(\frac{F_{\rm
pk}}{{\rm(1+z)\,Jy}}\right)^{\frac{-22}{19}}\left(\frac{D_{\theta}}{{\rm
Mpc}}\right)^{\frac{-44}{19}}\left(\frac{\nu_{\rm pk}}{5\leavevmode\nobreak\
{\rm GHz}}\right)^{4}\left(\frac{t_{\rm pk}}{{\rm days}}\right)^{2}{\rm
cm}^{-3}$ (5)

Additionally we have, for the internal shock energy $U=U_{\rm B}/\epsilon_{\rm
B}$,

$U=1.859\times 10^{46}\left(\frac{1}{\epsilon_{\rm
B}}\right)\left(\frac{\epsilon_{\rm e}}{\epsilon_{\rm
B}}\right)^{\frac{-11}{19}}\left(\frac{f}{0.5}\right)^{\frac{8}{19}}\times\\\
\left(\frac{F_{\rm
pk}}{{\rm(1+z)\,Jy}}\right)^{\frac{23}{19}}\left(\frac{D_{\theta}}{{\rm
Mpc}}\right)^{\frac{46}{19}}\left(\frac{\nu_{\rm pk}}{5\leavevmode\nobreak\
{\rm GHz}}\right)^{-1}{\rm erg}$ (6)

We assume equipartition ($\epsilon_{e}$=$\epsilon_{B}$=1/3), where the
magnetic energy density, the energy density in electrons and the energy
density in protons contribute equally as destinations for the converted
kinetic energy in the shock. We further assume $f=0.5$ for the filling factor.
If the emission region is modelled as a disc of radius $R$ and thickness $S$
on the sky, whose volume is $\pi R^{2}S$, an equivalent spherical volume can
be given by $4/3\pi R^{3}$. The filling factor is the fraction of this
equivalent spherical volume producing emission (Chevalier, 1998).

We list the inferred properties of AT 2023fhn’s blast-wave in Table 7. Results
for the fiducial parameters of $\epsilon_{e}=0.1$ and $\epsilon_{B}=0.01$ are
also listed. These properties are compared with other LFBOTs in Figures 9, 10
and 11. In LFBOTs the expanding blast-wave typically shows a SSA spectrum that
decreases in peak flux and frequency over time. However we note that AT2023fhn
shows an increase in peak flux between $\sim 90$ and $\sim 138$ days post
explosion. A similar increase was seen in CSS161010 between 69 and 99 days
post explosion (Coppejans et al., 2020). This could potentially be caused by
an increase in density, or inhomogeneities in the CSM, but we are not able to
test this scenario given our weak constraints on the SSA peak at $\sim 90$
days post explosion.

Finally, we calculate a dimensionless normalisation of the wind density
parameter $A_{\star}\propto n_{e}r^{2}\propto\dot{M}/v_{w}$ (Chevalier & Li,
2000),

$A_{\star}=\frac{\dot{M}}{(5\times 10^{11}\leavevmode\nobreak\ {\rm
g\leavevmode\nobreak\ cm^{-1}})\times 4\pi v_{w}}$ (7)

where $A_{\star}=1$ for a Wolf-Rayet-like wind with $\dot{M}=10^{-5}$M⊙yr-1
and $v_{w}=1000$km s-1. From our best fits to the radio data, we derive that
AT 2023fhn at $\sim$70–110 rest-frame days has $A_{\star}\sim 1$ ($\sim
0.1\times 10^{-4}$ M⊙ yr-1 for $v_{\rm w}$ = 1000 km s-1). This mass loss rate
is consistent with that of Wolf-Rayet stars. As shown in Figure 11, this
density is also consistent with that of the other LFBOTs. The constraints on
the synchrotron self-absorption peak at $\sim 90$ days post explosion were
unfortunately insufficient to constrain the density profile of the CSM around
AT2023fhn.

Figure 9: Radio observations of AT 2023fhn (see Table 3) placed in the context
of other LFBOTs. Upper limits from NOEMA and the VLA as reported by Ho et al.
(2023a) and Ho (2023) are also shown. Left: radio SED for AT 2023fhn, with a
broken-power law fit to the $t=138$ day (grey line) and $t=90$ day (green
line) data. Data point rest-frame times are indicated by the colourbar. The
90% confidence regions on the fits are shown by light grey/green shading.
Right: radio light-curve for AT 2023fhn (central frequencies indicated by the
colourbar) and other LFBOTs. The 10 GHz AT 2023fhn detections are connected by
a dashed orange line, to aid the eye in comparing with other LFBOTs. Data for
the other LFBOTs, all at (10$\pm$2) GHz, are from Ho et al. (2019, AT
2018cow); Margutti et al. (2019, AT 2018cow), Ho et al. (2020, ZTF 18abvkwla),
Coppejans et al. (2020, CSS161010), Bright et al. (2022), Ho et al. (2022, ZTF
20 acigmel) and Yao et al. (2022, AT 2020mrf).

Figure 10: Left: the product of rest-time $\Delta t$ and the rest-frame peak
frequency ${\nu}_{\rm pk}$ at that time, versus the peak radio spectral
luminosity $L_{\rm\theta\nu,pk}=L_{\rm\nu,pk}/(1+z)^{3}$, with lines of
constant $\dot{M}/V_{w}$ (in units of 10-4 M⊙ yr-1 / 1000 km s-1) and lower
limits on the blast-wave velocity shown. Both AT 2023fhn epochs are shown, we
note that constraints on the later point (138 days) are stronger and the
parameters at this epoch better constrained. All comparison data points adopt
$\epsilon_{e}=\epsilon_{B}=1/3$. Right: lower limits on the average blast-wave
velocity (blast-wave radius over the rest-frame time) in units of $c$ versus
the internal energy of the shock $U=U_{B}/\epsilon_{B}$. Other LFBOT data are
taken from Ho et al. (2019, AT 2018cow); Margutti et al. (2019, AT 2018cow);
Nayana & Chandra (2021, AT 2018cow), Ho et al. (2020, ZTF 18abvkwla),
Coppejans et al. (2020, CSS161010), Bright et al. (2022);Ho et al. (2022, ZTF
20 acigmel) and Yao et al. (2022, AT 2020mrf). The mildly-relativistic regime
is shaded. We have scaled the Bright et al. (2022) ZTF 20 acigmel point
following equations 2 and 6 to align with our assumption of equipartition.
Figure 11: Circumstellar density ne at the radius of the shock Rp for AT
2023fhn and previous LFBOTs. The densities for ZTF 20 acigmel (Bright et al.,
2022, Table 6) have been reduced by a factor $\sim$16 to align them with the
equipartition $\epsilon_{e}=\epsilon_{B}=1/3$ assumption used for all other
measurements (for reference, see how equation 5 scales with $\epsilon_{e}$ and
$\epsilon_{B}$). As in Figure 10, both AT 2023fhn epochs are shown, where the
best constraints are from the epoch at 138 days. Other LBFOT results are from
Ho et al. (2019, AT 2018cow); Nayana & Chandra (2021, AT 2018cow), Ho et al.
(2020, ZTF 18abvkwla), Coppejans et al. (2020, CSS161010), Bright et al.
(2022, ZTF 20 acigmel, their fit to ne(r) is adopted, shown as a red
solid/dash line either side of a possible break) and Yao et al. (2022, AT
2020mrf). Lines of constant $\dot{M}$ are shown for $v_{w}=1000$ km s-1. Note
that due to different assumptions in the modelling, the densities and/or mass
loss rates derived between different authors and objects can differ by up to a
factor 5 (DeMarchi et al., 2022). Table 7: Summary of radio SED fit results
using the $\sim$90 day data, left, and $\sim$138 day data, right, with
equation 1. Above the single solid lines we list the broken power-law fit
parameters. Below, we list the inferred event properties at each epoch under
the synchrotron blastwave model as described in Section 4.4, assuming
equipartition ($\epsilon_{e}$=$\epsilon_{B}$=1/3). The uncertainties on the
event properties are statistical only, and are underestimated due to the
presence of systematic errors arising from fixed values of $f$, $\epsilon_{\rm
e}$ and $\epsilon_{\rm B}$. We also allowed $s$ to vary between 0 and 1, with
$s=1$ providing the best-fit in each case. The (rest-frame) fit parameters
$\nu_{\rm pk}$ and Lν,pk are defined at the intersection point of the two
power laws (Chevalier, 1998). Below the double lines we give parameter values
calculated with $\epsilon_{e}=0.1$ and $\epsilon_{B}=0.01$ (note that only the
results with $\epsilon_{e}$=$\epsilon_{B}$=1/3 are plotted in the relevant
figures).

|  $t\sim 90$ days |
---|---|---
Parameter | Unit | Value
$\nu_{\rm pk}$ | GHz | 4$\pm$4
$L_{\rm\nu,pk}$ | erg s-1 Hz-1 | (4${}^{+5}_{-4}$)$\times 10^{29}$
$\beta_{1}$ | – | 3.0$\pm$0.7
$\beta_{2}$ | – | -0.66$\pm$0.04
$R_{\rm p}$ |  $10^{17}$ cm | 1.3$\pm$0.7
$v/c=\Gamma\beta$ | – | 0.7$\pm$0.4
$\dot{M}$/vw | 10-4 M⊙ yr-1 / 1000 km s-1 | 0.08$\pm 0.01$
$n_{e}$ | cm-3 | 21${}^{+33}_{-14}$
$B$ | G | 0.24$\pm 0.02$
$U$ |  $10^{49}$ erg | 2.2${}^{+4.3}_{-1.4}$
$R_{\rm p}$ |  $10^{17}$ cm | 1.2${}^{+0.6}_{-0.4}$
$v/c=\Gamma\beta$ | – | 0.6${}^{+0.3}_{-0.2}$
$\dot{M}$/vw | 10-4 M⊙ yr-1 / 1000 km s-1 | 1.0$\pm 0.2$
$n_{e}$ | cm-3 | (3.4${}^{+5.3}_{-2.2}$)$\times 10^{2}$
$B$ | G | 0.15$\pm 0.01$
$U$ |  $10^{49}$ erg | 19${}^{+37}_{-12}$

|  $t\sim 138$ days |
---|---|---
Parameter | Unit | Value
$\nu_{\rm pk}$ | GHz | 5$\pm$3
$L_{\rm\nu,pk}$ | erg s-1 Hz-1 | (6$\pm$4)$\times 10^{29}$
$\beta_{1}$ | – | 2.81$\pm$0.02
$\beta_{2}$ | – | -0.6$\pm$0.2
$R_{\rm p}$ |  $10^{17}$ cm | 1.2${}^{+0.3}_{-0.5}$
$v/c=\Gamma\beta$ | – | 0.4${}^{+0.1}_{-0.2}$
$\dot{M}$/vw | 10-4 M⊙ yr-1 / 1000 km s-1 | 0.32${}^{+0.10}_{-0.03}$
$n_{e}$ | cm-3 | (1.0${}^{+3.2}_{-0.5}$)$\times 10^{2}$
$B$ | G | 0.31${}^{+0.04}_{-0.02}$
$U$ |  $10^{49}$ erg | 2.8${}^{+2.6}_{-2.2}$
$R_{\rm p}$ |  $10^{17}$ cm | 1.1${}^{+0.3}_{-0.5}$
$v/c=\Gamma\beta$ | – | 0.4${}^{+0.1}_{-0.2}$
$\dot{M}$/vw | 10-4 M⊙ yr-1 / 1000 km s-1 | 4.0${}^{+1.2}_{-0.4}$
$n_{e}$ | cm-3 | (1.6${}^{+5.2}_{-0.7}$)$\times 10^{3}$
$B$ | G | 0.19${}^{+0.03}_{-0.01}$
$U$ |  $10^{49}$ erg | 25${}^{+23}_{-20}$

##  5 Discussion

In this Section, we discuss the host galaxy and derived properties of AT
2023fhn in the context of the other LFBOTs discovered thus far.

The host of AT 2023fhn, taking the spiral and satellite as one interacting
system, is broadly consistent with the host galaxies of core-collapse
supernovae, and slightly above four other LFBOT hosts in terms of specific
star formation rate (although below the host of ZTF 18abvkwla). The host
offset and faint, diffuse emission at the transient location (see Section 3.1)
are consistent with the tail of the core-collapse supernova distribution (see
also Chrimes et al., 2024). While the local and broader environment is
consistent with a core-collapse origin, it is interesting to consider whether
the high sSFR is related to tidal interaction between the spiral and satellite
galaxy. Such interactions may be associated with an elevated tidal disrupted
event (TDE) rate, which show a bias towards occurrence in post-starburst
galaxies and galaxies undergoing interactions/mergers (French et al., 2016).
The non-nuclear location of AT 2023fhn - at high offset from both the spiral
and satellite - is difficult to explain in such a scenario (Chrimes et al.,
2024). On the other hand, the measured optical magnitudes at the location of
AT 2023fhn (see Table 4) allow a contribution from a point source with
absolute magnitude as bright as $\sim$-14. A significant contribution from a
point source at the location of AT 2023fhn is disfavoured (as the precise
location has similar brightness to its immediate surroundings, as explained in
Section 3.1), but the presence of a globular cluster or ultra-compact dwarf
galaxy - which may host massive black holes (e.g. Seth et al., 2014) \- cannot
be ruled out. The presence of such an undetected cluster or ultra compact
dwarf galaxy would be consistent with the upper limit on the black hole mass
inferred from our late-time UV observations of $\lesssim 10^{5}$ M⊙ (Mummery
et al., 2024), given black hole - host galaxy/cluster mass relations (Kormendy
& Ho, 2013; Lützgendorf et al., 2013).

The UV-optical, X-ray and radio evolution of AT 2023fhn is broadly similar to
other LFBOTs. Notably, however, the X-ray to UV luminosity ratio of AT 2023fhn
is an order of magnitude lower than AT 2018cow at similar times, and up to 3
orders of magnitude lower than ZTF 20acigmel. As we show in Section 4.4, it is
difficult to attribute this variety to differences in the circumstellar medium
density or blast-wave propagation, as AT 2023fhn has a blast-wave velocity,
energy and CSM comparable with other LFBOTs. This is consistent with the
evidence from other LFBOTs thus far that the X-ray emission arises from a
distinct mechanism, namely central engine activity. AT 2023fhn is only the
third LFBOT with a mildly relativistic outflow ($v=0.4^{+0.1}_{-0.2}c$), in
common with CSS161010 and ZTF 18abvkwla, demonstrating that the blast-wave is
engine-driven. As can be seen in Figure 11, all LFBOTs with sufficient
constraints from radio observations thus far have a wind-like (in the sense
that density decreases with distance), albeit not $r^{-2}$, circumstellar
density profile. This suggests the CSM was produced by the progenitor system
(i.e. through winds), rather than the explosion occurring in a pre-existing
dense ISM, which would produce a flat density profile.

An alternative explanation for the variety in UV/X-ray ratios is the viewing
angle, where the asymmetric outflow and accretion disc are being viewed from
different angles. In this interpretation, the viewing angle to AT 2018cow was
closer to perpendicular to the plane of the accretion disc (although not
exactly perpendicular, Margutti et al., 2019). This conclusion was also
reached by Maund et al. (2023) based on the high polarization (and possibly
for AT 2022tsd, given the observation of late-time optical flares Ho et al.,
2023c). AT 2023fhn, meanwhile, would have been seen close to edge-on, well
off-axis from any asymmetric outflow (e.g. from a choked jet) and with the
inner accretion disc obscured (where choked jets and/or the inner disc
dominates the X-ray luminosity, Jonker et al., 2020). The effect of viewing
angle as an explanation for different LFBOT X-ray luminosities has also been
posited by Metzger (2022) and Migliori et al. (2024).

With the fundamental LFBOT requirement of a low 56Ni ejecta mass, and magnetar
central engines struggling to explain all aspects of LFBOT phenomenology (e.g.
the late-time emission in AT2018cow, Chen et al., 2023; Li et al., 2024),
constraints on the possible progenitor models are tightening. IMBH TDE models
remain plausible, if a dense wind-like CSM can be produced (e.g. by the
ejection of stripped mass during the disruption event). However, the star-
forming nature of the host galaxy population, and the locations of LFBOTs
within them, likely disfavour such an interpretation. Other plausible models
include the delayed merger of black holes and Wolf-Rayet stars (Metzger,
2022), and failed supernovae (Quataert et al., 2019). In AT 2023fhn, the mass-
loss wind parameter A${}_{\star}\sim 1$ \- higher than many radio loud
supernovae (Chevalier & Fransson, 2006) and collapsar GRBs (Gompertz et al.,
2018; Chrimes et al., 2022). Such a dense circumstellar environment likely
require a short-lived evolutionary stage with enhanced mass loss, for example
pre-explosion winds from a blue supergiant or Wolf-Rayet star (Margutti et
al., 2019).

##  6 Conclusions

We list here our conclusions about the nature of AT 2023fhn and its place in
the context of other LFBOTs and extragalactic transients more generally,

  1. 1.

Although relatively isolated compared with other LFBOTs and indeed most core-
collapse supernovae, AT 2023fhn is otherwise consistent with a core-collapse
event, associated with a typical star-forming galaxy and located in a young
(albeit diffuse) stellar population.

  2. 2.

The low X-ray to UV luminosity ratio demonstrates orders of magnitude of
variety in this parameter among LFBOTs, which may be indicative of differences
in viewing angle. In this interpretation, the relatively low X-ray luminosity
of AT 2023fhn is due to an edge-on viewing angle, such that the inner
accretion disc is obscured and we are well off-axis from any choked
jet/asymmetric outflow.

  3. 3.

The CSM properties are similar to previous LFBOTs, and are indicative of a
dense surrounding medium. Given the wind-like ne density profiles of other
LFBOTs, and our ne measurements of AT 2023fhn which continue this trend, it is
likely that the dense CSM was produced by wind-like mass-loss from the
progenitor system itself (rather than the progenitor exploding in a pre-
existing dense ISM).

  4. 4.

An IMBH TDE interpretation remains possible, only if there exists a pre-
existing dense CSM or if the early stages of the tidal disruption produce such
an environment. The host galaxy is likely undergoing tidal interactions, which
may elevate the TDE rate. While the non-nuclear location and host properties
rate favour a core-collapse origin, the explosion of AT 2023fhn in an
undetected globular cluster or ultra-compact dwarf galaxy cannot be ruled out.

Despite mounting evidence, the origin of LFBOTs is still ambiguous. Two
approaches will elucidate which of the proposed scenarios contribute to the
LFBOT population. The first is to grow the sample, enabling statistically
robust comparisons of offsets and host galaxy properties to be made with other
classes of transient. This will be possible with the advent of new wide-field,
deep sky surveys such as those performed by the Vera Rubin observatory (Ivezić
et al., 2019). The second is to perform detailed studies of future local
events - like AT2018cow - across the electromagnetic spectrum. Such events
offer the best opportunity to search for underlying clusters, monitor the
long-term evolution, understand the detailed emission physics, and ultimately,
determine their progenitors. Although there is much progress still to be made,
based on AT 2023fhn and the growing population of LFBOTs, we deem a massive
star progenitor with strong winds but low ejecta mass the most likely
scenario. This favours models such as black hole/Wolf-Rayet mergers or failed
supernovae.

###### Acknowledgements.

A.A.C. acknowledges support from the European Space Agency (ESA) as an ESA
Research Fellow. P.G.J. has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (Grant agreement No. 101095973). P.J.G. is partly supported by NRF
SARChI Grant 111692.
Observations analysed in this work were taken by the NASA/ESA Hubble Space
Telescope under program 17238. This research has made use of software provided
by the Chandra X-ray Center (CXC) in the application of the CIAO package
(Fruscione et al., 2006). The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc.
Computing facilities were provided by the Scientific Computing Research
Technology Platform of the University of Warwick. This research has made use
of the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project
funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00.
The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.
This publication makes use of data products from the Wide-field Infrared
Survey Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

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##  Appendix A SED fitting MCMC results

In this appendix we provide the joint posterior parameter distributions for
the host galaxy of AT 2023fhn, in the form of a corner plot (Figure 12)
including stellar mass, metallicity, extinction, population age and timescale
for an exponentially declining star formation history. These are provided as
outputs from emcee SED-fitting using prospector. For the MCMC initial values
(and flat priors) we use A${}_{\rm V}=0.05$ (0¡AV¡2), t${}_{\rm age}=1$ Gyr
and M$=10^{10}$ M⊙ ($10^{6}$¡M/M⊙¡$10^{12}$), with a flat prior on $\tau$ of
0.1¡$\tau$/Gyr¡100. For our fiducial run, the redshift is fixed at $z=0.238$
and the metallicity at $Z=0.5Z_{\odot}$. Also provided in Table 8 are results
when $Z$ is allowed to vary a free parameter.

Figure 12: emcee output from prospector for the host of AT 2023fhn. Produced using the corner.py code (Foreman-Mackey, 2016) via prospector. The metallicity is fixed at $0.5$Z⊙. Table 8: Host galaxy properties derived from prospector SED fitting, as in Table 6, but allowing the metallicity $Z$ to vary. Host property | Value
---|---
M⋆ / M⊙ | $(1.21^{+0.07}_{-0.05})\times 10^{10}$
SFR / M⊙ yr-1 | 7.3${}^{+1.2}_{-1.0}$
Z/Z⊙ | 0.08${}^{+0.02}_{-0.02}$
AV | 0.40${}^{+0.06}_{-0.06}$
tage/Gyr | 1.8${}^{+0.5}_{-0.4}$
$\tau$/Gyr | 1.1${}^{+1.2}_{-0.6}$