methodsMethods References

# An assessment of the Association Between a Fast Radio Burst and Binary
Neutron Star Merger

Alexandra Moroianu∗1,2 Linqing Wen∗1,2 Clancy W. James3 Shunke Ai4,5 Manoj
Kovalam1,2 Fiona Panther1,2 Bing Zhang4,5

###### Abstract

Fast radio bursts (FRBs) are mysterious bright millisecond-duration radio
bursts at cosmological distances[1, 2]. While young magnetars have been put
forward as the leading source candidate[3, 4, 5, 6, 7], recent observations
suggest there may be multiple FRB progenitor classes[2, 8]. It has long been
theorised that FRBs could be emitted from compact object mergers[9] —
cataclysmic events such as binary neutron star (BNS) mergers that may be
detectable in gravitational waves (GWs) by the ground-based Laser
Interferometer Gravitational Wave Observatory (LIGO)[10] and Virgo[11]. Here
we report a potential coincidence between the only BNS merger event
GW190425[12] out of 21 GW sources detected during the first six months of
LIGO-Virgo’s 3rd Science Run and a bright, non-repeating FRB event, FRB
20190425A[2], from a search using public GW and CHIME FRB data. The FRB is
located within the GW’s sky localization area, occurred 2.5 hours after the GW
event, and has a dispersion measure consistent with the distance inferred from
GW parameter estimation[13]. The chance probability of a coincidence between
unrelated FRB and GW events in the databases is estimated to be $0.0052$
($2.8\,\sigma$). We estimate the chance of CHIME detecting such an event to
range from 0.4% for a beam-centre detection to 68% if a bright burst is
detectable in a far sidelobe. This potential association is consistent with
the theory[14] that the BNS merger leaves behind a supramassive, highly
magnetized compact object, which collapses to form a black hole after losing
angular momentum due to spindown and makes an FRB through ejecting the
magnetosphere[15]. If such a physical association is established, the equation
of state of the post-merger compact object is likely stiff, with a Tolman-
Oppenheimer-Volkoff non-spinning maximum mass[16] $M_{\rm
TOV}>2.63_{-0.23}^{+0.39}M_{\odot}$ for a neutron star remnant, or $M_{\rm
TOV}>2.31_{-0.08}^{+0.24}M_{\odot}$ for a quark star remnant.

Australian Research Council Centre of Excellence for Gravitational Wave
Discovery (OzGrav)

Department of Physics, University of Western Australia, Crawley WA 6009,
Australia

International Centre for Radio Astronomy Research, Curtin University, Bentley,
WA 6102, Australia

Nevada Center for Astrophysics, University of Nevada, Las Vegas, NV 89154, USA

Department of Physics and Astronomy, University of Nevada, Las Vegas, NV
89154, USA

To date, more than 600 FRBs have been detected at radio frequencies between
$110\,\mathrm{MHz}$ and $8\,\mathrm{GHz}$[17, 18]. The high all-sky rate[2]
and event rate density[19, 20] of FRBs, combined with the fact that some FRB
sources emit repeated bursts[21, 2], suggest that the majority of FRBs are not
produced from cataclysmic channels such as compact object mergers. However, a
small sub-population of FRBs associated with cataclysmic events would be
difficult to detect in these analyses[2], and be consistent with cataclysmic
event rates [19]. Furthermore, extensive follow-up studies have failed to
detect repeating radiation from some nearby FRBs[1, 22]. There exist several
theories that predict the association of an FRB with a GW event due to compact
binary coalescence between two neutron stars, a neutron star and a black hole,
or even two charged black holes[9]. In particular, binary neutron star (BNS)
mergers have long been theorised to emit FRB-like signals before[23, 24],
during[25] or after[14] the merger. With the publicly available GW catalogue
GWTC-2[13] and the newly released first FRB catalogue[2] from the Canadian
Hydrogen Intensity Mapping Experiment FRB project (CHIME/FRB), it is possible
to test these theories by searching for GW-FRB associations. We conduct a
search for GW-FRB coincidences using CHIME/FRB’s first FRB catalogue
containing 535 new FRB sources[2] (observed July 2018 - July 2019), 171 of
which overlap with the first half of LIGO’s $3^{\rm rd}$ Science Run (O3a:
April 1, 2019 - October 1, 2019)[13]. Our search time window is chosen to be
asymmetrical and 26 hours wide, encompassing FRBs that occur up to 2 hours
before a GW signal[25] and 24 hours after[14] (see Methods). A GW-FRB pair is
considered to be coincident in time if an FRB falls within the time window of
a GW signal. CHIME/FRB localization[2] is accurate on the order of arcminutes,
more precise than even the best GW localization of tens of square degrees[26].
Therefore, we consider a GW-FRB pair spatially coincident if the FRB lies
within the 90% credible interval[13] of a candidate GW’s localization (see
Methods).

We find an apparently non-repeating FRB 20190425A[2] temporally and spatially
coincident with a GW merger event: GW190425[12, 13]. GW190425 was observed on
April 25, 2019 08:18:05 UTC by LIGO Livingston (LIGO Hanford was offline) with
a false alarm rate of $\rm FAR=1/69,000\ \mathrm{yr^{-1}}$. There was no
significant detection made by Virgo due to its lower sensitivity, which helps
constrain the sky localization of the event. GW190425 is a BNS merger event,
however the remnant mass of the system in the source frame, $M_{\rm tot}^{\rm
final}=3.23^{+0.33}_{-0.11}\ M_{\odot}$, is significantly larger than that
predicted by known Galactic BNS systems[13]. FRB 20190425A is a curiously
bright (see Methods) radio transient with fluence $31.6\pm 4.2\ \mathrm{Jy\
ms}$ (assuming a beam-centre detection) and burst width $3.799\pm 0.002\cdot
10^{-4}\ \mathrm{s}$. It has a broadband emission across CHIME’s 400–800 MHz
bandwidth, and a single-peaked morphology, which is observed in 30% of the
CHIME FRB population, and is associated with non-repeating FRBs. In contrast,
repeating FRBs typically exhibit narrow-band structure[2]. It also has an
unusually low dispersion measure (DM) of $128.2\ \mathrm{pc\ cm^{-3}}$,
indicating an origin within $z<0.0394$, assuming DM originates only from the
Milky Way and the intergalactic medium[27]. It was observed 2.5 hours after
GW190425 at 10:46:33 UTC at a peak frequency of 591.8 MHz, and localized to
J2000 celestial coordinates RA = $255.72\pm 0.14^{\circ}$, DEC = $21.52\pm
0.18^{\circ}$. This places it in the 66.7% credible interval of GW190425’s
refined GWTC-2 skymap[13] (Figure 1). Parameter estimation[13] localized the
BNS merger event to redshift $z=0.03^{+0.01}_{-0.02}$. This is within the
upper limit ($z<0.0394$) specified by FRB 20190425A’s DM (see Methods), making
the two signals coincident within the error margins of their distances.

Figure 1: Temporal and spatial coincidence of GW190425 and FRB 20190425A. Top
left: LIGO Livingston signal to noise ratio (SNR) of GW190425 (see Methods).
Top right: flux (in Jy) of FRB 20190425A[2], occurring $2.5\ \rm hours$ after
the merger. Bottom: Sky direction of FRB 20190425A (cyan) and the localization
of GW190425[13] (90% contour indicated by black line). Figure 2: The expected
dispersion measure (DM) distribution inferred from GW190425, compared to non-
repeating CHIME FRBs. Blue solid line: the probability distribution of DM
after subtracting the contribution from the Milky Way’s interstellar medium
(DM-DMMWISM; see Methods). Orange dashed line: the observed value for FRB
20190425A, compared to the number of non-repeating CHIME FRBs ($N_{\rm FRB}$,
green histogram).

To quantify the likelihood of this association being entirely coincidental, we
estimate the probability of chance coincidence of GW190425 and FRB20190425A
assuming that FRB and GW detections are independent. Evidence against this
hypothesis comes from three sources: the spatial, temporal, and DM
coincidence. We exclude repeating FRBs in this analysis (see Methods). The
likelihood of a chance temporal coincidence between GW190425 and FRB 20190425A
($P_{\rm T}$) is taken to be the probability of CHIME randomly detecting an
FRB in a 2.5 hour stretch of time. We estimate a CHIME FRB detection rate of
1.93 per day around the time of GW190425, leading to a Poisson probability of
$P_{\rm T}=0.18$. We define $P_{\rm S}$ to be the probability that a random
CHIME FRB would be detected during this 2.5 hour interval with equal to or
higher likelihood in the GW190425 skymap than FRB 20190425A (i.e. within the
66.7% credible interval). Using the estimated declination dependence of
CHIME’s exposure[2], we estimate $P_{\rm S}=0.265$ (see Methods). If we
instead use our initial temporal (26 hr time window) and spatial (90% credible
interval) selection criteria, we find 0.88 ($P_{\rm T}$) and 0.15 ($P_{\rm
S}$) respectively. The probability of an FRB originating at redshift $z$
having a dispersion measure DM has been estimated using a sample of localized
FRBs[27]. We produce the expected DM probability distribution for the
published redshift posterior distribution[12] of GW190425. We find that FRB
20190425A lies in the 46% credible interval of GW190425’s DM probability
distribution. Only one of 473 other FRBs exhibits a DM with a more-likely
value (Figure 2). We thus find $P_{\rm DM}$, the chance that a random CHIME
FRB would have a DM with an equal or better match to expectations, to be
$2/474\approx 0.004$.

CHIME has shown that the temporal, spatial and DM distributions of FRBs are
independent[28], except for a potential correlation[29] between FRBs with DM
$\sim$ 800 pc cm-3 and large-scale structure at $z\sim 0.4$. We use $P_{\rm
T}P_{\rm S}P_{\rm DM}=0.18\cdot 0.265\cdot 0.004=1.9\cdot 10^{-4}$ as evidence
against the null hypothesis of a chance coincidence. The chance probability of
finding an FRB with smaller product $P_{\rm T}P_{\rm S}P_{\rm DM}$, i.e. the
p-value, is $0.0052$ (see Methods). Note the close proximity of this FRB in
time, sky direction and distance, as implied by DM measurements, to GW190425
makes this association more significant than the random chance of finding any
FRBs within the search windows used for initial discovery (13.5% probability).
Of further interest, GW190425-FRB 20190425A is the only GW-FRB pair that
survived our time-spatial coincidence criteria and it is linked to the only
BNS event out of the 21 GW sources detected. This encourages us to consider a
potential astrophysical association between GW190425 and FRB 20191425A.

We search for a host galaxy inside the reported error ellipse of FRB
20190425A’s central localization (see Methods). We identify one candidate in
the NASA Extragalactic Database (NED)111The NASA/IPAC Extragalactic Database
(NED) is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology. within a redshift range
$0.001<z<0.08$ consistent with the BNS merger redshift range: UGC 10667
(Figure 3). This galaxy has a redshift consistent with the BNS merger and the
FRB DM. UGC 10667 has an offset of 5.05 arcminutes from the optimal FRB
location and a redshift of $z=0.03136\pm 0.00009$. The expected number of
galaxies[30] within the search volume is $N_{\mathrm{gals}}\sim 0.173$ (see
Methods) assuming a galaxy density of $\rho_{\mathrm{gals}}=2.35\cdot
10^{-3}\,\mathrm{Mpc}^{-3}$ and a maximum luminosity distance of
$d_{\mathrm{L}}=255.85\,\mathrm{Mpc}$. Therefore, to investigate the
association, we encourage follow-up observations of UGC 10667 to search for
evidence of the merger event, such as the afterglow emission of the ejecta in
the broad band, especially in the radio band at sub-GHz frequencies[31, 32].

Figure 3: Potential host association for GW190425-FRB 20190425A. We
investigate hosts within an error ellipse defined by the 1-$\sigma$
uncertainties in RA ($\pm 0.14^{\circ}$) and DEC ($\pm 0.18^{\circ}$) centered
on the optimal FRB location derived by CHIME[2] (red ellipse). Redshifts of
the identified extragalactic objects are listed in Methods. UGC 10667 (orange
cross) is the only host with a redshift consistent with the redshift derived
for the GW source. Background image: DSS2-red
(http://archive.eso.org/dss/dss).

Though we cannot definitively assign the potential GW-FRB association to a
single theory, it is consistent with the GW, short gamma-ray burst (sGRB) and
FRB association theory invoking the collapse of a post-BNS-merger
magnetar[14]. The FRB generation mechanism is the so-called “blitzar”
mechanism[15], which has been confirmed through numerical simulations[33].
Within this scenario, the 2.5 hour delay time between the FRB and the GW event
is the survival time of the supramassive neutron star before collapsing into a
black hole[14], which is consistent with the expected delay timescale range
for a supramassive magnetar both in theory and in observational data (see
Methods). The chance of CHIME detecting such a single burst within its
$1.3^{\circ}$–$2.5^{\circ}$ wide primary beam is 0.4–0.8%, increasing to 14%
when allowing for a detection in the far sidelobes (see Methods). The duration
of the FRB is of the order of light crossing time of the ejected magnetosphere
of the collapsing supramassive neutron star, which is of the order of its spin
period. This is consistent with the $\sim$ millisecond duration of FRB
20190425A. As an initially rapidly rotating supramassive neutron star
collapses to a black hole after losing angular momentum, the total ejected
electromagnetic (EM) energy[14, 33] is $E_{\rm EM}\sim 1.7\cdot 10^{44}\ {\rm
erg}\ (B/10^{14}\,\mathrm{Gauss})^{2}(R_{\rm NS}/10\,{\rm km})^{3}$, where $B$
and $R_{\rm NS}$ correspond to the surface magnetic field and the radius of
the neutron star, respectively. We calculate the FRB’s total isotropic radio
emission energy as $E_{\mathrm{FRB,iso}}=3.72\cdot 10^{38}\,\mathrm{erg}$
using the measured fluence of FRB 20190425A ($3.2\cdot
10^{-28}\,\mathrm{J\,m^{-2}}\cdot 400\,\mathrm{MHz}$) and the most probable
luminosity distance ($156\,\mathrm{Mpc}$) of GW190425. The true energy of the
emitter should be $E_{\mathrm{FRB,iso}}f_{b}\eta_{r}^{-1}$, where $f_{b}\leq
1$ is the beaming factor and $\eta_{r}$ is the radio emission efficiency. For
the blitzar FRB model, the EM energy injection is essentially isotropic[15,
33], so $f_{b}\sim 1$. This implies $\eta_{r}\sim 2\cdot 10^{-6}$, similar to
the reported value for the Galactic FRB 200428 (ref. [4, 5, 6, 7]). BNS
mergers eject dense neutron-rich material that could prevent the escape of
coherent radio emission. For an FRB to be observed following the merger, the
line of sight needs to be cleared by a sGRB jet[14]. However, the sGRB does
not need to be bright enough to be detected by current gamma-ray telescopes.
For example, a sGRB with the brightness of GRB 170817A would be able to clear
the ejecta and escape detection at the distance of $156\,\mathrm{Mpc}$ (ref.
[34, 35]). We note that an excess of gamma-rays was detected 0.5–5.9 s after
GW190425 by the International Gamma-Ray Astrophysics Laboratory (INTEGRAL)
using the SPI-ACS subsystem. This was reported as a candidate sGRB of marginal
significance associated with GW190425 by two independent analyses[36, 37].
Both the localization of the sGRB reported by INTEGRAL, and the non-detection
by FERMI,[37] is consistent with the FRB and GW association.

If confirmed, the astrophysical association between FRB 20190425A and GW190425
can constrain the poorly known equation of state (EoS) of the post-merger
compact object. GW parameter estimation reveals that the gravitational masses
of the two merger components in the source frame are
$M_{1}=2.03^{+0.58}_{-0.34}\ M_{\odot}$ and $M_{2}=1.35^{+0.26}_{-0.26}\
M_{\odot}$[13], with the final total mass of the merger product $M_{\rm
tot}^{\rm final}=3.23^{+0.33}_{-0.11}\ M_{\odot}$
(https://dcc.ligo.org/LIGO-P2000223/public). Assuming a uniformly rotating
neutron star for the merger remnant, we derive the final gravitational mass
$M_{\rm rem}=3.16^{+0.40}_{-0.24}\ M_{\odot}$ (see Methods), consistent with
the final total mass derived from the GW data. There is a universal maximum
mass ($M_{\rm TOV})$ that a non-rotating neutron or quark star can support
against gravitational collapse into a black hole[38, 39]. This depends on the
uncertain neutron star EoS, and is poorly constrained by data[40, 41, 42]. A
supramassive neutron star remnant can support a higher mass with an
enhancement factor up to $M_{\rm rem}/M_{\rm TOV}\sim 1.2$ for uniform
rotation[43, 38, 39]. If GW190425 produced a spin-supported supramassive
neutron star remnant, this constrains $M_{\rm TOV}>2.63^{+0.39}_{-0.23}\
M_{\odot}$. In addition, requiring that the remnant subsequently collapses
places an upper limit of $M_{\rm TOV}<M_{\rm
rem}/1.046=3.02^{+0.42}_{-0.25}\,\mathrm{M_{\odot}}$ (see Methods). Our
constraints on $M_{\rm TOV}$ are at the high end of, but still consistent
with, constraints derived from observations of GW170817 and X-ray emission of
Galactic pulsars (Figure 4, upper panel) [41, 40]. Given the high-mass, high-
pressure environment of a violent merger, quark deconfinement might occur for
the merger remnant[44, 45], making the enhancement factor as large as 1.4
(ref. [46]). Assuming $M_{\mathrm{rem}}=M_{\rm tot}^{\rm final}$, we find
$2.31_{-0.08}^{+0.24}\ M_{\odot}<M_{\rm TOV}<3.23^{+0.33}_{-0.11}\ M_{\odot}$,
consistent with existing constraints for quark star models[42] (Figure 4,
lower panel).

Figure 4: Constraints on the Tolman-Oppenheimer-Volkoff non-spinning maximum
mass ($M_{\rm TOV}$) for neutron stars (upper panel) and quark stars (lower
panel). Given the derived remnant mass $M_{\rm rem}$ of GW190425, the required
$M_{\rm rem}/M_{\rm TOV}$ enhancement factor as a function of $M_{\rm TOV}$ is
drawn as the black solid curve with the two associated dashed curves denoting
the error range. The maximum enhancement factor can be up to $\sim 1.2$ and
$\sim 1.4$ for a uniformly rotating neutron star[43, 38, 39] and quark
star[46], respectively. These are shown as the blue solid band in both panels
(the width of the band accommodates the possible range of different EoSs). The
minimum enhancement factor for a uniformly rotating star is $\sim 1.05$ for
neutron stars[39], and we assume $1$ for quark stars as the most conservative
limit, which are denoted as red bands in both panels. The allowed range of
$M_{\rm TOV}$ given a GW190425/FRB 20190425A association is derived from the
intersections of the colored bands and slanted curves; this is shown in dark
(light) gray shading when using the central value (including error ranges) of
$M_{\rm rem}$. Published constraints on the distribution of $M_{\rm TOV}$ are
presented as colored dotted lines[40, 42, 41] for comparison, with the
relevant probability density scale marked on the right axis.

Our constraints on $M_{\rm TOV}$ indicate that mergers with lower component
masses such as GW170817 (and its association with GRB 170817A)[47] would
produce a much longer-lived supramassive or stable neutron star. The late-time
X-ray rebrightening of the GW170817 remnant is consistent with the existence
of such a long-lived remnant [48, 49]. These mergers may produce FRBs that
repeat over a period of time much longer than 2.5 hours if the magnetar-FRB
mechanism applies. This then implies that repeating FRBs could be produced
from old stellar populations, such as repeating FRB 20200120E in a globular
cluster in M81[50, 8]. Since the rate density of BNS mergers is much smaller
than the inferred rate density of FRBs, this channel alone cannot account for
the FRB 20190425A-like FRBs in the CHIME sample. We encourage wide-field radio
observations concurrent with future GW observing runs in order to further test
our proposed GW–FRB association, and the use of FRB localisation data to
identify potential hosts galaxies to guide searches for a multiwavelength
counterpart.

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##  1 Methods

###  1.1 Search Method

We search for coincidences between GW signals[13] and published CHIME FRBs[2],
taking into account all existing theoretical models for potential GW-FRB
associations[23, 25, 14, wang2016]zhang2020. Our initial search considers
coincidence in time and sky direction, and aims to identify potentially
interesting events for further analysis — distance and dispersion measure are
considered only in the combined chance probability calculationAlex2021thesis.

#### Time

Our search time window is chosen to be asymmetrical and 26 hours wide,
encompassing FRBs that occur up to 2 hours before a GW signal and 24 hours
after. This covers pre-merger emission theories such as magnetospheric
interactions[23, wang2016]zhang2016 and magnetic braking[25], and post-merger
emission theories such as magnetar collapse[14] (note this theory relates only
to BNS merger events). We source our GW data from the published GW catalog
GWTC-2 available at the time of writing[13] and CHIME FRBs from the CHIME/FRB
Public Database (https://www.chime-frb.ca/catalog). Our GW sample consists of
39 events detected by LIGO and Virgo during the O3a observing run (April 1,
2019 – October 1, 2019) and 536 FRBs — 474 of which are apparent non-repeaters
— published in CHIME Catalog 1[2]. Within our sample, 21 GW events and 171
(150 non-repeating) FRBs have overlapping observing windows and are selected
to search for temporal coincidence. A GW and FRB are considered to be
coincident in time if the FRB lies within the designated 26-hr time window of
a GW, and this is found by simply iterating over the GPS times of the two
signals. Any signals that are not coincident in time are cut, and the
remaining candidates are screened for coincidence in sky direction.

#### Sky Direction

The accuracy of GW localization is mainly determined by the measured signal
arrival time between detectors, as well as the relative signal amplitude at
each detector[wen2010, fairhurst2011, klimenko2011, pankow2018]. As a result,
it is largely dependent on the number and geographical separation of
interferometers that successfully detect a signal. Bayesian methods are used
to map the sky direction of a GW source as a posterior probability
distribution on the skysinger2016, with a ‘credible interval’ value being
assigned to each RA and DEC coordinate. We obtain these credible interval
values from the published GWTC-2 data[13]. Note a smaller credible level value
indicates closer proximity to the optimal valuesivia2006. The current
sensitivities of the Advanced LIGO and Virgo network are able to localize GW
signals to sky areas of tens of square degrees[26] for confident detections by
all three interferometers. CHIME FRBs are localized using beam model
predictions with errors on the order of arcminutes[2]. Therefore, for our sky
direction cut, we consider a GW-FRB pair spatially coincident if the best-
fitting FRB coordinates lie within the 90% percent credible interval of
candidate GW signals. This is done using the find_greedy_credible_levels
function of the ligo.skymap.postprocess.util moduleligoskymap.

###  1.2 Search Results

Our search found $12$ out of $21$ ($\sim 57\%$) GW events coincident in time
with at least one CHIME FRB. This high fraction is not surprising considering
the high rate of CHIME FRB detections (see “Chance Probability Derivation”
section). One GW event initially included in GWTC-2 that was temporally
coincident with two CHIME FRBs — GW190424_180648 — has since been redacted due
to its significance being reduced upon further re-analysis and is not included
in any updated GWTC event lists (https://www.gw-openscience.org/GWTC-2.1).
Thus, we eliminate this candidate coincidence from the spatial search. Of the
remaining GW-FRB pairs, only one candidate coincidence passed the sky
direction cut: FRB 20190425A - GW190425. Remarkably, this is also the only BNS
event detected during O3a.

###  1.3 Chance Probability Derivation

Given the wide time window we are searching over, the high detection rate of
CHIME FRBs and the poor localization of GW events, random coincidences in time
and sky direction are expected. Furthermore, since the relation between
dispersion measure (DM) and redshift $z$ for FRBs shows large fluctuations[27]
— and due to the uncertainty in $z$ inferred from GW190425 itself — we have
not placed any a priori cuts on the predicted DM values from the estimated
luminosity distance of GW190425. Nonetheless, FRBs arriving closer in time,
from a sky direction consistent with the GW event localization, and with DMs
consistent with the inferred GW event distance given the ionized matter
content of the Universe, will present greater evidence against such a chance
association. We derive a joint probability of chance association by combining
probabilities of random temporal, spatial and DM (or distance) coincidences
defined as $P_{\rm T}$, $P_{\rm S}$, and $P_{\rm DM}$, respectively. As non-
repeating FRBs best suit compact object merger theories, we choose to analyse
the distributions of non-repeating CHIME FRBs only, though a conservative
value is also calculated using all CHIME FRBs (i.e. including repeaters).
Details of the calculation are below.

#### $P_{\rm T}$

The likelihood of a chance temporal coincidence, $P_{\rm T}$, is the
probability of CHIME randomly detecting an FRB in the 2.5 hour post-merger, as
per the blitzar scenario. GW190425 was the only BNS event detected during the
overlap of O3a and CHIME Catalog 1 — see P-Value Calculation for calculations
considering other scenarios, e.g. BH–BH mergers. CHIME’s operationality was
not constant throughout O3a, during which CHIME’s FRB detection efficiency was
affected by scheduled maintenance and unscheduled outages[2]. In particular,
the detection rate reduces for a short period in the days after GW190425. As a
result, we cannot assume a uniform distribution of CHIME FRB detections. To
derive a more accurate value of the rate of FRBs ($R_{\rm FRB}$) around the
time of GW190425, we group CHIME FRBs into 5-day bins, and use the time-
averaged number of detections within a 30-day period (see Extended Data Figure
5) to find $R_{\rm FRB}$. Thus we average over variability in CHIME
sensitivity on small timescales. The resulting rates are 1.93 FRBs per day for
non-repeaters, and 2.03 per day when including repeaters. The number of FRBs
expected to fall within a 2.5 hour time window is then $2.5\cdot 1.93/24=0.20$
for non-repeaters and $2.5\cdot 2.03/24=0.21$ for our conservative value
considering all CHIME FRBs.

Figure 5: CHIME FRB detection rates. Number $N_{\rm FRB}$ of all (blue
histogram) and non-repeating (orange histogram) CHIME FRBs per 5 days. Average
rate during the period surrounding GW190425 (dashed black line) for all and
non-repeating FRBs shown by the blue and red lines, respectively.

The number of once-off FRB detections in any given time period $T$ will follow
a Poissonian distribution with expectation value $\lambda=TR_{\rm FRB}\approx
0.20$ for a 2.5 hour window. The probability $P_{\rm T}$ to observe a random
CHIME non-repeating FRB with a tighter time coincidence than FRB 20190425A is
then given by:

$\displaystyle P_{\rm T}=1-\exp(-\lambda)\approx 0.18.$ (1)

for non-repeating FRBs. The periodic and/or bursty activity periods for
repeating FRBs will make the time distribution from these sources non-
PoissonianCHIME2020_periodic,Rajwade_121102_repetitions. Ignoring the non-
Poissonian nature of repeating FRBs, and using $\lambda\approx 0.21$ for the
coincidence window, produces a conservative $P_{\rm T}=0.19$.

If instead we consider only our search time window of $T=26$ hr, the expected
rate $\lambda=2.1$, and hence $P_{\rm T}=0.88$.

#### $P_{\rm S}$

We define $P_{\rm S}$ to be the probability that a random CHIME FRB would be
detected at a location with equal to or higher likelihood in the GW190425
skymap than FRB 20190425A (i.e. within the 66.7% credible interval). This is a
function of GW190425’s refined skymapabbott2021, weighted by the exposure time
of CHIME at each coordinate. This can be written as:

$\displaystyle P_{\rm S}$ $\displaystyle=$
$\displaystyle\int_{\Omega_{x}}E(\Omega)d\Omega,$ (2)

where $\Omega$ is a general 2D sky coordinate, $\Omega_{x}$ is the 66.7%
credible region and $E(\Omega)$ is the relative likelihood (‘exposure’) of
seeing an FRB at sky position $\Omega$.

CHIME’s instantaneous exposure is a function of its primary beamshape and
CHIME’s location at a latitude of $49^{\circ}19^{\prime}13^{\prime\prime}.08$
North[2]. We ignore declination dependent fluctuations due to the placement of
the synthesized beams, which are on scales much smaller (${\mathcal{O}}\sim
0.1^{\circ}$) than variations in the GW190425 skymap. We also approximate the
instantaneous coverage in local azimuth angle to be very small, which is valid
at the declinations considered here. Therefore, any background FRB detected in
the [0,2.5] hour window after GW190425 — i.e. the 2.5 hour window before FRB
20190425A — will necessarily fall in the RA ($\alpha$) range
$218.22^{\circ}\leq\alpha\leq 255.72^{\circ}$. This method implicitly accounts
for the favourable alignment of the LIGO and CHIME antenna patterns due to
their nearby geographical location, which causes the GW190425 skymap to
significantly overlap with the sky area covered by CHIME’s primary beam within
the 2.5 hr time window.

The CHIME/FRB Collaboration use a sophisticated pulse-injection method —
accounting for beamshape effects — to calculate the exposure $E(\delta)$ to an
FRB as a function of declination $\delta$ [4]. This exposure time is equal to
the detection probability per square degree to within a normalisation factor,
and is split into ‘upper’ and ‘lower’ transit curves representing sky regions
viewed above and below the Northern pole. The un-normalized exposure,
$E_{u/l}^{\prime}(\delta)$, is modelled by manually fitting a spline to the
upper ‘u’ and lower ‘l’ transit curves (Figure 5 in Ref. [2]) of this
function. The normalization constant, $C$, is then derived by integrating
$E^{\prime}(\Omega)$ over all declinations and the RA range of interest using
the upper transit curves, and the RA range offset by 12 hr for the lower
transit curves, i.e.

$\displaystyle C=\int_{218.22^{\circ}\leq\alpha\leq
255.72^{\circ}}E_{u}^{\prime}(\delta)d\Omega+\int_{38.22^{\circ}\leq\alpha\leq
75.72^{\circ}}E_{l}^{\prime}(\delta)d\Omega\approx 1658$ (3)

Using our derived value for C, we then integrate the normalized exposure
function, $E_{u/l}(\Omega)=E_{u/l}^{\prime}(\delta)/C$, over the 66.7%
credible sky area in the range $218.22^{\circ}\leq\alpha\leq 255.72^{\circ}$
($38.22^{\circ}\leq\alpha\leq 75.72^{\circ}$) for the upper (lower) transit
respectively as per Eq. (2) to find the total probability. This produces
$P_{\rm S}=0.265$. As a simple check of this method, we also took the optimal
measured sky positions of all non-repeating CHIME FRBs, and find that of the
56 in this RA range, 17 of them (30%) lie within the credible interval. If we
instead randomise the RA of all non-repeating CHIME FRBs uniformly over the RA
range, we find that 29.4% lie within the 66.7% credible sky area of GW190425’s
localization; while shuffling FRB RA values in the CHIME catalog with respect
to DEC finds 28.8% lie in this interval. We attribute the excess beyond our
estimates to be random fluctuations of the observed RA,DEC of FRBs compared to
expectations.

If we instead consider an FRB uniformly distributed in time over our [-2,+24]
hr time window (for which $P_{\rm T}=0.88)$, we find $P_{S}=0.154$ for the 90%
likelihood region. Thus the total chance of an event passing our initial
selection criteria is $P_{\rm pass}=$13.5%.

We observe that the distribution of CHIME FRBs has been extensively analysed
for deviations from a simple declination dependent sensitivity[28], with the
only observed anisotropy not due to $E(\delta)$ being a potential correlation
between FRBs with DM $\sim$ 800 pc cm-3 and large-scale structure at $z\sim
0.4$ [29]. The spatial scales of such structure are small compared to the
variation in the GW190425 skymap, and the distances involved are much larger
than those relevant to GW190425, so we ignore this here.

###  1.4 P-value calculation

We use the product $P_{\rm T}P_{\rm S}P_{\rm DM}$ as evidence against our null
hypothesis, $H_{0}$, of a purely chance association. To estimate the
probability of obtaining an equally small product under $H_{0}$ (i.e. the
p-value), we consider the 88% probability of observing an FRB in the time
range [-2,24] hr about the time of GW190425. We use a uniform time
distribution, with RAs located at the centre of the CHIME beam, and DECs
distributed according to CHIME’s exposure. We calculate $P_{\rm S}P_{\rm DM}$
for all such FRBs, rejecting those outside the 90% credible area. Sampling
$P_{\rm DM}$ uniformly from $0$ to $1$ allows us to calculate the probability
of observing a value of $P_{\rm T}P_{\rm S}P_{\rm DM}<1.9\cdot 10^{-4}$ under
$H_{0}$. We find a p-value of 0.0052, i.e. the significance of this event is
$2.8\,\sigma$.

BNS are the most commonly proposed merger scenario for FRB progenitors [9,
LVKchime2022]. However, pre-merger emission from the inspiral of binaries
involving a charged black hole has also been proposedZhang2016bbh. In such a
scenario, the possibility of a CHIME FRB occurring during the [-2,0] hr time
window prior to the other 20 GW events should be considered as a trial factor.
For this calculation, we use the mean CHIME FRB detection rate of 1.62
FRBs/day during the overlap period between O3 and the CHIME catalogue (138
once-off FRBs in 85 days), for an expected number of 2.7 coincident FRBs.
Using the GWTC 2.1 skymaps, and the same methods to calculate $P_{S}$ above,
we find that 0.41 of these would also be expected to pass our spatial
selection criteria. Compared to the 13.5% chance of a background event passing
these criteria for GW190425, this effectively counts as three extra trials.
Thus if this scenario is considered equally plausible — which it is not, due
to the incredibly large required charge ($3.3\times 10^{21}$ C M/M⊙) on the
BHs — our p-value should be raised to 0.021, i.e. 2.3$\sigma$.

#### Notes on GW190425 Localization

The sky localization of GW190425 is poorly constrained due to it being
detected significantly in only a single detector. FRB 20190425A lies within
the 66.7% credible interval for the most recently published GWTC-2 skymap for
GW190425[13] (used in our main analysis). The FRB sky direction is also
largely consistent with all skymaps available for the GW event at various
stages of its discovery (Extended Data Table 1). It has a better consistency
with the initial online rapid Bayestar localizationsinger2016; using this
skymap results in a 50% lower sky coincidence probability ($P_{S}$) for a
random spatial coincidence than the GWTC-2 result. Our FRB, however, is less
consistent with the online LALInference skymaplalinference. Using this
LALInference skymap results in a larger $P_{S}$, by 32%. The GWTC-2 skymap is
obtained using cleaned data and a better estimation of the noise level, while
the initial Bayestar and LALInference skymaps are obtained using the available
online data around the time of the detection. Therefore we conclude that
$P_{S}=0.265$.

Table 1: Credible interval that FRB 20190425A lies in for each of the published skymaps for GW190425, and corresponding probabilities for coincidence in sky direction ($P_{S}$, see text). All skymaps were sourced from https://gracedb.ligo.org/superevents/S190425z/view/.  Localization | Credible Interval | $P_{S}$ | Date Published
---|---|---|---
Bayestar | 25.0% | 0.14 | Apr 2019
LALInference | 90.2% | 0.35 | Apr 2019
Updated Superevent | 67.6% | 0.21 | Jul 2020
GWTC-2 | 66.7% | 0.265 | Oct 2020

#### $P_{\rm DM}$

An FRB produced at a given redshift, $z$, will have a likelihood distribution
$P({\rm DM|z})$ of dispersion measures, DM. The DM is a measure of the column
density of free electrons, $n_{e}$, along the line of sight $\ell$ from the
FRB source to the observer, in units of pc cm-3. Accounting for the redshift
of an extragalactic object, it is defined as

${\rm DM}=\int\frac{n_{e}(\ell)}{1+z}\ d\ell.$ (4)

The DM of extragalactic FRBs can be characterised in multiple ways. Here, we
use four components: two from the Milky Way, being its interstellar medium
(MWISM) and halo (MWhalo), and two extragalactic contributions, from the
intergalactic medium (IGM), and the host galaxy (host), two of which depend on
redshift $z$:

${\rm DM}(z)={\rm DM}_{\rm MW}+{\rm DM}_{\rm EG}(z)={\rm DM}_{\rm MWISM}+{\rm
DM}_{\rm MWhalo}+{\rm DM}_{\rm IGM}(z)+\frac{{\rm DM}_{\rm host}}{1+z}.$ (5)

We observe that in the CHIME Catalog 1 data, quoted ‘extragalactic’ values for
${\rm DM}_{\rm EG}$ include ${\rm DM}_{\rm MWhalo}$, i.e. ${\rm DM}_{\rm
EG}={\rm DM}-{\rm DM}_{\rm MWISM}$. The contribution from the ISM, ${\rm
DM}_{\rm MWISM}$, can be estimated using various electron density models, e.g.
NE2001cordes2002, YMW16yao2017, or YT20yamasaki2020, giving 48.79, 38.8 and
49.0 pc cm-3 respectively for FRB 20190425A. Such models can suffer from over-
fitting however, and may have poor predictive powerSchnitzeler2012DM. ${\rm
DM}_{\rm MWhalo}$ is uncertain — lower limits can be placed using pulsars from
the Large Magellanic CloudShannon2018, while upper limits can be placed using
nearby FRBsCHIME_M81_2021. ModellingProchaskaZheng2019 suggests ranges from
50–80 pc cm-3.

The extragalactic contributions, ${\rm DM}_{\rm IGM}+{\rm DM}_{\rm host}$,
have been estimated by fits to five localized FRBs[27]. Both contributions are
expected to have tails towards high DM values, from the few that intersect
many or dense clumps of matter along the line-of-sight, and/or originate from
dense regions within their host. Therefore DM values only poorly constrain the
distance to an FRB. However, a robust upper limit, $z_{\rm max}$, can be
estimated by setting ${\rm DM}_{\rm host}=0$, taking the lowest of model
values for $\rm DM_{\rm MWISM}$ (38.8 pc cm-3) and ${\rm DM}_{\rm MWhalo}$ (50
pc cm-3), and using the approximate relationInoue2004 in the nearby Universe
of $\rm DM_{\rm IGM}=1000\,{\rm pc\,cm}^{-3}\,z$. Such an estimate is
consistent with the nearby low-DM FRB discovered in M81[50]. Applying this to
FRB 20190425A produces $z_{\rm max}=0.0394$, or $\sim$180 MPc using standard
cosmologyade2016,Wright_2006_cosmology.

Deriving a realistic DM–z relation using the model described in [27] requires
considering variations in the component DM contributions. We use the NE2001
model for ${\rm DM}_{\rm MWISM}$, and assume ${\rm DM}_{\rm MWhalo}=50$ pc
cm-3. In this model, errors in ${\rm DM}_{\rm MWISM}$ and ${\rm DM}_{\rm
MWhalo}$ are absorbed into the distributions for ${\rm DM}_{\rm IGM}$ and
${\rm DM}_{\rm host}$. In their model, ${\rm DM}_{\rm IGM}$ is a function of
the total baryon content of the Universe, $\Omega_{b}$, and a ‘feedback’
parameter F governing how clumped those baryons are[27]. This DM model is also
explained in James2021, and implemented in publicly available Python
codefrb,zdm.

The feedback parameter F is poorly constrained by localized FRBs[27] — here,
we somewhat arbitrarily use F $=0.32$ — while the baryon content was
consistent with expectations from measurements of the cosmic microwave
backgroundPlanckCosmology2018. Most importantly for this work, fits to the FRB
host contribution ${\rm DM}_{\rm host}$ (which dominates over ${\rm DM}_{\rm
IGM}$ in the nearby Universe) used a log-normal distribution,

$\displaystyle p({\rm DM}_{\rm host}|\mu_{\rm host},\sigma_{\rm
host})=\frac{1}{{\rm DM_{\rm host}}}\frac{1}{\sigma_{\rm
host}\sqrt{2\pi}}\exp\left[-\frac{(\log{\rm DM}_{\rm host}-\mu_{\rm
host})^{2}}{2\sigma_{\rm host}^{2}}\right].$ (6)

Best-fit values of $e^{\mu_{\rm host}}=65-70$ pc cm-3 and $\sigma_{\rm
host}=0.4$ (where $\mu_{\rm host}$ and $\sigma_{\rm host}$ are the mean and
standard deviation of the fitted lognormal FRB host galaxy DM distributions,
respectively) are obtained using a “gold standard” sample of five localized
FRBs measured with the Australian Square Kilometre Array Pathfinder (ASKAP).

Figure 6: From left to right: probability distribution of redshift $z$ for
GW190425 (from https://dcc.ligo.org/LIGO-P2000223/public); and the probability
distributions of the mean and standard deviation of the fitted lognormal FRB
host galaxy DM distribution[27].

Incorporating uncertainties in $z$ from GW190425, $\mu_{\rm host}$, and
$\sigma_{\rm host}$ (shown in Extended Data Figure 6), the expected DM of an
FRB originating from GW190425 is therefore:

$p({\rm DM|GW190425})=\int p({\rm DM}|z,\mu_{\rm host},\sigma_{\rm
host})p(z)p(\mu_{\rm host})p(\sigma_{\rm host})dzd\mu_{\rm host}d\sigma_{\rm
host},$ (7)

where $p({\rm DM}|z,\mu_{\rm host},\sigma_{\rm host})$ is derived from (5) and
(6). Integrating over these distributions produces the expected DM
distribution. We plot in Figure 2 the expected distribution with the DMMWISM
contribution subtracted, to allow comparison with other once-off CHIME
FRBs[2].

We calculate the coincidence probability associated with the DM of FRB
20190425A by ordering all 474 non-repeating CHIME FRBs according to $p($DM-
DM${}_{\rm MWISM})$ and counting the number with equal or better
probabilities. Using the NE2001 model for DMMWISM, we find only one FRB with a
better-matching $p($DM-DM${}_{\rm MWISM})$. Thus, a simple estimation yields
$P_{\rm DM}=2/474\approx 0.0042$. The uncertainties in DMMWISM, $\mu_{\rm
host}$ and $\sigma_{\rm host}$ have also been derived using NE2001[27], i.e.
using NE2001 only is self-consistent. Nonetheless, we calculate a conservative
value of $P_{\rm DM}$ using two methods. Firstly, we simply use the YMW16
model to calculate DMMWISM for all CHIME FRBs. In this case we find four other
FRBs with a more probable DM value than FRB 20190425A, i.e. $P_{\rm
DM}=5/474\approx 0.0105$. We also simulate uncertainty in DMMWISM by randomly
generating these values from a Normal distribution with mean equal to the
average of NE2001 and YMW16, and standard deviation equal to the difference.
Out of 1000 random iterations, we find on-average 4.2 more-probable FRBs, i.e.
$P_{\rm DM}=5.2/474\approx 0.011$. We take this value as a conservative
estimate of $P_{\rm DM}$.

Therefore $P_{\rm tot}=P_{T}P_{S}P_{\rm DM}=0.18\cdot 0.265\cdot 0.004\
(0.19\cdot 0.265\cdot 0.011)=1.9\cdot 10^{-4}\ (5.5\cdot 10^{-4})$ is the
total (conservative) chance probability. These probabilities were derived
using a Frequentist approach, but we note that a Bayesian measure of
significance can also be appliedashton2018.

###  1.5 GW190425 SNR time series

We use modules from the PyCBC software packageNitz2021 to perform a matched
filteringFinn1992,Cutler1994 and obtain the SNR time series in Figure 1.
Public glitch subtracted, cleaned GW strain data is used for the filtering
(https://dcc.ligo.org/LIGO-T1900685/public) together with a TaylorF2 waveform
template for the most probable chirp mass of $1.48M_{\odot}$ [12].

###  1.6 Host galaxy association search

Name | z | RA | DEC
---|---|---|---
WISEA J170311.62+212626.6 | 0.078742 | 17 03 11.622 | +21 26 26.61
UGC 10667 | 0.031 | 17 02 38.976 | +21 34 35.91
WISEA J170310.07+212309.9 | 0.047523 | 17 03 10.07 | +21 23 09.9
Table 2: List of extra-galactic sources within the central 68% localization
uncertainty of FRB20190425 ($0.1\times 0.2\deg^{2}$) retrieved via the NASA
Extragalactic Database (NED) within a redshift range $0.001<z<0.08$ consistent
with the GW PE redshift distribution. Quoted redshifts are spectroscopic. We
exclude objects that do not have a listed spectroscopic redshift.

The properties of potential host galaxies found inside the error ellipse of
FRB 20190425A’s central localization are displayed in Extended Data Table 2.
The only host within the upper limit $z_{max}=0.0394$ is UGC 10667. To
investigate the significance of this host galaxy association we utilize the
methods described in [30]. The total number of galaxies expected within a
solid angle $\Delta\Omega$ at luminosity distance $d_{\mathrm{L}}$ is
$N_{\mathrm{gals}}=\rho_{\mathrm{gals}}\frac{4}{3}\pi
d_{\mathrm{L}}^{3}\frac{\Delta\Omega}{4\pi}$ in the nearby (Cartesian)
Universe. The density of galaxies can be derived from the Schechter function
associated with a galaxy catalog optimized for GW follow-up searches.[30] In
this work we utilize their value of $\rho_{\mathrm{Gals}}=2.35\cdot
10^{-3}\,\mathrm{Mpc}$, which considers galaxies that contribute to the top
50% of the luminosity function. Thus, for a luminosity distance of
$255.85\,\mathrm{Mpc}$ (the upper limit derived for the GW event[12]) one
expects $N_{\mathrm{Gals}}\sim 0.173$ within the CHIME 68% FRB 20190425 error
ellipse (i.e. $\sim 17\%$ chance of coincidence).

###  1.7 Delay time

Within the “blitzar” model for FRBs, the delay time between GW190425 and FRB
20190425A is defined by the survival time of the supramassive neutron star
(SMNS) formed at the merger before it collapsed into the black hole. The
collapse time scale depends on the mass of the SMNS. For the majority of the
cases, the collapse time likely coincides with the spindown timescale, which,
for a magnetic-dipole-dominated spindownshapiro83, can be estimated as

$\displaystyle t_{\rm sd,md}=\frac{E_{\rm rot}}{L_{\rm sd,md}}=3.0\times
10^{4}~{}s~{}\left(\frac{R_{NS}}{18~{}{\rm
km}}\right)^{-6}\left(\frac{B_{p}}{10^{14}~{}{\rm
Gauss}}\right)^{-2}\left(\frac{P_{i}}{0.8~{}{\rm
ms}}\right)^{2}\left(\frac{I}{8\times 10^{45}~{}{\rm g~{}cm^{2}}}\right),$ (8)

where $E_{\rm rot}=(1/2)I\Omega_{i}^{2}$ is the total rotational kinetic
energy of the SMNS, $L_{\rm sd,md}=B_{p}^{2}R_{s}^{6}\Omega_{i}^{4}/(6c^{3})$
is the spindown luminosity due to magnetic dipole radiation, $\Omega_{i}$ and
$P_{i}$ represent the initial angular velocity and period of the new-born
SMNS, $B_{p}$ stands for the strength of the surface magnetic field at the
pole, and $I$ is the momentum of inertia of the SMNS. These parameters have
been normalized to typical values at the maximum spin for an SMNS[gao20]. For
these nominal parameters, a collapse time at $2.5$ hr corresponds to
$B_{p}\sim 1.8\times 10^{14}$ G.

The light curves of a fraction of short GRBs are found to exhibit an X-ray
plateau followed by a steep decay rowlinson10,rowlinson13,lv15. These
“internal plateaus” are proposed to form from the wind emissions of an SMNS
that end with the collapse of the SMNS[14]. The distribution of the observed
plateau duration falls within the range of $10^{2}-10^{4}$slv15,Gao2016,
consistent with our interpretation of the FRB delay time.

###  1.8 Constraints on $M_{\rm TOV}$

We derive constraints on the universal Tolman-Oppenheimer-Volkoff non-spinning
maximum mass ($M_{\rm TOV}$) by constraining the gravitational mass of the
merger remnant at different post-merger phases. To achieve this, we first
derive the total post-merger baryonic mass (a conserved quantity). According
to GW parameter estimation[13], the gravitational masses of the binary neutron
stars in the source frame are $M_{1}=2.03^{+0.58}_{-0.34}M_{\odot}$ and
$M_{2}=1.35^{+0.26}_{-0.26}M_{\odot}$ with the sum of the two $M_{\rm
tot}=3.39^{+0.31}_{-0.11}M_{\odot}$. The remnant mass extracted from the GW
observation is $M_{\rm tot}^{\rm final}=3.23^{+0.33}_{-0.11}M_{\odot}$ in the
source frame (https://dcc.ligo.org/LIGO-P2000026/public). This is smaller than
$M_{\rm tot}$, indicating a fraction of its mass was radiated away in GWs. For
pre-merger NS, we use the non-spin or low-spin universal relation to estimate
the total baryonic mass $M_{b}$ of the system from its gravitational mass $M$:
$M_{b}=M+0.080M^{2}$, which is applicable to NSs that are not spinning near
the break-up limit (ref. timmes96,gao20). We can safely assume low-spins for
pre-merger NSs, as the spindown timescale (Equation 8) of a millisecond object
is about $1.3\times 10^{9}~{}{\rm yr}~{}(B_{p}/10^{8}~{}{\rm Gauss})^{-2}$.
Therefore, even if the initial spin of a BNS merger member is close to
milliseconds, it should have been spun down during the typical BNS merger
timescale $\sim 10^{9}$ yrwandermanpiran15, unless its $B$ field is lower than
a few $10^{8}$ G, which is very rare and never observed in the Milky Way. This
gives the total baryonic mass $M_{\rm b,tot}=3.86_{-0.31}^{+0.70}M_{\odot}$,
including $0.1M_{\odot}$ uncertainty introduced by the $M_{b}-M$ relation due
to the unknown neutron star EoS. During the merger, an order of
$0.06M_{\odot}$ baryonic mass is expected to have been ejected to power
kilonova emission[metzger17], therefore the baryonic mass of the final remnant
may be estimated as $M_{\rm b,rem}=3.80_{-0.31}^{+0.70}M_{\odot}$.

A neutron star post-merger remnant is expected to go through a brief
differential-rotation phase (< 1 second), before forming an essentially
uniformly rotating body[shapiro00, margalit19]. We therefore apply a universal
relation between baryonic mass $M_{b}$ and gravitational mass $M$ for
maximally rotating neutron stars, $M_{b}=M+0.064M^{2}$, to convert the
baryonic remnant mass $M_{\rm b,rem}$ to gravitational remnant mass $M_{\rm
rem}$ (ref. gao20). This leads to $M_{\rm rem}=3.16^{+0.40}_{-0.24}M_{\odot}$.
Note that $M_{\rm rem}$ is slightly lower than $M^{\rm final}_{\rm tot}$ as
$M^{\rm final}_{\rm tot}$ is not necessarily taken from the rigidly rotating
phase. Since uniform rotation can support a higher mass with a maximum
enhancement factor $M_{\rm rem}/M_{\rm TOV}\sim 1.2$ [43, 38]lasota96 (more
precisely, $1.201\pm 0.017$ [39]), a lower limit of $M_{\rm
TOV}>2.63^{+0.39}_{-0.23}M_{\odot}$ can be placed. The minimum enhancement
factor at the maximum rotation has been shown to be $1.046\pm 0.008$ [39].
This places a limit of $M_{\rm TOV}<3.02^{+0.42}_{-0.25}M_{\odot}$.

If a quark star is formed after the merger, due to the lack of a universal
$M_{b}-M$ relation, the gravitational mass of the remnant is difficult to
estimate. In this case, we use the final mass $M_{\rm tot}^{\rm final}$
extracted from the GW waveform as the remnant mass $M_{\rm rem}$ to constrain
$M_{\rm TOV}$. For rotating quark stars, the enhancement factor can be as high
as $M_{\rm rem}/M_{\rm TOV}\sim 1.4$[46]. On the other hand, since there is no
detailed calculation of the enhancement factor for maximum rotation, we adopt
the enhancement factor $\sim 1$ to represent a most conservative constraint on
the upper limit of $M_{\rm TOV}$ of quick stars. We then find that
$2.31_{-0.08}^{+0.24}M_{\odot}<M_{\rm TOV}<3.23^{+0.33}_{-0.11}M_{\odot}$.

In principle, $M_{\rm TOV}$ can be further constrained given the 2.5 hour
collapse time if the surface magnetic field strength of the post-merger
compact star is known[ravi14]. The combination of short GRB X-ray plateau
observations and theory suggests a collapse time ranging from minutes to
hours[lasky14, gao16, 46]. The observed 2.5 hours is consistent with this
range. For our case, if the magnetic field is very low, the increase of spin
period would be insignificant in 2.5 hours, in which case a $M_{\rm TOV}$
close to the lower limit is required to ensure the remnant collapse after the
star is slightly spun down; If the surface magnetic field is very high, most
of the angular momentum would have been lost in a short time. Then a $M_{\rm
TOV}$ close to the upper limit is required to prevent the supramassive compact
object from collapsing before 2.5 hours. In reality, the surface magnetic
field of the merger remnant is not well constrained. Therefore, the allowed
$M_{\rm TOV}$ range remains broad, as seen in the dark grey region of Figure
4.

###  1.9 Energetics

The estimated fluence of FRB 20190425A is $31.6\pm 4.2$ Jy ms[2]. This is a
lower limit, and is estimated assuming it occurs at CHIME’s beam centre. Using
the CHIME bandwidth of $400$ MHz, and assuming a luminosity distance of
$156\,\mathrm{Mpc}$, we calculate an isotropic equivalent energy of
$E_{\mathrm{FRB}}=3.72\cdot 10^{38}\,\mathrm{erg}$. The emitted FRB power is a
small/negligible fraction of the mass-energy of the remnant in the optimistic
scenario. In contrast, the GW mass-energy emitted in the merger that forms the
remnant is $\sim 7\%$ of the total mass of the merger product, i.e. a BNS
merger event is clearly capable of producing such a burst. If the emission is
beamed, $E_{\mathrm{FRB}}$ will be lower by the beaming factor, while if the
FRB was detected far from the CHIME beam centre, $E_{\mathrm{FRB}}$ will be
much higher.

Figure 7: Flux-DM distribution of CHIME FRBs. The majority of CHIME FRBs have
flux densities below $5\rm\ Jy$. FRB 20190425A (orange square) resides in the
low end of the DM spectrum, but has a somewhat exceptional flux density. Note
that these flux densities are lower limits, as CHIME flux measurements are
derived under the assumption that each burst is detected in the center of the
primary beam.

Here, we also wish to point out the curious brightness of FRB 20190425A.
Figure 7 highlights the flux density distribution of CHIME Catalog 1 FRBs. FRB
20190425A (orange square) exhibits a curiously high flux density for its DM,
with only four more notable outliers.

###  1.10 GRB association

Automated electromagnetic follow-up of the real-time detection of GW190425
(S190425z[GCN190425z]) resulted in the reports of a detection of a marginally
significant excess of gamma-raysINTEGRALGCN3 by the INTEGRAL telescope’s SPI-
ACS systemSavchenko2012. No significant signal was found by other subsystems
on-board INTEGRAL, including IBIS/PICsIT, ruling out a localization for the
source within the IBIS field of view (FoV). Subsequent analysis, correcting
for the local background variance at the time of the event resulted in the
updated report of an event detected by SPI-ACSINTEGRALGCN1 with a fluence
$F=2.9\cdot 10^{-10}$ – $2\cdot 10^{-9}\,\mathrm{erg\,cm^{2}}$ in the
$75-2000\,\mathrm{keV}$ range, six seconds after the GW event, assuming a
duration of $1\,\mathrm{s}$. The false alarm probability[36] is less than
$3\sigma$ however it cannot be ruled out that the event is physical. We find
that the localization provided does not exclude the location of FRB20190425A
nor a significant portion of the localization uncertainty for GW190425,
however it is noted[36] that the south-west arc of the localization contour is
slightly disfavored due to an absence of signal in the IBIS/Veto shield
instruments on-board INTEGRAL. A subsequent independent analysis of
INTEGRAL/SPI-ACS data by [37] reports the same sGRB event with a fluence of
$8\cdot 10^{-8}-2.4\cdot 10^{-6}\,\mathrm{erg\,cm^{-2}}$ with a significance
of $5.5\sigma$, wherein the authors utilize a different calibration model and
find an sGRB of significantly longer duration than in the initial prompt
analysisINTEGRALGCN1[36]INTEGRALGCN3.

We note that this work is complementary to the on-going international
LIGO–Virgo–KAGRA Collaboration effort to detect sub-threshold prompt GWs
associated with CHIME FRBs LVK_CHIME_2022.

###  1.11 Further Discussion

Capturing the FRB counterparts of a GW source is challenging given the fact
that the CHIME primary beamwidth is $1.3^{\circ}$–$2.5^{\circ}$ in RA, with
200 $\deg^{2}$ in FoV [2], covering only around 0.5% of the sky. What is the
chance that an FRB emitted from the post-merger remnant of GW190425 would
occur at a time in which it could be detected by CHIME?. The chance of an
event emitted at a random time, i.e. a random RA, at a declination of
$\delta=30^{\circ}$ occurring in this beamwidth is thus
($1.3^{\circ}$–$2.5^{\circ}$)/($360^{\circ}\cos\delta)=$0.4%–0.8%. On the
other hand, the chance of coincident detection could be improved by several
scenarios. A bright FRB could be detected far from beam centre, as was the
case with a radio flare from SGR 1935+2154, which was observed by CHIME
$22^{\circ}$ from the meridian [4]. This would increase the chance to capture
the FRB to $44^{\circ}/(360^{\circ}\cos\delta)$=14% ($44^{\circ}$ reflects
$22^{\circ}$ both sides of the beam). Furthermore, there is a slight
preference for GWs to be detected over a large sky area around the zenith (and
the nadir) of the LIGO detectors. In our case the GW event was detected
significantly only by the LIGO-Livingston detector whose zenith aligns well
with that of CHIME due to their geographical proximity. Constraining the time
interval to 2.5 hr, while assuming the FRB arises from the same location on
the sky, results in a chance detection probability of
($1.3^{\circ}$–$2.5^{\circ}$)/($37.5^{\circ}\cos\delta)=$4%–8% for in-beam
events, and $22^{\circ}/(37.5^{\circ}\cos\delta)$=68% for sidelobe events
(only one side of the beam counts, since only detections earlier than 2.5 hr
are considered).

Our favoured interpretation of FRB 20190425A is a blitzar event. Another
possibility is that the post-merger magnetar generates multiple repeating
bursts and FRB 20190425A is one of them. If this is the case, the likelihood
of detecting an FRB associated with the GW source would also have increased.
However, we disfavour this possibility for the following reasons: 1.
Observationally, FRB 20190425A is bright and carries the key observational
signatures of non-repeating FRBspleunis2021, e.g. single peak, short duration,
and broad spectrum. These are very different from the bursts detected from
repeating FRB sources, which typically have long widths, narrow spectra, and
very often multiple peaks. 2. Even within the non-repeater population, this
burst is brighter than others and is an outlier of the flux-DM relation of
most CHIME FRBs (Figure 7). This suggests that FRB 20190425A may have a
distinct physical origin from other FRBs. 3. Theoretically, interpreting
FRB20190425A within the blitzar framework already requires a large $M_{\rm
TOV}$ that is marginally consistent with other constraints on the NS EoS. The
repeater scenario requires that the post-merger product survive even longer
than 2.5 hours, which would further escalate the EoS tension with known
results.

The estimated merger rate of BNS (100–1700 Gpc-3 yr-1 LVK_merger_rates_2021)
is far lower than the estimated FRB rate $\sim 10^{5}$ Gpc-3 yr-1 [19,
20]james2022L. Thus blitzar FRBs initiated by BNS mergers can account for at
most 5% of the FRBs exhibiting broadband, single-peaked morphology observed by
CHIME, which themselves account for 30% of the population. If the association
between GW190425 and FRB 20190425A is indeed astrophysical and can be
attributed to the blitzar model, it implies the existence of “subpopulations
amongst subpopulations” of FRBs.

naturemag methods

We acknowledge the custodians of the land this research was conducted on, the
Whadjuk (Perth region) Noongar people and pay our respects to elders past,
present and emerging. This research has made use of data, software and/or web
tools obtained from the Gravitational Wave Open Science Center
(https://www.gw-openscience.org/), a service of LIGO Laboratory, the LIGO
Scientific Collaboration and the Virgo Collaboration. LIGO Laboratory and
Advanced LIGO are funded by the United States National Science Foundation
(NSF) as well as the Science and Technology Facilities Council (STFC) of the
United Kingdom, the Max-Planck-Society (MPS), and the State of
Niedersachsen/Germany for support of the construction of Advanced LIGO and
construction and operation of the GEO600 detector. Virgo is funded, through
the European Gravitational Observatory (EGO), by the French Centre National de
Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica
Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from
Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal,
Spain. This research has made use of the NASA/IPAC Extragalactic Database,
which is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology; NASA’s Astrophysics Data
System Bibliographic Services; and the Python libraries
Matplotlib[Matplotlib2007], NumPy[Numpy2011], SciPy[SciPy2019] and
Pandas[pandas, reback2020pandas]. This research has made use of the DSS-2
based on photographic data obtained using The UK Schmidt Telescope. The UK
Schmidt Telescope was operated by the Royal Observatory Edinburgh, with
funding from the UK Science and Engineering Research Council, until 1988 June,
and thereafter by the Anglo-Australian Observatory. The DSS was produced at
the Space Telescope Science Institute under US Government grant NAG W-2166.
AM, FHP and MK utilized the OzSTAR national facility at Swinburne University
of Technology. The OzSTAR program receives funding in part from the Astronomy
National Collaborative Research Infrastructure Strategy (NCRIS) allocation
provided by the Australian Government. LW, FHP and MK acknowledge funding
support from Australian Research Council Centre of Excellence for
Gravitational Wave Discovery (OzGrav) under grant CE170100004. MK acknowledges
the SIRF postgraduate scholarship from the University of Western Australia.
CWJ acknowledges support from the Australian Government through the Australian
Research Council’s Discovery Projects funding scheme (project DP210102103). SA
and BZ acknowledges a Top Tier Doctoral Graduate Research Assistantship
(TTDGRA) at University of Nevada, Las Vegas.

We acknowledge Volodymyr Savchenko and Simon Driver for useful correspondence
regarding the sGRB coincidence and galaxy luminosity function respectively,
Dr. Qi Chu for her knowledge sharing of GW signal extraction, Teresa Slaven-
Blair, Tara Murphy, Dougal Dobie, and Hao Qiu for initial discussions relevant
to this research, Patrick Sutton for valuable comments regarding the
calculation of $P_{S}$, and Vivek Gupta for information regarding the UTMOST
detection of the Crab pulsar.

AM led the GW-FRB coincidence search, GW190425/FRB 20190425A follow-up, chance
probability (temporal and spatial) and significance analysis, drafted the
initial paper and brought it to completion. LW conceived the original idea for
the work, designed the research framework, built the collaboration team,
supervised all aspects of the analysis, and contributed to the writing and
completion of the paper. CWJ jointly conceived the original idea for the work,
contributed to supervision of students in the project, performed the
dispersion measure analysis, assisted with significance analysis, and
contributed to writing the paper. FHP contributed the host galaxy search, GW
parameter estimation, FRB energetics, sGRB context and paper writing and
figure showing FRB-host galaxy coincidences. SA and BZ proposed the
theoretical interpretation to the data, performed constraints on $M_{\rm TOV}$
for neutron stars and quark stars, and contributed to the writing of the
theory part of the paper. MK generated the approximated GW waveform, whitened
the public GW strain data and performed matched filtering to construct the SNR
time series.

The authors declare that they have no competing financial interests.

The CHIME FRB data is publicly available at https://www.chime-frb.ca/catalog.
The public GW event data is available at
https://gracedb.ligo.org/superevents/public/O3/ (general information),
https://dcc.ligo.org/LIGO-T1900685/public (strain data),
https://dcc.ligo.org/LIGO-P2000223/public (GWTC-2 parameter estimation) and
https://www.gw-openscience.org/eventapi/html/GWTC-2/GW190425/v2 (GWOSC event
portal).

Processed data is presented in the tables and figures of the paper. Code used
for processing data is available upon reasonable requests to the corresponding
authors.