11institutetext: INAF-Istituto di Radio Astronomia (IRA), via Piero Gobetti
101, Bologna, Italy
11email<EMAIL_ADDRESS>22institutetext: Dipartimento di Fisica e
Astronomia, Universitá di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
33institutetext: South African Radio Astronomy Observatory, Black River Park,
2 Fir Street, Observatory, Cape Town, 7925, South Africa 44institutetext:
Department of Physics and Electronics, Rhodes University, PO Box 94, Makhanda,
6140, South Africa 55institutetext: INAF-Osservatorio Astronomico di Cagliari,
via della Scienza 5, I-09047, Selargius (CA), Italy 66institutetext:
Università degli Studi di Cagliari, Dipartimento di Fisica, SP Monserrato-
Sestu, I-09042 Monserrato (CA), Italy 77institutetext: INAF-Osservatorio di
Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129,
Bologna, Italy 88institutetext: Institute of Space Sciences and Astronomy
(ISSA), University of Malta, Msida, MSD 2080, Malta 99institutetext:
INAF/IAPS, via del Fosso del Cavaliere 100, I-00133 Roma (RM), Italy
1010institutetext: Università degli Studi di Roma ”Tor Vergata”, via della
Ricerca Scientifica 1, I-00133 Roma (RM), Italy 1111institutetext: SSDC/ASI,
via del Politecnico snc, I-00133 Roma (RM), Italy 1212institutetext: INAF-
Osservatorio Astronomico di Roma, via Frascati 33, 00078 Monte Porzio Catone
(RM), Italy

# The Northern Cross Fast Radio Burst project - III. The FRB-magnetar
connection in a sample of nearby galaxies

D. Pelliciari , 1122 G. Bernardi 113344 M. Pilia 55 G. Naldi 11 G. Pupillo 11
M. Trudu 5566 A. Addis 77 G. Bianchi 11 C. Bortolotti 11 D. Dallacasa 1122 R.
Lulli 11 G. Maccaferri 11 A. Magro 88 A. Mattana 11 F. Perini 11 M. Roma 11 M.
Schiaffino 11 G. Setti 1122 M. Tavani 991010 F. Verrecchia 11111212 C.
Casentini 99

(XXX-XXX-XXX)

###### Abstract

Context. Fast radio bursts (FRBs) are millisecond-radio transients observed at
cosmological distances. The nature of their progenitors is still under debate,
although magnetars are invoked by most models. The FRB-magnetar connection was
strengthened by the discovery of a FRB-like event from the Galactic magnetar
SGR J1935+2154.

Aims. We aim to further investigate the FRB-magnetar connection, in particular
how magnetars like SGR J1935+2154 can be considered progenitors of the FRB
population.

Methods. We carried out an FRB search in a sample of seven nearby (¡ 12 Mpc)
galaxies with the Northern Cross radio telescope for a total of 692 h. We
computed the rate of SGR-like events expected from our survey, as a function
of the energy slope, $\gamma$, and event rate per magnetar, $\lambda_{\rm
mag}$.

Results. We detected one 1.8 ms burst in the direction of M101 with fluence of
$58\pm 5$ Jy ms. Its dispersion measure of 303 pc cm-3 places it most-likely
beyond M101. Considering no significant detection coming indisputably from the
selected galaxies, we place a 38 yr-1 upper limit on the total - i.e.,
including the whole sample - burst rate at the 95% confidence level. This
upper limit constrains $\lambda_{\rm mag}<0.42$ magnetar-1 yr-1 or, if
combined with literature observations of a similar sample of nearby galaxies,
it yields a joint constraint of $\lambda_{\rm mag}<0.25$ magnetar-1 yr-1. We
also provide the first constraints on the expected rate of FRBs hypothetically
originating from ultraluminous X-ray (ULX) sources, since some of the galaxies
observed during our observational campaign host confirmed ULXs. Our
observations constrain the event rate to be $<13$ yr-1 per ULX on the total
sample of galaxies observed.

Conclusions. Our results indicate that bursts with energies $E>10^{34}$ erg
from magnetars like SGR J1935+2154 appear more rare compared to previous
observations, and further disfavours them as unique progenitors for the
cosmological FRB population, leaving more space open to the contribution from
a population of more exotic magnetars, not born via core-collapsed supernovae.

###### Key Words.:

Galaxies: Local Group – methods: observational – stars: magnetars

##  1 Introduction

Fast radio bursts (FRBs) are millisecond-long, highly dispersed radio signals
having an exceptionally high brightness temperature ($10^{32}-10^{35}$ K), of
extragalactic origin (Thornton et al., 2013; Cordes & Chatterjee, 2019;
Petroff et al., 2019, 2021; Pilia, 2021). Since their discovery (Lorimer et
al., 2007), about $600$ distinct FRB sources have been observed (The CHIME/FRB
Collaboration et al., 2021), with a host galaxy association for about 25 of
them (Tendulkar et al., 2017; Bannister et al., 2019; Ravi et al., 2019;
Prochaska et al., 2019; Macquart et al., 2020; Marcote et al., 2020; Bhardwaj
et al., 2021a; Ravi et al., 2021; Niu et al., 2021; Nimmo et al., 2022; Ryder
et al., 2022; Ravi et al., 2022; Bhandari et al., 2022a; Driessen et al.,
2023; Sharma et al., 2023). Moreover, 50 FRBs were found to be repeating (The
CHIME/FRB Collaboration et al., 2023), with recent statistical evidence
indicating that repeaters may represent a distinct class of sources (Hashimoto
et al., 2020; Pleunis et al., 2021; Zhong et al., 2022; Guo & Wei, 2022; The
CHIME/FRB Collaboration et al., 2023). Up to now only two repeaters, FRB
20180916B and FRB 20121102, have shown periodic activity, with periods of
$\sim 16.33\pm 0.12$ (Pleunis et al., 2021) and $\sim 161\pm 5$ days (Cruces
et al., 2021), respectively.

Among all progenitor candidates, magnetars, i.e. neutron stars (NS) powered by
the decay of their strong ($10^{14}-10^{16}$ G) magnetic field (Duncan &
Thompson, 1992; Rea & Esposito, 2011; Turolla et al., 2015; Kaspi &
Beloborodov, 2017), are the most widely considered. The FRB-magnetar
connection was strengthened by the detection of FRB 20200428, the first
Galactic FRB-like event (CHIME/FRB Collaboration et al., 2020; Bochenek et
al., 2020), observed simultaneously with an X-ray burst (Mereghetti et al.,
2020; Ridnaia et al., 2020; Li et al., 2021; Tavani et al., 2021), emitted by
the Soft Gamma Repeater J1935+2154 (SGR1935, hereafter), one of the most
active magnetars known (Stamatikos et al., 2014; Lien et al., 2014; Cummings,
2014; Kozlova et al., 2016; Younes et al., 2017). The reported isotropic-
equivalent energy emitted at radio wavelengths by this burst, $E_{\rm
SGR}\simeq 2\times 10^{34}$ erg (Bochenek et al., 2020; Margalit et al.,
2020), lies between the energetic pulsar giant radio pulses (see, e.g.,
Kuzmin, 2007) and extragalactic FRBs. Further observations revealed fainter
bursts from SGR1935 (Zhang et al., 2020; Burgay et al., 2020; Good & Chime/Frb
Collaboration, 2020; Alexander & Fedorova, 2020; Kirsten et al., 2021; Dong &
Chime/Frb Collaboration, 2022; Maan et al., 2022; Huang et al., 2022; Pearlman
& Chime/Frb Collaboration, 2022).

Since magnetars are connected to a young stellar population, they are expected
to be found in regions of star formation. While this has been observed for
some FRBs (Chatterjee et al., 2017; Marcote et al., 2017; Bassa et al., 2017;
Tendulkar et al., 2017; Ravi et al., 2019; Marcote et al., 2020; Bhardwaj et
al., 2021a; Niu et al., 2021; Piro et al., 2021; Tendulkar et al., 2021; Nimmo
et al., 2022), others have been found in galaxies with low star formation
rate, mainly in their outskirts (Heintz et al., 2020; Mannings et al., 2021;
Bhandari et al., 2022b). Notably, the repeating FRB 20200120E was recently
found in a globular cluster in the nearby galaxy M81 (Kirsten et al., 2022a).
Indeed, it is also theoretically possible to find young magnetised NSs in
globular clusters, formed either via the accretion-induced collapse of a white
dwarf (WD; Tauris et al., 2013; Wang & Liu, 2020) or the merger-induced
collapse of a compact binary system, precisely WD-WD, WD-NS or NS-NS
(Giacomazzo & Perna, 2013; Schwab et al., 2016; Zhong & Dai, 2020).

CHIME/FRB Collaboration et al. (2020) observed a sample of fifteen nearby
galaxies (within 12 Mpc) with star formation rate (SFR) higher than the Milky
Way in order to search for SGR1935-like FRBs, i.e. bursts with energy
$E_{0}>4\times 10^{34}$ erg. The advantage of targeting nearby galaxies over
the Milky Way (MW) is that the whole population of magnetars is simultaneously
observed, therefore increasing the probability to detect a burst with respect
to targeting individual magnetars. No bursts were observed, allowing them to
place a constraint on the burst rate of SGR1935-like events
$0.007<\lambda_{\rm mag}<0.4$ yr-1 magnetar-1, where the lower limit is set by
the detection of the SGR1935 burst itself (CHIME/FRB Collaboration et al.,
2020).

In this work we present long monitoring observations of a sample of nearby
galaxies (NGs) taken with the Northern Cross (NC) telescope, searching for
FRBs with the aim to study the FRB-magnetar connection, following CHIME/FRB
Collaboration et al. (2020). We note that some of the galaxies observed within
our observational campaign host confirmed ultraluminous X-ray (ULX) sources.
The latter are accreting binary systems with high X-ray luminosity, $L_{X}\geq
10^{39}$ erg s-1, way higher than any X-ray luminosity emitted by stellar
processes (Fabbiano, 1989; Kaaret et al., 2017).

The paper is structured as follows: Section 2 describes the observations and
the sample of NGs observed and Section 3 presents constraints on the FRB burst
rate coming from magnetars (Section 3.1) and ULXs (Section 3.2), exploiting
our observations. Finally, the implications that our constraints have on the
connection between FRBs and their progenitors, along with our conclusions, are
discussed in Section 4.

##  2 Sample description and observations

Table 1: Properties of the observed NG sample. Columns list: coordinates, distances ($D$), SFRs, the dispersion measure contribution from the Milky Way interstellar medium (ISM) DMISM, computed as the maximum between the YM16 (Yao et al., 2017) and NE2001 (Cordes & Lazio, 2002, 2003) models respectively, the total exposure time spent on source. SFRs are estimated from H$\alpha$ luminosities for all the galaxies but M82 and IC 342, for which infrared luminosities were used. References for distances are: [1] McConnachie et al. (2005); [2] Karachentsev et al. (2004); [3] Dalcanton et al. (2009); [4] Shappee & Stanek (2011); [5] Anand et al. (2018); [6] Newman et al. (2001); [7] Hoyt et al. (2019). References for SFR: [8] Rahmani et al. (2016); [9] Gao & Solomon (2004); [10] Förster Schreiber et al. (2003); [11] Kennicutt et al. (2008). | R.A. (J2000) | Dec (J2000) | D [Mpc] | SFR [$M_{\odot}\ \rm yr^{-1}$] | DMISM [pc cm-3] |  $\rm T$ [hr]
---|---|---|---|---|---|---
M31 | $00^{\rm h}42^{\rm m}44.3^{\rm s}$ | $+41^{\circ}16^{\prime}07.5^{\prime\prime}$ |  $0.79\pm 0.03$ [1] |  $0.35$ [8] | $142$ | $51$
IC342 | $03^{\rm h}46^{\rm m}48.5^{\rm s}$ | $+68^{\circ}05^{\prime}46.0^{\prime\prime}$ |  $3.3\pm 0.3$ [2] |  $2.8$ [9] | $178$ | $102$
M82 | $09^{\rm h}55^{\rm m}52.4^{\rm s}$ | $+69^{\circ}40^{\prime}46.9^{\prime\prime}$ |  $3.53\pm 0.04$ [3] |  $13$ [10] | $41.2$ | $184$
M101 | $14^{\rm h}03^{\rm m}12.6^{\rm s}$ | $+54^{\circ}20^{\prime}55.5^{\prime\prime}$ |  $6.4\pm 0.5$ [4] |  $2.9$ [11] | $30.9$ | $96$
NGC6946 | $20^{\rm h}34^{\rm m}52.3^{\rm s}$ | $+60^{\circ}09^{\prime}13.2^{\prime\prime}$ |  $7.7\pm 0.3$ [5] |  $4.3$ [11] | $145.8$ | $115$
M106 | $12^{\rm h}18^{\rm m}57.6^{\rm s}$ | $+47^{\circ}18^{\prime}13.4^{\prime\prime}$ |  $7.8\pm 0.6$ [6] |  $2.8$ [11] | $25.8$ | $84$
M66 | $11^{\rm h}20^{\rm m}15.0^{\rm s}$ | $+12^{\circ}59^{\prime}28.6^{\prime\prime}$ |  $11.1\pm 0.4$ [7] |  $2.7$ [11] | $31.1$ | $63$
Figure 1: Normalized NC beam-forming response (solid line) as the source
transits across the telescope field of view. Dashed lines represent the
average value of the telescope beam response for each delay bin.

Our sample consists of seven galaxies within a maximum distance of 12 Mpc,
whose characteristics are summarized in Table 1. We selected them based on
their reported high SFRs, since magnetars like SGR1935, born through core-
collapse supernovae (CCSNe), trace young star-formation sites. Apart from M31
and IC 342, all the other galaxies were already included in the sample
observed by CHIME/FRB Collaboration et al. (2020). We included M31 for its
proximity and similarity to the MW. As already mentioned, among the galaxies
observed, M82, M101, IC 342 and NGC 6946 host confirmed ULXs (M82 X-1 (Ptak &
Griffiths, 1999), M101 X-1 (Stetson et al., 1998), IC 342 X-1, IC 342 X-2
(Rana et al., 2015), NGC 6946 X-1 (Fabbiano & Trinchieri, 1987; Roberts &
Colbert, 2003)). Nowadays, these objects are believed to be the result of a
super-Eddington accretion onto a stellar mass black hole (e.g. Liu et al.,
2013), or a NS (Pintore et al., 2020, and references therein).

We monitored each galaxy daily during its transit through the telescope
primary beam using eight cylinders of the north-south arm of the array (we
refer the reader to Locatelli et al., 2020, for details of the system). Due to
limitations of the current acquisition software, a source cannot be tracked
continuously as it moves across the telescope field of view, therefore we
employed a “shift and track” strategy already used in Trudu et al. (2022),
where seven discrete delay values are approximately equally spaced in angular
size to cover the field of view. The resulting telescope beam pattern is shown
in Figure 1, where the seven peaks corresponding to the seven beamforming
delays are clearly visible. Such a beam pattern implies that the sensitivity
to the source varies up to 40% as it transits through the primary beam. As the
variation of the beam response within each delay bin is small ($\approx
10\%$), we will assume it to be constant in the following analysis, and equal
to its average value (dashed line in Figure 1). The energy detection threshold
$E_{\rm min}$ for a burst observed in the delay bin $j$ from the galaxy $i$
can be written as:

$E_{{\rm min},i,j}=4\pi D_{i}^{2}\,\Delta\nu\,\frac{F}{A_{j}},$ (1)

where $D_{i}$ is the source distance, $\Delta\nu=16$ MHz the observing
bandwidth, $A_{j}$ the average beam gain in the $j$-th delay bin and $F=38$ Jy
ms is the NC fluence threshold corresponding to the peak of the central beam
assuming a $10\sigma$ detection threshold (Trudu et al., 2022). In this work
we assumed 1 ms as the reference burst duration.

Observations started on December 26th 2021 and ended on August $21^{\rm st}$
2022, for a total of 692 hr. Data were stored to disk with a time resolution
of 138.24 $\mu$s and a frequency channel width of 14.468 kHz. We calibrated
our data using interferometric observations of Cas A (see Locatelli et al.,
2020, for details on the calibration procedure), carried out approximately at
the beginning, halfway and at the end of the observational campaign. Receiver
phases and amplitudes remained fairly constant over week-long timescales,
nevertheless, our observing campaign was interspersed with monthly
observations of the pulsar B0329+54 and the repeating FRB 20180916B (CHIME/FRB
Collaboration et al., 2019). Both sources served as calibration tests for the
stability of our system and, at the same time, FRB 20180916B was observed
within its window of expected activity (CHIME/FRB Collaboration et al., 2019;
Pastor-Marazuela et al., 2021; Pleunis et al., 2021; Trudu et al., 2022) with
the purpose of multiwavelength observations (Pilia et al., 2020; Tavani et
al., 2020; Trudu et al., 2022).

We regularly detected single pulses from B0329+54 at its nominal dispersion
measure DM $\sim 26.8$ pc cm-3 (Hassall et al., 2012) and detected two new
bursts from FRB 20180916B, in addition to those presented in Trudu et al.
(2022), in agreement with the expected repetition rate.

Figure 2: Bursts from FRB 20180916B observed on April $30^{\rm th}$ 2022 (left panel) and August $9^{\rm th}$ 2022 (right panel), respectively. Bottom panels show the dynamic spectra, while the top panels show the frequency averaged profiles.The best-fit DMs (in pc cm-3) at which the bursts were dedispersed are reported in the top right corner of each plot. Data were down-sampled to have 64 frequency channels, each $0.25$ MHz wide, and time bins with $2.2$ ms width for better display. Table 2: Properties of B4 and B5 bursts from FRB 20180916B. We report, from the top row to the bottom, the barycentric time of arrival (TOA) expressed as the modified julian day (MJD), the signal to noise ratio (S/N), the fit-optimized DM, the full width at half maximum (FWHM) duration, the flux density and the fluence of the bursts. Parameter | B4 | B5
---|---|---
TOA (MJD) | 59699.52603591 | 59800.25184782
S/N | $15$ | $20$
DM (pc cm-3) | $349.8\pm 0.1$ | $350.7\pm 0.1$
$\Delta t$ (ms) | $6.35\pm 0.1$ | $5.7\pm 0.3$
Flux density (Jy) | $15\pm 1$ | $19\pm 1$
Fluence (Jy ms) | $96\pm 6$ | $108\pm 5$

Figure 2 shows their dedispersed waterfall plots, labelled B4 and B5 to follow
the Trudu et al. (2022) nomenclature, and their best fit values are listed in
Table 2. These detections provide evidence for calibration stability across
the whole campaign.

The search for FRBs in our galaxy sample was performed using the SPANDAK
pipeline (Gajjar et al., 2018), which flags radio frequency interference (RFI)
through rfifind (Ransom et al., 2002) and searches for single pulses with
Heimdall (Barsdell et al., 2012). We used the same search setup described in
Trudu et al. (2022), within the $0<{\rm DM}<1000$ pc cm-3 range, with a signal
to noise ratio (S/N) greater than six and a boxcar duration shorter than 35
ms, in order to balance the search time and our scientific goals, whilst
remaining consistent with the observed width distribution of FRBs (Petroff et
al., 2021; The CHIME/FRB Collaboration et al., 2021).

###  2.1 FRB detection from the direction of M101

We found no candidates with a S/N $>10$ throughout the whole campaign, and
$\sim 100$ candidates with $6\leq{\rm S/N}\leq 10$ that were further visually
inspected and double checked. Most candidates were discarded due to the
presence of RFI contamination and noise properties that showed deviations from
a theoretical Gaussian distribution. The only candidate that conservatively
passed the selection, detected with a $\rm S/N\sim 11$, is shown in Figure 3.

We assess the likelihood of a candidate signal by computing the number of
false candidates with $\rm S/N$ higher than the detection threshold, expected
because of noise outliers. The number of false positive events is a function
of the S/N and can be computed as (Cordes & McLaughlin, 2003):

$N_{\rm false}(>{\rm S/N})=2N_{\rm DM}\,\frac{\Delta T}{{\rm d}t}\,P(>\rm
S/N),$ (2)

where $N_{\rm DM}$ is the number of DM trials considered in the FRB search,
set internally in Heimdall, $\Delta T$ the total duration of the observations,
${\rm d}t$ the time sample duration and

$P(>{\rm S/N})=\frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-z^{2}}{\rm
d}z\equiv\frac{1}{2}\Biggl{[}1-{\rm erf}\Biggl{(}\frac{{\rm
S/N}}{\sqrt{2}}\Biggr{)}\Biggr{]}$ (3)

is the probability that an event is due to a noise statistical fluctuation. In
our case $N_{\rm DM}\sim 3000$, $\Delta T=692$ h and ${\rm d}t\sim 138\ \mu$s,
obtaining $N_{\rm false}\sim 10^{-9}$ for $\rm S/N\geq 10$, hence we consider
our candidate as a genuine FRB.

The burst, hereafter FRB 20220320, was detected on 2022 March 30 UT =
01:14:02.40 (Barycentric time of arrival, $\infty$ MHz), in the direction of
M101 and its properties are listed in Table 3.

Table 3: Observational properties of FRB 20220320. The uncertainty on the FRB position corresponds to the beam FWHM. Parameter | Value
---|---
R.A. (J2000, deg) | $211(3)$
Dec. (J2000, deg) | $54.4(5)$
T.o.A | 2022-03-20 01:14:02.40 (UT)
S/N | $11$
DM (pc cm-3) | $303\pm 2$
$\Delta t\ (\rm ms)$ | $1.8\pm 0.3$
Flux density (Jy) | $32\pm 3$
Fluence (Jy ms) | $58\pm 5$

We measured a DM $=303\pm 2$ pc cm-3, which disfavours its local origin. The
DM contribution along the line of sight of M101 due to the ISM is $\rm DM_{\rm
ISM}\simeq 23-31$ pc cm-3, according to the NE2001 (Cordes & Lazio, 2002,
2003) and the YMW16 (Yao et al., 2017) electron density models, respectively,
while the contribution from the Galactic halo is $\sim 50$ pc cm-3 (Agarwal et
al., 2019; Macquart et al., 2020; Yamasaki & Totani, 2020; Lemos et al.,
2022). Finally, the intergalactic medium (IGM, considering $z\simeq 0.001$)
contributes to approximately $\sim 2$ pc cm-3 (Macquart et al., 2020),
although this value, for low redshift galaxies, depends on the line of sight
(Li et al., 2019). These contributions, if coming from M101, would imply a
moderately high $\rm DM_{\rm host}$, $\simeq 220$ pc cm-3. In our case, the
almost face-on inclination of M101 seems to disfavor a large $\rm DM_{\rm
host}$ for M101 (Xu & Han, 2015). Although James et al. (2022), by analysing
16 FRBs from ASKAP observations, found $\langle\rm DM_{\rm host}\rangle\sim
186\pm 50$ pc cm-3, which would be compatible with an origin from M101, other
works point towards lower values for the host DM contribution (Niino, 2020;
Zhang et al., 2020). This further supports an unlikely association with M101.

If we then consider the burst to be originating farther away, assuming a more
conservative value $\rm DM_{\rm host}\simeq 100$ pc cm-3, the burst would be
placed at a maximum redshift of $z\sim 0.18$, i.e. at a luminosity distance of
$\sim 870$ Mpc. For the distance estimation we considered a seven-year
Wilkinson Microwave Anisotropy Probe (WMAP7) cosmology (Komatsu et al., 2011)
to be consistent with Macquart et al. (2020). Given this maximum redshift, its
spectral luminosity would be at most $6.3\times 10^{33}$ erg s-1 Hz-1, well
within the range of extragalactic FRB spectral luminosities (Bochenek et al.,
2020; CHIME/FRB Collaboration et al., 2020; Luo et al., 2020)

Figure 3: Dedispersed profile of FRB 20220320. The top panel shows the
frequency averaged time series, while the bottom panel shows its dynamic
spectrum, coherently dedispersed at DM $=303$ pc cm-3.

##  3 Upper limits on the FRB repetition rate from our observations

In this section, we show how the observations conducted in our NG campaign
allow us to extract important upper limits on the FRB burst rate. In
particular, we develop a simple model to calculate the expected rate of FRB
events from the whole sample of galaxies of Table 1, considering as a first
case a single population of SGR1935-like magnetars as FRB progenitors. By
taking $\lambda_{\rm mag}$, the average burst rate per magnetar, and $\gamma$,
the power-law energy distribution slope for magnetar bursts, as free
parameters, we will discuss how the upper limits on the rate from the whole
galaxy sample translates into upper limits on $\lambda_{\rm mag}$ and
$\gamma$. We also discuss how our observations can constrain the FRB event
rate if FRBs hypothetically originate from ULXs. Indeed, accretion-based
mechanisms for the FRB engine have been proposed (Waxman, 2017; Katz, 2017,
2020; Sridhar et al., 2021).

###  3.1 SGR1935-like magnetars

We start by computing the total burst rate from our galaxy sample, considering
a single population of magnetars similar to SGR1935. This means that we
restrict our analysis to magnetars having radio efficiency $\eta\sim 10^{-5}$,
i.e. the ratio of energy radiated in the radio and X-ray bands by SGR1935
(Mereghetti et al., 2020; Tavani et al., 2021; Ridnaia et al., 2020; CHIME/FRB
Collaboration et al., 2020; Bochenek et al., 2020) and burst energetics $E\geq
E_{0}$, where $E_{0}=2\times 10^{34}$ erg being the isotropic radio energy
released by FRB 20200428 (Bochenek et al., 2020; Margalit et al., 2020;
CHIME/FRB Collaboration et al., 2020). This energy follows by considering
$d=7$ kpc as the distance of SGR1935 (Margalit et al., 2020).

Following CHIME/FRB Collaboration et al. (2020), we assume that the magnetar
burst rate $\mathcal{R}$ from a given galaxy is proportional to its SFR. In
this way, we compute the number of SGR1935-like magnetars residing in a
certain galaxy by scaling for $N_{\rm mag}/\rm SFR_{\rm MW}$, with $N_{\rm
mag}=29$ (Olausen & Kaspi, 2014; Kaspi & Beloborodov, 2017) the number of
Galactic magnetars and SFR${}_{\rm MW}=1.65\pm 0.19$ M⊙ yr-1 the Galactic SFR
(Licquia & Newman, 2015).

With these prescriptions, the rate expected from the galaxy $i$ of our sample
can be expressed as:

$\displaystyle\begin{aligned} \mathcal{R}(\lambda_{\rm mag},\gamma;>E_{{\rm
min},i,j})&=N_{\rm mag}\,\frac{\rm SFR_{i}}{\rm SFR_{\rm MW}}\times\\\
&\times\int_{E_{{\rm min},i,j}}^{E_{\rm
max}}K_{0}\,\left(\frac{E}{E_{0}}\right)^{-\gamma}\Theta[E-E_{0}]\,dE,\end{aligned}$
(4)

where $E_{{\rm min},i,j}$ is the minimum burst energy detectable from the
galaxy $i$ in the delay bin $j$ (Eq. 1). The integral is the burst rate energy
function, which we assume to follow a power law with index $\gamma$. Note that
the Heaviside function $\Theta$ restricts the case to SGR1935-like bursts,
i.e. with energy $E\geq E_{0}$. We considered the maximum energy $E_{\rm max}$
to be:

$E_{\rm max}=\eta\,E_{\rm mag},$ (5)

with $\eta\sim 10^{-5}$ and $E_{\rm mag}$ is the total magnetic energy
reservoir for a magnetar with magnetic field $B$ (Margalit et al., 2020):

$E_{\rm mag}=3\times 10^{49}\,\left(\frac{B}{10^{16}\,{\rm
G}}\right)^{2}\,\,{\rm erg}.$ (6)

We considered $B=2\times 10^{14}\ \rm G$, the magnetic field strength of
SGR1935 (Israel et al., 2016), and checked that a higher value for $B$ does
not appreciably affect our results.

The burst rate normalization $K_{0}$ can be expressed as a function of the
burst rate per magnetar $\lambda_{\rm mag}$:

$\lambda_{\rm mag}=\int_{E_{0}}^{E_{\rm
max}}K_{0}\,\left(\frac{E}{E_{0}}\right)^{-\gamma}\,dE,$ (7)

yielding:

$K_{0}=\lambda_{\rm mag}\frac{(1-\gamma)\,E_{0}^{-\gamma}}{E_{\rm
max}^{-\gamma+1}-E_{0}^{-\gamma+1}}.$ (8)

Figure 4: Expected burst rate (color-map) as a function of the energy
distribution slope $\gamma$ and the SGR1935-like burst rate per magnetar
$\lambda_{\rm mag}$ from the whole observing campaign of NGs. The red line is
the 95% confidence upper limit obtained by our observations.

Eq. 4 can therefore be re-written as:

$\displaystyle\mathcal{R}(\lambda_{\rm mag},\gamma;>E_{{\rm min},i,j})=N_{\rm
mag}\,\lambda_{\rm mag}\,\frac{\rm SFR_{i}}{\rm SFR_{\rm MW}}\,\frac{E_{\rm
max}^{-\gamma+1}-E_{{\rm min},i,j}^{-\gamma+1}}{E_{\rm
max}^{-\gamma+1}-E_{0}^{-\gamma+1}}\ .$ (9)

We can then compute the total expected burst rate from our NGs sample as the
sum of the rate for each galaxy in each delay bin, weighted by their
corresponding integration time:

$\mathcal{R}_{\rm tot}(\lambda_{\rm
mag},\gamma)=\frac{\sum_{i}^{N}\sum_{j}^{N_{b}}\mathcal{R}(\lambda_{\rm
mag},\gamma;>E_{{\rm
min},i,j})\,T_{i,j}}{\sum_{i}^{N}\sum_{j}^{N_{b}}T_{i,j}},$ (10)

where $N_{b}=7$ is the number of delay bins and $T_{i,j}$ is the total
integration time of the $i$-th galaxy in the delay bin $j$. The total expected
burst rate has a mild dependence upon the slope of the energy distribution and
a and a much more significant dependence upon the burst rate per magnetar as
can be visually assessed in Figure 4. Our observations led to a 95% confidence
level (CL) (Gehrels, 1986) upper limit on the total burst rate of
$\mathcal{R}_{\rm tot}<38$ yr-1. By imposing this upper limit, we obtain a 95%
CL constraint on the burst rate per magnetar that varies between $\lambda_{\rm
mag}<0.38$ magnetar-1 yr-1 for $\gamma\leq 1$ and $\lambda_{\rm mag}<0.47$
magnetar-1 yr-1 for $\gamma\simeq 3$. After marginalizing over the energy
distribution slope $\gamma$, we derive $\lambda_{\rm mag}<0.42$ magnetar-1
yr-1.

Previous works derived constraints for the magnetar burst rate. In particular,
CHIME/FRB Collaboration et al. (2020) obtained $0.007<\lambda_{\rm mag}<0.4$
magnetar-1 yr-1 at 95$\%$ CL from the detection of FRB 20200428 and the non-
detection from a sample of 15 nearby galaxies. However, the authors adopted
slightly different values than us for the distances and SFRs of the galaxies
that are common to our sample (see their Extended Data Table 1) and they
considered a lower $\rm SFR_{\rm MW}=1\ M_{\odot}$ yr-1. If we use their
values in our estimate, we obtain $\lambda_{\rm mag}<0.3$ magnetar-1 yr-1. By
combining our observations with CHIME/FRB Collaboration et al. (2020), we can
obtain an even further improved upper limit on $\lambda_{\rm mag}$. By
assuming distance and SFR values presented in Table 1 for both samples, we
recompute the total rate expected from the joint observations (eq. 9, 10),
which has to be compared with the upper limit obtained from the total
observing time ($\sim 1370\ \rm h$). As a result, we obtain $\lambda_{\rm
mag}<0.25$ magnetar-1 yr-1 at 95$\%$ CL, the most stringent upper limit on the
burst rate per magnetar to date. In Section 4 we will discuss this result in
the framework of the FRB-magnetar connection.

###  3.2 Ultraluminous X-ray sources

An alternative formation channel to the more standard magnetar models predicts
that FRBs can be produced by short-lived relativistic flares from super-
Eddington accreting NSs and BHs (Sridhar et al., 2021). The isotropic energy
emitted by this kind of FRB is postulated to lie in the range $10^{34}$ erg -
$10^{45}$ erg (Sridhar et al., 2021), which implies that these sources would
have been detected with the NC sensitivity. Therefore, the observing time
spent on these galaxies is useful for placing an upper limit on the rate of
FRBs produced by these accreting objects.

We follow the approach described in section 3 and express the rate
$\mathcal{R}_{u,i}$ expected from the population of ULXs in the galaxy $i$ of
our sample:

$\mathcal{R}_{u,i}(\lambda_{u})=N_{u,i}\,\lambda_{u},$ (11)

where $N_{u,i}$ is the number of ULX sources expected in the galaxy $i$ and
$\lambda_{u}$ is the average burst rate per ULX for energies in the
$10^{34}<E<10^{45}$ erg range. The number of ULX sources can be expressed as a
function of the SFR (Kovlakas et al., 2020):

$N_{u,i}=0.51\,\frac{{\rm SFR}_{i}}{{\rm M}_{\odot}{\,\rm yr}^{-1}}.$ (12)

We then expect from Eq. (12) a total number of $\sim 14$ ULXs in the galaxies
we observed. The total expected burst rate $\mathcal{R}_{u,{\rm tot}}$ from
our NGs sample then becomes:

$\mathcal{R}_{u,{\rm
tot}}(\lambda_{u})=\frac{\sum_{i}^{N}\sum_{j}^{N_{b}}\mathcal{R}_{u,i}(\lambda_{u})\,T_{i,j}}{\sum_{i}^{N}\sum_{j}^{N_{b}}T_{i,j}},$
(13)

The observed upper limit at 95$\%$ CL (Gehrels, 1986) on the total burst rate
is $\simeq 38$ yr-1, the same as recovered in Section 3.1, since it depends
only on the total observing time. Therefore, by imposing $\mathcal{R}_{u,{\rm
tot}}<38$ yr-1 we obtain $\lambda_{u}<13$ yr-1 for the average burst rate per
ULX. This is the first upper limit on the FRB repetition rate hypothetically
coming from ULXs. We note that this upper limit is 2-3 orders of magnitude
lower with respect to the reported repetition rate of most active repeaters
$r\sim 10^{3}$ yr-1 from FRB 20121102A and FRB 20180916B (Margalit et al.,
2020). We find this contrast by also computing the repetition rate for
confirmed ULXs only, i.e. without estimating the population of ULXs from Eq.
(12) but considering only already discovered ULXs in the galaxies we observed.
We report the upper limits obtained for each case in Table 4, and discuss the
possible implications of these results in the following Section.

Table 4: Upper limits for the FRB repetition rate (last column) coming from confirmed ULXs. In the $2^{\rm nd}$ column we report the number of ULXs present in a given galaxy. The last row consider the total expected ULXs ensamble derived from Eq. (12). ULX | $N_{\rm u}$ |  $\lambda_{\rm u}$ [yr-1]
---|---|---
IC 342 X-1, IC 342 X-2 | $2$ | $<128$
M82 X-2 | $1$ | $<140$
M101 X-1 | $1$ | $<273$
NGC 6946 X-1 | $1$ | $<227$
All | $14$ | $<13$

##  4 Discussion and conclusions

In this paper we presented a FRB search in a sample of seven NGs taken with
the NC radio telescope. The campaign was 692 h long and yielded the detection
of a 58 Jy ms, 1.8 ms-long burst with a DM = 303 pc cm-3, observed in the
direction of M101, although most likely coming from a more distant source.
Therefore we considered no detections from the monitored galaxies. We used
this result to investigate the connection between FRBs and magnetars, by
computing the total burst rate $\mathcal{R}_{\rm tot}$ expected from our
galaxy sample, assuming, as unique FRB progenitors, magnetars like SGR
J1935+2154, obtaining $\mathcal{R}_{\rm tot}<38$ yr-1 at the 95$\%$ CL. We
considered $\lambda_{\rm mag}$, the average burst rate per magnetar, and
$\gamma$, the slope of the burst energy distribution, as free parameters for
our SFR-based model. In addition, we derived the average FRB rate per ULX from
the same observations on NGs. Indeed, among the target galaxies of our
observational campaign, some host confirmed ULXs, from which, at least
theoretically, an FRB would have had enough energy (Sridhar et al., 2021) to
be detected by the NC.

Since the detection of the Galactic FRB-like signal, it has been tantalizing
to claim that magnetars like SGR1935, i.e. similar in energetics and formed
through core-collapse supernovae (CCSNe), represent the entire cosmological
population of FRBs. Although the implied volumetric rate from the detection of
FRB 20200428 is consistent with the faint energetic of the cosmological rate
density (Lu et al., 2022), SGR1935-like magnetars cannot explain the high
repetition rate of active repeaters (Margalit et al., 2020). Moreover, FRB
20200428 is about one order of magnitude fainter than the average FRB
luminosity (Bochenek et al., 2020; CHIME/FRB Collaboration et al., 2020; Luo
et al., 2020), although giant magnetar flares may be bright enough to fill the
gap (Margalit et al., 2020). The discrepancy in the repetition rate, along
with the discovery of the M81 repeater localized in a globular cluster
(Bhardwaj et al., 2021a; Kirsten et al., 2021), led to consider other, more
exotic NS formation channels (Kremer et al., 2021, 2023), challenging the
presence of a single population of magnetars as FRB progenitors.

Our observations do not constrain well the burst energy slope, although they
somewhat disfavour flat slopes ($\gamma<1$) over steeper ones ($\gamma>1$).
The average burst rate per magnetar is, instead, constrained to be
$\lambda_{\rm mag}<0.42$ magnetar-1 yr-1. This upper limit halves the range
for the magnetar burst rate implied by the STARE2 detection Bochenek et al.
(2020), $0.0036<\lambda_{\rm mag}<0.8$ magnetar-1 yr-1, consistently with the
results from CHIME’s NG observations, $0.007<\lambda_{\rm mag}<0.4$ magnetar-1
yr-1 CHIME/FRB Collaboration et al. (2020). We also showed how the upper limit
lowers to $\lambda_{\rm mag}<0.25$ magnetar-1 yr-1 if we considered our NG
observations combined with the monitoring reported in CHIME/FRB Collaboration
et al. (2020).

Considering the STARE2 detection, Margalit et al. (2020) already pointed out
that the cosmological FRB rate, including repeating sources, can be explained
only by adding a second magnetar population, younger and with a stronger
magnetic field with respect to the SGR1935-like ones (Margalit et al., 2019;
Blanchard et al., 2016). This second population includes more exotic
magnetars, not born through the usual supernovae core collapse, but through a
much more rare formation channel. Our constraints imply that the burst rate
per magnetar of SGR-like events is approximately a factor of two smaller than
previously reported, implying rarer events. In the perspective of a two-
population model, our results imply that rare magnetars should be more
prominent than considered earlier in order to compensate the smaller burst
rate from SGR1935-like magnetars. Moreover, the detection of FRB 20200120E in
a globular cluster (Bhardwaj et al., 2021b; Kirsten et al., 2022b) have
similar implications (Lu et al., 2022), being the formation of magnetars
possible inside globular clusters through compact object mergers, accretion
induced collapse or a WD merger induced collapse (Kirsten et al., 2022b;
Kremer et al., 2021, 2023). However, the $\rm ns$-structures observed in some
bursts from FRB 20200120E could be explained in terms of a recycled
millisecond pulsar origin (Majid et al., 2021; Kremer et al., 2021), hence it
is not clear whether M81-like FRBs could represent this needed population of
rarer FRB progenitors.

Among other exotic, but prominent progenitor models, we find accretion-based
mechanisms (Waxman, 2017; Katz, 2017, 2020; Sridhar et al., 2021). In
particular, the recent model of Sridhar et al. (2021) succeed in explaining
both the energetics, and the chromaticity behaviour seen in FRB 20180916B
(Pastor-Marazuela et al., 2021). Estimating a total number of 14 ULXs present
in our sample of galaxies, we constrained the average rate of FRB events per
ULX to be $\lambda_{u}<13$ yr-1 at the $95\%$ CL. We also provided individual
upper limits for each monitored ULX. These initial estimates show a
discrepancy of a few orders of magnitude when compared to the repetition rates
of the most active repeaters (Margalit et al., 2020). As already pointed by
Sridhar et al. (2021), a strongly-magnetised object in the compact pair could
be necessary in order to power cosmological FRB luminosities, making these
events much rarer and difficult to be detected. In conclusion, our limits on
the burst rate disfavour both magnetars and ULXs as progenitors of very active
repeating sources like FRB 20180916B and FRB 20121102A.

###### Acknowledgements.

We thank the anonymous referee for the useful comments, which helped us
improving the quality of the manuscript. The reported data were collected
during the phase of the INAF scientific exploitation with the Northern Cross
radio telescope.

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