# A search for hard X-ray bursts occurring simultaneously to fast radio bursts
in the repeating FRB 121102

Shangyu Sun Key Laboratory for Research in Galaxies and Cosmology, Shanghai
Astronomical Observatory, Chinese Academy of Sciences,
80 Nandan Road, Shanghai 200030, China.  Wenfei Yu  Key Laboratory for
Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, Chinese
Academy of Sciences,
80 Nandan Road, Shanghai 200030, China.  Yunwei Yu  Institute of Astrophysics,
Central China Normal University, Wuhan 430079, China  Dongming Mao  Key
Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical
Observatory, Chinese Academy of Sciences,
80 Nandan Road, Shanghai 200030, China.

###### Abstract

The nature of fast radio bursts (FRBs) is currently unknown. Repeating FRBs
offer better opportunity than non-repeating FRBs since their simultaneous
multi-wavelength counterparts might be identified. The magnetar flare model of
FRBs is one of the most promising models which predicts high energy emission
in addition to radio burst emission. To investigate such a possibility, we
have searched for simultaneous and quasi-simultaneous short-term hard X-ray
bursts in all the Swift/BAT event mode data which covered the periods when
fast radio bursts were reported detections in the repeating FRB 121102, by
making use of BAT’s arcmin level spacial resolution and wide field-of-view. We
did not find any significant hard X-ray bursts which occurred simultaneously
to those radio bursts. We also investigated potential short X-ray bursts
occurred quasi-simultaneous with those radio bursts (occurrence time differs
in the range from hundreds of seconds to thousands of seconds) and concluded
that even the best candidates are consistent with background fluctuations.
Therefore our investigation concluded that there were no hard X-ray bursts
detectable with Swift/BAT which occurred simultaneously or quasi-
simultaneously with those fast radio bursts in the repeating FRB 121102.

Radio bursts (1339), Radio transient sources (2008), Neutron stars (1108),
Magnetars (992), X-ray transient sources (1852), Non-thermal radiation sources
(1119)

##  1 Introduction

The fast radio burst (FRB) was a recently recognized class of astrophysical
transient phenomena (Lorimer et al., 2007; Thornton et al., 2013), with
features of short durations (millisecond timescale), high flux densities
($\sim$Jy), and large dispersion measures (DMs) implying cosmological
distances. The localization of several FRBs (Tendulkar et al., 2017; Bannister
et al., 2019; Ravi et al., 2019) even certifies their cosmological origin. The
FRB 121102 was the first discovered repeating FRBs (Spitler et al., 2014;
Petroff et al., 2015; Scholz et al., 2016; Spitler et al., 2016). Afterwards,
the CHIME/FRB Collaboration (CHIME/FRB Collaboration et al., 2019a) discovered
a second repeating one (FRB 180814.J0422+73; CHIME/FRB Collaboration et al.,
2019b) and soon eight more (The CHIME/FRB Collaboration et al., 2019). Many of
these repeating FRBs show more common features in their bursts: complex burst
morphology and sub-burst downward frequency drifts (CHIME/FRB Collaboration et
al., 2019b; Hessels et al., 2019; The CHIME/FRB Collaboration et al., 2019)
although these features are also seen in some nonrepeating FRBs (e.g. Champion
et al., 2016). The repetition of these sources naturally exclude cataclysmic
models for them. However, the physical nature of neither repeating nor
nonrepeating FRB sources is clearly understood.

The repetition of the FRB 121102 enabled interferometric localization of it
(R.A.: 05h31m58${}^{\rm s}.70$, decl.: +33∘08′52${}^{\prime\prime}.5$;
Chatterjee et al., 2017) and identification of its host galaxy ($z=0.19273$,
$\sim$970 Mpc; Tendulkar et al., 2017). The bursts from it show highly
variable spectra (Scholz et al., 2016; Hessels et al., 2019). Spitler et al.
(2016) and Chatterjee et al. (2017) reported a dispersion measure (DM) of
558.1$\pm 3.3$ pc cm-3. First of all, based on the feature of tremendous
energy released in milliseconds and repetition of bursts, its nature is
suspected to relate more to a young active neutron star, for example the
phenomena of magnetar flare and giant pulse (Popov & Postnov, 2010; Kulkarni
et al., 2014; Lyubarsky, 2014; Connor et al., 2016). Secondly, the high
rotation measures (RM) of FRB 121102 ($>10^{5}$ rad m-2; Michilli et al.,
2018) indicate extreme magneto-ionic surroundings of the burst source, and the
estimated magnetic field of such large strength can be explained by that of a
magnetar (for e.g. SGR J1745–2900 Eatough et al., 2013). Thirdly, Tendulkar et
al. (2017) identified the host galaxy of FRB 121102 as a compact (diameter
$\mathrel{\hbox{\hbox to0.0pt{\lower 2.36806pt\hbox{$\sim$}\hss}
\kern-3.00003pt\raise 1.72218pt\hbox{$<$}}}$ 4 kpc) dwarf ($\sim 6\times
10^{7}$ $M_{\odot}$), which is believed to be the crib of superluminous
supernovae or long-duration gamma-ray bursts. They are likely the progenitor
of a millisecond magnetar (Dai & Lu, 1998; Zhang & Mészáros, 2001; Woosley,
2010; Kasen & Bildsten, 2010; Yu et al., 2017), which is hence considered to
be the origin of FRB 121102. Therefore, the young magnetars responsible for
FRBs could be formed from some unusual core-collapse supernovae and then they
are harbored at the center of a supernova remnant (Metzger et al., 2017;
Margalit & Metzger, 2018; Metzger et al., 2019). For a more general
consideration, these young magnetars could also be born from the mergers of
double neutron stars (Dai et al., 2006; Metzger et al., 2008; Yu et al., 2018)
or from the accretion-induced collapse of white dwarfs (Canal et al., 1990;
Nomoto & Kondo, 1991). This possibility at least has been somewhat supported
by the observations of the non-repeating FRBs (Cao et al., 2018; Margalit et
al., 2019). In this case, the young magnetars cannot be associated with a
supernovae remnant, but can still be surrounded by a pulsar wind bubble (Dai
et al., 2017). Therefore, no matter which channel the magnetars originate
from, a persistent radio counterpart emission can be always generated by the
interactions between the ejecta, pulsar wind, and the surrounding medium. By
confronting with the flux of the persistent radio emission and the decreasing
DM of FRB 121102 (i.e., 10% decreasing in seven months Michilli et al., 2018),
the age of the neutron star can be tightly constrained to be about one hundred
years old (Cao et al., 2017; Metzger et al., 2017). In view of its highly
relevant to a young magnetar, it is very natural to expect FRB 121102 could be
accompanied by some high-energy emissions.

The Swift/BAT can cover the entire sky as efficiently as 80–90$\%$ per day
(Krimm et al., 2013) and offers a time resolution of $10^{-4}$ s for trigger
event mode data. It is good for detecting or monitor short-and-bright X-ray
transient sources, and therefore meets the requirement for addressing the
aforementioned scientific questions. A blind search for hard X-ray bursts in
the BAT data of one-year time (2016 October 1 to 2017 September 30) had been
conducted (Sun et al., 2019). Continuing the previous efforts, we searched for
X-ray bursts in all the BAT trigger event mode data that were simultaneous to
all the radio bursts from FRB 121102 that had been reported in the literature.
In addition to the search for simultaneous X-ray bursts, we also performed a
search for possible bursts which did not occur simultaneously in these data.
We present the method and our results achieved in our search for burst signals
in the direction of FRB 121102 with the Swift/BAT data in Sect. 2. Then we
discuss and conclude in Sect. 4.

##  2 Observations and analysis

Table 1: Radio burst detected from FRB 121102 since 2012-11-02. reference |  $N_{\rm rb}$ a | dates of bursts | radio | trigger-mode
---|---|---|---|---
|  | from | to | observatoryb | data
Spitler et al. (2014) | 1 | 2012-11-02 | 2012-11-02 | AO | 00537266000
Spitler et al. (2016) | 11 | 2012-11-02 | 2015-06-02 | AO | 00036376034
Scholz et al. (2016) | 6 | 2015-11-13 | 2015-12-08 | AO, GBT | 00051650045
Spitler et al. (2018) | 3 | 2016-08-20 | 2016-08-20 | Effelsberg | n/a
Law et al. (2017) | 9 | 2016-08-23 | 2016-09-18 | AO, VLA | 00034292075, 00020700007
Gourdji et al. (2019) | 42 | 2016-09-13 | 2016-09-14 | AO | 00034712006, 00081872001, 00020700002
Scholz et al. (2017) | 13 | 2016-09-16 | 2017-01-12 | AO, GTB | 00085966015, 00074948011, 00732188000
Michilli et al. (2018) | 17 | 2016-12-25 | 2017-08-26 | AO, GTB | 00087278003
Hardy et al. (2017) | 13 | 2017-01-16 | 2017-02-19 | Effelsberg | 00050100039
MAGIC Collaboration et al. (2018) | 5 | 2017-02-15 | 2017-03-02 | AO | 00034921009
Gajjar et al. (2018) | 21 | 2017-08-26 | 2017-08-26 | GBT | n/a
Zhang et al. (2018) | 93 | 2017-08-26 | 2017-08-26 | GBT | n/a
Josephy et al. (2019) | 1 | 2018-11-19 | 2018-11-19 | CHIME | n/a
a Number of detected bursts from FRB 121102 .
b Arecibo Observatory (AO); Canadian Hydrogen Intensity Mapping Experiment
(CHIME); Effelsberg Radio Telescope;
Robert C. Byrd Green Bank Telescope (GBT); Very Large Array (VLA).

All the fast radio bursts in FRB 121102 that had been reported in the
literature (since 2014, till August 2019) were investigated. The sample and
the corresponding references are listed in Table 1. We also referred to the
paper of Li et al. (2019) where part of the sample was also collected. Since
the radio bursts in the repeating FRB have a timescale of about milliseconds
in the radio band, to search for high-energy short-term bursts in association
with those radio bursts either simultaneously or quasi-simultaneously, we have
to make use of the event mode data in the Swift/BAT archive. These BAT
triggered event mode data have a time-resolution of about 100 $\mu$s, and the
corresponding time stamp of each photon detected by BAT was recorded.

We first aimed at a search for potential X-ray bursts occurred simultaneously
with those 234 fast radio bursts in the sample list in Table 1. Simultaneous
BAT triggered event mode data (spread in 14 observations of total exposure
about 64 ks) were found available to 46 radio bursts out of the sample.
However, FRB 121102 was not always in the field of view of BAT during these 14
observations, It turned out that there was only one radio burst covered with
simultaneous BAT exposure in the observation 00085966015, so we further
analyzed the dataset in more detail. Beyond the investigation of BAT event
data covering the radio burst, we also searched for any X-ray bursts occurred
before or after the radio bursts in the event data of those 14 observations
when BAT’s field-of-view covered FRB 121102 . This corresponds to a search for
hard X-ray bursts when the repeating FRB was in active radio bursting phases.

(a) BAT high time resolution light curve simultaneous to the radio burst from
FRB 121102 binned in milliseconds. Figure 1: The BAT light curve of FRB 121102
with a time resolution of millisecond around the radio burst which occurred at
04:10:17.434 on 2016-09-18 (referenced to infinite frequency at the solar
system barycenter) as reported by Scholz et al. (2017). This barycentric time
is converted to the Swift time, the $\pm 1$ ms interval of which is marked in
red in the light curve. Dashed lines denote the average and $\pm 3\sigma$ of
the rates. See the corresponding BAT sky image in Fig. 2.

The event mode data were processed by the software package HEASOFT v6.19
following _The SWIFT BAT Software Guide_. The batdetmask tasks were used to
produce the detector quality map from CALDB. The batdetmask tasks calculate
the mask weighting for each event file. The batbinevt tasks were run again to
produced the light curves (LCs) from event files corresponding to the
specified direction of FRB 121102 (R.A. 82${}^{\circ}.9946$, decl.
33${}^{\circ}.1479$) in the following four different energy bands, namely,
15–30, 30–60, 60–150, and 15–150 keV. To generate the sky maps, the batbinevt
tasks were run to convert those event lists to detector plane images (DPIs),
and the batfftimage task was used to covert them into sky maps with photon
counts or significance. As a result, the total exposure time of the event mode
data toward FRB 121102 was about 2.1 ks. The FRBs have millisecond timescales
in the radio band, and it is natural to search their X-ray counterparts on ms
timescales, but not limited in ms timescale alone. Our search for potential
short-term bursts was conducted on four representing timescales, namely 1 ms,
10 ms, 100 ms, and 1000 ms. We decide our shortest timescale is 1 ms because
small binning results in plenty of LC/image data and large uncertainty in
flux, and hence demands more computing resource.

In Figs. 1 and 2, we present the BAT LC (15–150 keV; time bin of millisecond)
and sky image which are simultaneous with the radio burst occurring on
2016-09-18 04:10:17.434 (referenced to infinite frequency at the solar system
barycenter) from FRB 121102 (reported by Scholz et al. (2017); see Table 1).
We convert times between the satellite and the barycenter with barycorr in
FTOOLS, taking into account the relative locations of the satellite, the
geocenter, and the barycenter. The LC time marked in red in Fig. 1 is the
result of converting the FRB barycentric time to that at Swift satellite. The
significances of the two BAT rate measurements in the $\pm 1$ ms time window
of the radio burst are both below 3$\sigma$ as shown in the LC (see in Fig. 1
the dashed lines for the average and $\pm 3\sigma$ of the rates, and red
markers for the $\pm 1$ ms time window) and the sky image (see in Fig. 2 the
red color indicating significance below 3$\sigma$, and the magenta dashed
circle marking the location of FRB 121102). Below we put constraints on the
X-ray flux simultaneous with the radio burst. Conservatively, the measurement
with a larger rate value and a larger uncertainty is used for estimating an
upper-limit of flux. The 3$\sigma$ upper limit of the count rate (= 3 $\times$
standard deviation of the rates; binned in milliseconds) we derived is 4.6
cts/s, which is equivalent to $6.9\times 10^{-7}$erg cm-2s-1 in the entire
energy band of 15–150 keV if we assume an energy spectrum with a photoindex of
2. The count rates in the 10 ms, 100 ms, 1000 ms binned LCs at the radio burst
time are checked, too, All of them below 3$\sigma$ of the rates, which
correspond to 1.2, 0.38, and 0.091 cts/s.

(a) Simultaneous BAT sky image. Figure 2: The BAT sky image in the direction
of FRB 121102 right at the moment when the radio bust occurred at 04:10:17.434
on 2016-09-18 (referenced to infinite frequency at the solar system
barycenter) as reported by Scholz et al. (2017). The magenta dashed circle
marks the nominal size of the point spread function of BAT coded-mask imaging.
The corresponding BAT light curve is shown in Fig. 1.  (a) burst 2 LC, time
bin of 1 ms. Figure 3: The BAT FRB 121102 LC before and after the X-ray pulse
(in red markers) with the highest s/n ratio among the search results as
reported in Table 2. Dashed lines denote the average and $\pm 3\sigma$ of the
rates. See the BAT sky image of this pulse in Fig. 4.

For the processing of the event mode data, we refer to the methods described
in paragraph 4, section 2 in our previous paper of Sun et al. (2019). To avoid
complexities due to bright sources entering into the BAT field-of-view, the
following segments were excluded from the original BAT event data in our
searches based on We are able to put an upper limitour investigations:

(1) large dips occasionally appearing in the LCs with an interval within 1
time bin and an amplitude larger than the standard deviation. After applying
these two conditions, about 85% of the data remains, and

(2) those segments with low signal-to-noise ratios:
$|$ count rate / statistical error $|<1$.

Using these criteria, we obtained the actual segments of the event data for
our burst search. We had performed searches for potential X-ray bursts in the
data sets on times scales of 1 ms, 10 ms, 100 ms and 1000 ms, as described in
paragraph 5, section 2 of the previous paper Sun et al. (2019).

After the computation of fluences ($=\displaystyle\sum_{i}^{\rm pulse}{\rm
rate}_{i}$; called _pulse integrals_ , PIs) of candidate bursts, we then
checked those bursts with fluences above a threshold. In the current study, we
set the fluence threshold as:
0.0035 counts = $0.1\times$ crab rate $\times$ 1 sec. For setting up this
criteria, we refer to the empirical rules used in the Swift/BAT project of
transient monitoring111https://swift.gsfc.nasa.gov/results/transients/, where
sources are considered detected under the following circumstances: (a) the
mean rate is at least 0.003 crab rate, or (b) the peak rate (1-day binned) for
the source is at least 0.03 crab rate with at least a 7-sigma significance.
When we applied 0.03 crab to our short-duration (1s–1ms) pulse search, there
are too many noisy pulses from background fluctuation, so that we need to
enhance the threshold. Furthermore, we check the s/n ratio (
$=\displaystyle\sum_{i}^{\rm pulse}{\rm rate}_{i}/\sqrt{\sum_{i}^{\rm
pulse}{\rm error}_{\rm stst.,i}^{2}}$ ): threshold of s/n ratio 5.0. Whenever
there is a candidate burst above these two thresholds, a sky map corresponding
to the specific time range is then generated for checking whether the
candidate burst has an astrophysical origin. In some cases, certain
instrumental effects caused significant flux fluctuation at the edge of the
sky map (due to small-portion illumination of the detectors by the sources at
the edge of the field of view). In some cases, cosmic ray events probably
caused widespread illumination of the detectors. We exclude these events and
remove the corresponding time intervals in the LCs.

##  3 Results

Table 2: X-ray pulses with the highest s/n ratios from the search. | pulse timea | pulse integralb | pulse
---|---|---|---
| start time (s) | stop time (s) | (cts) | s/n ratioc
search in 1 s binned and 0.1 s binned LCs
no candidate found
search in 0.01 s binned LCs
1 | 16539.365 | 16539.405f | 0.00762 | 3.63
search in 0.001 s binned LCs
2 | 15627.204 | 15627.209f | 0.00500 | 3.77
3 | 16167.264 | 16167.269f | 0.00503 | 3.70
4 | 16567.854 | 16567.859f | 0.00449 | 3.69
5 | 22030.669 | 22030.674f | 0.00470 | 3.73
a Swift time in seconds - 509200000
b $=\displaystyle\sum_{i}^{\rm pulse}{\rm rate}_{i}$ ; c
$=\displaystyle\sum_{i}^{\rm pulse}{\rm rate}_{i}/\sqrt{\sum_{i}^{\rm
pulse}{\rm error}_{\rm stst.,i}^{2}}$
The pulse searching was conducted with the following conditions:
threshold of pulse integral 0.0035 = $0.1\times$ crab unit $\times$ 1 s;
threshold of s/n ratio 3.5.
f In observation 00050100039 (obs. id).

As a result of searching in 1 ms, 10 ms, 100 ms and 1000 ms timescales with
the threshold of s/n ratio 5.0, there is no candidate passing all the filters.
To be careful with our search, we select pulses with highest s/n ratios to
check what they look like. As we lower the threshold of s/n ratio to 3.5, five
pulses are left, as reported in Table 2. There is one found from the search in
the 10 ms timescale; four from that in the 1 ms timescale. All of them have
the s/n ratios between 3.5 and 4, in observation 00050100039, which might be
associated with the radio burst occurring at 2017-02-19 16:37:48.114137
(referenced to infinite frequency at the solar system barycenter) reported by
Hardy et al. (2017). All the pulses are found in this observation because the
condition of BAT exposing toward FRB 121102 in this observation was the best
among all. Amongst the five pulses, pulse 2 has the shortest separation of
about 800 s after the radio burst. The other pulses have separations of about
930 s–7200 s. They all happen to be after the the radio burst because the
radio burst lied in the beginning of the BAT observation. We present the LCs
and sky images for pulse 2 (1 ms timescale) in Figs. 3 and 4. In the skymap of
the X-ray pulse, we see that in the source direction the significance
indicated by colors is only slightly higher than that in other regions, and
cannot regard them as astrophysical bursts.

(a) X-ray pulse 2, ms timescale Figure 4: The BAT sky image in the direction
of FRB 121102 taken during the time periods of the X-ray pulse with the
highest S/N ratio among the searches as reported in Table 2. The magenta
dashed circle marks the nominal size of the point spread function of BAT
coded-mask imaging. See the BAT LC before, on, and after the moment in Fig. 3.

For evaluation of the statistical significance, we calculate the number of
false positives above a given threshold to be expected from screening those
BAT count rates below null by assuming that the count rates are affected by
purely uncorrelated Gaussian noise. The number of false positive pulses
expected above the s/n ratio of 3.5 for the 10 ms timescale is 0.89, and for
the 1 ms timescale 7.6. The number of candidates from the search is 1 for the
10 ms timescale, and 4 for the 1 ms timescale. We find that the candidates are
compatible with being statistical fluctuations.

##  4 Conclusions

We have searched for simultaneous short duration hard X-ray bursts as well as
quai-simultaneous short duration bursts in the direction of FRB 121102 in the
Swift/BAT archival event mode data in which radio bursts were detected from
FRB 121102. There were existing BAT X-ray event mode data taken simultaneously
to a radio burst detected in FRB 121102, but there was no X-ray signal over
$3\sigma$ found in the event of the radio burst. We are able to put an upper
limit of $6.9\times 10^{-7}$erg cm-2s-1 of a hard X-ray burst in the energy
band 15–150 keV simultaneous to the radio burst from the repeating FRB 121102,
assuming a photo index of 2. This limit on flux, converted into luminosity
assuming isotropy and given the distance to the source ($\sim$970 Mpc
Tendulkar et al., 2017), is $7.8\times 10^{49}$erg s-1. In conclusion, we have
not found evidence that supports that the source of FRB 121102 radiates strong
hard X-ray burst emission detectable with current X-ray instrument like
Swift/BAT simultaneously with those radio bursts.

We noticed that recent detection of a bright radio burst (with two pulses)
from the magnetar SGR 1935+2154 (Scholz & Chime/Frb Collaboration, 2020;
Bochenek et al., 2020) while it was in active bursting phase (including
Swift/BAT; Palmer, 2020) and subsequent identifications of its association
with X-ray and soft gamma-ray bursts (Mereghetti et al., 2020; Tavani et al.,
2020; Zhang et al., 2020) have confirmed that X-ray bursts or burst activities
could be related to some FRBs in the local distances. The measured count rate
with BAT from SGR 1935+2154 was 350k counts/s on a 1 second timescale over the
full detector sensitivity range. If we consider to put it as far away as FRB
121102 (SGR 1935+2154: $<10$ kpc; FRB 121102: $\sim$970 Mpc Kozlova et al.,
2016; Tendulkar et al., 2017), then the predicted flux is still below the
upper limit that we derived in this paper.

We note that the topic is very relevant to the recent breakthrough made
through the study of SGR 1935+2154, but still any X-ray bursts in possible
association with the FRBs of the same mechanism but originated at cosmological
distances would still be well below the sensitivity of current wide field-of-
view X-ray instrument like Swift/BAT. W.Y. would like to thank Josh Grindlay
of Harvard University and Craig Markwardt of GSFC and Jean in’t Zand of SRON
for stimulating discussions in the past on Swift /BAT data. W.Y. and S.Y.S.
would like to thank David Palmer of LANL for very valuable comments on our
previous analysis of BAT data. This work was supported in part by the National
Program on Key Research and Development Project (Grant No. 2016YFA0400804) and
the National Natural Science Foundation of China (grant Nos. 11333005,
U1838203, and 11822302). S.Y.S. thank Zhen Yan and Stefano Rapisarda for
helpful discussions for this study. S.Y.S. also acknowledges support from the
International Postdoctoral Exchange Fellowship Recruitment Program of China
Postdoctoral Council in 2018. W.Y. also acknowledges the support by the FAST
Scholar fellowship in 2017, which is supported by special funding for advanced
users, budgeted and administrated by Center for Astronomical Mega-Science,
Chinese Academy of Sciences (CAMS). In this work, the authors used the data
supplied by NASA’s High Energy Astrophysics Science Archive Research Center in
the US. The authors used the data products from the Swift mission, which is
funded by NASA.

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