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

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.


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 (∼Jy), and large dispersion measures (DMs) implying cosmological distances.
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; Corresponding author: Shangyu Sun and Wenfei Yu sysun@shao.ac.cn, wenfei@shao.ac.cn 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.: 05 h 31 m 58 s .70, decl.: +33 • 08 ′ 52 ′′ .5; Chatterjee et al. 2017) and identification of its host galaxy (z = 0.19273, ∼970 Mpc; Tendulkar et al. 2017). The bursts from it show highly variable spectra Hessels et al. 2019). Spitler et al. (2016) and Chatterjee et al. (2017) reported a dispersion measure (DM) of 558.1±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 ∼ < 4 kpc) dwarf (∼ 6 × 10 7 M ⊙ ), 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 . 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.

OBSERVATIONS AND ANALYSIS
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 µs, 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 fieldof-view covered FRB 121102 . This corresponds to a search for hard X-ray bursts when the repeating FRB was in active radio bursting phases.
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 BAT-BINEVT tasks were run again to produced the light curves (LCs) from event files corresponding to the specified direction of FRB 121102 (R.A. 82 • .9946, decl. 33 • .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 ±1 ms time window of the radio burst are both below 3σ as shown in the LC (see in Fig. 1 the dashed lines for the average and ±3σ of the rates, and red markers for the ±1 ms time window) and the sky image (see in Fig. 2 the red color indicating significance below 3σ, 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 3σ upper limit of the count rate (= 3 × standard deviation of the rates; binned in milliseconds) we derived is 4.6 cts/s, which is equivalent to 6.9 × 10 −7 erg cm −2 s −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 3σ of the rates, which correspond to 1.2, 0.38, and 0.091 cts/s.  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 (= pulse ∑ i 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× crab rate × 1 sec. For setting up this criteria, we refer to the empirical rules used in the Swift/BAT The pulse searching was conducted with the following conditions: threshold of pulse integral 0.0035 = 0.1× crab unit × 1 s; threshold of s/n ratio 3.5. f In observation 00050100039 (obs. id).
project of transient monitoring 1 , 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 (1day 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 stst.,i ): 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.  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 ±3σ of the rates. See the BAT sky image of this pulse in Fig. 4.
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.
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.

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 (a) X-ray pulse 2, ms timescale  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. 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 3σ found in the event of the radio burst. We are able to put an upper limit of 6.9 × 10 −7 erg cm −2 s −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 (∼970 Mpc Tendulkar et al. 2017), is 7.8 × 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: ∼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.

ACKNOWLEDGMENTS
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.