First joint observation by the underground gravitational-wave detector, KAGRA, with GEO600

We report the results of the first joint observation of the KAGRA detector with GEO600. KAGRA is a cryogenic and underground gravitational-wave detector consisting of a laser interferometer with three-kilometer arms, and located in Kamioka, Gifu, Japan. GEO600 is a British--German laser interferometer with 600 m arms, and located near Hannover, Germany. GEO600 and KAGRA performed a joint observing run from April 7 to 20, 2020. We present the results of the joint analysis of the GEO--KAGRA data for transient gravitational-wave signals, including the coalescence of neutron-star binaries and generic unmodeled transients. We also perform dedicated searches for binary coalescence signals and generic transients associated with gamma-ray burst events observed during the joint run. No gravitational-wave events were identified. We evaluate the minimum detectable amplitude for various types of transient signals and the spacetime volume for which the network is sensitive to binary neutron-star coalescences. We also place lower limits on the distances to the gamma-ray bursts analysed based on the non-detection of an associated gravitational-wave signal for several signal models, including binary coalescences. These analyses demonstrate the feasibility and utility of KAGRA as a member of the global gravitational-wave detector network.

We report the results of the first joint observation of the KAGRA detector with GEO 600. KAGRA is a cryogenic and underground gravitational-wave detector consisting of a laser interferometer with three-kilometer arms, and located in Kamioka, Gifu, Japan. GEO 600 is a British-German laser interferometer with 600 m arms, and located near Hannover, Germany. GEO 600 and KAGRA performed a joint observing run from April 7 to 20, 2020. We present the results of the joint analysis of the GEO-KAGRA data for transient gravitational-wave signals, including the coalescence of neutron-star binaries and generic unmodeled transients. We also perform dedicated searches for binary coalescence signals and generic transients associated with gamma-ray burst events observed during the joint run. No gravitational-wave events were identified. We evaluate the minimum detectable amplitude for various types of transient signals and the spacetime volume for which the network is sensitive to binary neutron-star coalescences. We also place lower limits on the distances to the gamma-ray bursts analysed based on the nondetection of an associated gravitational-wave signal for several signal models, including binary coalescences. These analyses demonstrate the feasibility and utility of KAGRA as a member of the global gravitational-wave detector network.

Introduction
The first direct observation of gravitational waves (GWs) [1] opened a new branch of astronomy. In their first three observing runs, Advanced LIGO and Advanced Virgo have identified 90 candidates with probability of astrophysical origin greater than 50% [2][3][4][5], all of which were consistent with being produced by the inspiral and merger of compact-object binaries comprised of black holes (BHs) or neutron stars (NSs). During the most recent observing run, signals were detected at a rate of greater than 1 event per week [3,5], and this rate is expected to grow rapidly as detector sensitivity improves [6]. There is also the potential to detect GWs from other sources, such as core-collapse supernovae [7,8] cosmic strings [9,10], and long gamma-ray bursts (GRBs) [11][12][13][14], which would provide probes into the astrophysics of these objects [15,16] and further insights into fundamental physics [15,17,18].
Optimal use of GW data relies on observations by a network of detectors. Laser interferometer GW detectors are essentially all-sky monitors but have low sky-localization accuracy for short-duration transients. Determining the source position or host galaxy for short transients relies mostly on triangulation between widely separated detectors [6,[19][20][21][22][23]. Multiple detectors with different orientations are also required to disentangle the two wave polarizations, which in turn is required, for example, for some tests of general relativity [1,17,[24][25][26].
Measuring both polarizations is also required for determining the source orientation, which is needed to determine the distance to binary sources (vital for measurements of the Hubble constant [27][28][29][30]). It can also give information on GRB beaming [31]. Multiple detectors also provide redundancy against detector downtime and improve the sky coverage of the network.
In this paper we report the results of the first joint observation of a new detector in the global network: KAGRA. The KAGRA detector [32] took scientific data from April 7 through April 20, 2020, at the end of the third observing run (O3) of the LIGO-Virgo-GEO network. The LIGO and Virgo detectors were forced to terminate operations prematurely due to the COVID-19 pandemic, but the GEO 600 (abbreviated in this paper as GEO) detector continued operations and collected data jointly with KAGRA over this period.
We present the results of analyses of this joint GEO-KAGRA run data for transient GW signals. We perform four of the searches that are standard for LIGO-Virgo observing runs.
Two of these scan all of the data for signals arriving from any direction at any time: a search for binary NS (BNS) coalescences [2,3,33,34], and a search for generic unmodeled short transients (bursts) [35][36][37]. The other two analyses are dedicated searches for binary coalescence signals and GW bursts associated with GRB events observed during the joint run [38][39][40][41]. No significant candidate GW events are identified, which is expected given the sensitivity of KAGRA at this early stage in its commissioning. However, the sensitivity of KAGRA is expected to improve by more than two orders of magnitude over the coming years as its design sensitivity is achieved [6]. These analyses demonstrate the value KAGRA will have as a member of the global network as its sensitivity increases. This paper is structured as follows. In Section 2 we describe the KAGRA and GEO detectors, and the joint observing run. In Section 3 we present the all-sky search for BNS coalescences. In Section 4 we present the all-sky search for generic bursts. In Section 5 we present the compact binary coalescence (CBC) and burst searches following up GRBs observed during the joint run. We conclude with a discussion of the prospects for future joint observations in Section 6. The construction of KAGRA started in 2010. However, the start of tunnel excavation was delayed until 2012 due to a major earthquake on March 11, 2011. The tunnel excavation was completed by May 2014, then the installation of the laser interferometer started [32,44].

GEO-KAGRA Observing Run
The initial test of KAGRA with room temperature mirrors was completed by March 2016, and the first operation of the 3 km Michelson interferometer was done from March to April 2016 [32,44]. After the cryogenic systems and mirrors were installed, a test operation of the interferometer with one cryogenic mirror was performed from April 28 to May 6, 2018 [45].
By April 2019, most of the interferometer components had been installed, and the commissioning work started. In August 2019, the first lock of the Fabry-Perot Michelson interferometer configuration was achieved. The first lock of the power-recycled Fabry-Perot Michelson interferometer (PRFPMI) configuration was accomplished in January 2020. The signal readout scheme was upgraded from a conventional radio-frequency (RF) readout to a direct-current (DC) readout with an output mode cleaner in February 2020. The injected laser power was 5 W. The power recycling gain for the carrier field in the PRFPMI configuration was measured to be around 11-12. The circulating power in the Fabry-Perot arm cavities was 21-25 kW per arm.
Over the course of six months from August 2019, the detector noise floor was reduced by 3-4 orders of magnitude. A standard measure of interferometer sensitivity is the volumeand angle-averaged distance to which the inspiral of a 1.4 M -1.4 M binary system can be detected with a matched-filter signal-to-noise ratio (SNR) of at least 8 [6,46]. From February 25 to March 10, 2020, KAGRA conducted observations with a BNS observable range of about 600 kpc. After further commissioning work, the sensitivity of KAGRA was improved to reach a BNS observable range of approximately 1 Mpc by the end of March.
KAGRA then performed an observation run jointly with GEO from April 7 through 20, 2020. Since the thermal noise was not a major noise source at this point, the test-mass mirrors were not cooled during this run. Further details of the detector design and construction history are given in [32].
The sensitivity of KAGRA during the joint GEO-KAGRA run was limited at low frequencies (below 100 Hz) by the local control noise of the mirror suspensions, arising from insufficiently optimised damping control filters. Above 400 Hz, the sensitivity was limited by laser shot noise. At intermediate frequencies the noise is not well-modelled but shows some coherence with environmental acoustic noise, which may arise from scattered light coupling.
During the joint run, data is flagged as being in observing mode when the PRFPMI configuration is locked with DC readout. Fixed-frequency lines are added to the test-mass feedback control signals to calibrate the data. The feedback control signals are monitored for saturations or other anomalies, and the data acquisition system is checked offline for errors. If any anomalies are found in these checks, the observing mode flag is removed. The GW searches presented in this paper are performed exclusively on data that are flagged as observing mode, except for the analysis of GRB 200415A in Section 5. At the time of GRB 200415A, the detector was locked, but there were a few personnel still near the detector following earlier maintenance work. Thus, the data at this time was not flagged as observing mode. However, subsequent investigation of the data found no anomalies, and we conclude that we can use the data around the time of GRB 200415A for GW searches.

GEO 600
GEO [47][48][49] is a British-German interferometric GW detector with 600 m arms located near Hannover, Germany. Similar to other GW detectors, the design is based on a Michelson interferometer with a number of features to enhance the sensitivity. The GW signal is read out by controlling the differential arm length slightly off of the dark fringe in order to couple the differential arm motion to the direct-current power at the output. At high frequencies, the detector is limited by quantum shot noise. The shot noise originates as vacuum fluctuations entering the interferometer at the output. By replacing the normal vacuum fluctations with a squeezed vacuum, the quantum noise is reduced in the measurement quadrature [50].
In contrast to the KAGRA detector, the test masses of GEO are made of fused silica and operate at room temperature [51]. Their diameter, thickness and mass are 18 cm, 10 cm and 5.6 kg, respectively. The power injected is about 3 W, which leads to about 3 kW of circulating power in the power recycling cavity which is then 1.5 kW circulating power per arm. GEO uses folding in the arms to give an optical length of 1200 m for each arm [48,49].
Normally, the GEO detector is operated in data-taking astrowatch mode when the detector is not being used for instrument science research. For the joint GEO-KAGRA run period, the detector was operated in a stable configuration that included squeezed vacuum injection Right: BNS inspiral ranges for GEO and KAGRA over the joint run. The gap around day 6 and 7 was caused when both detectors were affected by bad weather and were unable to lock.
for increased sensitivity. The squeezer has a high duty cycle; squeezing was applied for 97.9% of the observation time.

Joint Observing Run and Data Quality
The GEO-KAGRA joint run period was between April 7 2020 08:00 UTC and April 21 2020 00:00 UTC. Figure 1 shows representative sensitivities of the detectors during the run, as measured by the amplitude spectral density of the calibrated strain output, and the evolution of the detectors' sensitivity over time, as measured by the BNS inspiral range. Table 1 shows the observing times and the duty cycles for two interferometers, the latter defined as the percentage of the total run duration in which the instruments were observing.
The duty cycle of KAGRA was lower than that of GEO for several reasons. One was that alignment sensing and control using wavefront sensors was not implemented by the time of the run, so that the interferometer could not be operated for long periods. Furthermore, following loss of lock of the interferometer it often took a long time to adjust the alignment in order to recover lock.
While the quiet underground environment of KAGRA provides advantages in the operation of the instrument, KAGRA is not completely free from the effects of bad weather.  Table 1 The time length of the observing mode and the duty cycle for GEO and KAGRA for the period April 7 2020 08:00 UTC to April 21 2020 00:00 UTC. data shown in Fig. 1 is a period when KAGRA could not operate due to a storm caused by a low-pressure system that passed through Japan at that time.
Following the joint run the vibration isolation control system has been improved and additional environmental monitors and the wavefront sensor system have been installed.
This has led to an increase in KAGRA's duty cycle.
The strain data from each interferometer is generated by processing and combining raw electronic signals coming from the differential arm length control using a detailed model of the control system including the optical response of the interferometer. Any errors in the measurements which inform the model will lead to a systematic error in the calibration.
In general, systematic error is complex-valued, frequency-dependent, and time-dependent.
The calibration uncertainty of the data used in this paper are within ±10% in amplitude and within ±10 deg in phase (68% C.L.) between 30 Hz and 1500 Hz and between 40 Hz and 6 kHz for KAGRA and GEO, respectively. In addition, a cleaning process [54] using auxiliary channels is applied to the GEO data to remove some bilinear noise from the gravitational wave strain data.
We have observed many short, transient noise fluctuations, known as glitches, in each detector. During the joint observing period, the median rates of glitch triggers generated by the data-monitoring program Omicron [55,56] with SNR larger than 6.5 were 10.3 per minute for GEO and 6.8 per minute for KAGRA. These values are significantly larger than the glitch rates during the first and the second parts of O3 (O3a and O3b) of LIGO-Virgo, which were 0.29-0.32 per minute, 1.1-1.2 per minute and 0.47-1.1 per minute for LIGO-Hanford, LIGO-Livingston and Virgo, respectively [3,5]. On the other hand, the glitch rates of GEO and KAGRA were comparable with the rate of 14 per minute in Virgo during the second observing run (O2) [3], which was the first observing period for the Advanced Virgo project. The investigation of sources of glitches in GEO and KAGRA is ongoing by identifying statistical coincidences and physical couplings between the auxiliary channels and the strain channel.
One method to reduce the impact of glitches on GW searches is through the use of dataquality flags, lists of time segments that identify the status of detectors or the likely presence of a particular instrumental artefact. Three categories of data-quality flags are used in GW searches [57,58]. Category 1 flags indicate that the data have been severely impacted by 20 noise and should not be used for astrophysical searches. Category 2 flags indicate that the data are predicted to contain non-Gaussian artefacts based on glitches in auxiliary channels and known physical couplings to the strain data. Category 3 flags indicate that the data are predicted to contain non-Gaussian artefacts based on glitches in auxiliary channels and statistically significant correlations between glitches in auxiliary channels and glitches in the strain data. GEO has introduced data-quality flags corresponding to Category 1 and Category 3. KAGRA had not introduced data-quality flags by the time of the joint run; they are planned to be introduced before the next observing run.

All-sky binary search
To search for compact binary coalescence (CBC) signals, we first perform a matched-filter search and then rank candidate events with a multi-dimensional classifier using the GstLAL library [59][60][61]. Because of their short duration, high-mass binary coalescences are difficult to distinguish from glitches. In this search, it was found that the brief observation period did not provide a sufficiently large data set to train the ranking statistic, leading to noise features being incorrectly assigned high statistical significance. In contrast, because of their longer duration, BNS waveforms are easier to distinguish from noise transients, and despite the short observation period there is sufficient data to train the GstLAL detection system to perform well for this class of GW source. For this reason we restrict the search to BNS sources only.
Except for restricting the mass parameter range to BNS sources, the GstLAL configuration for this search is the same as those for our most recent GW transient catalogs, GWTC-2.1 [4] and GWTC-3 [5], and for the O3a subsolar-mass binary search [62], with one change: the event clustering based on the matched-filter SNR is disabled, and instead a data reduction step based on SNR and the signal-consistency test statistic is newly introduced. This change improves the GEO-KAGRA sensitive range by approximately 10%. This new finding will also help improve future LIGO-Virgo-KAGRA analyses.
Matched filtering is done by comparing the data to a set of template waveforms called a template bank [63][64][65][66]. We use the same template bank as was used in the first Advanced LIGO observing run (O1) [67,68] but with the component masses restricted to the range 1 M to 3 M , which conservatively covers the range expected for NSs [5]. Templates are  [64,69,70] is used, while for higher masses the reduced-order model of the SEOBNRv4 approximant [71] is used. This subset of the O1 template bank was tested against a set of BNS signals with masses distributed uniformly across the search mass range and using noise power spectral densities typical of GEO and KAGRA during their joint run. The fitting factor [72] was above 0.9 for >99% of simulated signals, with the exceptions being simulations for the chirp mass larger than 2.4M . The fitting factor was above 0.97 (the threshold commonly used in LIGO-Virgo searches [5]) for all signals with chirp masses below 2 M , corresponding to component masses below 2.3 M for an equal-mass binary.
GstLAL defines triggers as the maximum of SNR over 1 s windows which exceed a threshold of 4. It defines coincident triggers as triggers from each detector associated with the same template and with coalescence times within 32.5 ms of each other. This time window accounts for the maximum light-travel time (27.5 ms) between GEO and KAGRA as well as the uncertainty in the inferred coalescence time at each detector. Candidate events comprise both coincident triggers and non-coincident triggers. We define the network SNR as the root-sum-square of the SNRs for coincident triggers, and simply the SNR for non-coincident triggers. We discard candidate events that have network SNR below 7 because there are so many noise background events at those low SNRs that it is hard to distinguish true signals from noise.
GstLAL ranks candidate events based on the logarithm of the likelihood ratio L, which is a measure of how signal-like a given event is. The likelihoods used in this analysis are constructed using the SNR, a signal-consistency test, the differences in time and phase between the triggers from different detectors when the candidate event consists of coincident triggers, the information of which set of detectors ({GEO}, {KAGRA}, or {GEO, KAGRA}) form the event, the sensitivity of the detectors to the exact template masses at the time of the event, the rate of triggers in each of the detectors at the time of the event, and the relative frequency with which signals are expected to be recovered by each template given the assumption that astrophysical sources are distributed uniformly in the logarithm of the masses.
GstLAL uses Monte Carlo techniques to estimate the distribution function f (ln L) for the log-likelihood ratios assigned to candidates resulting from the noise process. From f (ln L), the total number of candidates collected in the experiment, and the experiment's duration we compute the mapping from a log likelihood-ratio threshold ln L th to the false-alarm rate, FAR(ln L th ), which is the rate at which the noise process yields candidates at or above the given threshold.

Search results
For the GEO-KAGRA search, the total amount of data analyzed for each detector combination was 4.59 days for GEO-only, 0.90 days for KAGRA-only, and 6.21 days for two-interferometer observations, for a total of 11.70 days (0.032 years).

Search sensitivity
We estimate the sensitive spacetime volume (product of sensitive volume and livetime) of this search to CBCs by adding simulated signals to the data and repeating the analysis [73].
Since GEO and KAGRA were not sensitive enough to constrain the BNS merger rate beyond  Figure 3 shows the sensitive spacetime volume as a function of the iFAR threshold. This volume is computed by integrating detection efficiency over distance with appropriate weighting, where the efficiency is defined as the fraction of simulated signals that exceed the iFAR threshold within each distance bin. When we compute this fraction, we include GEO-only, KAGRA-only, and GEO-KAGRA times. The spacetime volume is a decreasing function of the threshold, approximately 3 × 10 −2 Mpc 3 years to 2 × 10 −2 Mpc 3 years for iFARs from one per year to one per million years. Figure 3 also shows the equivalent sensitive range, defined as the radius of a sphere of the same average spatial volume, which may be compared to Figure 1. The iFAR of the most significant candidate corresponds to a range of ∼0.6 Mpc, which can be taken as the approximate sensitive range of this analysis.

All-sky burst search
The search pipeline coherent WaveBurst (cWB) [79,80] is an algorithm for the detection and reconstruction of GW transient signals with durations of typically up to a few seconds.
The algorithm searches for coincident excess signal power in a network of GW detectors without assuming specific waveform models, and therefore is suitable for searching for GW transients from a range of different sources. It is used in all-sky burst searches [35,36,81], as well as for example in searches for GWs from binary coalescences [2,3,5] and core-collapse supernovae [82].
Analyses with cWB are performed in a wavelet domain [83] on normalized data transformed at various resolution levels. Wavelets with amplitudes above the typical fluctuations of detector noise are selected and grouped into clusters. Clusters that are correlated in multiple detectors are identified as coherent events. For coherent events, waveforms are reconstructed based on maximum-likelihood-ratio statistics [79]. Events are ranked by their coherent network SNR η c [79] and those with η c > 5 are stored for further processing.
Due to the high rates of glitches and a large number of noise coincidences found in the GEO-KAGRA network, we apply an additional constraint in which only one polarization component of a GW candidate event is reconstructed. This constraint has been employed in other LIGO and Virgo searches [35,36,81,82]. It is effective in mitigating the background event rate, and allows the analysis to search for the GW polarization to which the network has maximum sensitivity from each sky direction [84,85]. However, for non-aligned detectors, such as GEO and KAGRA, each detector can be sensitive to different polarizations at any given sky location. In this case the constraint may lead to the rejection of real events. Also, where the network is sensitive to both polarizations, a significant portion of the signal energy contributes to the noise estimate. In extreme cases, the contribution may be so large that the signal becomes undetectable. While reconstructing both polarizations may help reduce false negative rate, lifting this constraint would increase substantially the background event rate as well as the computational cost.
To reduce further the rate of noise events falsely identified as GW signals, we apply additional selection cuts. In this work we use the network correlation coefficient c c [79], which is a ratio between correlated and total energy of the signal. GW signals have c c ≈ 1; we exclude events with c c < 0.55. We also employ the effective number of time-frequency resolution levels used for event detection and waveform reconstruction [86]

Background and search results
Given that the GEO-KAGRA network sensitivity is limited both at frequencies 100 Hz and 1 kHz (see Figure 1), our analysis spans the frequency range of 64-1024 Hz. The data is down-sampled and periods of poor data quality are removed, similar to the all-sky searches for burst signals in O1 and O2 [35,36]. Intervals with at least 600 s of continuous coincident data are required, and the total analysed coincident time between GEO and KAGRA is equal to 4.38 days. The background event distribution is estimated by artificially time-shifting the data from one detector with respect to the other. The time shifts are multiples of 1 s, larger than the time required for a GW signal to travel between the detectors so that any identified signal is not of astrophysical origin. In total, a background livetime of 7.2 years is obtained.    It is consistent with the background and is not significant enough to be considered a GW event.

Search sensitivity
We estimate the search sensitivity to potential GW transients by adding simulated signals  Table 2. In addition to these ad hoc signals, two astrophysically motivated signals are used: the reconstructed signal of GW150914 [1] and a simulated core-collapse supernova waveform referred to as SFHx [87]. The simulated signals are distributed uniformly over the sky and in polarization angle.
For SG waveforms, we use both elliptical and circular polarizations: the sources of circular SGs are assumed to be optimally oriented while the sources of elliptical SGs have isotropically distributed orientations. GA waveforms are linearly polarized, while WNB waveforms have uncorrelated equal-amplitude polarizations. For SFHx, we use the optimal orientation as the waveform is only available at this observing angle. Each signal is simulated at a wide range of amplitudes, characterized by the root-sum-squared strain h rss : These signals are then recovered using the search method described above and the detection efficiency is defined as the fraction of signals that produce an event which passes the selection cuts and has an iFAR ≥ 1 year. Table 2 shows for each waveform type the h rss amplitude at which the detection efficiency reaches 50% and 90%. As mentioned earlier, the constraint employed in cWB affects the sensitivity of networks of two detectors. This effect is more prominent when the reconstructed waveform energy is distributed across different polarization components. As a result, the detection efficiencies for these waveforms are less than 90% even for large values of h rss .
For these waveforms, we put N/A in the column corresponding to 90% detection efficiency.
These h rss limits follow the network noise spectra (Figure 1).
Assuming isotropic and narrow-band emission by a source, the energy emitted in GWs is given by [81]: where r is the distance to the source and f 0 is the central frequency. This equation is valid for unpolarized signals such as WNBs, while for SG signals, the rotating system emission has to be accounted for by multiplying the right-hand side of Eq. (2) by a factor of 2/5 [88].
Using Eq. (2) and the h rss limits from Table 2, we can estimate the minimum energy needed to be radiated by a population of standard-candle sources at a distance of r = 10 kpc to give  Table 2 The GW morphologies used to quantify the search sensitivity. The first column shows the waveforms used. The second and third columns show the h rss values at which 50% and 90% detection efficiencies are achieved at an iFAR of 1 year. For the astrophysical waveforms the second and third columns show the luminosity distance at which these efficiencies are achieved.
a 50% detection efficiency. The results are shown in Figure 6. Again, the general behavior is determined by the power spectral density of the network (Figure 1).

Gamma-ray burst analyses
GRBs are targets of interest in GW astronomy because the astrophysical processes that power them, specifically massive stellar core collapse [7,8,[11][12][13][14] and CBCs [31], may also emit detectable GWs. By targeting GRBs with tailored search methods we can potentially detect weaker associated GWs than would be identified with non-targeted analyses [85,89]. GRBs display a bimodality in their joint duration-spectral-hardness distribution [90].
The physics governing the bulk motion of matter during these events is complex, so we do not have robust models of the resulting GW emission, though a number of speculative models for strong GWs emission have been proposed, such as long-lived bar-mode instabilities and disk fragmentation instabilities [11][12][13][14]. We therefore use a minimally modeled search algorithm X-Pipeline [85,94] to target these GRBs. Short-hard GRBs (duration < 2 s) can be produced by NS binary coalescences, a connection that was long proposed [95][96][97][98] and observationally confirmed by the multimessenger studies of GW170817/GRB 170817A [31,33,[99][100][101][102][103][104]. We therefore target them with a modeled CBC search algorithm PyGRB [89,105] in addition to the more generic minimally modeled During the joint GEO-KAGRA run, 4 GRBs were detected coinciding with science data taking in both GEO and KAGRA; see Table 3. Our minimally modeled search algorithm was able to analyze all of these given its data requirements. GRB 200415A and GRB 200420A were short duration, therefore our modeled search algorithm was also used to analyze them.
GRB 200415A was subsequently associated [106,107] with a magnetar giant flare in the nearby galaxy NGC253 at 3.5 Mpc based on its sky position, temporal and spectral properties and inferred energy. All GRB properties were taken from the Fermi Gamma-ray Burst Monitor (GBM) Catalog [108][109][110][111][112], with one exception: the minimally modeled analysis of GRB 200415A took sky position data from a preliminary IPN triangulation [113] for practical 29 GRB Name Data Source Type Analysis

200420A
Fermi -GBM Short X-Pipeline & PyGRB Table 3 GRBs observed during GEO-KAGRA run times when both detectors were taking science-quality data. GRB 200415A and GRB 200420A were short-duration GRBs, and so are analysed by both searches.
reasons. Given the coarse angular sensitivity of the GW detector network, the very small difference does not affect the results in any significant way.

Binary coalescence search targeting short GRBs
By targeting the times and sky positions of short GRBs, we can perform a deep, coherent matched filter analysis for associated GWs from BNS and NSBH binaries. This analysis is called PyGRB [89,105], and forms part of the larger PyCBC analysis toolkit [114] with key components in the LALSuite library [115]. This approach has been used in many previous observing runs of the LIGO and Virgo detectors [38][39][40][41] and here we deploy a PyGRB analysis that is functionally identical to that used in the most recent LIGO-Virgo analyses [40,41], with only some changes to the configuration that are appropriate for the data being analyzed, as outlined below.
The PyGRB search performs a matched filter coherently across the operational GW detector network around the time of each short GRB. In this analysis we filter in the frequency range 40-1000 Hz with a bank of template waveforms [66,116] generated with an aligned-spin point-particle model, IMRPhenomD, that includes inspiral, merger, and ringdown phases [117,118]. The bank includes waveforms representing BNS and NSBH systems, where NSs have dimensionless spins ≤ 0.05. 1 Within these bounds, NSBH templates are further constrained to the region in parameter space where the combination of masses and spins could give rise to tidal disruption of the NS, and therefore potentially produce a GRB following [121,122], assuming a very stiff 2H equation of state [123] and requiring a non-zero remnant mass. Additionally, we place an inclination constraint motivated by the expected 1 The fastest known spinning pulsar has a dimensionless spin magnitude of ∼0.4 [119] and masses bound by [1.00, 2.83] M and BHs have dimensionless spins ≤ 0.998 and masses bound by [2.83, 25.00] M . We restrict our template bank to NS spin magnitudes of ≤ 0.05 because it has been demonstrated [68,120] that due to the balance between signal recovery and false alarm rate, the overall search sensitivity for BNS systems with spins <0.4 is larger when the template bank is restricted to spins <0.05 than when it is expanded to include spins <0.4. [124][125][126][127] small inclination angles for GRB progenitors due to GRB beaming. This is imposed by filtering with only circularly polarized templates [89], corresponding to binary systems with inclination angles θ JN between the total angular momentum axesĴ and the line-of-sight N of 0 deg or 180 deg. This constraint improves sensitivity to signals with small inclinations ( 30 deg or 150 deg).
We tile the reported sky error region of each GRB and filter at each sky point with our constrained template bank [89] to obtain a coherent SNR statistic for the network. We place thresholds of 4 on single detector SNRs and 6 on the coherent network SNR. Surviving triggers are then re-weighted or cut according to signal consistency checks [89,105,128], to produce the search detection statistic.
We consider a 6 s window spanning [−5, +1) s about the reported GRB Earth-crossing time as the on-source where an associated GW event may be found. This is compared to an off-source window that is used to characterize the search background, which typically contains up to ∼ 90 min of data surrounding the on-source time. The loudest (most significant) candidate event in the on-source, as defined by the detection statistic, is compared to a list containing the most significant background events from each of the 6 s background trials within the off-source. Additional background trials are obtained by time shifting the data streams relative to one another by amounts greater than the light travel time between the detectors [89], similar to the approach described in Section 4. This comparison between on-source and background trials results in a p-value for the candidate on-source event.
In the case of no compelling candidate event being identified in the on-source, these simulated signals allow for exclusion distances to be quoted. A 90% exclusion distance corresponds to the distance within which 90% of a population of simulated signals were recovered with a detection statistic at least as large as the loudest on-source candidate event; at greater distances the recovered fraction of signals drops. For GRB 200415A we report 90% exclusion distances of 0.91 Mpc for BNS systems, 1.08 Mpc for isotropically spinning NSBH, and 1.45 Mpc for aligned-spin NSBH. At a distance of 3.5 Mpc, corresponding to NGC 253, exclusion confidences for these three populations are 0%, 2%, and 9% respectively, too low to be able to confidently exclude any such binary merger as the progenitor of GRB 200415A. These exclusion curves are shown in Figure 7. For GRB 200420A we report 90% exclusion distances of 0.15 Mpc for BNS systems, 0.21 Mpc for isotropically spinning NSBH, and 0.17 Mpc for aligned-spin NSBH. The injection recovery was limited in this case by the large sky error of the GRB. The reported GBM 1σ statistical uncertainty (averaged over the error ellipse [111]) was 27.3 deg [141], and was used to generate a two-dimensional normal distribution on the sky from which injection sky positions were drawn. This resulted in a population of injections spanning a large area on the sky within which the interferometer sensitivities varied significantly, including regions with severely reduced range. As a result, a non-negligible fraction of nearby injections were undetectable.

Search for generic bursts associated with GRBs
X-Pipeline [85,94] is an analysis package that combines data from multiple detectors coherently to detect minimally modeled GW transient signals associated with events such as GRBs, core-collapse supernovae, and fast radio bursts. It is used regularly for such searches of LIGO-Virgo data [31,[38][39][40][142][143][144].
For each GRB X-Pipeline constructs a grid of sky positions covering that GRB's sky localisation error box. For this analysis linear grids are used, which have been shown to be a computationally efficient way to cover large error boxes for two-detector networks without significant loss of sensitivity [145]. For each grid point a coherent analysis is performed.
The frequency range of the search is increased from the standard values of [20,500] Hz to [30,1100] Hz to account for GEO's better sensitivity at higher frequencies. The on-source window is [−600 s, +max(60 s,T 90 )] about the GRB Earth-crossing time, where T 90 is the reported GRB duration. This window is large enough to account for any reasonable time delay between the GW and gamma-ray emission [146][147][148][149][150][151][152][153][154][155]. An exception to this window choice is made for GRB 200415A, for which KAGRA was not operating in a stable locked state until less than 600 s before the GRB event. For this GRB we use an on-source window  to the remaining off-source and simulation clusters. The surviving on-source clusters are our candidate events. Each is assigned a p-value by comparing to the distribution of surviving off-source events. The sensitivity as a function of signal amplitude or source distance is evaluated as the fraction of simulated signals that give surviving events with p-values lower than the lowest p-value of the on-source events.
Of the four GRBs analysed, the lowest p-value for any on-source event was p = 0.132 for GRB 200412A. This is consistent with the null hypothesis given the number of GRBs analysed. We therefore conclude there is no evidence for GW emission associated with any of the four GRBs analysed. Figure 8 shows the 90% confidence level lower limit on the distance for each of the GRBs for several emission models: the accretion-disk instability model A of [156,157]; and circularly polarized sine-Gaussian [38] signals with central frequencies of 150 Hz, 500 Hz, and 1000 Hz where we assume an energy emission of 10 −2 M c 2 (1.8 × 10 52 erg) in GWs. We see that in each case our exclusion distances are of order 100 kpc (the analyses of GRB 200412A and GRB 200420A did not produce 90% exclusion distances for the 1000 Hz sine-Gaussians above 10 kpc). This is not enough to test the magnetar giant flare hypothesis for GRB 200415A [107]. 34 6 Summary and Discussion We have presented the results of the first joint observation of the KAGRA detector with GEO, performed during April 7-20 2020. The coincident observational data from GEO and KAGRA were analysed jointly to look for transient GW signals, including neutron-star binary coalescences and generic unmodeled transients. We also performed dedicated searches for CBC signals and generic transients associated with GRBs observed during the joint run. No candidate GW events were identified.
In the all-sky BNS search, the most significant candidate from the analysis of 0.032 years of data has an iFAR of 0.033 years, consistent with background. The sensitive spacetime volume to BNS coalescences was estimated as a function of iFAR, and we found that the iFAR of the most significant event corresponds to a sensitive distance of ∼0.6 Mpc, comparable to that expected from the noise spectra.
In the all-sky burst search, the most significant candidate from the analysis of 0.012 years of data has an iFAR of 0.097 years which is not significant enough to be considered a likely GW event. The sensitivity of the search was estimated in terms of the minimal detectable root-sum-square signal amplitude and minimum detectable signal energy at a fixed distance.
We find minimal detectable energies of around 10 −6 M c 2 to 10 −3 M c 2 for sources at 10 kpc.
These sensitivities are consistent with the amplitude spectral densities of the detectors.
The searches for CBCs and generic transient signals associated with GRBs found no candidate events, with the lowest p-value for any GRB being 0.132. For GRB 200415A, the dedicated CBC search set a 90% exclusion distance of 0.91 Mpc for BNS systems, 1.08 Mpc for generically spinning NSBH, and 1.45 Mpc for aligned-spin NSBH. At a distance of 3.5 Mpc, corresponding to NGC 253, the exclusion confidences for these populations are 0%, 2% and 9% respectively. The sensitivity of the generic burst search was evaluated for several GW emission models, giving 90% exclusion distances of order 100 kpc for sources emitting 10 −2 M c 2 energy in GWs. These results are not strong enough to test the binary merger or magnetar hypotheses for the progenitor of GRB 200415A.
The lack of detected GWs in this run is expected given the sensitivity of the GEO-KAGRA network at the time. However, the sensitivity of KAGRA is expected to improve by more than two orders of magnitude later in this decade [6], becoming comparable to that of the LIGO and Virgo detectors. Our analyses have demonstrated the ability to incorporate KAGRA data into standard transient search pipelines that have been used to detect GWs in LIGO and Virgo data. Adding KAGRA to the LIGO-Virgo network will improve the skylocalization accuracy and increase the number of events detected with 3 or more detectors simultaneously [21,158]. KAGRA is planning to join the forth observing run of the advanceddetector network. We look forward to KAGRA's scientific contributions in the coming years as a member of the global GW detector network.

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The full O3GK detector strain data and data products associated with this paper are available through Gravitational Wave Open Science Center [159].