Magnetars-highly magnetized neutron stars-exhibit intermittent bursts of hard X-rays and soft gamma-rays with typical peak luminosities 10 43 erg s -1 (see Kaspi & Beloborodov 2017, for a review). Galactic (Evans et al. 1980;Hurley et al. 1999Hurley et al. , 2005;;Mereghetti et al. 2005;Boggs et al. 2007) and extragalactic (Mazets et al. 2008;Abadie et al. 2012;Burns et al. 2021;Svinkin et al. 2021) giant flares have peak luminosities up to five orders of magnitude larger. Although the mechanisms that cause these bursts and giant flares are not well understood, many models predict accompanying gravitationalwave emission from excited core and/or crust oscillations (Ioka 2001;Ciolfi et al. 2011;Corsi & Owen 2011;Kashiyama & Ioka 2011;Zink et al. 2012). This hypothesis is enhanced by the identification of quasiperiodic oscillations (QPOs) in the tails of giant flares (Barat et al. 1983;Israel et al. 2005;Strohmayer & Watts 2005, 2006;Watts & Strohmayer 2006), and possibly fainter bursts (Huppenkothen et al. 2014a(Huppenkothen et al. , 2014b)), which have been attributed to various oscillations of the stellar crust and core (e.g., Duncan 1998;Messios et al. 2001;Piro 2005;Glampedakis et al. 2006;Strohmayer & Watts 2006;Levin 2007;Colaiuda & Kokkotas 2011;Glampedakis & Jones 2014).
Initial estimates for the potential gravitational-wave emission from giant flares were optimistic that the fundamental oscillation mode ( f-mode) of magnetars could be excited by the catastrophic rearrangement of the star's interior magnetic field. These f-modes are excited at frequencies between ∼1 and 3 kHz, and could potentially emit up to ∼10 49 erg (Ioka 2001;Corsi & Owen 2011) for ∼100 ms (Lindblom & Detweiler 1983;McDermott et al. 1988;Wen et al. 2019), making them detectable with the Advanced LIGO (Aasi et al. 2015), Advanced Virgo (Acernese et al. 2015), and KAGRA (Akutsu et al. 2019(Akutsu et al. , 2021) ) gravitational-wave observatories (Abbott et al. 2018). Detailed calculations of the rearrangement of the neutron star's magnetic field using analytic calculations (Levin & van Hoven 2011) and numerical relativity simulations (Ciolfi et al. 2011;Ciolfi & Rezzolla 2012;Zink et al. 2012;Tsokaros et al. 2021) yield more realistic estimates for the gravitationalwave energy emitted in the f-mode during these events. These models suggest that gravitational waves associated with Galactic magnetar flares are not observable with the current generation of observatories, but instead require the sensitivity of at least third-generation observatories such as the Einstein Telescope (Punturo et al. 2010) or Cosmic Explorer (Reitze et al. 2019;Evans et al. 2021), or dedicated kilohertz facilities such as the proposed NEMO observatory (Ackley et al. 2020).
Other oscillation modes in the star, which are generally longer lived and at lower frequencies than the f-mode, may be excited. These include buoyancy modes (g-modes) and Alfvén modes where the magnetic field provides the oscillation restoring force. The latter of these modes has been suggested as potential long-lived gravitational-wave sources from magnetar giant flares (Kashiyama & Ioka 2011;Zink et al. 2012), with the resonant frequency correlated to the initial rise time of the magnetar giant flare (Hurley et al. 1999(Hurley et al. , 2005;;Mazets et al. 2008). The damping time and mode excitation amplitude of these modes are largely unknown, making them interesting candidates for longer-lived gravitational-wave signals.
Only one Galactic giant flare has been observed coincident with a LIGO-Virgo observing run: the 2004 giant flare from SGR 1806-20. Upper limits on the gravitational-wave energy associated with the burst were determined to be between ∼10 46 and 10 52 erg, depending on the assumed waveform model (Kalmus et al. 2007;Abbott et al. 2008a;Kalmus 2009). A stacked search was performed on a series of bursts from the same magnetar occurring in the same minute, reducing the above upper limits to ∼10 45 and 10 50 erg assuming the same fmode frequency and damping time for each burst (Abbott et al. 2009;Kalmus 2009;Kalmus et al. 2009). Further searches for f-modes in 1279 bursts from six different magnetars yielded upper limits between ∼10 44 and 10 47 erg (Abadie et al. 2011), while the first search for f-modes in the advanced era of gravitational-wave interferometers yielded comparable upper limits for four bursts from two magnetars (Abbott et al. 2019;Schale 2019). These energy upper limits are in the range of possible gravitational-wave energies given the most optimistic predictions (Ioka 2001;Corsi & Owen 2011).
Longer-duration searches initially targeted the QPO frequencies in the tail of the giant flare of SGR 1806-20, with upper limits of various modes at 10 46 erg (Abbott et al. 2007;Matone & Márka 2007), comparable to the electromagnetic energy emitted from the giant flare. A study was performed on a method to detect gravitational waves targeting repeated QPOs (Murphy et al. 2013). A search for long-duration gravitational waves from four magnetar bursts was performed using LIGO's sixth science run (S6) data (Quitzow-James 2016; Quitzow- James et al. 2017). The best upper limits from magnetar bursts come from recent observations in the Advanced LIGO-Virgo second observing run (O2), with gravitational-wave energies constrained to less than ∼10 44 -10 48 erg, again depending on the signal model, frequency, and damping time (Abbott et al. 2019;Schale 2019). We previously placed limits on gravitational-wave emission from purported extragalactic magnetar giant flares (Abbott et al. 2008b;Abadie et al. 2012), 296 with long-duration searches constraining the gravitational-wave energy emitted to between ∼10 49 and 10 52 erg for four different giant flares (Macquet et al. 2021).
In this paper, we report on a search for gravitational waves coincident with 13 magnetar short bursts from SGR 1935 +2154, Swift J1818.0-1607, and three electromagnetic bursts from an unidentified source (or sources) during the LIGO-Virgo-KAGRA third observing run (O3). Targeted gravitational-wave searches associated with magnetar bursts can broadly be split in two categories following theoretical predictions of short-duration and long-duration signals. For each magnetar burst we carry out a short-duration and longduration search. We find no evidence of gravitational-wave signals and hence place upper limits on the gravitational-wave strain and energy for each burst considered.
The O3 observing run extended from 2019 April 1 to 2020 March 27, with three gravitational-wave detectors taking data: LIGO Hanford Observatory (LHO), LIGO Livingston Observatory (LLO), and Virgo, all of which had been upgraded so that the binary neutron star inspiral ranges increased by a factor of 1.53 for LLO, 1.64 for LHO, and 1.73 for Virgo (Davis et al. 2021) compared to their performance during O2. For each detector, several data quality checks are performed to mitigate terrestrial noise (Davis et al. 2021). In addition, multidetector analyses are used to mitigate nonastrophysical features present in the data. In 2020 January, a new technique was implemented to mitigate the impact in LIGO detectors of scattered light, a transient noise coupled with ground motion. Data available for bursts that occurred in February and March show a lower transient noise rate.
The list of magnetar short bursts and giant flares from Hurley (2021) provides the source object and observation time for each burst. In both the long-duration and short-duration searches, we describe the data in which we look for a signal as the "onsource" window, while the time around this composing the background as the "off-source" window. Analysis requirements include at least two gravitational-wave detectors in observation mode, sufficiently good data quality, and sufficient data available in the burst's on-source window. Several bursts did not meet the two-detector criterion (one detector available for bursts 2651, 2658, 2659, and 2667in Hurley 2021;;and none for 2662, 2663, and 2664), had poor data quality (2650 and 2672), or had very little data available in the on-source window (2650). Considering these requirements, 12 magnetar short bursts from known sources and three electromagnetic bursts thought to likely be magnetar short bursts from an unknown source or sources occurred when at least two detectors were in observation mode with sufficiently good data quality and are included in this search. In addition, although burst 2651 occurred when LHO was in observation mode and 87 s before Virgo was in observation mode (LLO was not taking data), data were available for most of the long-duration search on-source window, thus the burst was analyzed by the long-duration search only. 11 of the short bursts were from SGR 1935+2154 (Cummings et al. 2014), a magnetar that emitted a fast radio burst in 2020 April (Kirsten et al. 2020), and two of the short bursts were from Swift J1818.0-1607, a magnetar discovered in 2020 (Evans et al. 2020).
The source or sources of the remaining three electromagnetic bursts, detected by Fermi-GBM (Meegan et al. 2009), are unknown as they have very poor sky localization. These three electromagnetic bursts were accompanied by a fourth burst which did not meet the two-detector condition necessary for our analysis, but all four of these bursts occurred in a 33 hr window of time between 2020 February 3 and February 4. Because of their temporal proximity, we search for a signal assuming that they were emitted by the same magnetar. Only two known Galactic magnetars are in the 3σ sky position error region of all four electromagnetic bursts. In order to run a directional search and obtain the upper limits, we consider the source of these bursts to be 1 RXS J170849 at 3.8 kpc (Durant & van Kerkwijk 2006), and note that the directional sensitivity of the detector network changes very little between neighboring sky positions. The sources, times, active detectors, and the isotropic electromagnetic energy (E EM iso ) of each burst included in this search are listed in Table 1; fluence information for some of the bursts from SGR 1935+2154 were obtained from Lin et al. (2020) and used to estimate E EM iso . Note. The on-source interval is centered around the magnetar burst time. Note. FBS is reported for the long-duration search, and the p-value for the short-duration searches. A p-value of 1 indicates that there were no clusters in the on-source window that survive the cluster selection process. We follow Abbott et al. (2019) to search for short-duration signals (as potentially emitted by f-modes) and long-duration signals (such as might accompany an observed QPO). Each search combines the data from two (or more when available in the case of the short-duration search) detectors into a timefrequency map and then forms groups of pixels, called clusters, to search for gravitational-wave signals. The three electromagnetic bursts without a known source are only analyzed with the short-duration search. The searches are described in the following sections.
The search for short-duration transient gravitational waves (milliseconds to seconds) is motivated by a potential signal associated with f-mode oscillations in the magnetar's core. Because the frequencies of the expected gravitational-wave signals can be as high as several kilohertz (Wen et al. 2019;Ho et al. 2020), the search ranges in frequency from 50 to 4000 Hz, extending to higher frequencies than the other unmodeled searches (most notably LIGO-Virgo-KAGRA's burst searches Abbott et al. (2023); the expectation value is calculated assuming a uniform distribution of p-values (given by the null hypothesis), with each point having a 90% probability of landing in the shaded region. The lowest p-value in the delayed on-source search is 3.5 × 10 -3 from burst 2653, and is determined to be most likely an instrumental artifact through arguments invoking both astrophysics and the characteristics of the detector. Several centered on-source search clusters fall outside of the 90% confidence interval, which is not unlikely given how few data points there are, and many of them have properties inconsistent with what one would expect from an astrophysical source. Although the most significant of these, which appears in burst 2656, has a p-value (8.6 × 10 -3 ) and a peak frequency (1577 Hz) which are consistent with expectations for an f-mode, we provide arguments for why this is not the case in Section 3.1.
Figure 2. Spectrograms of the LHO data (left) at the time of the most significant cluster found in the on-source window of burst 2653, and an instrumental artifact appearing also in the LHO data (right). The time separation between these two events is ∼15,277 s, which is larger than the size of the background window in our analysis, and therefore the instrumental artifact was not included in the background. These two spectrograms display very similar structure, with similar double shortduration transients separated in both cases by ∼0.3 s. Several instrumental artifacts of this nature are found by Omicron (Robinet et al. 2020) within the day of burst 2653. The second most significant cluster in the same delayed on-source analysis of burst 2653 also has this same double-peaked structure. associated with gamma-ray bursts, Abbott et al. 2021Abbott et al. , 2022;;and fast radio bursts, Abbott et al. 2023).
We analyze the data using X-pipeline: an unmodeled, coherent search pipeline (Sutton et al. 2010;Was et al. 2012). The X-pipeline algorithm coherently combines the data from each detector in the network to produce a multiresolution timefrequency map displaying the energy in each pixel. The brightest 1% of these pixels are then selected, and neighboring bright pixels are combined into clusters, which are then assigned a ranking statistic. A large fraction of background clusters are rejected by vetos built from the coherent and incoherent power across the detector network. Other details on the parameters of the short-duration search are summarized in Appendix A.
The search for short-duration gravitational waves is comprised of two components: an 8 s on-source window centered on the magnetar burst time (a "centered" on-source window) to optimize sensitivity when gravitational-wave emission is most probable, and a 500 s on-source window beginning just after the centered on-source window (a "delayed" on-source window). The longer delayed on-source window is intended to search for short-duration signals emitted during the time following the burst, analogous to the QPOs that have been observed in some giant flares. For each on-source window, we calculate the significance of clusters using 3 hr of data taken symmetrically about the burst time with a gap of 16 s before and after the onsource window. values are marked by filled-in shapes, and the h rss 90% values are not filled in. The vertical axis notes the waveform, where "SG" means sine-Gaussian and "RD" means ringdown. The frequency and duration of each injection are given as well. All of the sine-Gaussian and ringdown waveforms are eliptically polarized except for the ones denoted by " * ," which are circularly polarized. The numerical values of h rss 50% can be found in Tables 678, while the numerical values of h rss 90% can be found in Tables 91011.
Since the delayed on-source window starts just after the end of the centered on-source window and has a 500 s duration, it overlaps the off-source window for the centered on-source search. This introduces the possibility of a signal detected in the delayed on-source window being included in the background of the centered on-source window. We mitigate this possibility by examining the results of the delayed on-source window and verifying the absence of a signal before viewing the results of the centered on-source window. A summary of the pipeline, time window, and frequency range for the shortduration searches (and long-duration search) is reported in Table 2.
Following previous searches (Quitzow -James 2016;Quitzow-James et al. 2017;Abbott et al. 2019), we use the Stochastic Transient Analysis Multidetector Pipeline (STAMP; Thrane et al. 2011) to analyze data for the long-duration search. STAMP builds signal-to-noise ratio (S/N) time-frequency maps using the cross-power between two detectors. We then use STAMPʼs seedless clustering algorithm, which generates clusters with quadratic Bézier curves (Thrane & Coughlin 2013), to search for long-duration transient gravitationalwave signals. Restricting the variation of the clusters in frequency to a maximum of 10% allows us to target nearly monochromatic gravitational-wave signals potentially emitted from the mechanisms responsible for QPOs while reducing computational resources (Abbott et al. 2019). Clusters are ranked according to their S/N, defined as the sum of the S/N of the pixels that compose the cluster (Thrane & Coughlin 2013).
The on-source window starts 4 s before the burst time and ends 1600 s after, for 1604 s in total. Additional details are provided in Appendix B and in Thrane et al. (2011). The frequency range is 24-2500 Hz, limited by seismic noise at low frequencies, and going to just above the QPO's highest frequency observed in the tail of the 2004 giant flare (Mereghetti et al. 2005). Data from LHO and LLO are used when available, with data from Virgo used for bursts that also have data from either LHO or LLO (see Table 1 for the available detectors for each burst).
The background for each burst is estimated using 59,040 s of off-source data as close as possible to the burst's on-source window while excluding the on-source windows of all of the other bursts. These data are broken up into 36 off-source analysis windows. We combine the data from one detector from each of these analysis windows with the data from the other detector from every other analysis window to create 1260 (36 2 -36) S/N time-frequency maps (which we will refer to as background segments) in order to produce a background cluster distribution for each burst.
The results of the short-duration and long-duration searches for each burst are presented in the following sections. Clusters found in the on-source windows of the short-duration search are ranked by their p-value, which is the probability of having a cluster of such significance in the on-source window under the null hypothesis. They are calculated considering the clusters in the background with a ranking statistic larger than the onsource cluster. Similarly we characterize the significance of the on-source clusters of the long-duration search with the fraction of background segments (FBS) as
Total where N is the number of segments in the respective burst's background whose loudest cluster has an S/N greater than or equal to the on-source cluster's S/N, and N Total is the total number of segments in that background. The p-value in the short-duration search is found similarly to Equation (1), but where N and N Total include all clusters in the background with a S/N higher than the on-source cluster rather than only the loudest cluster from each time segment.
The upper limit h rss 90% (E GW 90% ) is the value of the root-sumsquare strain (gravitational-wave energy) of the magnetar signal such that 90% of a population of signals with that amplitude (energy) would have given rise to gravitational-wave candidates more significant than those found by our search. We also present the analogous upper limits pertaining to a 50% detection efficiency, h rss 50% and E GW 50% . To estimate h rss 50% and h rss 90% for each burst, we inject waveforms into the data and calculate the amplitudes for which 50% and 90% of the signals have a detection statistic equal to or greater than the respective most significant on-source cluster. These waveforms are meant to encapsulate a broad range of different signals that could be produced in association with magnetar bursts, but are not associated with specific emission mechanisms.
We then derive the rms of the integrated incident gravitational-wave strain (h rss ) and gravitational-wave energy (E GW ) for these amplitudes. The definition of h rss is
where h + (t) and h × (t) are the two signal polarizations. In Appendix C we derive h rss and E GW for the different waveforms used in the analysis.
When calculating E GW , we use 9 kpc for SGR 1935+2154 (Zhong et al. 2020). The distance to Swift J1818.0-1607 is estimated to be in the range of 4.8-8.1 kpc (Karuppusamy et al. 2020); we calculate E GW with the larger distance of 8.1 kpc to be conservative. For the magnetar bursts with unknown source (s), we consider 1 RXS J170849 as the source and use 3.8 kpc for the distance (Olausen & Kaspi 2014). The gravitationalwave energy upper limits corresponding to the h rss upper limits are calculated according to the discussion in Appendix C, and in all cases the energy is proportional to the source distance Figure 5. Distributions of background and on-source clusters found by the long-duration search for each burst analyzed with data from LHO, LLO, and Virgo. The background of each burst is displayed along with the S/N of its on-source cluster, denoted by a circle. The dashed black line is the mean, and the gray contours are the one, two, and three standard deviations of the distribution of FBS obtained simulating Gaussian noise colored with the Advanced LIGO design sensitivity curve (Barsotti et al. 2018).
squared. Any uncertainty in these distances will also effect the energy upper limits.
All bursts listed in Table 1 have been considered by the short-duration search except bursts 2651 and 2665 because of missing data in the on-source windows. For the bursts considered, the short-duration centered and delayed on-source searches find clusters whose p-values are reported in Table 3. The cumulative distribution of these p-values is represented in Figure 1. The two most significant (p-value < 1%) clusters found for bursts 2653 and 2656 by the short-duration search are discussed.
Burst 2653. Two significant clusters are detected by the delayed on-source search. The most significant cluster has a p-value of 3.5 × 10 -3 , a peak frequency of 97 Hz, and duration of 31 ms. This is the outlier displayed in Figure 2. X-pipeline identifies another loud cluster 50 s earlier with the same p-value, a peak frequency of 228 Hz, and a duration of 7.8 ms. Given their frequency and duration, each of these clusters is only a couple of cycles long. Both clusters display similar characteristics in the LHO data, appearing in spectrograms as a short-duration, low-frequency spike. In both cases, another high-S/N spike is seen in the data ∼0.3 s from the time of the cluster as shown in Figure 2. Several other of these high-S/N features are detected on the same day as trigger 2653, and these are also in groups of two spaced out by ∼0.3 s. While X-pipeline does not reconstruct either of these neighboring spikes in a coherent cluster, their presence at such a consistent and short time separation from the cluster strongly suggests that each of these clusters has a terrestrial origin. While X-pipeline conducts a coherent search, there remains poor coherence across the two-detector network for these clusters. When the energy per time-frequency pixel is standardized to be 1 unit for Gaussian data, this signal is detected with 165.3 units in LHO, and only 6.2 units and 12.8 units of energy in LLO and Virgo, respectively. The ratio between the LHO and LLO energies is more than can be accounted for by the ratio of antenna factors squared, which gives a measure of the directional sensitivity (4.8 for LHO-LLO and 1.3 for LHO-Virgo) at the time of the burst. Finally, neither of these clusters is visibly identifiable in the LLO nor the Virgo time-frequency maps, meaning they are likely instrumental artifacts in LHO only.
Burst 2656. The most significant cluster found by the centered on-source search has a p-value of 8.6 × 10 -3 . This cluster is 63 ms long, and its frequency extends from 1560 to 1608 Hz, which matches the expected frequency range of neutron star f-mode oscillations. The cluster appears ∼3.1 s before the burst time. There are no known physical mechanisms produce gravitational waves so long before the electromagnetic emission; while this does not rule out this cluster being astrophysical, it makes it less plausible.
Unlike the clusters found for burst 2653, this one is only visible in the LLO data spectrogram shown in Figure 3, which also illustrates that no high-S/N glitches are present in the ambient noise at the time of the burst. The imbalance in detector energies for this cluster also suggests that it is an instrumental artifact.
When considering the number of analyses in the long-duration and short-duration searches (40 in total across the three onsource windows of 16 bursts), the probability of having a pvalue as low as that of burst 2656 is 29%. This, and the high probability that the cluster is due to an instrumental artifact, imply it is highly unlikely to be a signal of astrophysical origin. Nevertheless, we can calculate the strain and gravitational-wave energy required for such a signal assuming it is of astrophysical origin. Using the ringdown waveform with a 100 ms damping time and 1590 Hz frequency, h rss 50% and E GW 50% are 2.2 × 10 -22 Hz -1/2 and 1 × 10 47 erg, respectively. This implies a ratio of gravitational-wave energy to electromagnetic energy of E E 6 10 GW 50% EM iso 6 . It is difficult to imagine a physical scenario whereby this much more energy is deposited into gravitational rather than electromagnetic waves, adding further weight to the conclusion that this cluster is not of astrophysical origin.
In the short-duration searches, simulated signals are added into the on-source data and the resulting time-frequency maps are processed similarly to the on-source time-frequency maps. The injected signals are chosen such that they adequately model a short-duration transient consistent with a magnetar fmode signal, and also such that they cover a reasonable range of frequencies outside of the f-mode frequency range. We inject sine-Gaussian waveforms, described in Appendix C, at a range of frequencies between 70 and 3560 Hz and standardize the damping time of each injection to be the inverse of the frequency. We also inject a series of ringdown waveforms characterized by sinusoids with an exponentially decaying amplitude as described in Appendix C. These ringdown waveforms have damping times of 100 ms and 200 ms, and frequencies ranging from 1500 to 2020 Hz for consistency with previous searches. We also include a series of white noise burst (WNB) signals ranging in frequency from 100 to 1000 Hz to probe h rss upper limits at lower frequencies. The ringdown and sine-Gaussian waveforms are eliptically polarized such that the analysis makes no assumptions on the source orientation. The exception to this are two circularly polarized sine-Gaussian waveforms injected at 1600 and 2020 Hz, which assume an optimally oriented source and are used for comparison with previous searches.
In Figure 4, we present the h rss 50% and h rss 90% values of the most sensitive burst from each source for the short-duration search. Overall, the h rss upper limits follow the detectors' sensitivity frequency evolution and we also see that for most waveforms, h rss 90% is approximately a factor of 2 greater than the values are less than a factor of 1.5 greater than their corresponding h rss 50% . The numerical values of the upper limits pertaining to SGR 1935+2154 can be found in Table 12, while the upper limits for Swift J1818.0-1607 can be found in Table 13. ote. When no value is specified, the search was run with the default parameters, including frequency ranging from 50 to 4000 Hz, a symmetric background window 10,800 s in length, and a 0°error region. The background asymmetry factor is defined as the fraction of the background time before the burst time, with 0.5 corresponding to a symmetric background. The error region is defined as the 1σ uncertainty in the sky position of the source. Using a nonzero error region on a point source can sometimes optimize the h rss and E GW upper limits because it counters the effects of the Earth's rotation during the on-source window. Note. The energy is calculated assuming a distance of 9 kpc. Taking into account the uncertainty on the distance to SGR 1935+2154 given in the caption of Table 1, the energies could scale by a factor ranging from 0.52 to 1.6. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. The energy is calculated assuming a distance of 8.1 kpc, the most conservative value in the range of accepted distances. Taking into account the distance range to Swift J1818.0-1607 given in the caption of Table 1, the energies could scale by a factor as low as 0.35. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. The energy is calculated assuming a distance of 3.8 kpc. Taking into account the uncertainty on the distance to 1 RXS J170849 given in the caption of Table 1, the energies could scale by a factor ranging from 0.75 to 1.3. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. The energy is calculated assuming a distance of 9 kpc. Taking into account the uncertainty on the distance to SGR 1935+2154 given in Table 1, the energies could scale by a factor ranging from 0.52 to 1.6. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. The energy is calculated assuming a distance of 8.1 kpc, the most conservative value in the range of accepted distances. Taking into account the distance range to Swift J1818.0-1607 given in the caption of Table 1, the energies could scale by a factor as low as 0.35. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. The energy is calculated assuming a distance of 3.8 kpc. Taking into account the uncertainty on the distance to 1 RXS J170849 given in Table 1, the energies could scale by a factor ranging from 0.75 to 1.3. All waveforms are elliptically polarized, except those denoted by an " * ," which have circular polarization, and the WNBs, which are unpolarized.
(This table is available in machine-readable form.) Note. Burst 2656 had the lowest upper limits for 50% detection efficiency. The value of E GW is proportional to d 2 , where d is the distance to the source. The energies are calculated assuming a distance of 9 kpc (the distance to SGR 1935+2154 is 9.0 ± 2.5 kpc; Zhong et al. 2020); given the uncertainty on the distance to SGR 1935 +2154, the energies could scale by a factor ranging from 0.52 to 1.6.
(This table is available in machine-readable form.)
corresponding h rss 50% . In Table 4 we provide h rss 90% and E GW 90% for two waveforms that best model the f-mode for each burst. Finally, in Appendix D we give for each waveform the lowest value of h rss 50% and E GW 50% considering all bursts from SGR 1935 +2154, Swift J1818.0-1607, the unknown source for each waveform in Tables 678, respectively. The lowest values of h rss 90% and E GW 90% are in Tables 91011.
All bursts from Table 1 have been analyzed by the longduration search except the three bursts from the unknown source(s). The search results for each burst are shown in Table 3, which lists the FBS of the most significant cluster for each burst. No interesting cluster has been found as the most significant cluster has an FBS of 0.02. Figure 5 compares the most significant on-source cluster to the corresponding background distribution for each burst.
As in the O2 search (Abbott et al. 2019), two families of waveforms, half sine-Gaussians and ringdowns, are injected at five frequencies (55, 150, 450, 750, and 1550 Hz) and two damping times (150 and 400 s). The lowest value of h rss 50% comes from burst 2656, identified with SGR 1935+2154, which has the largest sum squared antenna factors. The results for burst 2656 indicate an improvement in h rss 50% from O2 to O3, ranging from a factor of 1.25-2, which follow roughly the detectors' sensitivity improvement between the runs, although it also depends on additional considerations such as the detector antenna factors at the time of the burst. The half sine-Gaussian h rss 50% values for burst 2656 are plotted against representative sensitivity curves of LHO, LLO, and Virgo during O3 (Buikema et al. 2020;Kissel 2020;Verkindt 2021) in Figure 6, along with h rss 50% from O2 as a comparison. In Figure 7, we plot h rss 50% and h rss 90% for bursts 2656 and 2674 (2673 for waveforms at 55 Hz with a damping time of 400 s for Swift J1818.0-1607), which provide the lowest values at 50% detection efficiency among all bursts emitted by SGR 1935 +2154 and Swift J1818.0-1607, respectively. Tables 12 and13 provide the 50% and 90% detection efficiency upper limits on h rss and E GW for these same bursts for each waveform.
In this study, we search for and find no evidence of gravitational waves coincident with 16 bursts (13 magnetar short bursts and three electromagnetic bursts thought to be magnetar short bursts but with no identified source object) during O3. We search for both short-duration signals produced by excited f-modes in the neutron star's core, and for longduration signals that may be generated from core buoyancy or Alfvén modes. The detection statistics for both the shortduration and long-duration searches are consistent with background noise: the most significant cluster found that was not clearly identified as an instrumental artifact has a p-value of 0.00857; a cluster with this p-value or lower has a 29% probability of appearing in one or more of the 40 searches performed over all of the bursts under the null hypothesis.
For bursts with known sources, the lowest E GW 50% in the shortduration search for waveforms with frequencies from 1500 to 2020 Hz ranged from 4 × 10 46 to 6 × 10 47 erg. The E GW 90% Note. The upper limits are given for burst 2673 for 55 Hz waveforms with τ = 400 s and given for burst 2674 for all other waveforms; these bursts had the lowest upper limits for 50% detection efficiency for these respective waveforms. The energy upper limits are calculated conservatively assuming a distance of 8.1 kpc for Swift J1818.0-1607, although we note that these upper limits could scale by a factor as low as 0.35 if the source is at the close end of its distance range (4.8 kpc).
(This table is available in machine-readable form.)
values of these waveforms ranged from 7 × 10 46 erg to 3 × 10 48 erg. In Tables 678, we report the lowest h rss 50% values over all bursts for each waveform; the lowest h rss 90% values are given in Tables 9-11. The only injected waveforms with exactly the same parameters as the O2 search are the WNBs; see a factor of improvement in h rss 50% of 1.1 for the 100-200 Hz, 11 ms WNB. To obtain an approximate metric of improvement, we compare injected circularly polarized sine-Gaussian waveforms at 1600 Hz and 2020 Hz from O3 to sine-Gaussian waveforms of 1500 Hz and 2000 Hz in O2 and see factors of improvement of 1.5 and 1.7 in h rss 50% , respectively. This is roughly in agreement with the detector's sensitivity improvement between O2 and O3.
The long-duration search sets the lowest upper limits on long-duration gravitational-wave emission from magnetar bursts to date. We report the long-duration upper limits for each waveform for the burst which had the lowest h rss values at 50% detection efficiency in Table 12 for SGR 1935+2154 and in Table 13 for Swift J1818.0-1607. Of these results, the half sine-Gaussian waveform injected into burst 2656 (from SGR 1935+2154) at 450 Hz produced the lowest h rss 90% upper limit of 1.1 × 10 -22 Hz . This corresponds to a gravitationalwave energy of 2.8 × 10 45 erg. The lowest E GW 90% values from these results for SGR 1935+2154 and Swift J1818.0-1607 are measured by the sine-Gaussian waveform at 55 Hz, and are 1.0 × 10 44 erg and 0.5-1.3 × 10 44 erg, respectively. The energy upper limits scale with the distance squared to the source, and here we give the full range of E GW 90% for Swift J1818.0-1607 that corresponds to the distance range of 4.9-8.1 kpc.
We also place upper limits on the ratio of gravitational-wave energy to electromagnetic energy emitted by SGR 1935+2154 (the only source whose bursts have published electromagnetic fluences) using the calculated isotropic electromagnetic energies given in Table 1. For the short-duration search, the most constraining ratio when taking the gravitational-wave energy from the 1590 Hz, 100 ms ringdown waveform is E E 3.0 10 for a band surrounding the 92.5 Hz QPO in the giant flare's tail (Abbott et al. 2007(Abbott et al. , 2008a)).
With the current sensitivities of the LIGO and Virgo detectors, we can now probe well below the potential energy budgets available to generate gravitational waves from catastrophic rearrangements of the star's internal magnetic field (Ioka 2001;Corsi & Owen 2011). However, even the lowest upper limits provided here are well above the expected gravitational-wave energy one would expect from f-mode emission from giant flares (e.g., Levin 2007;Ciolfi & Rezzolla 2012;Zink et al. 2012), let alone the lower-energy bursts being considered here. As gravitational-wave observatories continue to improve in sensitivity, and more observatories such as KAGRA (Akutsu et al. 2019) reach comparable sensitivity, searches for gravitational waves from magnetar bursts will eventually probe several orders of magnitude below the electromagnetic energy of giant flares, increasing the probability of a discovery of gravitational waves from magnetar flares. This project has made use of the data of the Interplanetary Network (ssl.berkeley.edu/ipn3/index.html), which was maintained by Kevin Hurley. We would like to remember all of the contributions Kevin made to many LIGO-Virgo-KAGRA searches over the years.
We would like to thank all of the essential workers who put their health at risk during the COVID-19 pandemic, without whom we would not have been able to complete this work.
Search It should be noted that the burst times are distributed such that the standard 3 hr symmetric background in the shortduration searches would in some cases include the time of the previous or subsequent burst. We mitigate this by either reducing the background length or adjusting the background asymmetry factor (the fraction of background time before the burst) to optimize the amount of background data that could be used for each burst. Full details of these modifications are provided in Table 5.
In addition to modifying the length and background asymmetry factor to exclude neighboring bursts, there are also modifications to the search that we do in order to optimize the upper limits of h rss 50% and h rss 90% for each burst. These include vetoing events in specific frequency bands that display high non-Gaussianity and introducing an error region around the source direction to adjust for the motion of the Earth during the on-source window. A full list of these changes is given in Table 5.
Data are required both before and after each pixel in the long-duration time-frequency map to estimate the pixel background (see Thrane et al. 2011 for details). In this search, we use 18 s of data before and after each pixel, as was done in Quitzow-James (2016), Quitzow- James et al. (2017), andAbbott et al. (2019). Thus, any data removed from the longduration on-source window include up to an additional 36 s, with 18 s both before and after the interval to be removed. We note that 1640 s of data are required for the full 1604 s longduration on-source window.
Two on-source windows are missing data. One of these is the on-source window of burst 2651, which starts 87 s after the burst; since the on-source window starts 4 s before the burst and 18 s is needed to estimate the pixel background, the time-frequency map starts 109 s after the start of the on-source window (105 s after the burst). Data are available for the first 1121 s of the on-source window of burst 2665, leading to the time-frequency map ending after 1103 s. The on-source windows for bursts 2652, 2660, and 2665 each had 8 s of data removed due to data quality issues, leading to gaps of 44 s in the time-frequency maps. As was done in previous searches (including the O2 search; Abbott et al. 2019), noisy spectral lines, such as 60 Hz power-line harmonics, are identified and removed from the time-frequency maps for each detector pair. Of special note, 55 and 150 Hz are removed for the LHO/ Virgo detector pair and 150 Hz for LLO/Virgo; thus, these detector pairs are not sensitive to injected waveforms in these respective frequencies. The Bezier curves for the clusters are generated identically to the other windows, with the missing times (and data removed due to noisy lines) not included in the calculation of the cluster S/N. The background segments are treated identically to their respective on-source windows.
For both short-duration and long-duration searches, we consider sine-Gaussian and ringdown waveforms whose plus (+) and cross (×) polarizations are given respectively by where ι is the inclination angle and τ is the damping time. An injection is circularly polarized in the case where cos is 1 or -1, linearly polarized when cos 0, and elliptically polarized when cos is between -1 and 1. All waveforms in the long-duration search (half sine-Gaussians and ringdowns) have circular polarization. For the short-duration search, the ringdown and most of the sine-Gaussian waveforms are elliptically polarized so as not to assume a source orientation. The polarization angle around the line of sight to the source is set to zero for the long-duration search (which results in an overall phase shift for circularly polarized waveforms), and is uniformly distributed from 0 to π for the waveforms in the short-duration search.
We calculate E GW 50% (E GW 90% ) for the short-duration search from the corresponding h rss 50% (h rss 90% ) using the rotating system emission formula in the narrow-band approximation given by Equation (17) of Sutton (2013)
where d is the distance to the source and f 0 is the central frequency. We note that Equation (17) of Sutton (2013) is valid regardless of waveform polarization. We calculate the E GW 50% and E GW 90% of the WNB waveforms using Equation (11) of Sutton (2013) for isotropic emission, with correction factors to account for our waveforms being broadband. Specifically, we use For Q f 2 1 0 , this can be approximated as
The E GW of a half sine-Gaussian is half of the E GW of a sine-Gaussian, and the h rss of a half sine-Gaussian is the h rss of a sine-Gaussian divided by 2 . The h rss of a half sine-Gaussian with ι = 0 is (Quitzow-James 2016) The E GW of a half sine-Gaussian waveform with Q f 2 1 0 can be approximated as (Quitzow-James 2016)
The h rss of a ringdown waveform can be derived from Equation (2) as It is important to note that the short-duration ringdown waveforms include a ringup right before the injection time for the purpose of avoiding a discontinuous jump in the signal. This ringup has a rise time that is one-tenth of the ringdown damping time. When including this ringup, the h rss of the total waveform is the h rss of the ringup and ringdown added in quadrature while the E GW of the ringup and ringdown are add linearly. This gives
The Astrophysical Journal, 966:137 (32pp), 2024 May 1 Abbott et al.
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GRB 070222, included in a search targeting gamma-ray bursts(Aasi et al. 2014), was later determined to likely be an extragalactic magnetar giant flare(Burns et al. 2021;Macquet et al. 2021).