INTEGRAL search for magnetar giant flares from the Virgo Cluster and in nearby galaxies with high star formation rate

ABSTRACT

Giant flares from magnetars can reach, for a fraction of a second, luminosities greater than 10|$^{47}$| erg s|$^{-1}$| in the hard X-ray/soft |$\gamma$|-ray range. This makes them visible at distances of several megaparsecs. However, at extragalactic distances (farther than the Magellanic Clouds), they are difficult to distinguish from the short |$\gamma$|-ray bursts, which occur much more frequently. Since magnetars are young neutron stars, nearby galaxies with a high rate of star formation are optimal targets to search for magnetar giant flares (MGFs). Here, we report the results of a search for MGFs in observations of the Virgo cluster and in a small sample of nearby galaxies obtained with the IBIS instrument on the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) satellite. From the currently known MGF sample, we find that their energy distribution is well described by a power law with slope |$\gamma$| = 2 (with 90 per cent c.l. interval [1.7–2.2]). From the lack of detections in this extensive data set (besides 231115A in M82), we derive a 90 per cent c.l. upper limit on the rate of MGF with |$E > 3 \times 10^{45}$| erg of |${\sim}2\times 10^{-3}\,{\rm yr}^{-1}$| per magnetar and a lower limit on |$R(>E) $| of |${\sim} 4\times 10^{-4}\,{\rm yr}^{-1}$| magnetar|$^{-1}$| for |$E < 10^{45}$| erg.

1 INTRODUCTION

Magnetars are young isolated neutron stars whose electromagnetic emission (mostly at energies between |$\sim$|0.1 and few hundreds keV) is powered by the dissipation of their intense magnetic fields (generally |${>}10^{14}$| G in the magnetosphere and up to |$\sim 10^{16}$| G in the NS interior). They exhibit strong variability on all time-scales, from milliseconds to months (see e.g. Mereghetti, Pons & Melatos 2015; Kaspi & Beloborodov 2017, for reviews). The most spectacular, although quite rare, variability events observed in these objects are the so called giant flares, during which a hard X-ray luminosity up to |${\sim}10^{47}$| erg s|$^{-1}$| can be reached for a fraction of a second. The extreme properties of the first discovered giant flare, the famous event of 5 March 1979 (Mazets et al. 1979; Cline et al. 1980), were among the main motivations to invoke neutron stars endowed with ultra-strong magnetic fields, which are at the basis of the magnetar model (Duncan & Thompson 1992; Paczynski 1992).

After the March 1979 event that was produced by a magnetar in the Large Magellanic Cloud, only two other giant flares were observed, from two different Galactic magnetars (see Table 1). These three magnetar giant flares (MGFs) shared a common characteristic in their light curves: an initial short (⁠|$\lesssim$|0.2–0.3 s), very energetic (⁠|$E \gtrsim 10^{46}$| erg) hard X-ray pulse, always followed by a long, fainter tail of softer emission, periodically modulated at the magnetar spin period of a few seconds (Mereghetti 2008). These periodic tails are the telltale ‘signature’ that allows us to recognize a MGF and to associate it with a known source, even in the lack of positional information, as it occurred for the MGF of 27 December 2004 from SGR 1806-20 (Borkowski et al. 2004).

It was soon realized that the luminous initial pulses of MGFs could be detected up to distances of a few tens of Mpc, while the pulsed tails would remain undetectable. Thus, a MGF from a source in a distant galaxy appears very similar and difficult to distinguish from a short Gamma-Ray Bursts (GRBs; Mazets et al. 1982). Several studies were carried out to determine the fraction of the short GRB population that could be due to extragalactic MGFs. However, the paucity of candidates makes the resulting estimates quite uncertain, with reported values in the wide range from 1 per cent up to 40 per cent (see e.g. Hurley et al. 2005; Nakar et al. 2006; Ofek 2007; Svinkin et al. 2015).

A few candidate MGFs have been identified among short GRBs with positions consistent with bright galaxies outside the Local Group. Although an MGF origin cannot be proven with absolute certainty in all these cases, at least some of them appear very plausible (Roberts et al. 2021; Svinkin et al. 2021; Mereghetti et al. 2024). Furthermore, significant evidence for a population of extragalactic MGFs emerges from a collective statistical analysis of these candidates (Burns et al. 2021). Their main properties are compared to those of the three confirmed MGFs in Table 1.

During giant flares, magnetars emit a significant fraction of their total magnetic energy budget. This limits the number of the most energetic events that can be emitted in a magnetar’s lifetime. It is therefore interesting to derive observational constraints on the rate of MGFs as a function of energy. Given the low rate of Galactic MGFs, it is clear that targeted searches in more distant galaxies could be a promising way to enlarge the sample and derive constraints on the MGFs rate of occurrence. Regions of high star formation rate (SFR) offer the best prospects, since magnetars are believed to originate from massive stars undergoing core-collapse supernova explosions. Here, we report on a search for MGFs in INTEGRAL observations of the Virgo cluster and in a few other nearby galaxies with high SFR.

2 DATA ANALYSIS AND RESULTS

We use data obtained with the IBIS instrument on board INTEGRAL. IBIS is a coded-mask imager composed of two detectors, ISGRI and PICsiT, covering the 15 keV–10 MeV energy range. In this work, we use only the data of ISGRI (Lebrun et al. 2003), which operates in the nominal 15–1000 keV range, providing timing information with a resolution of 61 |$\mu$|s for each detected count. Thanks to its wide field of view, |$29^{\circ }\times 29^{\circ }$| (with a central |${\sim}9^{\circ }\times 9^{\circ }$| region at full sensitivity), it allows to simultaneously monitor several sources and is well suited to observe the Virgo cluster, which extends over a sky region centred at R.A. = 188°, Dec. = 12° with a radius of ∼8°. The angular resolution of ISGRI is 12 arcmin, but sources can be located with an accuracy of a few arcminutes.

To optimize the imaging performance, INTEGRAL points to the sky according to a predefined dithering pattern. Therefore, the data are split into many short pointings with fixed attitude and typical duration between 30 and 60 min each, called science windows (ScWs), interleaved by short slews. As a first step, we searched for bursts by analysing the light curves of all the individual ScWs selected as described below. All the burst candidates found in this search were then checked with an interactive imaging analysis in order to eliminate events caused by background variations, instrumental effects (e.g. noisy pixels) and sources unrelated to the galaxies under study.

For the light curves analysis, we followed the procedure described in Mereghetti et al. (2021). Briefly, this consists in evaluating the background level of each ScW through an iterative 3|$\sigma$| clipping, and then searching for count rate excesses on different time-scales. We used a threshold corresponding to a false alarm probability of 10|$^{-3}$| in each ScW. The ScWs with strongly variable background over their whole duration were excluded from the burst search. This resulted in a reduction of less than 4 per cent of the total exposure time. The imaging analysis was carried out with the software developed for the Integral Burst Alert System (IBAS, Mereghetti et al.2003).

2.1 Virgo cluster

At a distance of ∼16.5 Mpc, Virgo is the closest cluster of galaxies and it has been extensively observed by INTEGRAL. We considered all the galaxies reported in the Extended Virgo Cluster Catalog (EVCC, Kim et al. 2014), excluding the dwarf galaxies. We then extracted from the INTEGRAL archive all the ScWs covering the positions of the 975 selected galaxies. This resulted in 10 886 ScWs between May 2003 and August 2023, yielding a total observation time of 34.8 Ms On average, a single galaxy was observed for 22 Ms in 6700 ScWs. Since in general each ScW contains several galaxies, we did not apply any spatial selection and extracted light curves using the counts from the whole detection plane of ISGRI. This was done in the nominal 15–300 keV energy range in eight integration times with logarithmically spaced durations between 0.01 and 1.28 s. Statistically significant count rate peaks found in adjacent time bins and/or in overlapping time-scales were grouped and considered as a single burst candidate. All the burst candidates were then examined by producing the sky images of the corresponding time intervals, but none of them could be confidently interpreted as a real burst from one of the Virgo galaxies in the field of view. Note that at the Virgo cluster distance, the pulsed tail of a MGF would produce a hard X-ray fluence of the order of 10|$^{-9}$|–10|$^{-8}$| erg cm|$^{-2}$| over a time interval of few hundreds seconds. Since this is below the sensitivity of ISGRI, we concentrated on the search for short duration events.

2.2 Nearby galaxies

We considered the seven nearby galaxies with high SFR listed in Table 2. To search for bursts, we applied the same procedure described above, with the only difference that the light curve of each galaxy was extracted selecting only the ISGRI detector pixels illuminated by the source for more than 50 per cent of their surface. Also in this case, no significant bursts from the considered galaxies were found.

3 DISCUSSION

The results of our search for MGFs in the INTEGRAL data can be used to constrain the rate of occurrence of these events. To do this, we need the energy distribution of MGFs and an estimate of the expected numbers of MGFs in our data sets.

3.1 Energy distribution of MGFs

Given that the energy distribution of MGFs is only poorly constrained by the three confirmed events seen up to now, we assume that it can be described by a power law with index |$\gamma$| in the range [E|$_{\min}$|⁠, E|$_{\max}$|] and estimate the most likely parameters using a larger set of events selected among those listed in Table 1 as described below.

The expected number of MGF with energy in the range [E|$_1$|⁠, E|$_2$|] detectable in an observation of duration T is given by

where the normalization |$\tilde{k}$| represents the total number of MGF per year per magnetar and |$N(E)$| is the number of magnetars from which an event of energy E would be detectable.

As discussed in Burns et al. (2021), the whole sky was covered down to a limiting fluence of |$S_\mathrm{IPN}=2\times 10^{-6}$| erg cm|$^{-2}$| with the instruments of the InterPlanetarty Network (IPN) during the last 30 yrs. Therefore, we set T = 30 yrs in equation (1) and select from Table 1 the MGFs with fluence above |$S_\mathrm{IPN}$| observed in this time period. Only 790305 and 231115A do not satisfy these two requirements and thus are excluded, leading to a complete sample of seven MGFs.

To estimate |$N(E)$| we consider all the galaxies within |$d_\mathrm{max} = \sqrt{E/4\pi S_\mathrm{IPN}}$| reported in the z0MGS catalogue (Leroy et al. 2019), and assume that each of them contains a number of magnetars |$N_i$| proportional to its SFR: |$N_i = N_\mathrm{\rm MW+MC} ~({\rm SFR}_i/{\rm SFR}_{\rm MW+MC})$| = 30 (⁠|${\rm SFR}_i/1.85\,{\rm M}_\odot$| yr|$^{-1}$|⁠). We have assumed 30 magnetars in the Milky Way and Magellanic Clouds, based on the number of known magnetars. This is probably an underestimate due to the presence of still undiscovered quiescent magnetars. All the derived rates scale linearly with |$N_\mathrm{\rm MW+MC}$|⁠.

We then apply a maximum likelihood method to determine the |$\tilde{k}$| and |$\gamma$| values that best reproduce the observed data, considering that the observed number of MGFs with energy |$E_1 < E < E_2$| follows a Poisson distribution with average |$\mu _{12}$|⁠. In this way, we find |$\gamma = 1.97$| and |$\tilde{k} = 3.5\times 10^{-3}$| yr|$^{-1}$| magnetar|$^{-1}$|⁠, with 90 per cent c.l. intervals of [1.73, 2.21] and [1.3, 6.7] |$\times$|10|$^{-3}$|⁠, respectively. The corresponding distribution, in its integral form, is shown by the red line in Fig. 1, where the shaded area indicates the 90 per cent c.l. uncertainty.

3.2 Expected number of MGFs

We can calculate the expected number of MGFs in the INTEGRAL observations of the Virgo cluster by summing the contributions of all the individual galaxies:

where |$R_\mathrm{GF}(S)$| is the rate of GF with fluence |$S = \frac{E}{4\pi d_i^2}$| emitted by a single magnetar. We took |$d_i$| = 16.5 Mpc for all the Virgo cluster galaxies. |$T_i(\lt S)$| is the total time in which galaxy i has been observed with sensitivity better than S. In the computation of |$T_i(\lt S)$|⁠, we took into account the dependence of the ISGRI sensitivity on the position in the field of view and on the background level measured in each ScW. The instrument sensitivity in the energy range used for the search depends also on the spectral shape of the burst. We assume an exponentially cut-off power-law spectrum (⁠|$F(E) = k E^{\alpha } {\rm exp}(-(E(2+\alpha)/E_{\rm p}))$| ph cm|$^{-2}$| s|$^{-1}$| keV|$^{-1}$|⁠).

We expect that the number of magnetars per galaxy is proportional to the rate |$R_\mathrm{SN}$| of core collapse supernovae. Therefore, we estimate it by scaling the number of Galactic magnetars: |$N_i = N_{\rm MW} R_i^\mathrm{SN}/R_{\rm MW}^\mathrm{SN}$|⁠. The rate of core collapse supernovae depends on the luminosity and morphological type of each galaxy: |$R^{\rm SN} = k_\mathrm{morph} L_{\rm g}$|⁠. We used the g band luminosities |$L_{\rm g}$| reported in the EVCC and the values of |$k_\mathrm{morph}$| given in Table 3.

As a representative spectral shape for a MGF initial spike, we take the parameters measured with INTEGRAL for 231115A in M82: |$\alpha$| = 0.04 and |$E_{\rm p}$| = 551 keV (Mereghetti et al. 2024). For these values, equation (2) gives an expected number of |$N_\mathrm{GF} = 0.15$| in our Virgo cluster observations. By varying the spectral parameters in the range observed in other MGFs (⁠|$\alpha$| = [–1.0, 0.6] and |$E_{\rm p}$| = [300, 2300] keV), |$N_\mathrm{GF}$| varies from 0.05 to 0.3.

3.3 Constraints on the MGF rate

Given that no MGF was detected in Virgo, we computed the rate upper limit as

with |$N_\mathrm{up}=2.303$|⁠, which corresponds to the 90 per cent c.l. (Gehrels 1986). The corresponding limit on the rate as a function of MGF energy E is indicated by the orange line in Fig. 1, where the shaded region reflects the uncertainty given by varying the spectral parameters in the range mentioned above.

Owing to the relatively large distance of the Virgo cluster, these observations cannot constrain the rate of MGFs with energy below a few 10|$^{45}$| erg. On the other hand, this can be done with the results obtained for the seven galaxies of Table 2, which globally are expected to contain less magnetars, but are closer than the Virgo cluster. In this case, one MGF was detected with INTEGRAL (231115A in M82, Mereghetti et al. 2024). Therefore, using the formalism described above, we can put both an upper and a lower limit to the MGF rate. As indicated by the two blue lines in Fig. 1, the limits (at 90 per cent c.l.) obtained from these seven galaxies (plus those in the Virgo cluster) extend to lower values of E.

In Fig. 2, we compare the limits obtained in our work with the estimates derived by different authors (Popov & Stern 2006; Ofek 2007; Svinkin et al. 2015; Burns et al. 2021). We converted all these measurements to the same units (yr|$^{-1}$| magnetar|$^{-1}$|⁠) and 90 per cent c.l. for the upper limits and, when needed, we also renormalized them to the same number of assumed Galactic magnetars (30). The black histogram shows the constraints derived using only the three confirmed MGFs in the Milky Way and Large Magellanic Cloud (LMC).

4 CONCLUSIONS

We searched for MGFs in ∼35 Ms of INTEGRAL data on the Virgo cluster with negative results. With the reasonable assumption that the number of active magnetars in each galaxy scales with the rate of star formation, we derived a 90 per cent c.l. upper limit of about one giant flare with |$E > 3\times 10^{45}$| erg every ∼500 yr per magnetar. We also put some constraints on the rate of MGFs with lower energies, thanks to INTEGRAL observations of a few nearby galaxies with high SFR. The analysis of this sample, with the detection of only one MGF in M82, implies a rate lower limit of |$R({>}E) > 4\times 10^{-4}$| yr|$^{-1}$| magnetar|$^{-1}$|⁠, for energies |$E < 10^{45}$| erg.

These findings, in agreement with those obtained in similar analysis based on data from other satellites, demonstrate the importance of enlarging the sample of MGFs through searches extending beyond the Local Group of galaxies. Although the detection of pulsating tails, which would unambiguously confirm the MGFs candidates, is difficult with the current instrumentation, the most recent discoveries show that quick and precise localizations with instruments providing good spectral/timing capabilities coupled to rapid multiwavelength follow-ups are key elements to advance in this field.

ACKNOWLEDGEMENTS

The results reported in this article are based on data obtained with INTEGRAL, an ESA mission with instruments and science data centres funded by ESA member states, and with the participation of the Russian Federation and the USA. This work received financial support from INAF through the Magnetars Large Program Grant (PI S. Mereghetti).

DATA AVAILABILITY

All the data used in this article are available in public archives.

REFERENCES