Abstract Giant flares from magnetars can reach, for a fraction of a second, luminosities greater than 1047 erg s−1 in the hard X-ray/soft γ-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 γ-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 INTEGRAL satellite. From the currently known MGF sample we find that their energy distribution is well described by a power law with slope γ=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 × 1045 erg of ∼2 × 10−3 yr−1 per magnetar and a lower limit of R(E) > ∼4 × 10−4 yr−1 magnetar−1 for E < 1045 erg.
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