Scale-invariance in soft gamma repeaters

Abstract

The statistical properties of the soft gamma repeater SGR J1550-5418 are investigated carefully. We find that the cumulative distributions of fluence, peak flux and duration can be well fitted by a bent power law, while the cumulative distribution of waiting time follows a simple power law. In particular, the probability density functions of fluctuations of fluence, peak flux, and duration have a sharp peak and fat tails, which can be well fitted by a q-Gaussian function. The q values keep approximately steady for different scale intervals, indicating a scale-invariant structure of soft gamma repeaters. Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields.

Statistical similarity between soft gamma repeaters and the repeating fast radio bursts

“…Hence in this paper we study the statistical properties of the dimensionless fluctuation, defined as zn = Zn/σ. The fluctuations of bursts of SGR J1550-5418 and repeating FRB 121102 have been shown to follow the Tsallis q-Gaussian distribution (Chang et al 2017;Lin & Sang 2020). The Tsallis q-Gaussian function (Tsallis 1988;Tsallis et al 1998) is defined as…”

“…The magnetar association of FRBs motivate us to study the common properties shared by the two transients. For example, the power law distribution of the energy have been found in both SGRs (Cheng et al 1996;Göǧüş et al 1999Göǧüş et al , 2000Chang et al 2017;Cheng et al 2020) and repeating FRB 121102 (Wang & Yu 2017;Wang et al 2018;Wang & Zhang 2019;Lin & Sang 2020). Besides the power law property, the scale invariance of the size fluctuations has also been investigated in SGR (Chang et al 2017;Wei et al 2021) and repeating FRB 121102 (Lin & Sang 2020;Wei et al 2021).…”

“…For example, the power law distribution of the energy have been found in both SGRs (Cheng et al 1996;Göǧüş et al 1999Göǧüş et al , 2000Chang et al 2017;Cheng et al 2020) and repeating FRB 121102 (Wang & Yu 2017;Wang et al 2018;Wang & Zhang 2019;Lin & Sang 2020). Besides the power law property, the scale invariance of the size fluctuations has also been investigated in SGR (Chang et al 2017;Wei et al 2021) and repeating FRB 121102 (Lin & Sang 2020;Wei et al 2021). The power law distributions and the scaleinvariant structure of the energy fluctuations are predicted by self-organized criticality (SOC) systems (Bak et al 1987), which occurs in many natural systems exhibiting nonlinear energy dissipation.…”

“…Cheng et al (1996) compared the statistical properties of the 111 bursts of SGR 1806-20 and earthquakes and found that the cumulative energy distribution of bursts similar to the well-known earthquake Gutenberg-Richter power law. The properties of scale invariance of earthquakes and SGR were firstly found by Wang et al (2015) and Chang et al (2017), respectively. These studies on the statistical properties of SGRs and earthquakes support the idea that SGRs are powered by crustquakes of magnetars.…”

Probing the anisotropic distribution of baryon matter in the Universe using fast radio bursts

“…Except for an extremely active repeating source, FRB 121102, from which hundreds of bursts have been detected [11][12][13][14], most of the rest repeating sources found by the Canadian Hydrogen Inten-sity Mapping Experiment (CHIME) telescope only repeat two or three times [15]. Statistical analysis of FRB 121102 shows that the burst energies from this source follow the bent power-law and are scale-invariant [16], implying that there are some similarities between FRBs and soft gamma repeaters (SGRs) [17]. Recently, the CHIME/FRB Collaboration [18] found an unexpected long period of 16.35 days with an approximately 4-day active window in FRB 180916.J0158+65.…”