A giant glitch from the magnetar SGR J1935+2154 before FRB 200428

In this work, the observations from NICER, NuSTAR, Chandra and XMM-Newton are utilized to study the spin evolution of SGR J1935+2154 as listed in Appendix Table 1.

NICER is a payload onboard the International Space Station devoted to the study of neutron stars through soft X-ray timing (Gendreau et al., 2016). Its X-ray Timing Instrument (XTI) is an aligned collection of 56 X-ray concentrator optics (XRC) and silicon drift detector (SDD) pairs, which records individual photons with good spectral resolution and time resolution to $\sim 0.1$ $\mu$s relative to the Universal Time. The cleaned events data in 0.8-4.0 keV are used for profile and timing analyses by using the standard nicerl2 command with “$\rm underonly\_range=0-200$”. The arrival time of each event to barycentre is corrected via barycorr with coordinates $\alpha=19^{\rm h}34^{\rm m}55^{\rm s}.68$ and $\delta$=21^∘53^′48^′′.2 (Israel et al., 2016). The solar ephemeris for Solar System Barycentre (SSB) correction is DE405.

SGR J935+2154 was observed by NuSTAR around May 02 and 11 (OBSID 80602313002, 80602313004), 2020, with corresponding exposure times of 38 and 31 ks (Harrison et al., 2013). In this work, we analyze data from two telescopes on NuSTAR (usually labeled by their focal plane modules, FPMA and FPMB) using HEASoft (version 6.29). We utilize nupipline with NuSTAR CALDB v20180312 to create GTIs and select a circular region of radius $180^{\prime\prime}$ centred on the pulsar position to extract the source spectrum. The arrival time of each photon is corrected to SSB with the same solar ephemeris.

We processed the data collected by PN of XMM-Newton from 2014 to May, 2020 (Jansen et al., 2001) using the Science Analysis System (SAS) (v14.0.01) software. The time intervals contaminated by flaring particle background are discarded. Events in a circular region with a radius of $50^{\prime\prime}$ centred on the pulsar position are selected to ensure that all the source events are included. Only PN data are utilized to perform the timing analysis considering the time resolution. The arrival time of each photon is corrected to SSB with the same solar ephemeris.

Chandra observed SGR J1935+2154 four times in 2014 and 2016, with the ObsIDs of 15874, 15875, 17314, and 18884, respectively. The corresponding time resolutions in these observations are, 0.44 s, 2.85 ms, 2.85 ms, and 2.85 ms. Therefore, these four observations are used for timing analyses, as listed in Table LABEL:table:obs. The data were reprocessed with the Chandra Interactive Analysis of Observations software (CIAO, version 4.14) using the calibration files available in the Chandra CALDB 4.9.6 data base. The scientific products were extracted following the standard procedures, but adopting extraction regions with different sizes in order to properly subtract the underlying diffuse component. For 15874, we extract the events from a circular region with radius of 1.5^′′ for the timing analysis. While for observations 15875, 17314 and 18884 at continuous clocking (CC) mode, events in rectangular boxes of 3^′′ x 2^′′ sides aligned to the CCD readout direction are used to perform timing analysis. For the timing analysis, we applied the Solar system barycentre correction to the photon arrival times with AXBARY.

We perform both partially phase-coherent timing (PPCT) analysis and fully phase-coherent timing (FPCT) analysis for SGR J1935+2154 to study its timing behaviors using TEMPO2 (Hobbs et al., 2006). The PPCT analysis can mitigate the pronounced effects of timing noise on the long term evolution and show spin evolution clearly (Ferdman et al., 2015), while the FPCT analysis can get more accurate spin parameters of the pulsar, because the timing noise such as glitches revealed by PPCT analysis can be included in the new timing model. To perform PPCT analysis, we need to have spin frequencies and times of arrival (ToAs) in different epochs, which are obtained with $Z^{2}_{1}$ searching, i.e., the frequency making the folded profile deviating the most from a uniform distribution as represented by the $Z^{2}_{1}$ value is taken as the spin frequency at the time of each observation, and the phase of the minimum point in each profile is then taken as the TOA of that observation (Ge et al., 2012; Younes et al., 2020).

The data used for timing analysis span in about 2300 days from MJD 56853 to 59172. Two obvious abnormalities of SGR J1935+2154 are recognised since the frequencies obtained with $Z^{2}_{1}$ searching in two epochs deviate obviously from the extrapolation of the earlier data. In order to show the spin evolution clearly, as discussed above, the PPCT analysis is performed (Ferdman et al., 2015; Ge et al., 2019), and the resulted spin parameters in different epochs are given in Table 1. The spin parameters obtained from the above mentioned time spans are then fitted with equation (1) in TEMPO2.

where $\nu_{0}$, $\dot{\nu}_{0}$ are frequency and frequency derivative at the reference time $t_{\rm 0}$, and $t$ corresponds to the center of each sub-data set.

Based on the above preliminary timing results of SGR J1935+2154, we can further perform FPCT analysis to get more accurate timing solutions using the data around G1 and G2 respectively, with equation (2) shown below.

where $\nu_{0}$, $\dot{\nu}_{0}$ are frequency and frequency derivative at epoch $t_{\rm 0}$, $\Delta\nu_{\rm p}$ and $\Delta\dot{\nu}_{\rm p}$ are the persistent offsets of frequency and frequency derivative at the glitch epoch $t_{\rm g}$, $\Delta\nu_{\rm d1}$, $\Delta\nu_{\rm d2}$, $\tau_{\rm d1}$ and $\tau_{\rm d2}$ are the parameters of the two exponential components. The overall amplitudes of the glitches can be then inferred with $\Delta\nu=\Delta\nu_{\rm p}+\Delta\nu_{\rm d1}+\Delta\nu_{\rm d2}$ and $\Delta\dot{\nu}=\Delta\dot{\nu}_{\rm p}-\Delta\nu_{\rm d1}/\tau_{\rm d1}-\Delta\nu_{\rm d2}/\tau_{\rm d2}$. Furthermore, the recover factor $Q=\Delta\nu_{\rm d2}/\Delta\nu$ can be calculated as usually defined (Dib & Kaspi, 2014; Lower et al., 2021). The detailed timing parameters for the two glitches are listed in Table 2. The errors of spin parameters are obtained from TEMPO2 software.

For SGR J1935+2154, the timing results have not been affected by the timing accuracy of different telescopes. For NICER and NuSTAR, their time resolutions are 0.1 $\mu$s and 0.1 ms, respectively Gendreau et al. (2016); Bachetti et al. (2021), which much shorted the spin period of SGR J1935+2154. The time resolutions of XMM-Newton and Chandra observations are not as good as NICER and NuSTAR but they do not show differences on the timing results as reported in Israel et al. (2016).

The long time evolution and short time variations of $\nu$ and $\dot{\nu}$ could be illustrated directly as in Figure 1, which shows two spin-up glitches on MJD 57822 and 58964.5, which are named G1 and G2. The information about the first glitch (G1) is quite limited due to the incomplete time coverage and not concerned in this work. Unfortunately, as no timing information about SGR J1935+2154 is available between MJD 58110 and 58965, we do not know the exact rotation state of SGR J1935+2154 before the burst forest and FRB 200428. However, as shown in Figures 1 and 2, the timing behaviors around FRB 200428, which are obtained with both PPCT and FPCT analysis from the observations, are very typical for a glitch, which has three components, the persistent, the delayed spin-up and the recovering components, similar to the big glitches in the Crab pulsar (Ge et al., 2020). The fitting parameters as listed in Table 2 show that G2 is a giant glitch happened on MJD 58964.5(2.5) with $\Delta\nu/\nu=(6.4\pm 0.4)\times{10}^{-5}$ and $\Delta\dot{\nu}/\dot{\nu}=-4.4\pm 0.7$, where both $\Delta\nu$ and $\Delta\dot{\nu}$ include the delayed spin-up component that will be discussed later. There are two exponential components following G2. The first exponential component with $\tau_{\rm d1}=8\pm 1$ day represents the delayed spin-up process that was previously only detected in large glitches of the Crab pulsar and magnetar 1E 2259+586 (Ge et al., 2020; Woods et al., 2004). The second one is a slow recovery process with $\tau_{\rm d2}=131\pm 6$ day and $\Delta\nu_{\rm d2}=2.50\pm 0.16{\rm{\mu}Hz}$. Remarkably, in the evolution of the spin-down rate, a large persistent offset ($\Delta\dot{\nu}_{p}$) of $-2.031\pm 0.019$ pHz s^-1 is present, which is 1.4 times of the spin-down rate $\dot{\nu}$ before the glitch and is about one order of magnitude larger than the slow recovery component. Such a persistent offset should be due to an increase in the external torque caused by a rearrangement of the magnetosphere (Link et al., 1992; Zhang et al., 2022), and the large value implies that the magnetosphere changes dramatically at the glitch, consistent with the large pulse profile changes after G2 (Younes et al., 2020) (Figure 3).

The overall timing analyses have not given a very tight constraint on the occurrence time of G2. We therefore discuss whether it happened before FRB 200428 or not with detailed studies on timing behaviors and profiles, since it is crucial for understanding the possible causal connection between the glitch and FRB 200428. The data are divided into two part according to the epoch of FRB 200428 as plotted in Figure 4. In Figure 5, we give the $Z_{1}^{2}$ variations with spin frequency for the pre-FRB data, the post-FRB data and the whole dataset, respectively. The $Z_{1}^{2}$ values for the three datasets all reach their respective maxima at frequency around $0.3079468(12)$ Hz, and the value of the whole dataset is the highest, which is also consistent with the results from Younes et al. (2020) and Borghese et al. (2020). The difference of peak frequencies is smaller than $1.2\,\mu$Hz, much smaller than $19\,\mu$Hz, the frequency jump of G2, meaning that G2 must happened in advance, i.e., before FRB 200428. We also fold the pre- and post-FRB pulse profiles of this magnetar with the same set of spin parameters obtained above. As shown in Figure 6, the two profiles are not different from each other significantly and share the same minimum phase, supporting the previous conclusion from another aspect. Therefore, G2 happened at least before MJD 58967.2, which is 0.4 day before FRB 200428. From these two aspects, G2 occurred at least 0.4 days before FRB 200428 and probably occurred at $3.1\pm 2.5$ day earlier than FRB 200428.

We compare the delayed spin-up component of G2 with that of the glitches in the Crab pulsar and 1E 2259+586, as presented in Figure 7. Interestingly, in the $\Delta\nu/\nu$ -$\tau_{\rm d1}$ diagram, where $\tau_{\rm d1}$ is the timescale of the spin-up component, all the spin-up events can be roughly fitted with a power-law function ($\alpha=2.0$). This indicates that the mechanisms for angular momentum transfer of the glitches in the Crab pulsar, 1E 2259+586 and SGR J1935+2154 are similar. The existence of the rather long timescale spin-up components in the Crab pulsar and the non-detection of such components from the Vela pulsar and PSR J0537-6910 are suggested to be due to the different states of their crusts and interiors (Ge et al., 2020), i.e., the Crab pulsar is younger and hence less solidified. The existence of the delayed spin-up component of SGR J1935+2154 thus implies that it is young. It is worth noting here that the delayed spin-up components may have been detected from several other magnetars even though their timing properties are not well resolved (Woods et al., 2004; Dib & Kaspi, 2014), indicating that they are also young as widely believed.

From the known glitch sample of isolated pulsars, this event of SGR J1935+2154 is among the largest two in terms of the relative glitch amplitudes in the $\Delta\nu/\nu$-$\Delta\dot{\nu}/\dot{\nu}$ diagram (Dib & Kaspi, 2014; Espinoza et al., 2011; Lower et al., 2021) as shown in Figure 8. The other glitch-like event in magnetars with a comparable relative amplitude is associated with the super burst of SGR 1900+14 around MJD 51050 (Woods et al., 1999). Although the $\Delta\nu$ and $\Delta\dot{\nu}$ values of the large glitches in the Crab pulsar, Vela pulsar, PSR J0205+6449 and PSR J0537-6910 are comparable with those of G2 in SGR J1935+2154 (as shown in Figure 8 (b)), the relative change of the rotation frequency is much greater than those of the pulsars considering that this magnetar rotates much more slowly than the pulsars. Moreover, among the magnetar glitch sample, G2 has the largest $\Delta\nu$ value while SGR 1900+14 has the largest $\Delta\nu<0$ value (Woods et al., 1999).