# Rapid spin changes around a magnetar fast radio burst

Chin-Ping Hu, Takuto Narita, Teruaki Enoto, George Younes, Zorawar

Wadiasingh, Matthew G Baring, Wynn C.G Ho, Sebastien Guillot, Paul S

Ray, Tolga Guver, et al.

► To cite this version:

Chin-Ping Hu, Takuto Narita, Teruaki Enoto, George Younes, Zorawar Wadiasingh, et al. Rapid spin changes around a magnetar fast radio burst. Nature, 2024, 626 (7999), pp.500-504. 10.1038/s41586-023-07012-5. hal-04470709

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# Rapid spin changes around a magnetar fast radio burst

https://doi.org/10.1038/s41586-023-07012-5

Received: 19 May 2023

Accepted: 21 December 2023

Published online: 14 February 2024

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Chin-Ping Hu<fnref n="1" />,²,<fnref n="16" />✉, Takuto Narita³, Teruaki Enoto²,³,<fnref n="16" />✉, George Younes⁴,<fnref n="16" />✉,
Zorawar Wadiasingh⁴,<fnref n="5" />,⁶,<fnref n="16" />✉, Matthew G. Baring⁷,<fnref n="16" />, Wynn C. G. Ho⁸, Sebastien Guillot⁹,
Paul S. Ray¹⁰, Tolga Güver¹¹,¹², Kaustubh Rajwade¹³, Zaven Arzoumanian⁴, Chryssa Kouveliotou¹⁴,
Alice K. Harding¹⁵ & Keith C. Gendreau⁴

Magnetars are neutron stars with extremely high magnetic fields (≥10¹⁴ gauss) that exhibit various X-ray phenomena such as sporadic subsecond bursts, long-term persistent flux enhancements and variable rotation-period derivative<fnref n="1" />,². In 2020, a fast radio burst (FRB), akin to cosmological millisecond-duration radio bursts, was detected from the Galactic magnetar SGR 1935+2154 (refs. 3–5), confirming the long-suspected association between some FRBs and magnetars. However, the mechanism for FRB generation in magnetars remains unclear. Here we report the X-ray observation of two glitches in SGR 1935+2154 within a time interval of approximately nine hours, bracketing an FRB that occurred on 14 October 2022⁶,⁷. Each glitch involved a significant increase in the magnetar's spin frequency, being among the largest abrupt changes in neutron-star rotation⁸⁻¹⁰ observed so far. Between the glitches, the magnetar exhibited a rapid spin-down phase, accompanied by an increase and subsequent decline in its persistent X-ray emission and burst rate. We postulate that a strong, ephemeral, magnetospheric wind¹¹ provides the torque that rapidly slows the star's rotation. The trigger for the first glitch couples the star's crust to its magnetosphere, enhances the various X-ray signals and spawns the wind that alters magnetospheric conditions that might produce the FRB.

SGR 1935+2154, the most active Galactic magnetar of the past decade with a spin period of 3.25 s and a dipole (polar) magnetic-field strength of $4 \times 10^{14}$ G (ref. 12), has shown several major X-ray and radio outbursts¹³,¹⁴. The most recent outburst episode of SGR 1935+2154 occurred in October 2022 and lasted several days, during which it emitted hundreds of short X-ray bursts¹⁵⁻¹⁷. At Coordinated Universal Time (UTC) 19:21:47 (topocentric time of the Canadian Hydrogen Intensity Mapping Experiment, hereafter CHIME) on 14 October 2022, this magnetar emitted a fast radio burst (FRB) with multiple radio peaks measured with CHIME and the Robert C. Byrd Green Bank Telescope (GBT)⁶,⁷.

Alerted before this activity¹⁵, we initiated a series of Neutron Star Interior Composition Explorer (NICER) observations with 75-ks exposure and Nuclear Spectroscopic Telescope Array (NuSTAR) X-ray observations with 96-ks exposure from all scans starting from 17:32:40 UTC on 12 October until 6 November 2022 (Extended Data Table 1). Hereafter, we use the elapsed time *t* since the FRB detection at barycentric-corrected modified Julian date (MJD) 59,866.80817034 at infinite frequency. Our high-cadence X-ray observations achieved

67% temporal coverage bracketing the FRB, -17 h < *t* < 10 h, but did not cover the FRB itself due to Earth occultation. Nevertheless, this cadence enabled a detailed investigation of the spin-frequency evolution of the magnetar. After removing short bursts lasting milliseconds to around 10 seconds, the stellar rotational frequency *v* was revealed by pulsed thermal emission from the stellar surface using NICER data from the 2–8 keV energy band and NuSTAR data from the 3–8 keV energy band. Initially, the spin behaviour showed a spin-down rate of $\dot{v} = -1.7(6) \times 10^{-11}$ Hz s⁻<fnref n="1" /> (Fig. 1a), with parentheses indicating the 1σ uncertainty on the last digit.

A precise timing model was obtained using phase-coherent analysis, that is, tracking the X-ray-pulse times of arrival (TOAs) and optimizing parameters of a predictive model¹⁸. In the phase evolution (Fig. 1a and Extended Data Fig. 1), a concave trend is observed in the range of -4.4 h ≤ *t* ≤ 4.4 h, followed by a long-term convex quadratic trend. These data points are well fitted by a model (Methods) incorporating two spin-up glitches at $t_{g1} = -4.4^{+0.3}_{-0.5}$ h (MJD 59,866.63$^{+0.01}_{-0.02}$) and $t_{g2} = 4.4^{+0.4}_{-0.5}$ h (MJD 59,866.99 ± 0.02). With an uncertainty of

<footnote n="1">¹Department of Physics, National Changhua University of Education, Changhua City, Taiwan. ²Extreme Natural Phenomena RIKEN Hakubi Research Team, Cluster of Pioneering Research, RIKEN, Wako, Japan. ³Department of Physics, Graduate School of Science, Kyoto University, Kyoto, Japan. ⁴Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA.</footnote>

<footnote n="5">⁵Department of Astronomy, University of Maryland College Park, College Park, MD, USA. ⁶Center for Research and Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, MD, USA. ⁷Department of Physics and Astronomy, Rice University, Houston, TX, USA. ⁸Department of Physics and Astronomy, Haverford College, Haverford, PA, USA. ⁹Institut de Recherche en Astrophysique et Planétologie, UPS-OMP, CNRS, CNES, Toulouse, France. ¹⁰Space Science Division, US Naval Research Laboratory, Washington DC, USA. ¹¹Science Faculty, Department of Astronomy and Space Sciences, Istanbul University, Istanbul, Turkey. ¹²Observatory Research and Application Center, Istanbul University, Istanbul, Turkey. ¹³ASTRON, The Netherlands Institute for Radio Astronomy, Dwingeloo, The Netherlands. ¹⁴The George Washington University, Washington DC, USA. ¹⁵Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA.</footnote>

<footnote n="16">¹⁶These authors contributed equally: Chin-Ping Hu, Teruaki Enoto, George Younes, Zorawar Wadiasingh, Matthew G. Baring. e-mail: cphu0821@gm.ncue.edu.tw; enoto.teruaki.2w@kyoto-u.ac.jp; george.a.younes@nasa.gov; zorawar.wadiasingh@nasa.gov</footnote>
<figure><img src="image_3.png" /></figure>

**Fig. 1 | Evolution of pulse timing, short X-ray bursts and flux near the double-glitch epoch.** The time-zero epoch, marked by a vertical red dashed line, is defined as the occurrence time of the CHIME FRB. The dashed-dotted and dotted vertical lines denote the times of the first glitch and second glitch, respectively. **a.** The evolution of the pulse arrival phase with respect to the pre-glitch timing model. The orange line denotes the best-fit timing solution and the grey-filled area is the $1\sigma$ confidence interval obtained with MCMC simulations. The black and grey horizontal lines (labelled A to E) denote the time intervals of spectral analysis. **b.** The frequency evolution derived from the

best-fit timing model (orange line) and the corresponding $1\sigma$ confidence interval (grey-filled area). The data points are best-fit frequencies obtained from 15 consecutive arrival phases with a moving window of one data point. **c.** The evolution obtained using the same procedure as in **b. d.** The evolution of the burst occurrence rate, where blue circles denote the values obtained with NICER and green squares denote those obtained with NuSTAR. **e.** The count rate with a time bin size of 16 s of the persistent emission after removing the bursts. The error bars are statistical $1\sigma$ uncertainties.

approximately ±30 min, these are the best-constrained glitch epochs in magnetars and pulsars at high energies$^{8,19}$. We attempted to fit the TOAs with a high-order polynomial but its reduced $\chi^2$ value was much higher compared with the best-fit two-glitch model (Methods).

At the first glitch, the frequency jumps by $\Delta\nu_1 = 3.0(3) \times 10^{-5}$ Hz, corresponding to a fractional change of $\Delta\nu_1/\nu = 1.0(1) \times 10^{-4}$. The spin-down rate $\dot{\nu}$ also changed by $\Delta\dot{\nu}_1 = -1.5(3) \times 10^{-9}$ Hz s$^{-1}$. The second glitch has a smaller $\Delta\nu_2 = 1.9(3) \times 10^{-5}$ Hz ($\Delta\nu_2/\nu = 6(1) \times 10^{-5}$) with $\Delta\dot{\nu}_2 = 1.5(3) \times 10^{-9}$ Hz s$^{-1}$. Uncertainties are obtained through Markov chain Monte Carlo (MCMC) simulations (Methods). This observation suggests the glitch-recovery timescale could be much shorter than typical pulsar glitches (about 100 days), possibly only a few hours. The second glitch approximately compensates for the excess recovery between the two glitches. Notably, the post-glitch $\dot{\nu} = -4.9(1) \times 10^{-12}$ Hz s$^{-1}$ is just 30% of its pre-glitch magnitude but remains four times higher than the long-term baseline ($\dot{\nu} = -1.35 \times 10^{-12}$ Hz s$^{-1}$; ref. 12). Figure 2 compares the detected glitches with previous ones in magnetars and pulsars$^{8,10,11,20,21}$,

demonstrating that these two glitches are among the largest observed so far. The rotational energy increases for these two glitches are $3.9 \times 10^{41}$ erg and $2.6 \times 10^{41}$ erg, respectively (Methods).

Figure 1b,c shows the frequency evolution and its derivative using the two-glitch model. In addition, we obtained the local spin ephemeris by overlapping consecutive TOAs and avoiding intervals crossing glitch epochs. The $|\dot{\nu}|$ between the two glitches increased by a factor of about 100 compared with the pre-glitch value, indicating a rapid spin-down bracketing the FRB time.

The short-burst occurrence rate in this episode is shown in Fig. 1d. The burst-active epoch lasted for at least two days, during which the rate remained at approximately one burst per minute. Subsequently, the rate peaked at over four bursts per minute at $t \approx -2$ h and subsequently dropped to less than 10% of the pre-glitch level at $t_{g2}$. This declining phase is contemporaneous with the occurrence of the FRB. Such interplay between the X-ray bursts and FRB is similar to the behaviour seen during the previous outburst of SGR 1935+2154 in 2020$^{14,22}$.
<figure><img src="image_4.png" /></figure>

**Fig. 2 | Pulse frequency discontinuities for known pulsar glitches.** Glitch size distribution of previously reported rotation-powered pulsars (circles) and magnetars (squares)⁸,¹⁰ in the phase space of changes of stellar spin frequencies (ordinate) and their derivatives (abscissa) between glitches. The data are shown as absolute values. The error bars are statistical σ uncertainties. The glitches of rotation-powered pulsars are bimodally distributed, where glitches of

Vela-like pulsars (blue circles filled with pink) mainly lie at the top of the figure, and glitches of other pulsars follow a power-law distribution.⁸ The two magnetar glitches observed in this work are indicated by red diamonds. They have extremely large changes in |Δv| compared with all pulsars, and |Δv| comparable to those of Vela-like pulsars.

We extracted the non-burst X-ray photons and plotted the 64-s binned count rates of the persistent X-ray emission (Fig. 1e). The NICER and NuSTAR count rates at the early outburst phase (−51 h < *t* < −2.5 h) were approximately 1.0 and 0.5 counts per second, respectively. The persistent X-ray flux remained constant until a sudden increase at *t* = −2.5 h, reaching a NuSTAR count rate exceeding 50 counts per second in a minute, then declining to approximately 0.5 count per second over 10 hours.

We explored the energy dependence of the pulse profile using the best-fit two-glitch model. NICER data were divided into two energy bands: 2–5 keV and 5–10 keV. NuSTAR data were divided into four energy bands: 3–5 keV, 5–10 keV, 10–20 keV and 20–79 keV (Fig. 3). The broadband pulse profile is double-peaked: the soft X-ray component (below 10 keV) peaks at phase zero and the hard X-ray component (above 10 keV) shows a 0.5-phase offset from the soft X-ray one. Notably, the phase of the FRB roughly aligns with the hard X-ray peak. We validated our timing solution using two methods: an energy-resolved two-dimensional period search and monitoring profile variability in both soft and hard X-ray bands. Both approaches confirm the observed phase evolution and argue against hotspot migration.

We also investigated the NICER and NuSTAR X-ray spectral behaviour surrounding the FRB (Fig. 4). We divided the data into six time periods: A, the early stage $t < t_{g1}$; B, from $t_{g1} < t < -2.5$ h, the peak of the X-ray emission; C, $-2.5$ h $< t < -0.2$ h; D, $0.5 < t < t_{g2}$; E, the decaying phase at $t_{g2} < t < 10$ h (Fig. 1a); F, the returning to quiescence at 11.5 days $< t < 12.2$ days (Extended Data Table 3). The best-fit spectral parameters are summarized in Extended Data Table 4. The quiescent spectrum is well characterized by two components, as reported in other magnetars²³: a blackbody from a hotspot on the stellar surface with a temperature of $kT = 0.42_{-0.03}^{+0.04}$ keV and a radius $R = 1.8_{-0.3}^{+0.5}$ km when

assuming a distance *d* = 6.6 kpc, where *k* is the Boltzmann constant and *T* is the blackbody temperature (ref. 24), and a non-thermal power-law component from the magnetosphere with a photon index of Γ = 1.2 ± 0.1.

At epoch A, the persistent X-ray flux increased to five times the quiescent level. The spectrum is modelled by the same two-component model but with a hotter blackbody temperature at $kT = 0.51 \pm 0.03$ keV with *R* = 2.1 ± 0.2 km and Γ = 1.1 ± 0.1. At epoch B, no significant flux change was observed. Subsequently, the flux increased by a factor of >10 at 2.5 hours before the FRB (epoch C), with the power-law component dominating the X-ray spectrum (Methods). After the FRB (epoch D), the flux gradually decreased and returned to a similar value to that of epoch A after the second glitch (epoch E) with a soft Γ of 1.6–1.8. At epoch F, the flux halved from epoch E but remained three times higher than the quiescent level.

The total isotropic-equivalent radiative energy of the persistent emission is estimated as $5.0 \times 10^{40} (d/6.6 \text{ kpc})^2 \text{ erg}$ between the two glitches. The burst emission at epochs B, C and D has a total energy of $2.3 \times 10^{40} (d/6.6 \text{ kpc})^2 \text{ erg}$ when fitted with a power-law spectrum. This X-ray radiative output, $7.3 \times 10^{40} (d/6.6 \text{ kpc})^2 \text{ erg}$, is one order of magnitude lower than the spin-down inferred energy but two orders of magnitude higher than the normal quiescent energy of $\le 10^{39} (d/6.6 \text{ kpc})^2 \text{ erg}$ within the same time span (Extended Data Table 4).

We outline one possible picture of the unique behaviour detailed above, which may provide clues to the environment that permits or triggers the observed FRB, and radio bursts from SGR 1935+2154 in general. Owing to the absence of major changes in the count rate, pulse profile and spectra around $t_{g1}$, the first glitch was probably triggered by a mechanism internal to the magnetar. Spin-up glitches in normal pulsars⁸⁻¹⁰ and some magnetars¹⁹ are thought to result from angular-momentum transfer from superfluid neutrons in the rapidly
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | Energy-resolved pulse profile of SGR 1935+2154. Pulse profiles obtained with NICER are divided into 2–5 keV and 5–10 keV energy bands and NuSTAR data were divided into 3–5 keV, 5–10 keV, 10–20 keV and 20–79 keV</figcaption></figure>

energy bands. The red dashed line and the red dotted line indicate the phase of the FRB emission detected by CHIME and GBT, respectively. The error bars are statistical 1σ uncertainties.

rotating inner crust (and possibly core) to the other parts of the star²⁵, with the latter being slowed over long times by magnetospheric torques. The rapid spin-down after the first glitch quickly regenerated the spin lag between the superfluid and the rest of the star, leading to the second glitch. Using angular-momentum-conservation arguments (Methods), the short time interval of 8.8 hours between glitches suggests a superfluid component of several tens of per cent of the magnetar's moment of inertia. This suggests that a substantial part of the core and most free neutrons in the inner crust are in a superfluid state.

Long-term magnetic activity in the outer layers can provide heat or excite oscillations, leading to the unpinning of superfluid vortices in deeper layers²⁶,²⁷. The motion of a large number of superfluid vortices could move superconducting flux tubes in the core. The latter would change the surface-layer magnetic-field geometry, stress the crust and heat outer layers, thereby possibly producing the increased persistent emission and burst rate a few hours after the first glitch (Methods). These seismic stresses rupture the crust in a starquake near the magnetic poles where the field is strongest. The associated heating to super-Eddington temperatures can lead to the expulsion of large amounts of ion-rich plasma, forming an optically thick and collimated relativistic wind that torques the star, robbing the magnetar of angular momentum. This ephemeral wind can naturally explain the rapid spin-down epoch between the glitches, provided that the cumulative mass expelled is sufficient (Methods). The wind twists field lines in the magnetosphere above the poles, concomitantly increasing the magnetic-field energy density²⁸,²⁹. As the wind abates, it untwists the field back towards its more permanent configuration and clears the magnetosphere of current, perhaps seeding the decline of the X-ray flux and burst rate before the radio burst (Fig. 1d,e).

A possible FRB scenario is the ignition of pair cascades by a magnetar short burst as the magnetosphere evolves to a more charge-starved state³⁰. Such phenomenology generally aligns with the April 2020 FRB event, which occurred many hours into the waning phase of intense burst activity¹⁴, and the post-spin-down-glitch radio burst in October 2020¹¹. Future high-cadence observations of SGR 1935+2154 and other magnetars in X-rays, like those presented here and in conjunction with radio monitoring, will help identify the conditions required for generating FRBs.

## Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-023-07012-5.

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<figure><img src="image_6.png" /><figcaption>**Fig. 4** | X-ray spectral variations near the double-glitch epoch. X-ray spectral evolution of the persistent emission (red) of SGR 1935+2154 after removing short bursts, obtained with NICER and NuSTAR in time epochs A to F (see Fig. 1a). NICER spectra are shown in crosses, and NuSTAR FPMA and FPMB spectra are shown in circles and triangles, respectively. As a reference, we compare each of these active-state spectra with one quiescent spectrum (grey) obtained on 16</figcaption></figure>

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# Methods

## NICER data reduction

NICER is a non-imaging X-ray observatory with a large collecting area of 1,900 cm² at 1.5 keV and an excellent time resolution of <300 ns aboard the International Space Station³¹. It consists of 56 co-aligned X-ray concentrating optics and associated silicon-drift detectors, of which 52 are in operation. We reprocessed the NICER data using NICERDAS version 9, part of the HEASOFT version 6.30.1 package, and the calibration database version 20210720. The unfiltered data were calibrated and screened using the nicer12 pipeline with default settings, resulting in clean scientific event lists. We further removed a few background flares near Good Time Interval (GTI) boundaries. We corrected the arrival time of each photon to the barycentre of the Solar System using the barycorr command with the Jet Propulsion Laboratory Solar System ephemeris DE405. Photons with energies below 2 keV, due to significant absorption, and above 8 keV, due to reduced NICER sensitivity, were excluded from the analysis. A summary of the NICER data used in this research can be provided in Extended Data Table 1.

## NuSTAR data reduction

NuSTAR consists of two identical focal plane modules (FPMs), FPMA and FPMB. Each module is equipped with conical Wolter-I optics that achieve a point spread function with a half-power diameter of around 60 arcsec. Each FPM houses a detector with an energy range of 3–79 keV, a field of view of 12' × 12', an energy resolution of 0.4 keV at 10 keV, and a timing resolution of 65 ms (ref. 32). The data were reduced using NUSTARDAS version 2.1.2 with the calibration database version 20211020. We performed data calibration and screening using the nupipeline script. Images, event lists, light curves and spectra were extracted using nuproducts. The source photons were extracted from a circular region with a radius of 0.85 arcmin centred on the position of SGR 1935+2154. This guarantees that around 85% of the source X-ray photons were encircled. We extracted the background spectra from a circular source-free region within a radius of 2.5 arcmin centred on right ascension 19:34:46.6029 and declination +21:46:55.710 in the J2000 reference frame.

## Burst identification

We used the Bayesian block technique (https://docs.astropy.org/en/stable/api/astropy.stats.bayesian_blocks.html), which is designed to detect local variability by dividing data into variable-sized time blocks, to search for significant flux changes³³. The search energy ranges for the NICER and NuSTAR events were 2–8 keV and 3–79 keV, respectively. The prior was computed with a false alarm probability of $p_0 = 0.01$. We first identified blocks with a duration shorter than 4 s, and then merged nearby blocks as bright and long bursts are typically identified as several consecutive blocks. Next, we assessed the likelihood of the total counts in each block being a Poisson random fluctuation around the count rate present approximately 1 s before and after the block. We considered all bursts with a probability lower than $3 \times 10^{-7}$ (corresponding to a detection significance of $5\sigma$) to be confirmed bursts and marked the rest as burst candidates. We removed all the confirmed bursts and burst candidates from the analysis of the persistent count rate and rotation frequency. In addition, NuSTAR captured a flare with multiple peaks that occurred approximately two hours before the time of the FRB emission. The persistent emission during the peak of the flare increased by two orders of magnitude and showed multiple peaks, making it challenging to identify individual bursts. We do not attempt to identify the numerous small peaks within the 200-s-long flare. We conservatively count it as a single burst and remove it from further timing analysis as the persistent emission between peaks may be heavily contaminated. Therefore, the burst rate at the flux peak in Fig. 1d may be underestimated. A total of 368 short-burst candidates were identified in the NICER

dataset and 720 in the NuSTAR dataset. Before the FRB, SGR 1935+2154 showed a high burst rate of ≥1 short bursts per minute, which then dropped to ≤0.1 bursts per minute within a timescale of about 5 hours.

## Timing analysis and glitch model

We first collected X-ray photons detected with NICER before the FRB and performed a two-dimensional $Z^2$ test with two harmonics ($n = 2$)³⁴. As the time span increased, we stopped the $Z_2^2$ search when the spin-down rate could be significantly determined, which was $\nu = 0.3075277(1)$ Hz and $\dot{\nu} = 2.0(6) \times 10^{-11}$ Hz s⁻¹ at a time-zero epoch of MJD 59865.678 (barycentric dynamical time). This corresponds to a spin-period derivative of $\dot{P} = 2.1(6) \times 10^{-10}$ s s⁻¹, an order of magnitude higher than the long-term value of $\dot{P} = 1.43(1) \times 10^{-11}$ s s⁻¹ (refs. 12, 35). This result suggests that the spin behaviour of SGR 1935+2154 significantly changed after the initial activity detected on 10 October¹⁵.

To ensure high accuracy in tracing the TOAs, we divided the NICER observations into segments of integer orbits. Each segment was chosen to contain a sufficient number of photons to give a small uncertainty of $\sigma_\phi \le 0.05$ for each TOA. Near the peak of the flare, a NICER orbit was further divided into three segments owing to a large number of collected photons. The TOAs were determined using the unbinned maximum-likelihood method¹⁸,³⁶. A pulse profile with the highest signal-to-noise ratio was selected to construct a non-parametric template by smoothing it with a Gaussian filter and interpolating it to a bin size of $10^{-4}$ cycles. This same step size was used to compute the phase shift $\Delta\phi$ of each TOA. To estimate uncertainties, we computed the likelihood, and the resulting distribution followed the $\chi^2$ distribution. This characterization holds given our practice of deriving a single TOA from a dataset containing thousands of photons. Accordingly, we can calculate the $1\sigma$ statistical uncertainty. The same analysis procedure was also performed on the NuSTAR data in the 3–8 keV energy range.

Then, we traced the phase evolution of the TOAs based on the aforementioned ephemeris (Extended Data Fig. 1):

$$ \phi(t) = v(t - t_0) + \frac{1}{2}\dot{v}(t - t_0)^2 + \frac{1}{6}\ddot{v}(t - t_0)^3 + \dots \quad (1) $$

where those terms higher than the first derivative term ($\dot{v}$) are ignored for the first trial. It was clear that the initial timing solution failed to accurately predict the subsequent evolution. The phases of the TOAs showed a drop of approximately 0.2 cycles over a timescale of ≤0.5 days, starting about 4.4 hours before the CHIME FRB detection. Interestingly, the evolution formed a concave quadratic curve, indicating a fast spin-down over half a day. After approximately 4.4 hours following the CHIME FRB, the evolution showed a long-term convex quadratic curve, implying a much slower spin-down thereafter. Consequently, we fit the TOAs with a two-glitch model:

$$ \begin{cases} \phi(t) = \phi_0(t) = v(t-t_0) + \frac{1}{2}v(t-t_0)^2 & \text{for } t < t_{g1} \\ \phi(t) = \phi_1(t) = \phi_0(t) + \Delta v_1(t-t_{g1}) + \frac{1}{2}\Delta\dot{v}_1(t-t_{g1})^2 & \text{for } t_{g1} < t < t_{g2} \\ \phi(t) = \phi_1(t) + \Delta v_2(t-t_{g2}) + \frac{1}{2}\Delta\dot{v}_2(t-t_{g2})^2 & \text{for } t > t_{g2} \end{cases} \quad (2) $$

where $t_{g1}$ and $t_{g2}$ are glitch times. The sudden changes in frequency and spin-down rate are denoted as $\Delta v_1$ and $\Delta \dot{v}_1$ for the first glitch, and $\Delta v_2$ and $\Delta \dot{v}_2$ for the second glitch, respectively. The best-fit parameters for this model are listed in Extended Data Table 2. The best-fit timing model is shown as the orange curve in Fig. 1 and Extended Data Fig. 1. This model yields a fit statistic $\chi^2$ value of 83.2 with 64 degrees of freedom, and the residual did not show significant long-term trends.

The best-fit parameters and their corresponding $1\sigma$ uncertainties were obtained through an MCMC simulation. We sampled the full
parameter space of the two-glitch model using the emcee MCMC sampler³⁷ and assumed flat prior probability densities for all parameters. The MCMC was run with 32 walkers for 10⁵ steps, and the first 10⁴ samplings were discarded. The posterior probability density distributions are shown in Extended Data Fig. 2, and the values and 1σ uncertainties are summarized in Extended Data Table 2. The 1σ intervals of the best-fit model are plotted as the grey shaded area in Fig. 1 and Extended Data Fig. 1.

Compared with the pre-glitch epochs, the post-glitch ephemeris is more precisely defined owing to its long time span. To verify our timing solution, we cross-checked it by calculating the phases of the TOAs based on the post-glitch second-order ephemeris with a reference epoch of $t_0 = \text{MJD} 59,868.87136$, $v = 0.3075264$ Hz and $\dot{v} = -4.9 \times 10^{-12}$ Hz s⁻¹. A zoom-in view of the phase evolution near the FRB is presented in Extended Data Fig. 3. The parameters and the $\chi^2$ statistic of the best-fit model are in full agreement with those obtained previously. Furthermore, we tried to fit the phase evolution with an eighth-order polynomial, including terms up to $d^8v/dt^8$ in equation (1). Although this high-order polynomial has the same number of free parameters as the two-glitch model, it results in a much higher $\chi^2 = 378.8$ with 64 degrees of freedom. The residuals (as shown in Extended Data Fig. 3c) show a noticeable long-term trend, implying that the two-glitch model provides a much better fit. We also examined a fit of the TOAs with a long-term spin-up and a local fourth-order polynomial, but this did not yield better statistics.

The two glitches observed in this outburst are among the largest of all glitches determined in pulsars and magnetars, as shown in Fig. 2. We plotted the values of $\Delta v$ versus $\Delta \dot{v}$ and compared them with previously recorded glitches in pulsars and magnetars obtained from the literature and the Jodrell Bank glitch catalogue⁸,¹¹,²¹.

The rotational energy change involved in a glitch is $E_{glitch} \approx 4\pi^2|v\Delta v$, where $|v|$ (about $10^{45}$ g cm²) is the stellar moment of inertia. Thus the energies associated with these two glitches are $3.9 \times 10^{41}$ erg and $2.6 \times 10^{41}$ erg. The change in rotational energy between the glitches is estimated to be

$$ \Delta E_{\text{rot}} = \int_{t_{g1}}^{t_{g2}} \dot{E}_{\text{rot}} \, dt \approx -6.5 \times 10^{41} \text{ erg}, \quad (3) $$

where $\dot{E}_{\text{rot}} = 4\pi^2|v\Delta v$ is the inferred rotational energy loss rate during the period of enhanced torque. This value of $\Delta E_{\text{rot}}$ is approximately equal to the total energy associated with the two glitches.

## Energy-resolved pulse profile

We investigated the energy dependence of the pulse profile to gain insights into the emission mechanisms. To this end, we obtained the energy-resolved pulse profiles based on the best-fit two-glitch model by dividing the NICER data into two energy bands, 2–5 keV and 5–10 keV, and the NuSTAR data into four energy bands, 3–5 keV, 5–10 keV, 10–20 keV and 20–79 keV. The results are presented in Fig. 3. The soft X-ray peak is evident at a phase of $\phi \approx 0$ and the hard X-ray peak is found at $\phi \approx 0.5$. The soft X-ray peak dominates the profile below 10 keV but vanishes at energies above 20 keV. The hard X-ray peak is present above 5 keV and becomes the dominant feature above 10 keV.

We also calculated the spin phase of the FRB. The barycentric-corrected time of the CHIME FRB⁶ was calculated to be MJD 59,866.80817034 using pintbary, a command line tool of the pulsar timing software package pint³⁸ (http://ascl.net/1902.007). Similarly, we calculated the barycentric correct time of the brightest of the GBT FRBs⁷ as MJD 59,866.80817889. These times were extrapolated to infinite frequency based on a dispersion measure of 332.8 pc cm⁻³ (ref. 6). The phase of the FRB was found to be approximately 0.38 based on CHIME detection or 0.5 based on the GBT result, which is close to the peak of the 20–79 keV band (Fig. 3).

## Verification of the spin-down rate between glitches

From the analysis of the energy-resolved pulse profile, it is evident that the pulsed emission has multiple origins. The soft X-ray band may be dominated by thermal emission from the neutron star’s surface, whereas the hard X-ray emission would originate from the magnetosphere. This suggests that the timing solution based on photons below 8 keV could be affected by the pulse-profile change due to the motion of hotspots on the surface during the outburst. To investigate this, we attempted to trace the evolution of the phase of the 20–79 keV profile, but the large uncertainty due to the limited number of photons collected (approximately 2,200 counts between the two glitches) made it difficult to trace the evolution in detail.

As an independent verification, we performed an energy-resolved two-dimensional $Z_2^2$ test search for $v$ and $\dot{v}$ between the two glitches. Using NuSTAR events collected between the two glitches, we divided the events into four energy bands as defined in the energy-resolved pulse-profile analysis. The number of photons in each energy band was 7,991 in the 3–5 keV range, 14,478 in the 5–10 keV range, 6,484 in the 10–20 keV range and 2,275 in the 20–79 keV range. The results of the two-dimensional $Z_2^2$ test for each energy band, as well as the broadband (3–79 keV) events, are presented in Extended Data Fig. 5. The result obtained from the broadband events suggests a spin-down rate of $\dot{v} = -1.7(4) \times 10^{-9}$ Hz s⁻¹, which is in full agreement with the value obtained from the TOA analysis (−1.5(3) × 10⁻⁹ Hz s⁻¹). The spin-down rate in each energy band was determined to be −1.9(9) × 10⁻⁹ Hz s⁻¹ for 3–5 keV, −1.5(5) × 10⁻⁹ Hz s⁻¹ for 5–10 keV, −1.8(7) × 10⁻⁹ Hz s⁻¹ for 10–20 keV and −1.3(9) × 10⁻⁹ Hz s⁻¹ for 20–79 keV. These results point to a large spin-down rate that is consistent with that obtained from the TOA analysis.

Observational evidence for surface hotspot migration would most notably be (1) a change in the soft X-ray pulse profile and (2) a change in the relative phases of peaks in the quasi-thermal soft X-ray and non-thermal hard X-ray pulse profiles (under the largely secure assumption that these components trace different emission regions and physics). To examine this possibility, we obtained the soft X-ray profile 2–8 keV NICER data and 20–79 keV NuSTAR data in three epochs: $t < t_{g1}$, $t_{g1} < t < t_{g2}$ and $t > t_{g2}$ before the end of the first NuSTAR observation, as shown in Extended Data Fig. 4. Those X-ray photons collected within one hour of the two glitch epochs are not included to avoid possible coverage of the glitch time. The NICER soft X-ray profile remained single peaked although we note that a small secondary peak can be found at a phase of approximately 0.5. This small peak is occasionally seen in the profile of a few TOAs but they did not affect the stability of the main soft X-ray peak. The minima of the NuSTAR hard X-ray profiles are at around phase zero and no significant phase shift of the hard X-ray profile can be observed when folding the light curve with respect to the soft X-ray ephemeris. This suggests that the recovered phase evolution is secure and not a misinterpretation of hotspot migration.

## Spectral analysis

We extracted NICER and NuSTAR (FPMA and FPMB) persistent spectra with burst-removed and barycentric-corrected GTIs (Extended Data Table 3). NICER spectra were extracted with xselect version 2.5a following the standard procedure, where the background of NICER data was produced with the NICER background estimator tool nibackgen3C50 version v7b³⁹. The persistent spectra of epochs A, D and E were extracted from the time intervals where NICER and NuSTAR observed the target simultaneously, whereas those of epochs B, C and F do not strictly rely on time intervals with simultaneous observations.

We also extracted the burst spectra of NICER and NuSTAR (FPMA and FPMB) by accumulating all the detected burst at epochs B, C and D using the barycentric-corrected burst GTIs.
We used the XSPEC software version 12.12.1 with the $\chi^2$ statistic in the following analysis. We fitted the persistent spectra at each epoch (Fig. 4) and the burst accumulated spectrum (Extended Data Fig. 6), where the information of observation and the best-fit spectral parameters are shown in Extended Data Tables 4 and 3, respectively. The absorbed blackbody and power-law model, (tbabs*(bbodyrad+pegpwrlw)), was used for the persistent spectra except for epoch C. The solar abundance value was used to calculate the absorption$^{40}$. An absorbed power-law model (tbabs*pegpwrlw) was used for epoch C as the blackbody component is negligible compared with the power law. The accumulated burst spectrum was fitted with an absorbed blackbody plus a power law with a high-energy exponential roll-off (tbabs*(bbodyrad+cutofffl)). We added a constant term (about three) in the spectral model to cross-calibrate the normalization between NICER and NuSTAR because these two instruments cover emissions from different bursts. Best-fit spectral parameters, including the hydrogen column density $N_H$, black-body temperature $kT$, its radius $R$ and the photon index $\Gamma$ of the power law, are tabulated in Extended Data Table 4. These parameters were set free except for the spectra of epoch B, where the blackbody parameters were frozen to those of epoch A as no NICER observation was available and the NuSTAR spectral shape was more similar to that of epoch A than that of epoch C.

The absorbed 2-70 keV X-ray flux of persistent spectra was calculated with the flux command of XSPEC and the NICER and NuSTAR spectra were used for low-energy (2-10 keV) and high-energy (10-70 keV) bands, respectively. The absorption-corrected flux of persistent spectra was calculated from the normalization factors of the blackbody and power-law models. The absorbed and absorption-corrected flux of burst spectra were calculated from normalization factors of the blackbody and power-law models with only NuSTAR spectra because of the difficulty of estimating the effect of the constant value. Moreover, NuSTAR suffered dead time issues during a few of the most luminous bursts. Therefore, the flux of these bursts may be only estimated to an order of magnitude.

The hydrogen column density $N_H$ was determined to be (2.1-3.4) × 10$^{22}$ cm$^{-2}$ from the persistent spectra. Comparing the quiescent spectra, the blackbody temperature $kT$ increased to 0.51-0.68 keV around the FRB (epochs A-E) and returned to the quiescent value 12 days after the FRB (epoch F). However, the blackbody radius $R$ was similar to the quiescent value. Around the peak of the count rate in the X-ray bands (epoch C), the power-law spectrum became softer (from $\Gamma \approx 1.2$ to $\Gamma \approx 1.6$) and extended from the hard X-rays to lower energies, making it difficult to measure the blackbody parameters. In contrast, burst spectra have a high $N_H$ (4.2$^{+0.2}_{-0.1}$ × 10$^{22}$ cm$^{-2}$) and a soft $\Gamma$ (1.40 ± 0.02).

We also compared the above fitting results around the glitch (epochs A-E) with those considering the SCORPEON background model (obtained with the tool nicerl3-spec of NICERDAS v10). A few fitting parameters vary from the values obtained with the 3C50 background model, but the difference is at most around 20% (Extended Data Table 4). The difference could be larger than their $1\sigma$ statistical uncertainty and could be inherent in modelling the background. However, they did not change our order-of-magnitude estimate of the total energy and the spectral evolution.

## Theoretical interpretation

The main deliverables of this observational campaign are the two spin-up glitches that bracket a strong spin-down epoch that persists for several hours, the enhanced soft and hard X-ray activity evident mostly between the glitches, and the emission of the FRB during this activity interval. All these arise during an active epoch of X-ray bursts. The ephemeral wind picture presented here to address these features is derived from that presented in ref. 11 for the spin-down glitch observed from SGR 1935+2154 in 2020 during a period where source monitoring was much sparser than for this event.

## Constraining the superfluid component

First, the focus is on the timing results. Spin-up glitches impart abrupt re-adjustments to the rotational equilibrium of the entire star$^{25,41}$. Large glitch sizes typically require moments of inertia $I_{sf}$ of the superfluid neutron component in the inner crust of around a few per cent of that (I) of the entire star$^{42-45}$. This ratio can be estimated using angular-momentum-conservation arguments$^{42,46}$, yielding

$$ \frac{I_{sf}}{I} \approx \frac{\Delta v}{|\dot{v}| \Delta T_g} \qquad (4) $$

where $\Delta T_g$ is the time interval between glitches and is about 8.8 hours in the case here. This estimate suggests a superfluid component comprising several tens of per cent of the entire star.

## The inter-glitch torque driven by a strong wind

The rapid spin-down episode following the first glitch leads to a net increment $\Delta v \approx -4.7 \times 10^{-5}$ Hz in the hours before the second glitch. This evolution could be attributed to an external torque on the star and probably linked to the magnetosphere. The October 2020 spin-down glitch ($\Delta v = -1.8 \times 10^{-6}$ Hz) detailed in ref. 11 was interpreted as due to a strong, ephemeral wind lasting around 10 hours or less in its peak phase. This wind loads portions of the magnetosphere that are tied to the active surface region with plasma, altering the magnetic configuration and opening field lines near the pole$^{47}$. Thus the wind introduces a monopolar component to the field geometry that renders the polar fields more radial, approaching that of the morphology and strength of a split monopole$^{28,29,48}$ in the limit of extremely large winds and strong twists.

Such a picture can be also envisaged for the SGR 1935+2154 timing data for October 2022 presented here. The expected crustal stresses associated with the first glitch, amplified by the superstrong magnetic field, could precipitate plastic flows or rupturing, and localized heating and mechanical transport that could eject plasma from the surface near the magnetic pole into the magnetosphere. There, the locally zenith-directed fields permit rapid energy and mass transport vertically, and the thermal radiation pressure is above the Eddington limit, driving baryon-loaded plasma into the magnetosphere as a wind. Only mass transfer on open field lines can shed angular momentum to infinity and slow down the crust's rotation.

The wind required to drive the high spin-down episode between the glitches is highly optically thick$^{11}$, yet quite confined in its magnetic colatitudes in the inner magnetosphere. The polar cap colatitude of the last open field line footpoint at the surface for a dipolar configuration is $\theta_{cap} \approx \sqrt{2\pi R_{ns}/P_c} \approx 0.46^\circ$ for a rotational period of $P = 3.25$ s, where $R_{ns}$ is the radius of the neutron star and c is the speed of light. Thus, even with a modest expansion of the polar cap due to twists at the surface, the wind collimation at low altitudes is sufficient that it does not significantly obscure the surface soft X-ray emission: the inferred blackbody emission zone radii of $R_{bb} \approx 2$ km in Extended Data Table 4 suggest that the soft X-ray hotspot subtends angles $\theta_{bb} \approx R_{bb}/(R_{ns}/\sqrt{\pi}) \approx 7^\circ$. This is for a source distance of 6.6 kpc, which is not well constrained, thereby introducing some uncertainty into this $\theta_{bb}$ estimate. Near the surface, the wind is far less dense than the plasma that radiates the much more impulsive magnetar giant flares, and its motion is much less relativistic$^{11}$, thereby not being subject to strong Doppler boosting. Accordingly, its effective temperature lies at or below the NICER band$^{11}$, indicating that the wind's periphery may contribute to the soft X-ray signal, but not overwhelm it with hard X-rays. Yet such a wind does not occult the persistent hard X-ray signals at relatively low altitudes on closed field lines (see below).

The analysis of ephemeral mass loss delivered in ref. 11 that leads to the conclusion of high optical depth in the wind needs to be adapted for the high $|\Delta v|$ observed here between the glitches. Using total
angular-momentum conservation, the time-integrated mass loss $\delta m$ for a star of mass $M$ and radius $R_{\text{ns}}$ can be expressed via the ratio $\delta m/M \approx 2/5 (R_{\text{ns}}/R_{\text{eq}})^2 |\Delta v|/v$ for a spin-down increment $\Delta v$ in $v$; see equation (3) in ref. 11 and associated discussion for details. Here $R_{\text{eq}}$ is the radius of equipartition between the energy densities of the flowing plasma and the magnetic field. For the dipole field geometry focused on in ref. 11, one quickly infers $R_{\text{eq}} \approx 5 R_{\text{ns}}$ and a mass loss ratio of about $2.4 \times 10^{-6}$. This high value is not a realistic estimate because the plasma loading of the polar magnetosphere is sufficient to enhance the local field strengths$^{29}$ substantially when approaching a split monopole configuration, wherein the field strength scales roughly as $1/R$ with altitude $R$. This twisted field enhancement moves the equipartition radius to around $R_{\text{eq}} \approx 20-50 R_{\text{ns}}$, leading to the estimate of a fraction $\delta m/M \approx 2.4 \times 10^{-8}-1.5 \times 10^{-7}$ of the stellar mass expelled during a nom-inal 8.8-hour wind phase. This constitutes a mass loss roughly on the scale of that expected for giant flares. To provide a more precise esti-mate requires a detailed study of the dynamics of radiation-coupled plasma winds and angular-momentum expulsion in magnetar magne-tospheres; this will be the subject of a future study.

This wind can persist as long as the heat/mechanical energy source near the crustal active zone is maintained, and then abates as the surface regions 'heal', and the polar magnetosphere untwists. Observationally, this timescale is $\lesssim 9$ hours, offering an important constraint for theoreti-cal models for how subsurface conditions associated with magnetar glitches are generated. The cumulative spin-down during this epoch was sufficient to return the rotational configuration in about 9 hours to a critical state; this may be why a second glitch of similar magnitude ensued. The wind's abatement suggests at least partial crustal stress relaxation or healing. It is noted that mass that is shed on peripheral closed field lines (spillover 'wind') can potentially influence emission from the closed portions of the atmosphere and magnetosphere.

## Enhanced X-ray activity between the glitches

Two hours after the first glitch, there is a sharp rise in the burst rate and the persistent hard X-ray emission flux from SGR 1935+2154 (see Figs. 1 and 4). Assuming that these radiative changes are associated with the glitch, the time delay can be used to constrain the crustal location of heating within the magnetar, through the thermal timescale $\tau_{\text{th}} \approx (C/\kappa)z^2$, where C is heat capacity, $\kappa$ is thermal conductivity and $z$ is depth below the surface. For typical C and $\kappa$ of strongly magnetic neutron stars (see, for example, ref. 49), a two-hour thermal timescale occurs at a depth $z \approx 10$ m and density of $10^7$ g cm$^{-3}$ for polar locales where efficient heat transport occurs along the magnetic field approximately in the radial direction. This timescale probably exceeds that for the onset of the wind, as this outflow emanates from very near the surface; yet it may indicate when the wind enters its most powerful phase. The temporal correlation of the burst rate and persistent emission enhancement and decline following the first glitch suggests they are driven by the same subsurface energy deposition, with concurrent evolution and relaxation of the crust, atmosphere and magnetosphere.

Concerning the spectroscopy, there may be a causal coupling between the observed heating of the surface soft X-rays in the NICER data and the enhanced persistent signal seen above 10 keV by NuSTAR between the glitches. The leading paradigm for the generation of the persistent hard X-ray emission above 10 keV in magnetars is by resonant inverse Compton scattering (RICS) of soft X-ray photons emanating from the stellar surface by relativistic electrons accelerated in the magnetosphere$^{50,51}$. The scattering cross-section is resonant at the cyclotron frequency. The electrons are accelerated by magnetospheric electric fields, coherent or non-stationary, and given that the NuSTAR signal is enhanced and not abated between the glitches, we can presume that the collimated wind does not impair lepton acceleration in the pertinent electric field zone. This region is probably on closed field lines as most of the RICS signal, which is highly anisotropic and beamed, originates in quasi-equatorial locations where the magnetic field is low enough

for the scattering to access the cyclotron resonance. Moreover, for these locations, an observer who samples the Doppler-boosted RICS emission along field tangents$^{52}$ will naturally see a hard X-ray pulse peak at a different phase from that for the soft X-ray surface signal, as is evident in Extended Data Fig. 4. The intensity of the RICS emission is roughly proportional to the number density of the surface thermal photons$^{53}$, which for a blackbody scales as $T^3$. Accordingly, the roughly 60% increase in $T$ between the quiescent epoch and interval D as listed in Extended Data Table 4 should naively yield an enhancement in the RICS signal by a factor of about 4. In addition, the temperature increase might significantly extend the volumes of the inner magnetosphere for which the cyclotron resonance that controls the RICS emissivity is accessible, thereby further increasing the RICS flux. Combined, these influences would account for about half or more of the enhancement in the NuSTAR spectrum evident in Fig. 3, the remaining portion perhaps due to increases in the relativistic electron density associated with a spillover 'wind'.

## The fast radio burst

If the electric fields that accelerate the electrons that generate the RICS signal are left unmodified by the polar wind, then their persistence may continue pair creation that contributes to an enhanced RICS signal that can then further lead to enhanced pair cascading. The absence or presence of plasma where a burst occurs is probably connected to the generation of an FRB$^{30,54}$. Thus, the timing of the FRB during the epoch of amplified and abating hard X-ray emission between the glitches may in fact be a causal association. As a putative spillover wind abated and the system relaxed after the local persistent flux peak 2-3 hours after the first glitch (time interval C), this region became increasingly charge-starved to errant bursts during the span where the highest torque, and probably also stresses, were inflicted on the crust. This phenomenology is reminiscent of the April 2020 FRB, which also occurred in the waning phase of the burst storm on its track to relative source dormancy. Furthermore, it is noteworthy that the phase-connected arrival time of the FRB is roughly coincident with the peak of the hard X-ray signal in Extended Data Fig. 4, and offset in phase with the peak of the soft X-rays. Thus it appears probable that in this case both the FRB and the persistent hard X-rays both originate from quasi-equatorial locations, although probably not at the same altitudes.

## The October 2022 and October 2020 glitch comparison

It is of interest to compare this October 2022 event with the spin-down glitch in SGR 1935+2154 of the October 2020 epoch, which was not afforded the same high-quality observational cadence$^{11}$. The 2020 spin-down glitch was inferred using timing data spanning over 50 days, and arose during a data gap of approximately 3 days duration. An FRB-like burst was detected at about 3 days after the putative time of the spin-down glitch, and pulsed radio emission ensued thereafter, both during a period when the X-ray timing was re-established and at the post-glitch v (ref. 11). No X-ray enhancement before or after the spin-down glitch was seen. For the October 2022 events studied here, if instead, the source had been subject to a similar observational data gap of duration 1-2 days that bracketed the two glitches, none of the enhancement in persistent X-ray emission, the FRB and the glitches themselves would have been detected. In fact, the subsequent relatively sparse timing data might actually accommodate a spin-down-glitch solution for the October 2022 event, albeit probably of different magnitude in $\Delta v/v$. Clearly, the two events are different, particularly in terms of the eventual pulsed radio emission seen in 2020. Yet they do present similarities, principally rapid spin-down episodes, and this motivates the position that an ephemeral wind can drive the strong torque on the star for several hours between the two glitches. Moreover, the events do pose the question of what subsurface physics dictates a glitch recurrence timescale of around $\tau_{\text{rec}} \approx 2$ years in SGR 1935+2154. Glitch models of pulsars predict a range of $\tau_{\text{rec}}$ times and distributions$^{41}$.
Comparing these two events clearly indicates that the excellent data cadence we present here for October 2022 highlights the rich nature of information afforded by such temporally dense observations.

## Data availability

NICER raw data and calibrated level-2 data files were generated at the Goddard Space Flight Center large-scale facility. These data files are publicly available and can be found on HEASARC data archive (https://heasarc.gsfc.nasa.gov/FTP/nicer/data/obs/). NuSTAR data files are also publicly available at NUMASTER table (https://heasarc.gsfc.nasa.gov/W3Browse/all/numaster.html).

## Code availability

Reduction and analysis of the data were conducted using publicly available codes provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. For NICER and NuSTAR, we used NICERDAS version v009 and NUSTARDAS version v2.1.2, respectively, part of HEASOFT 6.31 (https://heasarc.gsfc.nasa.gov/docs/software/lheasoft). Spectral analysis was conducted using Xspec version 12.13.0 (https://heasarc.gsfc.nasa.gov/xanadu/xspec/). The emcee MCMC sampler is a public software available at https://emcee.readthedocs.io/en/stable/. The PINT is a public software available at https://nanograv-pint.readthedocs.io/en/latest/index.html. The custom codes for the timing analysis routines are available upon reasonable request from the corresponding authors.

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**Acknowledgements** This work was supported by the National Aeronautics and Space Administration (NASA) through the NICER mission and the Astrophysics Explorers Program. This research has also made use of data obtained with NuSTAR, a project led by Caltech, funded by NASA and managed by NASA/JPL, and has utilized the NUSTARDAS software package, jointly developed by the ASDC (Italy) and Caltech (USA). This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. C.-P.H. acknowledges support from the National Science and Technology Council in Taiwan through grants 109-2112-M-018-009-MY3 and 112-2112-M-018-004-MY3. T.E. acknowledges the RIKEN Hakubi project, JST grant number JPMJFR2020 (Sohatsu), and JSPS/MEXT KAKENHI grant number 22H01267. Z.W. acknowledges support by NASA under award number 80GSFC21M0002. W.C.G.H. acknowledges support through grants 80NSSC22K0397 and 80NSSC23K0078 from NASA. M.G.B. acknowledges the support of the National Science Foundation through grant AST-1813649 and NASA through grant 80NSSC20K1564. S.G. acknowledges the support from the CNES. K.R. acknowledges support from the Vici research programme 'ARGO' with project number 639.043.815, financed by the Dutch Research Council (NWO). NICER research at NRL is supported by NASA.

**Author contributions** C.-P.H. led the data analysis, performed the timing analysis and contributed to writing the paper. T.N., T.E., T.G. and S.G. performed the spectral analysis and contributed to writing the paper. T.E. led the NICER and NuSTAR collaboration. G.Y. and T.E. triggered the NICER DDT and joint NICER/NuSTAR GO ToO programme (NICER Cycle 4 proposal number 5076), respectively. G.Y. and P.S.R. supported the timing analysis and contributed to writing the paper. Z.W., W.C.G.H. and M.G.B. led the theoretical interpretations and contributed to writing the paper. K.R., C.K., Z.A., A.K.H. and K.C.G. contributed to writing the paper.

**Competing interests** The authors declare no competing interests.

**Additional information**

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41586-023-07012-5.

**Correspondence and requests for materials** should be addressed to Chin-Ping Hu, Teruaki Enoto, George Younes or Zorawar Wadiasingh.

**Peer review information** Nature thanks Jason Hessels and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

**Reprints and permissions information** is available at http://www.nature.com/reprints.
<figure><img src="image_7.png" /></figure>

**Extended Data Fig. 1** | Phase evolution of TOAs between 2022 October 12 and November 6 with respect to the pre-glitch ephemeris. The orange line is the best-fit two-glitch model, where the red vertical line denotes the time of the CHIME FRB detection. The times of two glitches are shown as the vertical dashed-dotted line (first glitch) and the dotted line (second glitch). The gray box denotes the zoom-in region shown in Fig. 1. The residual is shown in the lower panel.
<figure><img src="image_8.png" /></figure>

**Extended Data Fig. 2** | Posterior probability density distributions of the emcee sampler. The total simulation steps is 100,000. Two spin-up glitches are needed, where the first one is accompanied by an increase in the spin-down rate, while the second glitch is accompanied by a decrease in the spin-down rate.

The change in the spin-down rate of these two glitches is mostly canceled out. In the 1-D histograms, the dashed lines represent the best-fit value along with its 1σ standard deviation.
<figure><img src="image_9.png" /></figure>

**Extended Data Fig. 3** | Phase evolution of TOAs determined with NICER and NuSTAR based on the post-glitch ephemeris. The symbols used here are the same as those in Extended Data Fig. 1. The red dashed curve is the best-fit polynomial ephemeris up to the 8th order time derivative of $v$. This model has exactly the same number of free parameters as that of the two-glitch model. The residual of the two-glitch model is shown in panel (b), while that of the 8th-order polynomial is shown in panel (c).
<figure><img src="image_10.png" /><figcaption>**Extended Data Fig. 4** | Time-resolved pulse profiles obtained with NICER and NuSTAR. The left panel shows the pulse profile obtained with NICER in 2–8 keV in time intervals of $t < t_{g1}$, $t_{g1} < t < t_{g2}$, and $t > t_{g2}$. The right panel depicts the evolution of the 20–79 keV hard X-ray profile obtained with NuSTAR.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

**Extended Data Fig. 5** | Two-dimensional $Z_2^2$-test searching result between two glitches. We performed searches in the a. 3–79 keV, b. 3–5 keV, c. 5–10 keV, d. 10–20 keV, and e. 20–79 keV bands using NuSTAR data. X- and y-axes of panels b–d are the same as that of panel a. The color map of each panel denotes the

$Z_2^2$ values, while the peak is marked with the green plus sign. The green contours denote $Z_2^2(\text{max}) - 2.3, Z_2^2(\text{max}) - 6, \text{and } Z_2^2(\text{max}) - 15$ where $Z_2^2(\text{max})$ is the maximum $Z_2^2$ value of the peak.
<figure><img src="image_12.png" /></figure>

**Extended Data Fig. 6 | Spectral fitting results for burst emission from SGR 1935+2154 at the epochs between two glitches (Epochs B, C, and D).** The data are extracted from NICER (black), NuSTAR FPMA (red), and NuSTAR FPMB (green). All the detected burst events are accumulated. The total exposure of the NuSTAR data is 824 s. The accumulated spectrum is fitted by a model with an absorbed blackbody plus a power law with an exponential roll-off. Top, middle, and bottom panels show the count spectral components, fitting residuals, and spectra in $vF_v$ form, respectively.
Extended Data Table 1 | Data sets used in this work

<table><thead><tr><th>Observatory</th><th>ObsID</th><th>Start Date</th><th>Exposure (s)</th></tr></thead><tbody><tr><td>NICER</td><td>3020560159</td><td>2020-10-16T21:40:00</td><td>1349</td></tr><tr><td>NICER</td><td>5020560106</td><td>2022-10-12T17:40:27</td><td>1260</td></tr><tr><td>NICER</td><td>5020560107</td><td>2022-10-13T00:03:40</td><td>14913</td></tr><tr><td>NICER</td><td>5576010101</td><td>2022-10-13T16:44:01</td><td>3302</td></tr><tr><td>NICER</td><td>5576010102</td><td>2022-10-14T03:34:37</td><td>10332</td></tr><tr><td>NICER</td><td>5576010103</td><td>2022-10-14T23:58:20</td><td>7757</td></tr><tr><td>NICER</td><td>5576010104</td><td>2022-10-16T02:16:40</td><td>9990</td></tr><tr><td>NICER</td><td>5576010105</td><td>2022-10-17T01:14:37</td><td>2633</td></tr><tr><td>NICER</td><td>5576010106</td><td>2022-10-18T03:54:40</td><td>2472</td></tr><tr><td>NICER</td><td>5576010107</td><td>2022-10-19T04:20:01</td><td>2845</td></tr><tr><td>NICER</td><td>5576010108</td><td>2022-10-20T06:58:40</td><td>1693</td></tr><tr><td>NICER</td><td>5576010109</td><td>2022-10-21T00:00:00</td><td>3091</td></tr><tr><td>NICER</td><td>5576010110</td><td>2022-10-22T02:02:12</td><td>2034</td></tr><tr><td>NICER</td><td>5020560108</td><td>2022-10-23T21:44:37</td><td>260</td></tr><tr><td>NICER</td><td>5020560109</td><td>2022-10-25T06:17:53</td><td>678</td></tr><tr><td>NICER</td><td>5576010111</td><td>2022-10-26T08:20:34</td><td>6592</td></tr><tr><td>NICER</td><td>5576010112</td><td>2022-11-03T13:22:00</td><td>1297</td></tr><tr><td>NICER</td><td>5576010113</td><td>2022-11-06T08:16:30</td><td>1094</td></tr><tr><td>NICER</td><td>5020560110</td><td>2022-11-05T09:05:40</td><td>1194</td></tr><tr><td>NICER</td><td>5020560111</td><td>2022-11-06T00:42:00</td><td>729</td></tr><tr><td>NuSTAR</td><td>90602332004</td><td>2020-10-16T21:16:09</td><td>18585</td></tr><tr><td>NuSTAR</td><td>80802317002</td><td>2022-10-14T02:12:57</td><td>49624</td></tr><tr><td>NuSTAR</td><td>80802317004</td><td>2022-10-26T08:35:11</td><td>46266</td></tr></tbody></table>
Extended Data Table 2 | Best fit spin parameters between
2022 October 12 and November 6

<table><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>Epoch (MJD)</td><td>59865.6782217</td></tr><tr><td>ν (Hz)</td><td>0.3075277(6)</td></tr><tr><td>ν̇ (Hz s<sup>-1</sup>)</td><td>-1.7(6) × 10<sup>-11</sup></td></tr><tr><td>t<sub>g1</sub> (MJD)</td><td>59866.63<sup>+0.01</sup><sub>-0.02</sub></td></tr><tr><td>Δν<sub>1</sub> (Hz)</td><td>3.0(3) × 10<sup>-5</sup></td></tr><tr><td>Δν̇<sub>1</sub> (Hz s<sup>-1</sup>)</td><td>-1.5(3) × 10<sup>-9</sup></td></tr><tr><td>ν̇<sup>*</sup><sub>1</sub> (Hz s<sup>-1</sup>)</td><td>-1.5(3) × 10<sup>-9</sup></td></tr><tr><td>t<sub>g2</sub> (MJD)</td><td>59866.99(2)</td></tr><tr><td>Δν<sub>2</sub> (Hz)</td><td>1.9(3) × 10<sup>-5</sup></td></tr><tr><td>Δν̇<sub>2</sub> (Hz s<sup>-1</sup>)</td><td>1.5(3) × 10<sup>-9</sup></td></tr><tr><td>ν̇<sup>†</sup><sub>2</sub> (Hz s<sup>-1</sup>)</td><td>-4.9(1) × 10<sup>-12</sup></td></tr><tr><td>Δν<sup>‡</sup><sub>12</sub> (Hz)</td><td>3.9(4) × 10<sup>-5</sup></td></tr><tr><td>χ<sup>2</sup>/dof</td><td>83.2/64</td></tr></tbody></table>

Timing information for the glitches at times $t_{g1}$ and $t_{g2}$, inter-glitch and post-glitch frequency derivative, and frequency shift between two glitches are also included.

* inter-glitch frequency derivative.

† post-glitch frequency derivative.

′ frequency shift between two glitches.
Extended Data Table 3 | Information of observations at each epoch around the glitches

<table><thead><tr><th rowspan="3">Epoch</th><th rowspan="3">Start/End time (NICER MET)</th><th colspan="2">Exposure (s)</th><th colspan="2">Count Rate (counts s<sup>-1</sup>)</th></tr><tr><th>NICER</th><th>NuSTAR</th><th>NICER</th><th>NuSTAR</th></tr><tr><th colspan="2">FPMA/FPMB</th><th colspan="2">FPMA/FPMB</th></tr></thead><tbody><tr><td>Quiescent</td><td>214350080/214355957</td><td>1349</td><td>18580/18460</td><td>(4.9 ± 0.2) × 10<sup>-1</sup></td><td>(2.1 ± 0.1) × 10<sup>-2</sup>/(2.6 ± 0.1) × 10<sup>-2</sup></td></tr><tr><td>A</td><td>277061890/277225150</td><td>2034</td><td>2129/2111</td><td>1.27 ± 0.03</td><td>(1.58±0.09) × 10<sup>-1</sup>/(1.47±0.09) × 10<sup>-1</sup></td></tr><tr><td>B</td><td>277225150/277232029</td><td>—</td><td>3166/3137</td><td>—</td><td>(2.02±0.08) × 10<sup>-1</sup>/(1.79±0.07) × 10<sup>-1</sup></td></tr><tr><td>C</td><td>277232029/277240909</td><td>1455</td><td>67/67</td><td>13.5±0.1</td><td>4.8±0.3/4.2±0.3</td></tr><tr><td>D</td><td>277240909/277256736</td><td>377</td><td>490/485</td><td>3.7±0.1</td><td>(2.8±0.2) × 10<sup>-1</sup>/(3.4±0.3) × 10<sup>-1</sup></td></tr><tr><td>E</td><td>277256736/277274900</td><td>1593</td><td>2101/2080</td><td>2.33±0.05</td><td>(2.15±0.01) × 10<sup>-1</sup>/(2.36±0.01) × 10<sup>-1</sup></td></tr><tr><td>F</td><td>278238215/278288601</td><td>6592</td><td>46270/45850</td><td>(7.89±0.01) × 10<sup>-1</sup></td><td>(9.39±0.02) × 10<sup>-2</sup>/(9.42±0.01) × 10<sup>-2</sup></td></tr><tr><td>Burst</td><td>277225150/277256736</td><td>94</td><td>824/823</td><td>(4.90±0.02) × 10<sup>2</sup></td><td>(3.96±0.02) × 10<sup>-1</sup>/(3.61±0.02) × 10<sup>-1</sup></td></tr></tbody></table>
Extended Data Table 4 | Best-fit spectral parameters of the persistent X-ray emission

<table><thead><tr><th>Epoch</th><th>Absorbed/Unabsorbed flux *<br>10<sup>-11</sup> erg s<sup>-1</sup> cm<sup>-2</sup></th><th>N<sub>H</sub><br>10<sup>22</sup> cm<sup>-2</sup></th><th>kT<br>keV</th><th>R @6.6 kpc<br>km</th><th>Γ</th><th>spectral model‡</th></tr></thead><tbody><tr><td colspan="7">3C50 Background model for NICER data</td></tr><tr><td>Quiescent</td><td>0.49 ± 0.05 / 0.52 ± 0.05</td><td>2.1<sup>+0.5</sup><sub>-0.4</sub></td><td>0.42<sup>+0.04</sup><sub>-0.03</sub></td><td>1.8<sup>+0.5</sup><sub>-0.3</sub></td><td>1.2 ± 0.1</td><td>BB+PL</td></tr><tr><td>A</td><td>3.1<sup>+0.2</sup><sub>-0.3</sub> / 3.3 ± 0.3</td><td>2.6 ± 0.2</td><td>0.51 ± 0.03</td><td>2.1 ± 0.2</td><td>1.1 ± 0.1</td><td>BB+PL</td></tr><tr><td>B</td><td>3.3<sup>+0.3</sup><sub>-0.4</sub> / 4.1 ± 0.3</td><td>2.4 (fixed)</td><td>0.55 (fixed)</td><td>1.9 ± 0.2</td><td>1.2 ± 0.1</td><td>BB+PL</td></tr><tr><td>C</td><td>93<sup>+4</sup><sub>-5</sub> / 95 ± 4</td><td>3.13<sup>+0.06</sup><sub>-0.07</sub></td><td>—</td><td>—</td><td>1.22<sup>+0.03</sup><sub>-0.02</sub></td><td>PL</td></tr><tr><td>D</td><td>5.4<sup>+0.9</sup><sub>-1.1</sub> / 5.8<sup>+0.9</sup><sub>-0.6</sub></td><td>2.4<sup>+0.3</sup><sub>-0.4</sub></td><td>0.68 ± 0.05</td><td>1.8<sup>+0.3</sup><sub>-0.2</sub></td><td>1.6<sup>+0.2</sup><sub>-0.3</sub></td><td>BB+PL</td></tr><tr><td>E</td><td>3.1 ± 0.2 / 3.3 ± 0.2</td><td>2.5<sup>+0.2</sup><sub>-0.1</sub></td><td>0.61 ± 0.05</td><td>1.3<sup>+0.3</sup><sub>-0.2</sub></td><td>1.8 ± 0.1</td><td>BB+PL</td></tr><tr><td>F</td><td>1.56<sup>+0.03</sup><sub>-0.05</sub> / 1.67 ± 0.03</td><td>3.4 ± 0.2</td><td>0.34 ± 0.02</td><td>4.4<sup>+0.3</sup><sub>-0.2</sub></td><td>1.53 ± 0.2</td><td>BB+PL</td></tr><tr><td>Burst</td><td>488 ± 2 / 525 ± 2</td><td>4.2<sup>+0.2</sup><sub>-0.1</sub></td><td>0.17 ± 0.1</td><td>3.2<sup>+0.3</sup><sub>-0.2</sub> × 10<sup>2</sup></td><td>1.40 ± 0.02†</td><td>BB+CPL</td></tr><tr><td colspan="7">SCORPEON Background model for NICER data</td></tr><tr><td>A</td><td>4.0<sup>+0.03</sup><sub>-0.03</sub> / 4.1 ± 0.3</td><td>1.47<sup>+0.06</sup><sub>-0.10</sub></td><td>0.62<sup>+0.03</sup><sub>-0.02</sub></td><td>1.48 ± 0.12</td><td>1.20<sup>+0.09</sup><sub>-0.10</sub></td><td>BB+PL</td></tr><tr><td>B</td><td>3.3<sup>+0.3</sup><sub>-0.4</sub> / 4.1 ± 0.3</td><td>2.4 (fixed)</td><td>0.55 (fixed)</td><td>1.9 ± 0.2</td><td>1.2 ± 0.1</td><td>BB+PL</td></tr><tr><td>C</td><td>75<sup>+5</sup><sub>-5</sub> / 77 ± 4</td><td>2.21<sup>+0.05</sup><sub>-0.06</sub></td><td>—</td><td>—</td><td>1.33 ± 0.03</td><td>PL</td></tr><tr><td>D</td><td>4.8<sup>+0.4</sup><sub>-0.5</sub> / 5.3 ± 0.4</td><td>2.31<sup>+0.20</sup><sub>-0.19</sub></td><td>0.54<sup>+0.07</sup><sub>-0.08</sub></td><td>2.2<sup>+1.0</sup><sub>-0.5</sub></td><td>1.91 ± 0.14</td><td>BB+PL</td></tr><tr><td>E</td><td>3.9 ± 0.2 / 4.2 ± 0.2</td><td>1.92<sup>+0.12</sup><sub>-0.11</sub></td><td>0.56 ± 0.04</td><td>1.77<sup>+0.33</sup><sub>-0.21</sub></td><td>1.65 ± 0.08</td><td>BB+PL</td></tr></tbody></table>

<footnote>* Fluxes are calculated in the energy range of 2-70 keV except for absorbed flux of epoch B and burst (10-70 keV).</footnote>

<footnote>† The photon index of the power-law with an exponential rolloff at 37 keV.</footnote>

<footnote>‡ Corresponding Xspec models are, BB: bbodyrad, PL: pegpwrlw, and CPL: cutoffpl.</footnote>