The 2022 High-energy Outburst and Radio Disappearing Act of the Magnetar 1E 1547.0–5408

Regular monitoring of 1E 1547.0−5408 with an approximately 10 day cadence has been undertaken with Murriyang, the 64 m Parkes radio telescope, under the P885 project since its discovery as a radio-loud magnetar in 2007 (Camilo et al. 2007). Our observations from 2019 January have been performed using the Ultra-Wideband Low (UWL) receiver system (Hobbs et al. 2020), where two independent pulsar-search-mode data streams are recorded with the pulsar digital filterbank v4 (PDFB4) and GPU-based medusa signal processors. Individual observations lasted between 2 and 15 minutes. For this work, we analysed a subset of the PDFB4 data spanning from 2021 June to 2022 August and medusa data covering 2021 December to 2022 August. Data collected by PDFB4 were taken with 1 ms time sampling at a center frequency of 3100 MHz with 512 channels covering 1024 MHz of bandwidth. Full Stokes data collected with medusa were recorded with a 128 μs time resolution with 3328 channels covering the full UWL band from 704 to 4032 MHz, and coherently dedispersed at a dispersion measure (DM) of 830 pc cm⁻³. Both data sets were subsequently folded at the rotation period of the magnetar using dspsr (van Straten & Bailes 2011), such that a single pulse period is covered by 1024 phase bins. Frequency channels affected by radio-frequency interference (RFI) were excised using the paz and pazi tools in psrchive (Hotan et al. 2004; van Straten et al. 2012). The folded medusa data were then flux and polarization calibrated following the procedures outlined in Lower et al.(2020).

The Neutron star Interior Composition ExploreR (NICER) is a nonimaging, soft X-ray telescope mounted on the International Space Station, with a $\approx 5^{\prime}$ diameter field of view (FoV; Gendreau et al. 2016). NICER provides a large collective area peaking at 1900 cm² at 1.5 keV and a timing resolution <300 ns. We initiated a series of NICER target-of-opportunity observations of 1E 1547.0−5408 two days after the 2022 April 7 Swift-BAT detection of a magnetar-like burst coincident with 1E 1547.0−5408. The NICER monitoring consisted of about 1 ks of observations every few days, starting on 2022 April 9. We provide the observations log in Table 1.

We cleaned and calibrated all NICER data utilizing NICERDAS version v008c as part of HEASoft version 6.30.1. We applied the standard filtering criteria as described in the NICER Data Analysis Guide. ²¹  Moreover, detectors 14 and 34 can show larger than normal background noise, hence, were excluded from all analyses. Finally, we compared the light curve (binned with a 5 s resolution) created in the energy range 1–6 keV (where the source is supposed to dominate the emission) to the one created in the 13–15 keV energy range. Almost all the counts in the latter band are due to the high-energy particle background. We eliminated any simultaneous flaring background intervals that appeared in both light curves. These were mostly present at the start and/or end of a good time interval (GTI) due to imprecise modeling of the South Atlantic Anomaly. We provide the total GTIs of each NICER observation in Table 1. We utilize Xselect as part of HEASoft version 6.30.1 to extract the source spectra, and estimated the background contribution for each observation utilizing the 3C50 model (Remillard et al. 2022).

The Nuclear Spectroscopic Telescope ARray (NuSTAR; Harrison et al. 2013) is a focusing hard (3–79 keV) X-ray telescope, consisting of two identical focal plane modules (FPMs), FPMA and FPMB. Each module is formed by an array of 2 × 2 detectors providing a total of about $12^{\prime} \times 12^{\prime}$ FoV. Prompted by the increase in the soft X-ray flux, we requested NuSTAR director discretionary time and 1E 1547.0−5408 was observed for 24 ks on 2022 April 21. We utilized NuSTARDAS software version 2.1.2 to clean and calibrate the event files. We employed the task nuproducts to extract source events, light curves, and spectra from a circular region with a 50'' radius around the source central brightest pixel, which corresponds to 70% of the encircled-count fraction of the detectors point-spread function. This choice of extraction region is driven by the desire to maximize source counts, while limiting the stray-light background, which is present in both NuSTAR modules in proximity to the source. Similarly, we extracted the background files from a source-free region on the same detector as the source with the same radius. For comparison purposes, we analysed two archival NuSTAR observations taken on 2016 April 23 and 2019 February 15, following the same procedures outlined above. Table 1 summarizes the NuSTAR observations.

The X-ray Telescope (XRT) on board Swift is an imaging charge-coupled device, sensitive to photons in the energy range of 0.2–10 keV (Burrows et al. 2005). XRT observed 1E 1547.0−5408 on several occasions in 2022 March, May, and July, bracketing the time of the outburst. Thus, these observations provide the source soft X-ray spectral state shortly before the outburst onset, and a confirmation of its properties as observed with NICER following the outburst. For these observations, XRT was operating in windowed-timing mode, affording a 1D image with a time resolution of 1.7 ms. We utilized XRTDAS version 3.7.0 to reduce and calibrate the data. We extracted source events from each GTI of a given observation separately. We used a circular region with a 20 pixel radius centered on the brightest pixel. We extracted background events from an annulus with inner and outer radii of 80 and 120 pixels, respectively, centered at the same position as the source. We created the ancillary files using xrtmkarf, and used the response matrices in CALDB version 20220803. We excluded all GTIs where the source landed within a three pixel distance from a bad column or the edge of the CCD due to an increase in the systematic uncertainties. ²²  For the remaining good GTIs, we add the source and background spectra, as well as the ancillary and response files using the HEASOFT tool addspec. We provide the XRT observation IDs, dates, and total GTIs in Table 1.

BAT, also on board Swift, is a coded aperture telescope which images a ∼1.5 sr FoV in the energy range of 15–150 keV. Images are generated by the onboard software in response to count rate increases at timescales from 4 ms to 24 s or, in the absence of rate increases, on minute and longer timescales. Bursts from sources outside of the FoV can often be detected due to the leakage of photons through the instrument shielding, yielding a count rate increase without a corresponding image peak. These can be used to confirm the astrophysical nature of count rate increases seen by other instruments and constrain their direction of origin.

The Gamma-ray Burst monitor (GBM; Meegan et al. 2009) is a nonimaging instrument on board the Fermi Gamma-ray Space Telescope that is sensitive to photons in the 8–1000 keV range. GBM is capable of automatic onboard triggers, with one of the software algorithms tailored to magnetar-like short bursts. Apart from the triggered data, GBM also provides continuous time-tagged events (CTTE), with a time resolution of 2 microseconds. We utilized the CTTE data to search for any untriggered bursts from the direction of 1E 1547.0−5408 from its last radio detection on 2022 March 16 until the confirmed BAT burst on 2022 April 7. This analysis provides an estimate of the start time of the 2022 outburst.

Unlike other radio-loud magnetars which fade into radio silence in the months to years after an outburst, 1E 1547.0−5408 has remained radio-loud for well over a decade since the 2009 outburst (F. Camilo et al. 2023, in preparation). Following the 2008 and 2009 outbursts, detections of radio pulses were intermittent (see, e.g., Israel et al. 2021), possibly reflecting the highly dynamic nature of its magnetosphere during that period. Intermittent detections continued up to 2013, after which radio pulses were consistently detected during every observation. 1E 1547.0−5408 remained in this persistently radio-loud state until our two observations on 2022 March 16 and April 9, where we failed to detect radio pulses from the magnetar. Radio pulses were redetected during the 2022 April 19 observation, ∼12 days after the BAT-confirmed trigger, and have persisted up to at least our Parkes-UWL observation on 2022 August 3.

Using a high signal-to-noise ratio (S/N) observation taken on 2022 July 9, we measured a structure-optimized DM of 697 ± 1 pc cm⁻³ with the DM_phase package (Seymour et al. 2019). The updated DM is a significant improvement on the previously reported value of 830 ± 50 pc cm⁻³ (Camilo et al. 2007). This is likely due to differences in the methods applied to compute the DM (profile structure versus S/N optimization) in addition to the substantially larger instantaneous bandwidth afforded by the UWL. Using the NE2001 (Cordes & Lazio 2002) and YMW16 (Yao et al. 2017) electron density models, this updated DM corresponds to estimated distances of 8.3 kpc and 5.9 kpc, respectively. The latter distance is comparable to the commonly assumed distance of ∼4.5 kpc inferred from dust-scattering halos detected after the 2009 outburst (Tiengo et al. 2010), when considering the large systematic uncertainties that are associated with any of these methods, which are on average 50%. Similarly, we obtained an updated rotation measure (RM) of −1847.6 ± 0.5 rad m⁻² by directly fitting the Stokes Q and U spectra in the 2000–4032 MHz range (to avoid complications from scatter broadening) with RMNest (Lower et al. 2022). Our updated RM is consistent with the previously reported value of −1860 ± 20 rad m⁻² (Camilo et al. 2008).

The shape of the average radio profile detected throughout 2022 January–August was highly variable, and can be broadly categorized into three general archetypes:

• 1.  
  Profile A: strong leading component with one to three trailing components.
• 2.  
  Profile B: complex, multicomponent profile, sometimes with a central peak.
• 3.  
  Profile C: two dominant profiles joined by weaker subcomponents or a flat bridge of emission.

Examples of all three profile types are shown in Figure 1, all of which were dedispersed and de-Faraday rotated using our updated DM and RM values. Note, these categorizations are purely qualitative. For instance, the complex 2022 June 13 profile (bottom-middle panel in Figure 1) is largely double peaked, and could also be classified as Profile C. Transitions between profile types tend to be sudden and reminiscent of transient profile changes reported in earlier observations of this magnetar (e.g., Figure 5 of Halpern et al. 2008) and those seen in emission mode-changing/state-switching pulsars (Wang et al. 2007). The radio profiles of 1E 1547.0−5408 in Figure 1 display clear epoch-to-epoch variations in flux density. We computed the frequency-averaged radio flux density as

$$\begin{eqnarray}&&{F}_{f}=\displaystyle \frac{1}{{N}_{\mathrm{bin}}}\displaystyle \sum _{i}^{{N}_{\mathrm{on}}}{F}_{f,i},\end{eqnarray} \tag{ 1 }$$

where N_bin = 1024 is the number of phase bins covering a full rotation of the magnetar, N_on is the number of bins covering the on-pulse region, and F_f,i is the flux of the ith phase bin. Uncertainties in the flux density were computed from the rms of the off-pulse region

$$\begin{eqnarray}&&{\sigma }_{F,f}=\displaystyle \frac{\sqrt{{N}_{\mathrm{on}}}}{{N}_{\mathrm{bin}}}\sqrt{\displaystyle \sum _{i}^{{N}_{\mathrm{off}}}{F}_{f,i}^{2}},\end{eqnarray} \tag{ 2 }$$

where N_off is the number of off-pulse phase bins. The measured flux densities from our observations are displayed in the bottom panel of Figure 2. We used Equation (2) to set sensitivity limits for our observations on 2022 March 26 and April 9 where we failed to detect radio pulses, obtaining limiting flux densities of 1.3 ± 0.3 mJy and 0.9 ± 0.2 mJy, respectively. Visually, there appears to be a shallow increase in the revived radio flux over time. However, a direct connection between this apparent secular evolution and the outburst cannot be confirmed without a comparison to the long-term flux history of the magnetar.

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Also indicated in Figure 2 are the corresponding profile types seen during each observation. In terms of relative numbers, we observed the Profile B state in more than half (25/49) of our observations, while Profiles A and C were seen in 17 and seven, observations respectively. The appearance of any one mode appears to be largely stochastic, though there is a clear preference for Profile B after the outburst up until 2022 May 13 (MJD 59712) where the magnetar was in the Profile A state. No further systematic change in the profile or the mode-changing behavior is apparent after this date. It is possible that this preference may be related to changes in the emission region plasma following reactivation. However such profile variations persist among radio-loud magnetars for many months to years after an outburst (Levin et al. 2012; Lower et al. 2021b). Additionally, the swing of the linear polarization position angle (PA) across the profile remains largely flat and unchanged both before and after the outburst. This is consistent with previous observations of 1E 1547.0−5408 in 2007, where rotating vector model fits indicated that the magnetar is a near-aligned rotator (Camilo et al. 2008). Occasional departures from the smooth PA swing are detected in individual epochs, an example of which is shown in the top-right panel of Figure 1. The relatively smooth evolution of the PA swing persists at higher observing frequencies where the effects of interstellar scattering are negligible, indicating these features are due to either an unusually smooth transition between two orthogonal polarization modes or the result of birefringent propagation effects in the near-field environment (Dyks 2020). Birefringent propagation effects would also explain the unusually high circular polarization fraction (up to ∣V∣/I = 0.54) as well as changes in the handedness between observations. A more detailed investigation is left for future work.

The variable radio profile of 1E 1547.0−5408 is not conducive to pulsar timing methods that use a single reference template. Instead, we obtained pulse times of arrival (ToAs) from the Parkes/PDFB4 data by using the get_toas tool in PRESTO (Ransom 2011) to fit a single Gaussian template to individual observations via the fast Fourier transform based approach of Taylor (1992). We added an extra 0.05 s uncertainty in quadrature with the formal ToA uncertainties to account for excess epoch-to-epoch scatter in the ToAs that arise from the varying radio profile (often referred to as "jitter").

For NICER, we merged all barycenter-corrected event files and only accepted counts in the 1–5 keV energy range, which maximized the source pulse signal according to the Z² power (Buccheri et al. 1983). We then split the data into time intervals that contain ≈1000 counts each, without allowing individual intervals to exceed a 3 day integration. We employed a nonbinned maximum likelihood estimation (MLE) method to measure the X-ray pulse ToAs (Livingstone et al. 2009; Ray et al. 2011). First, we model a high S/N pulse profile with a Fourier series including only the fundamental harmonic; adding higher-order harmonics did not improve the quality of the fit. Second, we fit, using MLE, each unbinned data segment to the same model, only allowing for a phase shift Δϕ. The best-fit phase shift is the value that corresponds to the minimum of the negative log likelihood, $-\mathrm{log}{({ \mathcal L })}_{\min }$. The 1σ uncertainty on the phase shift was established by stepping over the full parameter space Δϕ ∈ [0, 2π) and noting a change in $-\mathrm{log}{({ \mathcal L })}_{\min }$ by 0.5 (corresponding to the ±34% or 1σ confidence interval of a χ² distribution with 1° of freedom).

We obtained an initial phase-connected solution by using the Hidden Markov Model (HMM)-based glitch detector of Melatos et al. (2020), ²³  which tracks the spin frequency (ν) and spin-down rate ($\dot{\nu }$) of the magnetar over time. This enabled robust integer pulse numbering to be applied to each ToA and provided estimates of any changes in ν and $\dot{\nu }$ at the time of the outburst.

Once the phase-connected solution was obtained, we then used the glitch plugin to tempo2 (Edwards et al. 2006; Hobbs et al. 2006) to perform independent local fits to ν and $\dot{\nu }$. The results of our local fits are shown alongside the HMM tracking in Figure 3. Both sets of spin frequency/spin-down-rate measurements generally agree with one another and display approximately the same secular evolution. A timing anomaly with clear jumps in both ν and $\dot{\nu }$ occurred in coincidence with the high-energy outburst, with the HMM recovering step changes of Δν = (9 ± 4) × 10⁻⁷ Hz and ${\rm{\Delta }}\dot{\nu }=(-1.6\pm 0.5)\times {10}^{-12}$ s⁻². There is also a clear, secular increase in the spin-down rate of the magnetar ($\dot{\nu }$ is becoming more negative) over time, where $\dot{\nu }$ appears to follow an approximately linear trend over the first 120 days postoutburst. This is also reflected by the downward curve in the evolution of ν over time. Increasing spin-down rates are also commonly observed in the postoutburst behavior of other magnetars, including recent outbursts in the radio-loud magnetars PSR J1622−4950 (Camilo et al. 2018) and XTE J1810−197 (Caleb et al. 2022). A linear fit to the spin-down evolution gives an apparent $\ddot{\nu }=-1.95(5)\times {10}^{-19}$ s⁻³. Similar behavior was previously observed in 1E 1547.0−5408 following the 2008 outburst (Israel et al. 2010).

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In order to constrain both the longer-term rotational properties of 1E 1547.0−5408 and the outburst-induced changes in its timing better, we modeled the anomaly as a pulsar glitch where the corresponding change in rotation phase is given by

$$\begin{eqnarray}\begin{array}{rcl}{\phi }_{{\rm{g}}}(t) & = & {\rm{\Delta }}{\phi }_{g}+{\rm{\Delta }}{\nu }_{p}(t-{t}_{{\rm{g}}})+\displaystyle \frac{1}{2}{\rm{\Delta }}{\dot{\nu }}_{p}{\left(t-{t}_{{\rm{g}}}\right)}^{2}\\ & & +\,\displaystyle \frac{1}{6}{\rm{\Delta }}{\ddot{\nu }}_{p}{\left(t-{t}_{{\rm{g}}}\right)}^{3}-{\rm{\Delta }}{\nu }_{d}{\tau }_{d}{e}^{-(t-{t}_{{\rm{g}}})/{\tau }_{d}}.\end{array}\end{eqnarray} \tag{ 3 }$$

Here, t_g is the glitch epoch, Δϕ_g is a phase jump to account for residual ambiguities in the rotation phase of the magnetar after the event, Δν_p is the permanent step change in the spin frequency, ${\rm{\Delta }}{\dot{\nu }}_{p}$ the step change in the spin-down rate, and Δν_d is the exponentially recovered change in the spin frequency that occurred over a characteristic timescale, τ_d . We also included a glitch-induced second spin-frequency derivative (${\rm{\Delta }}{\ddot{\nu }}_{p}$) term to account for the postoutburst linear increase in $\dot{\nu }$ that we discussed above.

The gap in our timing between the last Parkes detection on 2022 March 16 and the first NICER observation on April 9 makes it difficult to determine the precise glitch epoch. Since magnetar glitches are often associated with radiative events (Dib & Kaspi 2014), we use the date of the short burst detected by Fermi-GBM from the direction of 1E 1547.0−5408 as the nominal glitch epoch (i.e., t_g = MJD 59672; 2022 April 3; see Section 3.3.3). Note, the exact choice of glitch epoch between April 1 and April 7 has a strong impact on the recovered Δν_p , which we discuss further below. Using tempo2 and the FITWAVES plugin, we fit the glitch parameters alongside a set of 10 harmonically related sine waves to account for strong timing noise in the residuals. This returned values of Δν_p = 2.0(1) × 10⁻⁶ Hz, ${\rm{\Delta }}{\dot{\nu }}_{p}=-1.23(2)\times {10}^{-14}$ s⁻², and ${\rm{\Delta }}{\ddot{\nu }}_{p}=-1.86(3)\times {10}^{-19}$ s⁻³. A significant Δν_d of −2.1(1) × 10⁻⁶ Hz was recovered. The negative value of Δν_d signifies a resolved rise in the spin frequency over a period of τ_d = 13(1) days as opposed to a postglitch decay.

To verify the existence of this apparent delayed rise in ν, we sampled the posterior distributions for each parameter using the TempoNest Bayesian inference plugin to tempo2 (Lentati et al. 2014). This also allowed us to model the timing noise of the magnetar simultaneously as a power-law (PL) red-noise process. The power spectral density of the red-noise model is given by

$$\begin{eqnarray}&&P(f)=\displaystyle \frac{{A}_{{\rm{r}}}^{2}}{12{\pi }^{2}}{\left(\displaystyle \frac{f}{1\,\mathrm{yr}}\right)}^{-{\beta }_{{\rm{r}}}}\,{\mathrm{yr}}^{-3},\end{eqnarray} \tag{ 4 }$$

where A_r is the red-noise amplitude (in units of yr^3/2) and β_r the spectral index. Two separate fits were performed: one that included a resolved rise in the spin frequency, and another where Δν_d is fixed to zero for an instantaneous (unresolved) glitch. Comparing the recovered log-evidence from the resulting fits, we obtain a Bayes' factor of $\mathrm{ln}{ \mathcal B }=-2.8$ in favor of a resolved rise. The negative value indicates there is no significant evidence for the presence of a resolved versus an instantaneous change in the spin frequency. Our results for the unresolved glitch model are summarized in Table 2.

Table 2. Timing and Pulsar Parameters for 1E 1547.0−5408 from Our Joint Parkes/NICER Timing

Pulsar parameters
R. A. (J2000) a	15h50m5412386
Decl. (J2000) a	−54°18'241141
ν (Hz)	0.478836(3)
$\dot{\nu }$(s−2)	−3.63(3) × 10−12
${\mu }_{\alpha }\cos \delta$ (mas) a	4.8
μδ (mas) a	−7.9
Timing epoch (MJD TDB)	58350
Position epoch (MJD TDB)	54795
DM (pc cm−3)	697(1)
RM (rad m−2)	−1847.6(5)
Time span (MJD)	59368–59808
Number of ToAs	202
Solar system ephemeris	DE436
${\mathrm{log}}_{10}({A}_{{\rm{r}}})$ (yr3/2)	−5.1(2)
βr	5.7(8)
Glitch parameters
tg (MJD)	59672
Δνp (Hz)	2(1) × 10−7
${\rm{\Delta }}{\dot{\nu }}_{p}$ (s−2)	−2.4(1) × 10−12
${\rm{\Delta }}{\ddot{\nu }}_{p}$ (s−3)	−2.0(1) × 10−19

Note. Values in parentheses are the 1σ uncertainties on the last digit.

^a Fixed to values from Deller et al. (2012).

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We present the one- and two-dimensional posterior distributions for the glitch and timing noise parameters in Figure 4. There is a strong correlation between ${\rm{\Delta }}{\dot{\nu }}_{p}$ and ${\rm{\Delta }}{\ddot{\nu }}_{p}$, indicating these two parameters induce a similar signal across the relatively short postglitch timing of 1E 1547.0−5408. While ${\rm{\Delta }}{\dot{\nu }}_{p}$ agrees with the value recovered by the HMM at the 68% confidence interval, the TempoNest derived value of Δν_p is smaller by a factor of ∼4.5. As for the postoutburst rotational evolution, our recovered value of ${\rm{\Delta }}{\ddot{\nu }}_{p}$ is consistent with that inferred from a simple linear fit to $\dot{\nu }$ over time.

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The difference in the Δν_p values is a direct result of our choice of the glitch epoch and the large increase in the spin-down rate. This is apparent in the TempoNest runs where we assumed earlier and later values of t_g, where earlier glitch epochs result in a larger recovered value of Δν_p to match the postoutburst timing. Going the other way, setting the glitch epoch to the date of the Swift-BAT short burst (MJD 59676; 2022 April 7) results in a value of Δν_p that is consistent with zero at the 68% confidence interval, i.e a pure spin-down glitch. While several glitches in other magnetars have been associated with minimal instantaneous changes in ν (e.g., the 2012 outburst of 1E 1048.01−5937; Archibald et al. 2015), the lack of ToAs between the radio shutdown of 1E 1547.0−5408 and beginning of our NICER monitoring prevents us from ruling out a nonzero Δν_p .

3.3.1. Spectral Analysis

We employed Xspec version 12.12.1 for our X-ray spectral analysis. We used the tbabs model to account for the line-of-sight absorption toward the source, along with the Wilms et al. (2000) solar abundances. We binned all spectra to have 5 counts per bin and used the W-statistic (C-stat in Xspec) to estimate the best-fit model parameters and their associated uncertainties. For the NICER spectra, however, we used the pgstat statistic, which is a more appropriate choice given the modeled nature of the background (Remillard et al. 2022). Finally, we added a numerical factor to account for any cross-calibration uncertainties when fitting spectra from different instruments simultaneously. We find a ≲2% and ≲10% deviation between the two NuSTAR spectra and the NICER/Swift-XRT and NuSTAR spectra, respectively, commensurate with the expected values (Madsen et al. 2015).

We fit the NuSTAR and NICER observations taken on 2022 April 21 simultaneously, which provides the highest S/N broadband spectral shape of 1E 1547.0−5408 during this most recent outburst. We also fit the preoutburst 2016 and 2019 simultaneous Swift-XRT and NuSTAR observations (Coti Zelati et al. 2020) to quantify the source spectral variability better. We modeled all spectra in the 1–70 keV range using a three-component construction: two absorbed blackbodies (BBs; BB_warm and BB_hot) plus a PL, suitably representative of the magnetar broadband X-ray spectral shape (Götz et al. 2006; Kuiper et al. 2006; den Hartog et al. 2008a, 2008b; Enoto et al. 2017). We linked the absorption hydrogen column density N_H among all the spectra and left the rest of the model parameters free to vary. We establish the goodness of fit by running the Xspec goodness command to simulate 1000 spectra drawn from the best-fit model and compare their fit statistic to the observed data. We find that 16% of the spectra have a fit statistic smaller than the actual value, implying that the model adequately explains the data. We measure a best-fit N_H = (3.67 ± 0.02) × 10²² cm⁻², a factor of 1.75 times higher than the value predicted by the N_H–DM relation of He et al. (2013). We display the source spectrum and best-fit model in Figure 5, and present the best-fit parameters and their 1σ uncertainties in Table 3.

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Table 3. Broadband X-Ray Spectral Results

Date	kTwarm	${R}_{\mathrm{warm}}^{2}$	kThot	${R}_{\mathrm{hot}}^{2}$	Γ	Fwarm/Fhot/FPL	FS/FH	LX
	(keV)	(km2)	(keV)	(km2)		(10−12 erg s−1 cm−2)	(10−12 erg s−1 cm−2)	(1034 erg s−1)
2016-03-23	0.59 ± 0.03	${2.3}_{-0.5}^{+0.7}$	${1.16}_{-0.08}^{+0.1}$	${0.03}_{-0.01}^{+0.02}$	0.2 ± 0.1	${14.1}_{-0.8}^{+0.9}$ / ${2.9}_{-0.6}^{+0.7}$ / ${8.9}_{-0.5}^{+0.5}$	${17.2}_{-0.8}^{+0.9}$ / ${8.7}_{-0.4}^{+0.4}$	${6.3}_{-0.2}^{+0.2}$
2019-02-15	0.67 ± 0.02	1.3 ± 0.2	1.4 ± 0.2	0.008 ± 0.004	0.0 ± 0.1	${13.7}_{-0.5}^{+0.5}$ / ${1.7}_{-0.3}^{+0.5}$ / ${8.7}_{-0.6}^{+0.7}$	${15.5}_{-0.5}^{+0.5}$ / ${8.7}_{-0.5}^{+0.5}$	${5.9}_{-0.1}^{+0.2}$
2022-03-21	${0.64}_{-0.05}^{+0.04}$	${2.0}_{-0.3}^{+0.5}$	1.0 ± 0.1	${0.09}_{-0.06}^{+0.14}$	0.4 ± 0.2	${17}_{-3}^{+2}$ / ${6}_{-2}^{+3}$ / ${9.0}_{-1}^{+1}$	${23}_{-1}^{+1}$ / ${8.7}_{-0.8}^{+0.8}$	${7.7}_{-0.3}^{+0.3}$

Note. The BB emitting areas and luminosity are derived assuming a distance of 4.5 kpc (Tiengo et al. 2010). F_S and F_H are the 0.5–10 keV and 10–70 keV absorption-corrected fluxes, respectively.

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We find that the 2022 April 21 observation, 2.5 weeks after the GBM short burst detection (2 weeks after the confirmed BAT detection), exhibits a flux that is about 50% larger than the preoutburst level. This increase is solely due to an increase in the soft 0.5–10 keV X-ray flux (Figure 5), and particularly seen in the BB_hot contribution. The flux of this component has increased by a factor 3 and 5 since 2016 and 2019, respectively. On the other hand, the increase in the BB_warm component is a factor 1.2 and 1.3 larger compared to 2016 and 2019, respectively. Finally, the hard X-ray PL flux is consistent between all three observations at the 1σ level. This implies that either the hard X-ray flux was not impacted by this most recent outburst, or it followed a steeper temporal decay trend compared to the soft X-ray flux.

While the source exhibited a change in the overall flux, the broadband spectral curvature in 2022 remained relatively stable compared to the previous epochs. We find no significant variability in the temperature of either of the two BBs, nor in the hardness of the PL component. This points to an increase in the overall area of the hot thermally emitting region as the origin of the soft X-ray flux increase (Table 3).

To study the long-term high-energy evolution of the 1E 1547.0−5408 outburst, we modeled the NICER and Swift-XRT spectra in the 1–6 keV range (beyond 6 keV the data for both instruments were mainly background dominated). We used a simple absorbed BB model and fixed the hydrogen column density N_H to the best-fit value as derived above. This model sufficed to describe all the spectra except for the NICER observation on 2022 April 9 (ID 5020300101; Table 1) which required a second BB component to result in a statistically acceptable fit. The resulting 0.5–10 keV absorption-corrected flux evolution is shown in the upper panel of Figure 2. At the start of the NICER monitoring on 2022 April 9, we find a source flux that is a factor 3.5 larger than the preoutburst value, as established with Swift-XRT on 2022 March 5 (green circles in Figure 2, upper panel; see also Coti Zelati et al. 2020). This confirmed that 1E 1547.0−5408 was experiencing yet another high-energy outburst, its first since its major 2009 outburst. The source flux decayed back to the same preoutburst persistent flux level on 2022 April 26, i.e., 17 days later, and remained there until the end of our monitoring in 2022 August. We find that the bulk of the flux increase throughout the outburst occurred at energies >2 keV, consistent with the result of the NICER+NuSTAR broadband modeling.

3.3.2. X-Ray Timing Analysis

Given the complexity of the glitch timing model (Section 3.2), we fold the NICER barycenter-corrected events with a (strictly) postglitch variant of the combined radio/X-ray timing solution in Table 2. To account for red noise in the timing residuals, we fit for spin-frequency derivatives up to d⁵ ν/dt⁵, at which order the residuals are dominated by white noise. Due to the limited exposure of most individual NICER observations, we merged several consecutive ones until we accumulated about 6000 counts in the 1.5–6 keV interval. This ensured a proper sampling of the pulse shape in two energy bands, namely 1.5–3 keV and 3–6 keV. During the outburst decay phase (2022 April 9–26), the stretch of each interval that fulfilled our criterion was on average 2 days, and increased to 10 days after the source returned to its preoutburst flux level. We present these pulse profiles in Figure 6. Each row displays the pulsations per time interval starting from the date of the initial NICER observation on 2022 April 9 (day 0), while the left and right panels show the 1.5–3 keV and 3–6 keV pulse profiles, respectively; note that the pulse in red is from the NICER observation that is simultaneous with the NuSTAR one for 2022 April 21.

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The soft 1.5–3 keV pulsations are quasi-sinusoidal throughout our monitoring campaign. On the other hand, the 3–6 keV profile exhibits pronounced variability. For instance, during the outburst decay phase, there is an evident shoulder leading to the pulse peak. Moreover, the peak is slightly broader early in the outburst and displays complex shape, likely formed of two or more peaks. This complexity is confirmed with NuSTAR as we show below. The 3–6 keV pulse shape turns quasi-sinusoidal starting on day 17 from the first NICER observation, coincident with the return of the flux to the preoutburst level (Figure 2). We derive the rms pulsed fraction (rms PF) for each of the light curves in Figure 6 (see, e.g., Woods et al. 2004 for details). For this purpose, we fit each background-subtracted pulse profile to a Fourier series including three harmonics, which was sufficient to provide an acceptable fit to the data. We find PFs ranging from 19% to 25% and 29% to 34% in the 1.5–3 keV and 3–6 keV energy bands, respectively, with a typical 1σ uncertainty of about 3%. This implies a lack of significant variability in the PF at soft X-rays concurrent with the outburst flux enhancement.

The NuSTAR observation of 1E 1547.0−5408 on 2022 April 21 caught the tail end of the outburst. We display the pulse profiles during this observation in three separate energy bands, namely, 3–6 keV, 6–10 keV, and 10–15 keV (Figure 7). We confirm the NICER results which show, in the energy range 3–6 keV, a nonsymmetric profile with a shoulder leading to a multipeaked pulse maximum; this fine structure in the peak is reminiscent of that seen during the 2020 outburst of SGR 1830-0645 (Younes et al. 2022b). Similar pulse profile morphology is apparent in the 6–10 keV range: the pulse exhibits considerable asymmetry with a shoulder leading to the pulse peak. All these features are clearly absent from the 2016 and 2019 NuSTAR monitoring; the pulse profile in the same energy range shows a purely sinusoidal form (Coti Zelati et al. 2020; Figure 5). On the other hand, the pulse profile at high energies between 10 and 25 keV exhibits a quasi-sinusoidal shape, consistent with the result of the earlier NuSTAR observations. Note, however, the lower S/N in this band compared with that at energies below 10 keV. We do not detect significant pulsations at energies >25 keV, despite the detection of the source at the ≳10σ confidence level.

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Finally, we measure the NuSTAR energy-resolved rms PF following the same recipe we utilized for NICER. We find an increasing trend at soft energies, from about 30% and up to 45% at 10 keV. The PF drops to 30% in the energy range 10–25 keV. Moreover, the latter profile appears slightly offset from the soft-energy ones (Figure 7), yet a formal measurement is complicated by the difference in shape between the profiles. Lastly, we derive a 3σ upper-limit of 25% on the PF at energies >25 keV. These elements are broadly consistent with the 2016 and 2019 NuSTAR findings of Coti Zelati et al. (2020).

3.3.3. Short Burst Searches