Two New Outbursts and Transient Hard X-Rays from 1E 1048.1-5937

1E 1048.1−5937 was monitored regularly with the Swift-XRT since 2011 July as part of a campaign to study several magnetars (see e.g., Scholz et al. 2014; Archibald et al. 2015, 2017). The XRT was operated in windowed-timing mode for all observations, having a time resolution of 1.76 ms, and only one-dimension of spatial resolution.

Data were downloaded from the HEASARC Swift archive, reduced using the xrtpipeline standard reduction script, and time-corrected to the solar system Barycenter using HEASOFT v6.22. Following this, we processed the data in the same manner described by Archibald et al. (2017).

Observations, typically 1–1.5 ks long, were taken in groups of three, with the first two observations within approximately 8 hr of each other and the third approximately a day later. This observation strategy was adopted due to the source's prior unstable timing behavior, in which maintaining phase coherence using a longer cadence was only possible for several-month intervals (Kaspi et al. 2001; Dib et al. 2009). In total, 655 XRT observations totaling 1.0 Ms of observing time spanning 2011 July through 2018 April were analyzed in this work.

Following the detection of the first new outburst reported in Section 3.1, we received NuSTAR Director's Discretionary Time (DDT) to observe 1E 1048.1−5937 in outburst. The NuSTAR observation (ObsID 90202032002) was taken on 2016 August 5 (MJD 57605) with an exposure time of 55 ks.

NuSTAR data were reduced using the nupipeline scripts, using HEASOFT v6.20, and time-corrected to the solar system barycenter. Source events were extracted within a 1' radius around the centroid. Background regions were selected from the same detector as the source location, and spectra were extracted using the nuproducts script.

Using grppha, channels 0–35 (<3 keV) and 1935–4095 (>79 keV) were ignored, and all good channels were binned to have a minimum of one count per energy bin.

As shown in Figure 1, 1E 1048.1−5937 is clearly detected across the NuSTAR band, including at energies above 20 keV allowing the spectral analysis described in Section 3.2.

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Following the data reduction described in Section 2.1, we fit the XRT observations using an absorbed blackbody model. N_H was held constant at 5.8 × 10²¹ cm⁻², the best-fit value for the source before the 2012 outburst. Observations within one day of each other were grouped for this analysis.

Several individual observations, most notably in 2012 November, are significantly elevated from the long-term trend. These are most likely due to catching 1E 1048.1−5937 during a period of post-burst tail emission lasting several kiloseconds, as reported by An et al. (2014).

The long-term light curve over the XRT campaign is dominated by three outbursts. We fit phenomenological models to the flux decay following each outburst, fixing the baseline flux to that measured before the 2011 December outburst, and fixing the outburst start time to that of the first observation with elevated flux. We first fit a single exponential decay, as well as power-law decays, to the flux following each outburst. For the first two long outbursts, such single-component models did not adequately describe the data.

When fitting two-component models, those consisting of exponentials were statistically preferred to power-law models, using χ² goodness of fit as a metric. The optimal parameters for a two-exponential model for each outburst are shown in Table 1.

Table 1.  Characterization of the Flux Decay During the 2016 and 2017 Outbursts of 1E 1048.1−5937

tb	0.5–10 keV Flux Decay Fita	${\chi }_{\nu }^{2}$
MJD	10−11 erg s−1 cm−2
55,926	$(1.1\pm 0.15)$ ${{\rm{e}}}^{\tfrac{-(t-{t}_{b})}{550\pm 50}}$+$(1.9\pm 0.13)$ ${{\rm{e}}}^{\tfrac{-(t-{t}_{b})}{50\pm 10}}$	1.1
57,592	$(1.0\pm 0.13)$ ${{\rm{e}}}^{\tfrac{-(t-{t}_{b})}{440\pm 70}}$+$(1.5\pm 0.16)$ ${{\rm{e}}}^{\tfrac{-(t-{t}_{b})}{51\pm 9}}$	0.75
58,120	b $(1.2\pm 0.2)$ ${{\rm{e}}}^{\tfrac{-(t-{t}_{b})}{62\pm 12}}$	1.5

Notes.

^at and t_b are in units of days. ^bAfter subtraction of the flux decay fit from the July 2016 outburst; see Section 3.1.

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For the 2017 December outburst, as the 2016 July outburst had not yet fully decayed, we subtracted the best-fit model of that latter outburst before fitting. As is evident from Figure 2, by the last observation reported here (2018 April), the effects of the 2017 December outburst have waned, with the last reported fluxes consistent with the extrapolation from the 2016 July outburst.

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Note that for the two longest outbursts, both the short ∼50- and long ∼500 day exponential timescales are consistent at the 1σ level with each other. In addition, the third outburst has a timescale consistent with the shorter ∼50 day timescale. Also, within the limited available precision, the spectral variations are similar in the three outbursts (see Figure 2).

A NuSTAR observation was taken approximately 13 days after the Swift-XRT-detected flux increase, as indicated in Figure 2. We first verified that there were no short, magnetar-like bursts contaminating the data by conducting a burst search following the method described by Scholz & Kaspi (2011). To constrain the soft X-ray spectrum, we co-fit the NuSTAR observation with the Swift observations (observation ids 00032923252 and 254) taken on 2016 August 5–8, coincident to within days of the epoch of the NuSTAR observation.

We used Cash statistics (Cash 1979) for fitting and parameter estimation of the unbinned data. N_H was fit using the tbabs model with wilm abundances (Wilms et al. 2000) and vern photoelectric cross sections (Verner et al. 1996).

1E 1048.1−5937 is detected above 20 keV with a background subtracted 20–79 keV count rate of $(5.3\pm 0.6)\times {10}^{-3}$ photons per second. The spectrum is well fit by an absorbed blackbody and broken power law; the best-fit parameters are shown in Table 2. Here, ${{\rm{\Gamma }}}_{S}$ and ${{\rm{\Gamma }}}_{H}$ refer to the power-law index below and above the break energy, respectively. The X-ray spectrum and residuals are shown in Figure 3. All the uncertainties in the spectral parameters are quoted at 90% confidence.

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Table 2.  NuSTAR and Swift-XRT Spectrum of 1E 1048.1−5937 in Outburst

Absorbed Blackbody and Broken Power Law
Parameter	Value
NH (${10}^{22}\,{\mathrm{cm}}^{-2}$)	3.7 ± 0.3
${C}_{{NuSTAR}}$ a	0.85 ± 0.05
kTBB (keV)	0.88 ± 0.02
${{\rm{\Gamma }}}_{S}$	4.4 ± 0.1
${{\rm{\Gamma }}}_{H}$	${0.5}_{-0.2}^{+0.3}$
Break Energy (keV)	${13.4}_{-0.6}^{+0.6}$
C-Stat/$\mathrm{dof}$	1809.7/1965
Goodnessb	$49.7 \%$
Flux (0.5–10 keV)c	${31.2}_{-1.5}^{+0.7}$
Flux (3–79 keV)c	$20{.}_{-2}^{+1}$
Flux (20–79 keV)c	${4.8}_{-1.2}^{+1.4}$

Notes.

^aFitted relative normalization for NuSTAR. ^bPercentage of C-Stat statistic simulation trials from model parameters that are less than the fit statistic. ^cAbsorbed flux in units of ${10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$.

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In a 2013 NuSTAR observation of 1E 1048.1−5937 in relative quiescence, neither Weng & Göğüş (2015) nor Yang et al. (2016) found any evidence of X-ray flux from 1E 1048.1−5937 above 20 keV, setting a 3σ upper limit on the total, phase-averaged flux in the 20–79 keV band of ∼3–4 $\times \,{10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, just below our detection of a flux of ${4.8}_{-1.2}^{+1.4}\times {10}^{-12}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$.

In Figure 4, we show the pulse profiles of 1E 1048.1−5937 during the NuSTAR observation in units of photons per kilosecond, per focal plane module, folded using the timing solution from the Swift campaign (see Section 4). We calculated the rms pulsed fraction of 1E 1048.1−5937 in several energy bands, using the method described in the appendix of An et al. (2015). To determine the significance of the pulsed signal, we used the H-test (de Jager et al. 1989). Motivated by the spectral break in the power law at ${13.4}_{-0.6}^{+0.6}$ keV, we used this value as a fiducial cut to search for a pulsed signal in the hard X-ray band. A pulsed signal is detected up to 20 keV, and no significant pulsations are seen above this energy. In Table 3 we report the H-test false-alarm-probabilities (P_FA), and pulse fractions, where upper limits are given at the 99% confidence level. Due to a paucity of pulsed counts in the hard X-ray band, we can neither comment on the energy-dependence of the pulsed fraction, nor do meaningful phase-resolved spectroscopy of 1E 1048.1−5937.

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Here we have presented the detection of 1E 1048.1−5937 at energies above 20 keV. This, however, is not the first high energy detection of the source. Leyder et al. (2008) detected 1E 1048.1−5937 at 22–100 keV with International Gamma-ray Astrophysics Laboratory during observations of η Carinae. Their observation totals 1.1 Ms and is drawn from several observing epochs, but one of those epochs (MJD 52787–52827) corresponds to the peak of the 2001–2002 outburst of 1E 1048.1−5937. This is therefore consistent with the picture of 1E 1048.1−5937 being bright in hard X-rays during outburst.

Hard X-ray emission from magnetars is ubiquitous in persistently bright magnetars (e.g., Kuiper et al. 2006; Vogel et al. 2014; Enoto et al. 2017; Younes et al. 2017a). Additionally, in transient magnetars, similar hard X-ray components are observed near epochs of enhanced flux. For example, in SGR 0501+4516, for which in the first four days of an outburst, Suzaku detected a hard power law with ${\rm{\Gamma }}={0.79}_{-0.18}^{+0.20}$ (Enoto et al. 2010)—similar to the spectrum we have observed in 1E 1048.1−5937. As well, in SGR 1935+2154 (Younes et al. 2017b), a hard X-ray component was observed at the peak flux of an outburst. Thus, the phenomenon of a transient hard X-ray component appearing in outburst seems common for the magnetar class.

This hard X-ray emission is thought to be due to decelerating electron/positron flow in large twisted magnetic loops of the pulsar magnetosphere (Beloborodov 2013). In this picture, the flux evolution of magnetars following outbursts involves the untwisting of the magnetosphere (e.g., Beloborodov 2009; Parfrey et al. 2013; Chen & Beloborodov 2017). The transient hard X-ray emission we observed in 1E 1048.1−5937, and other magnetars in outburst, is then consistent with this picture where hard X-ray emission is only detectable during the peak of this outburst when the magnetosphere is maximally twisted. We would then generally expect the evolution of the hard X-ray flux to proceed on a similar timescale to that of the soft X-ray flux (Chen & Beloborodov 2017). Future systematic hard X-ray observations of magnetars in outburst are needed to put this to the test, although the hard X-ray relaxation of the high-magnetic-field radio pulsar PSR J1119−6127 has recently been shown to proceed on a timescale similar to that of the soft X-ray relaxation post-outburst (Archibald et al. 2018).

A correlation has been observed between the surface magnetic field (or alternately the spin-down rate) of a magnetar and its hard X-ray power-law index (Kaspi & Boydstun 2010; Enoto et al. 2017). Indeed, Kaspi & Boydstun (2010) predicted that ${{\rm{\Gamma }}}_{H}$ for 1E 1048.1−5937 should fall between 0 and 1, albeit in quiescence. Interestingly, this is in agreement with our measurement of ${{\rm{\Gamma }}}_{H}={0.5}_{-0.2}^{+0.3}$ in outburst.

In Enoto et al. (2017), the hardness ratio of fluxes in the 15–60 keV and 1–10 keV bands is shown to be correlated with the spin-down rate of the magnetar. If we take the quiescent spin-down rate of 1E 1048.1−5937 (∼9 × 10⁻¹² s s⁻¹), the predicted hardness ratio for 1E 1048.1−5937 is ∼0.4. We measure ${F}_{15\mbox{--}60\mathrm{keV}}=(3.2\pm 0.6)\times {10}^{-12}$ erg cm⁻² s⁻¹ and ${F}_{1-10\mathrm{keV}}=(31\pm 1)\times {10}^{-12}$ erg cm⁻² s⁻¹ for a hardness ratio of 0.10 ± 0.02, which is broadly consistent with the trend, especially given the large fluctuations in $\dot{P}$ observed in 1E 1048.1−5937, as well as the scatter in the observed distribution (Enoto et al. 2017).

In Figure 5 we show the last 20 yr of evolution in the X-ray flux, and spin-down rate for 1E 1048.1−5937, as monitored by RXTE⁶ and Swift. Note that the fluxes are in different energy bands (0.5–10 keV versus 2–20 keV), and that RXTE fluxes are pulsed only, and have been scaled to match the Swift flux during the period of overlap.

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The time delay between the 2011 December and the 2016 July outbursts was 1670 ± 10 days. This can be compared to separations of 1800 ± 10 and 1740 ± 10 days between the prior flares as discussed by Dib & Kaspi (2014) and Archibald et al. (2015). While this outburst timing is consistent with the quasi-periodicity suggested in Archibald et al. (2015), the occurrence of the 2017 December outburst suggests that this repeated timescale is spurious. However, this last outburst is decaying on a faster timescale than the major outbursts on which the claimed quasi-periodicity is based—similar to the precursor flare noted in 2001 (e.g., Tam et al. 2008; Dib & Kaspi 2014). It will be interesting to continue monitoring 1E 1048.1−5937 to see if there is another outburst on the timescale the quasi-periodicity predicts, i.e., in ∼2021.

Additionally, the torque variations following the 2016 July outburst follow the trend of decreasing amplitude noted in Archibald et al. (2015). Following the four major outbursts observed thus far, the peak torque reached values of 12.3(1), 7.32(5), 4.4(1), and finally 1.73(1) times higher than the quiescent rate. The monotonic decrease in amplitude of these unexplained torque variations is curious, as it implies that our monitoring of 1E 1048.1−5937 was started at a special time, perhaps after a major but unobserved event. If the decline continues, by the next outburst, the torque variations should be smaller than order unity times the quiescent value. However, the monotonic decrease may also be purely coincidental. Further monitoring will be illuminating.

While the repetition, and monotonic decline in amplitude, of the torque variations from 1E 1048.1−5937 are striking and unique, rapid, extreme variability in the torque ($\dot{\nu }$) evolution appears to be a common feature following magnetar outbursts. In addition to that observed now repeatedly in 1E 1048.1−5937, similar variations have been observed in 1E 1547−5408 (Dib et al. 2012), PSR J1622−4950 (Scholz et al. 2017; Camilo et al. 2018), and in XTE 1810−197 (Camilo et al. 2016). Thus, in a large fraction of magnetar outbursts for which the spin-down rate has been tracked for over a decade, these extreme torque variations are observed, and can dominate the long-term spin evolution of these sources.

In the magnetar model, increased torque associated with outbursts, just as the enhanced hard X-ray emission, is due to a twist in the magnetosphere (e.g., Thompson et al. 2002; Beloborodov 2009). As the spin-down rate of the star is dominated by the relatively small number of open field lines, there is no reason for a strict correlation between the hard X-ray emission and spin-down rate, as it depends on the geometry of the magnetosphere (Beloborodov 2009; Kaspi & Beloborodov 2017). In the untwisting model, the spin-down rate of the star is only affected once the twist reaches an amplitude of ∼1 radian. The delay between the peak X-ray flux and peak torque of ∼100 days observed in 1E 1048.1−5937 would then be due to the initial twist not exceeding this threshold value (Beloborodov 2009).