THE SPIN-DOWN OF SWIFT J1822.3−1606: A NEW GALACTIC MAGNETAR

On 2011 July 14, the Swift/Burst Alert Telescope (BAT) triggered on several bursts of hard X-ray emission from the direction of a previously unknown source, subsequently named Swift J1822.3−1606 (Cummings et al. 2011). The spin period of the new source was soon identified to be P = 8.4377 s (Göğüş et al. 2011). The simplest interpretation of these initial observations is that Swift J1822.3−1606 is a previously unknown Galactic magnetar.

However, because of suggested similarities between Swift J1822.3−1606 and the unusual Be X-ray binary J1626−5156, it was suggested that perhaps Swift J1822.3−1606 is a Be X-ray binary (Göğüş et al. 2011; Bandyopadhyay et al. 2011). This hypothesis was challenged by Halpern (2011), who, due to the lack of an optical counterpart (de Ugarte Postigo & Munoz-Darias 2011), argued that the properties of Swift J1822.3−1606 are in line with those of other magnetars, in particular, the transient magnetar XTE J1810−197. Here we report on timing and flux properties of Swift J1822.3−1606 that agree strongly with the magnetar identification.

Magnetars are neutron stars powered by the decay of extreme magnetic fields (Thompson & Duncan 1995, 1996; Thompson et al. 2002). Soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are thought to be observational manifestations of magnetars, and we refer to them as such here. Magnetars exhibit X-ray bursts, spin periods in the relatively narrow range⁴ of P = 2–12 s, and are observed to spin-down with time. As inferred from P and spin-down rate $\dot{P}$ via the conventional vacuum dipole model which implies an inferred dipole magnetic field strength of $B = 3.2 \times 10^{19} (P \dot{P})^{1/2}$ G, their inferred B-fields tend to be significantly larger than for classical pulsars, typically B > 10¹⁴ G. Magnetars are also observed to display variability in nearly all of their observed properties: flux and pulsed flux, spectrum, pulse profile, timing noise, and glitches (see Mereghetti 2008; Rea & Esposito 2011 for reviews).

The true underlying distribution of magnetar B strengths is an open question. The recent discovery of a magnetar with a very low inferred magnetic field of B < 7.5 × 10¹² G (Rea et al. 2010) has raised the question of how low the dipolar field can be for magnetar-like activity to be observed. Moreover, the discovery of a magnetar-like outburst from the high-B rotation-powered pulsar (RPP) PSR J1846−0258 (Gavriil et al. 2008; Kumar & Safi-Harb 2008) highlights the question of whether RPPs and magnetars represent two distinct classes of objects, or if magnetars represent the high-B tail of a single population.

In this Letter, we present analyses of Rossi X-ray Timing Explorer (RXTE), Swift, and Chandra X-ray Observatory (Chandra) data. We perform a phase-coherent timing analysis and show that the spin evolution is consistent with a constant spin-down rate. We present an analysis of the decay of the source's intensity after the outburst, and show that the pulsed fraction is steady after increasing for ∼20 days after the outburst. We argue that these properties confirm that Swift J1822.3−1606 is a new Galactic magnetar.

2.1. Swift Observations

2.2. RXTE Observations

2.3. Chandra Observations

3.1. Phase-coherent Timing Analysis

Our timing analysis of Swift J1822.3−1606 follows the phase-coherent approach, in which we account for each rotation of the pulsar and utilized a combination of data from RXTE, Swift, and Chandra. Events were reduced to barycentric dynamical time (TDB) at the solar system barycenter using the XRT position of R.A. = 18^h22^m18^s, decl. = −16°04'268 (J2000; Pagani et al. 2011) and the JPL DE200 solar system ephemeris. Events were then binned into time series with 31.25 ms time resolution.

Each RXTE (2–10 keV), Swift (2–10 keV), and Chandra (0.3–8 keV) time series was folded with 64 phase bins using a spin-period determined from a periodogram analysis. We found an initial timing solution and used this to re-fold each profile to produce higher quality pulse times of arrival (TOAs). For RXTE data, using 128 phase bins created good pulse profiles with optimal TOA uncertainties. For Swift and Chandra data, 64 bin profiles resulted in higher significance pulse profiles and TOA uncertainties. Template profiles with 128 and 64 bins were created by aligning and summing all RXTE profiles.

Different energy ranges and telescope responses between RXTE, Swift, and Chandra result in small but significant differences in the resulting pulse profiles. To account for this, we fit for a constant phase offset between TOAs from different telescopes. We used a subset of the available data to fit for the phase offsets (MJD 55758 – 55781), which were then held fixed for the remainder of the analysis.

We searched for time variability in the pulse shape and found that individual profiles are consistent with the template, except for the first RXTE observation (96048-02-01-00). Here, the variation is significant, differing from the normalized template with χ²_ν/ν = 5.2/124, but subtle, at the ∼0.015 phase level. We accounted for this by multiplying the corresponding TOA uncertainty by three.

For each profile, we implemented a Fourier domain filter, using six harmonics in the cross-correlation procedure. Cross-correlation produces a TOA for each observation with a typical uncertainty of 0.3%P for RXTE TOAs, 0.7%P for Swift TOAs, and 0.1%P for Chandra TOAs. TOAs were fitted with TEMPO⁸; the resulting parameters are given in Table 1.

Table 1. Spin Parameters for Swift J1822.3−1606

Parameter	Value
Dates (Modified Julian Day)	55758 – 55842
Epoch (Modified Julian Day)	55761.0
Number of TOAs—RXTE	25
Number of TOAs—Swift	26
Number of TOAs—Chandra	3
P (s)	8.43771969(6)
$\dot{P}$	2.55(22) × 10−13
rms residuals (ms)	25.1
rms residuals (periods)	0.0029
Derived Parameters
Surface dipolar magnetic field, B (G)	4.7(2) × 1013
Spin-down luminosity, $\dot{E}$ (erg s−1)	1.7(1) × 1031
Characteristic age, τc (kyr)	525(45)

Note. Uncertainties are formal 1σ TEMPO errors.

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The top panel of Figure 1 shows timing residuals with P fitted, while the bottom panel shows residuals with $\dot{P}$ also fitted. Fitting $\dot{P}$ improves the root-mean-squared (rms) residuals by a factor of 1.7 and the χ²_ν/ν from 3.91/52 to 1.43/51. Resulting residuals show some evidence for an unmodeled trend. We verified that this trend is not explained by an exponential decay in P, as often observed after a glitch, by fitting the data in two subsets and looking for a trend in the measured $\dot{P}$ values. No such trend was found, thus, the most likely explanation for the remaining phase residuals is timing noise, a common phenomenon in magnetars. The best-fit values of P and $\dot{P}$ imply a surface dipolar magnetic field of B = (4.7 ± 0.2) × 10¹³ G.

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3.2. Source Intensity Evolution

To measure the source intensity and decay after the outburst, we first checked for the presence of dust scattering rings, such as those observed around 1E 1547−5408 (Tiengo et al. 2010), because these can bias the inferred source count rate. We checked for deviations from the point-spread functions in the first Swift PC mode and Chandra observations following the outburst, and we found no evidence for dust scattering.

To measure the evolution of the total flux, we measured a flux for each Swift WT mode observation using XSPEC, by assuming several different models. We found that the flux is relatively model independent, varying by <10% between models. A detailed spectral analysis will follow in a subsequent paper.

To measure the 2–10 keV pulsed count rate for each Swift and Chandra observation, barycentered time series were folded with the ephemeris (Table 1), with 16 phase bins. For the RXTE data, barycentered photons were selected only from PCU2, to minimize instrumental effects. Events were then folded as above. The pulsed count rate for each folded profile was then determined using a rms method as described in Dib et al. (2008), using five Fourier harmonics of the pulse profile. The pulsed fraction was determined by dividing the pulsed count rate by the total source count rate. Because the PCA is not a focusing instrument, the pulsed fraction could not be accurately determined from these data.

Figure 2 shows the evolution of the source intensity (top panel, as measured with Swift), the pulsed source intensity (middle panel, as measured with Swift and RXTE), and the pulsed fraction (bottom panel, as measured with Swift and Chandra). To describe the total flux decay quantitatively, we fit the 1–10 keV flux evolution of Swift J1822.3−1606 with a power law, an exponential plus constant model, and with a double-exponential model. We find that the double-exponential model provides the best fit to the data with timescales of 9 ± 1 and 55 ± 9 days and a χ²_ν/ν of 1.0/21. The single-exponential model provides a poorer fit with a best-fit decay timescale of 14.6 ± 0.5 days and a χ²_ν/ν of 1.6/22. The power-law model was a much worse fit with a χ²_ν/ν of 7.3/23.

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To describe the pulsed flux decay quantitatively, we fit the 2–10 keV pulsed count rate evolution with the same models as above, also including data from RXTE. Pulsed count rates from a given source for RXTE and Swift will differ owing to instrumental effects (e.g., effective area), but should be offset by a constant, with the same trends between instruments, as observed here. Thus, RXTE PCA pulsed count rates were scaled to the Swift XRT pulsed count rates, such that the scaling factor minimized the residuals of the fit. With a χ²_ν of 3.25 for 49 degrees of freedom, the best-fit decay timescale is 15.9 ± 0.2 days. A power-law model provided a much worse fit with a χ²_ν of 84 for 50 degrees of freedom. The fit to a double exponential model did not provide a significant improvement over the fit to the single exponential. If we constrain the decay timescales to be the same as for the total flux (see above), we find that the χ²_ν is 6.95 for 50 degrees of freedom.

The bottom panel of Figure 2 shows the 2–10 keV pulsed fraction of Swift J1822.3−1606 with Swift and Chandra data. The pulsed fraction increases from ∼35% to 45% during the first 20 days after outburst, after which it is statistically consistent with being constant (χ²_ν/ν of 1.8/27).

The regular spin-down we report for Swift J1822.3−1606, together with flux and pulsed flux decays similar to those seen in other magnetar outbursts, demonstrates that this source indeed shares critical properties with other known magnetars; we hence classify it as such. The inferred surface dipole B for Swift J1822.3−1606 of 4.7 × 10¹³ G is smaller than those of all but one confirmed magnetar, SGR 0418+5729 (Rea et al. 2010), though it is close to that of AXP 1E 2259+586 (B = 5.9 × 10¹³ G; Gavriil & Kaspi 2002). Further, Swift J1822.3−1606's B is similar to that measured for several RPPs, including the lone RPP observed to display magnetar-like outbursts, PSR J1846−0258, which has B = 4.9 × 10¹³ G (Gotthelf et al. 2000).

If Swift J1822.3−1606 suffered a large glitch with recovery at the outburst, as seen in some other magnetars (e.g., Kaspi et al. 2003), the following exponential decay in P could contaminate our measurement of $\dot{P}$ and thus B. Then, the true value of B would be smaller than the one reported here. However, the exponential recovery timescale for such a glitch in Swift J1822.3−1606 would have to be significantly longer than those observed in other magnetar glitches (e.g., 17 days for 1E 2259+586), since there is no evidence of a recovery in the 84 day timing solution reported here. Thus, any contamination of B owing to glitch recovery is likely to be small.

The post-outburst flux evolution of Swift J1822.3−1606 is best characterized by a double exponential decay with timescales of 9 ± 1 and 55 ± 9 days. This is reminiscent of the flux decay observed after the outburst from the transient AXP XTE J1810−197, which was fit with a two exponential decay model, albeit with longer decay timescales of 250 and 370 days (Bernardini et al. 2009).

Exponential flux decays as observed here are similar to what has been observed after several other magnetar outbursts (e.g., Rea et al. 2009; Gavriil et al. 2008), though power-law decays are also common (e.g., Woods et al. 2001; Kouveliotou et al. 2003). Lyubarsky et al. (2002) predicted power-law decays in magnetar outbursts assuming crustal cooling following an impulsive heat injection. Beloborodov & Thompson (2007), by contrast, considered magnetar outbursts as a result of sudden twisting of magnetic field lines in the magnetosphere, with the relaxation a result of their untwisting. In this model, the relaxation is predicted to be approximately linear, a functional form observed in one outburst of 1E 1048.1−5937 (Dib et al. 2009). Beloborodov (2009) showed that other functional forms for the decay, including exponential, are possible, as the untwisting is predicted to be strongly non-uniform, being erased by a propagating "front" whose speed depends on the initial twist configuration. The diversity in functional forms for the flux decays of magnetars hence favors the model put forth by Beloborodov (2009).

Although the flux (both pulsed and total) of Swift J1822.3−1606 clearly shows exponential decay, no comparable decay in P is seen, arguing for decoupling between the two evolutions. Indeed no such correlated evolution has been seen in other magnetar outbursts, and large glitches with recovery have been observed in magnetars showing no radiative changes (e.g., Dall'Osso et al. 2003; Dib et al. 2008). Hence, the flux decay provides no evidence for possible contamination of $\dot{P}$ by glitch recovery and the value we measure is likely to be due to dipolar spin alone.

Interestingly, the most recently discovered magnetars (including SGR 0418+5729 and Swift J1822.3−1606, but also SGRs 0501+4516, 1833−0832, and Swift J1834.9−0846; Göğüş et al. 2010a, 2010b; Rea et al. 2010; Kuiper & Hermsen 2011) all have B ≲ 1 × 10¹⁴ G, effectively lowering the "average" inferred B-field for magnetars. This raises the question of what is the true distribution of magnetar field strengths. In Figure 3, we plot the distributions of the periods and inferred magnetic fields of all confirmed magnetars, as well as of all known B > 10¹² G radio pulsars.

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The P distribution of magnetars remains narrow, spanning less than an order of magnitude, in great contrast to those of radio pulsars. We note that the period distribution for magnetars within the observed range appears consistent with being flat; a fit to the histogram mean yields a χ²_ν of 0.63. If borne out by future discoveries, this will need to be addressed in any population studies. The B distribution for observed magnetars, by contrast, appears peaked in the 10¹⁴–10¹⁵ G range, even with the relatively low B we have measured for Swift J1822.3−1606, albeit with the possible low tail represented by SGR 0418+5729. This is apparent as a "gap" between the peak of the magnetar distribution and the tail of the radio pulsar distribution. If magnetars represent the high-B tail of the birth B distribution of neutron stars, then their peaked B distribution may indicate that burst rates of magnetars fall rapidly with decreasing B, since the majority of magnetars have been discovered via bursting behavior. This would be broadly consistent with the theoretical findings of Perna & Pons (2011), who calculate expected burst rates in neutron stars and show that all neutron stars can exhibit magnetar-like bursts, though the burst rate drops with decreasing B and increasing age. That the number of radio pulsars plummets rapidly above B ∼ 10¹³ G could genuinely be due to falloff in the intrinsic distribution, or to smaller radio beams for these preferentially longer-period pulsars, but may also indicate that radio emission is harder to produce at higher B (e.g., Baring & Harding 2001). Although radio emission has been observed for three magnetars (Camilo et al. 2006, 2007; Levin et al. 2010), their radio spectra and radiative stabilities are vastly different from those for conventional radio pulsars, suggesting a distinct emission mechanism. Hence, if indeed we can "unify" radio pulsars and magnetars as described above, we expect the lowest B magnetars to be the most likely to produce observable traditional radio-pulsar-like radio emission, and the highest B RPPs to be the likeliest to show magnetar-like X-ray outbursts. The latter is consistent with the behavior of PSR J1846−0258 (Gavriil et al. 2008), while as yet, there is no evidence to support the former prediction. Such a unification would suggest that there exists a large population of as yet undetected B ∼ 10¹³ G neutron stars that could one day be discovered via their occasional magnetar-like bursts.

The characteristic age ($\tau _c=P/2\dot{P}$) for Swift J1822.3−1606 is 525 kyr, comparable to that of AXP 1E 2259+586 but larger than for all other magnetars, except for SGR 0418+5729 (>24 Myr). 1E 2259+586 is firmly associated with the supernova remnant CTB 109 which is thought to be ∼9 kyr old (Sasaki et al. 2004), much smaller than the AXP's characteristic age of 250 kyr. This demonstrates that τ_c can be an unreliable indicator of the true age, which can perhaps be ascribed to epochs of greater spin-down torque earlier in the star's history, when the dipolar field was larger. This hypothesis can explain the large τ_c of SGR 0418+5729, although the latter's greater distance from the Galactic Plane suggests it may indeed be the oldest known magnetar (but see Alpar et al. 2011 for an alternative discussion). Turolla et al. (2011) suggest that the observed properties of SGR 0418+5729 are consistent with it being an aged magnetar in which the external B has decayed significantly. Further evidence for SGR 0418+5729 being older than other magnetars includes lower energy bursts and a very low quiescent luminosity. Whether Swift J1822.3−1606 more closely resembles SGR 0418+5729 or 1E 2259+586 remains to be seen. The measurement of its flux in quiescence and the discovery of an associated supernova remnant would help resolve this issue.

We thank the Chandra and Swift teams for scheduling ToO observations. This research utilized data obtained from HEASARC, provided by NASA-GSFC. V.M.K. holds the Lorne Trottier Chair in Astrophysics and Cosmology and a Canada Research Chair. This work is supported by NSERC via a Discovery Grant, by FQRNT and CRAQ, by CIFAR, and a Killam Research Fellowship. C.Y.N. is a Tomlinson and CRAQ postdoctoral fellow.