Magnetar Broadband X-ray Spectra Correlated with Magnetic Fields:
Suzaku Archive of SGRs and AXPs Combined with NuSTAR, Swift, and RXTE
Studies were made of the 1–70 keV persistent spectra of fifteen magnetars as a complete sample observed with Suzaku from 2006 to 2013. Combined with early NuSTAR observations of four hard X-ray emitters, nine objects showed a hard power-law emission dominating at 10 keV with the 15–60 keV flux of 1– ergs s cm. The hard X-ray luminosity , relative to that of a soft-thermal surface radiation , tends to become higher toward younger and strongly magnetized objects. Updated from the previous study, their hardness ratio, defined as , is correlated with the measured spin-down rate as , corresponding with positive and negative correlations of the dipole field strength () and the characteristic age (), respectively. Among our sample, five transients were observed during X-ray outbursts, and the results are compared with their long-term 1–10 keV flux decays monitored with Swift/XRT and RXTE/PCA. Fading curves of three bright outbursts are approximated by an empirical formula used in the seismology, showing a 10–40 d plateau phase. Transients show the maximum luminosities of erg s, which is comparable to those of the persistently bright ones, and fade back to erg s. Spectral properties are discussed in a framework of the magnetar hypothesis.
Subject headings:catalog — pulsars: general — stars: magnetars — stars: magnetic field — stars: neutron — X-rays: stars
Soft Gamma Repeaters (SGRs) and Anomalous X-ray Pulsars (AXPs) are growing to a new population of young neutron stars. These two subclasses were historically discovered in different ways (Kouveliotou et al., 1998; Mereghetti & Stella, 1995), but now are believed to have common observational properties (for recent reviews, see Woods & Thompson 2006; Kaspi 2007; Mereghetti 2008); (a) a narrow range of slow spin periods, 2–12 s, (b) high spin-down rates of =– s s, (c) young characteristic ages as –100 kyr (d) X-ray luminosities, – erg s, that are brighter than the spin-down power erg s– erg s, where period and its derivative are normalized as and , respectively, (e) sporadic burst activities, and (f) occasional associations with supernova remnants.
The magnetar hypothesis for SGRs and AXPs (Duncan & Thompson, 1992; Thompson & Duncan, 1995, 1996) has become the most popular model in the last decade. This scenario describes that both SGRs and AXPs are isolated ultra-strongly magnetized neutron stars with their dipole magnetic field strength reaching – G. In this model, high X-ray luminosity, –, is interpreted as a release of magnetic energies stored in the stellar interior. The “magnetar” model has come to be widely recognized as a fascinating concept, for example, in the context of supernova explosions (Nicholl et al., 2013), and in the extreme fundamental physics exceeding the quantum critical field G (Harding & Lai, 2006), where , , , and are the electron rest mass, electron charge, speed of light, and Planck’s constant, respectively.
Despite the accumulated evidence for the magnetar model, there are also alternative hypotheses proposed to explain the observational features of SGRs and AXPs in terms of, e.g., accretion from a fossil disk (Alpar, 2001a; Trümper et al., 2010), invoking a quark star model (Ouyed et al., 2004), or as fast rotating massive white dwarves (Malheiro et al., 2012). Therefore, it is imperative at this stage to observationally examine the radiation properties of this group of objects, and understand their radiation properties in a unified way.
Nearly 23 confirmed SGRs and AXPs are now known on the Galactic plane as displayed in Figure 1 with their timing properties in Figure 2 (see the detailed catalog, Olausen & Kaspi 2014). Some are persistently bright with stable , intensively studied since the early days of X-ray astronomy: e.g., 4U 0142+61 (e.g., White et al. 1996; Enoto et al. 2011; Dib & Kaspi 2014). The soft X-ray spectrum is approximately an optically-thick radiation with its blackbody temperature at 0.5 keV which is thought to originate from the stellar surface or vicinity as a quasi-thermal emission (Zane et al., 2009). In this paper, we call this soft radiation below 10 keV “Soft X-ray Component (SXC)”.
Recent observations have revealed a new distinctive “Hard X-ray Component (HXC)” dominating above 10 keV. First detected with INTEGRAL from persistently bright sources (Kuiper et al., 2006; den Hartog et al., 2008a, b), the HXC was later reconfirmed by Suzaku and NuSTAR (Morii et al., 2010; Enoto et al., 2011; An et al., 2013a). This HXC extends up to 100 keV or more with a hard photon index , but must cuts off at some energies because of an upper limit by the CGRO/COMPTEL at 1 MeV. This power-law HXC is now believed to be an optically thin emission presumably from a pulsar magnetosphere in the magnetar scheme (e.g., Beloborodov 2013a).
There are also subsequent discoveries of transient objects, mainly discovered by burst activities: e.g., SGR 0501+4516 (e.g., Enoto et al. 2009; Rea et al. 2009). Such transient sources occasionally cause surges in persistent X-rays by a few orders of magnitude, followed by a gradual decay (Rea & Esposito, 2011). During these “outburst” states, sporadic short bursts with short time-scale durations (1 s) have been detected (Nakagawa et al., 2007; Israel et al., 2008). Although a complete picture has yet to come, bursts are thought to be originate from magnetic reconnection (Lyutikov, 2003) or cracking of the crust with starquakes (Thompson et al., 2002).
The SXC and HXC match ideally with the simultaneous 0.2–600 keV broadband coverage of the Suzaku satellite (Mitsuda et al., 2007). Our previous study of 9 SGRs and AXPs utilizing Suzaku (Enoto et al. 2010a, hereafter Paper I) suggested that 1) phase-averaged X-ray radiation of SGRs/AXPs commonly consists of the SXC below 10 keV and the HXC above 10 keV in both quiescent states and transient outbursts, 2) depends on and , and 3) their wide-band spectral properties are tightly correlated with and .
As the detailed description following Paper I, this paper provides a summary of Suzaku observations of SGRs and AXPs, combining the systematic spectral study of all the Suzaku sources and the X-ray decaying behavior of transient sources.
|Name||ObsID||Start Time||Epoch||Exp.||Nominal||XIS Mode||Process|
|( G)||(ks)||Pointing||(XIS0, 1, 3)||Version|
|Persistently Bright Sources|
|SGR 180620||24||401092010||2006-09-09 22:13:43||AO1||48.9||HXD||(full, full, full)||184.108.40.206|
|–||401021010||2007-03-30 15:08:00||AO1||19.6||HXD||(1/8, 1/8, 1/8)||220.127.116.11|
|–||402094010||2007-10-14 05:35:49||AO2||42.7||HXD||(full, full, full)||18.104.22.168|
|1E 1841045 (SNR Kes 73)||7.1||401100010||2006-04-19 10:51:40||PV||97.0||HXD||(1/8, 1/8, 1/8)||22.214.171.124|
|SGR 190014||7.0||401022010||2006-04-01 08:42:57||AO1||0.9||HXD||(1/4, 1/8, 1/4)||126.96.36.199|
|–||404077010||2009-04-26 18:23:44||Key||40.6||HXD||(1/4, 1/4, 1/4)||188.8.131.52|
|CXOU J171405.7381031||5.0||501007010||2006-08-27 01:27:07||AO1||75.6||XIS||(full ,full ,full )||184.108.40.206|
|1RXS J170849.0400910||4.7||404080010||2009-08-23 16:25:08||Key||50.9||HXD||(1/4, 1/4, 1/4)||220.127.116.11|
|–||405076010||2010-09-27 14:41:52||Key||47.0||HXD||(1/4, 1/4, 1/4)||18.104.22.168|
|1E 1048.15937||4.2||403005010||2008-11-30 23:02:01||AO3||85.0||HXD||(full, full, full)||22.214.171.124|
|4U 014261||1.3||402013010||2007-08-13 04:04:13||AO2||71.9||HXD||(1/4, 1/4, 1/4)||126.96.36.199|
|404079010||2009-08-12 01:41:15||Key||82.7||HXD||(1/4, 1/4, 1/4)||188.8.131.52|
|406031010||2011-09-07 15:43:32||ToO||36.7||XIS||(full, full, 1/4)||184.108.40.206|
|408011010||2013-07-31 10:05:39||AO8||79.8||XIS||(1/8, 1/4, 1/4)||220.127.116.11|
|1E 2259586||0.59||404076010||2009-05-25 20:00:17||Key||89.2||HXD||(1/4, 1/4, 1/4)||18.104.22.168|
|AX J1818.81559||406074010||2011-10-15 13:17:36||AO6||88.5||XIS||(1/8 ,1/8 ,1/8 )||22.214.171.124|
|1E 1547.05408||3.2||903006010||2009-01-28 21:34:12||ToO||10.6||HXD||(psum, 1/4, 1/4)||126.96.36.199|
|–||405024010||2010-08-07 03:52:07||AO5||34.1||HXD||(1/4, 1/4, psum)||188.8.131.52|
|SGR 05014516||1.9||903002010||2008-08-26 00:24:42||ToO||43.3||XIS||(1/4, 1/4, 1/4)||184.108.40.206|
|–||404078010||2009-08-17 20:21:51||Key||29.5||HXD||(1/4, 1/4, 1/4)||220.127.116.11|
|–||405075010||2010-09-20 17:27:15||Key||49.1||HXD||(1/4, 1/4, 1/4)||18.104.22.168|
|–||408013010||2013-08-31 23:25:40||AO8||41.2||XIS||(1/8, 1/4, full)||22.214.171.124|
|SGR 18330832||1.8||904006010||2010-03-27 09:03:32||ToO||35.7||HXD||(1/8, full, full)||126.96.36.199|
|CXOU J164710.2455216||1.6||901002010||2006-09-23 06:59:17||ToO||38.7||XIS||(1/8, 1/8, 1/8)||188.8.131.52|
|Swift J1834.90846||1.4||408015010||2013-10-17 07:17:57||AO8||30.4||XIS||(full, full, full)||184.108.40.206|
|Swift J1822.31606||0.14||906002010||2011-09-13 09:59:07||ToO||36.1||HXD||(1/8, full, full)||220.127.116.11|
2. Observation and Data Reduction
2.1. Suzaku Observations
2.1.1 Persistently bright or transient sources
Table 1 summarizes all SGRs and AXPs which Suzaku has observed as of 2013 December. In this table, the “transient sources” exhibit prominent soft X-ray increases by 2–3 orders of magnitudes and subsequent decays on timescales of months to years, while the “persistently bright ones” are relatively stable with their X-ray luminosities around erg s. This is illustrated in Figure 3 as long-term X-ray flux records of representative sources. Since this “persistent” and “transient” classification is somehow phenomenological without a clear consensus (e.g., Pons & Rea 2012a), we classified in this paper relatively variable sources as “transients”.
Our Suzaku sample in Table 1 includes 16 pointings of 9 persistently bright sources and 10 target of opportunity (ToO) observations to follow-up 6 transient objects. This covers 15 objects of all the 29 sources or candidates known to date111The latest magnetars and candidates are listed in http://www.physics.mcgill.ca/~pulsar/magnetar/main.html (see also., Olausen & Kaspi 2014. Due to operational constraints, we were unable to observe recent transients SGR 04185729 and SGR 174529. In the following analyses, we reprocessed all the published data while adding newly observed objects, and performed comprehensive phase-averaged spectroscopic analyses.
2.1.2 Reduction of broad-band Suzaku spectra
We reprocessed the X-ray Imaging Spectrometer (XIS, 0.2–12 keV; Koyama et al. 2007) and the Hard X-ray Detector (HXD, 10–600 keV; Takahashi et al. 2007; Kokubun et al. 2007) data using FTOOLS “aepipeline” of the HEADAS version 6.14 or later with latest calibration database (CALDB) and the standard screening criteria. Only the full window, 1/4, or 1/8 window modes of XIS0, 1, and 3 (Table 1) are analyzed, since XIS2 has been out of operation due to damage by a micro meteorite in 2006 November. As for the HXD, only the HXD-PIN data were utilized since the typical SGR/AXP intensity in hard X-rays (1 mCrab; Paper I) is below the detection limit of HXD-GSO.
The on-source and background XIS spectra were extracted from a circular region of radius and an annulus with the inner radius of and outer radius centered on the source, respectively. The XIS spectra of our magnetar sample are free from the pile-up effect, less than 1% (Yamada et al., 2012). The response matrix file (rmf) and auxiliary response file (arf) were produced using the FTOOLS xisrmfgen and xissimarfgen (Ishisaki et al., 2007). Two XIS0 and XIS3 spectra were summed up, with the rmf and arf also combined.
From the deadtime-corrected HXD-PIN spectrum of each source, we subtracted the Non X-ray Background (NXB), created with the LCFITDT method (Fukazawa et al., 2009), and filtered with the same criteria as those used in the observed on-source data. The Cosmic X-ray Background (CXB) was modeled as described by Enoto et al. (2010b) utilizing the refined spectral model as given by Moretti et al. (2009). Corresponding standard response files are used for this HXD-PIN spectrum. Thanks to the collimated field of view (34’34’ FWHM), the spectra are free from source contamination except for three sources: CXOU J164710.2-45516 (a nearby bright X-ray source GX 340+0, Naik et al. 2008), AX J1818.8 (a nearby hard source AX J1819.21601), and CXOU J171405.7381031 (a potential contamination from a surrounding supernova remnant CTB 37B, Nakamura et al. 2009).
The Galactic Ridge X-ray emission (GRXE; e.g., Krivonos et al. 2007) was further subtracted from the HXD-PIN spectrum when targets are close to the Galactic center222 The GRXE are subtracted from SGR 180620, 1RXS J170849.0400910, SGR 18330832, and 1E 1547.05408. For example, a blank-sky data (ObsID 500008010) was used for SGR 180620, while an observation of supernova remnant G25.5+0.0 (ObsID 504099010), which emits negligible signals in the HXD band, was utilized for SGR 18330832.. We fixed the GRXE photon index at 2.1 (Valinia & Marshall, 1998) and employed normalization adjusted to reproduce near-by blank sky observations. The GRXE contribution is typically 3% of the NXB.
In the following analyses, all uncertainties quoted are given at the 68% (1) confidence level for one parameter of interest unless stated otherwise.
2.1.3 Detections of the soft and hard X-rays
Figure 4 illustrates nine examples of the 1–10 keV XIS and 15–60 keV HXD-PIN spectra derived by the procedures in §2.1.2. The SXC below 10 keV was clearly detected with the XIS from all the observations in Table 1 except Swift J1834.90846 which had already been faded to become undetectable. Hereafter, we analyze the other sources.
|ObsID||Obs. Date||(ks)||ObsID||Obs. Date||(ks)|
|1E 1841045||30001025[04,06,08,10,12]||13 Sep 5-23||273||00080220004||13 Sep 21||1.8|||
|4U 0142+61||300010230[02,03]||14 March 27–30||168||000800260[01–03]||14 March 27–30||24|||
|1E 2259586||300010260[02,03,05]||13 April 24–27||157||000802920[02,03,04]||13 April 25–28||30|||
|1E 2259586||30001026007||13 May 16–18||88||000802920[05,07]||13 May 16–18||8.7||—|
After the NXB and CXB subtractions, we tabulate in Table 2 the 15–60 keV HXD-PIN source count rates together with 1 statistical and systematic uncertainties. The systematic uncertainty of the HXD-PIN background is a sum of 1% level of the NXB (reproducibility of the LCFITDT model; Fukazawa et al. 2009) and 10% of the CXB (1 sky-to-sky fluctuation). The associated 15–60 keV flux was calculated via power-law fitting of the HXD data. If the HXC is undetectable, we set 3 upper-limits on the count rates, which were converted to those on assuming spectral shapes of detected sources (caption of Table.2). We assigned 3 upper limits on 1E 2259586, 1E 1048.1537, Swift J1822.31606, and latter observations of SGR 05014516. The upper limit on 1E 2259586 is consistent with a recent detection by NuSTAR (Vogel et al., 2014).
As reported in Paper I and references therein, we have detected the HXC from 7 sources with 3 significance (see the caption in Table 1). Out of 10 new observations of 6 sources added to Paper I, the HXC was reconfirmed from 4U 0142+61 in 2011, 2013 and RXS J170849.0400910 in 2010. A signature of the HXC was suggested in SGR 18330832, but is rather weak compared with other sources, and the detection is marginal. Thus, we do not use this source in the correlation fittings in §3. Figure 5 illustrates a comparison of and . Suzaku has detected the HXC down to ergs cm s in the 15–60 keV band.
2.2. NuSTAR Observations
The Nuclear Spectroscopic Telescope Array (NuSTAR, Harrison et al. 2013) provides a high spectral sensitivity in the 3–79 keV band, and has already observed bright AXPs (An et al., 2014b, 2013a, a; Vogel et al., 2014; Tendulkar et al., 2015; Yang et al., 2015). In order to verify our results performed by the non-imaging instrument HXD, here we analyze initial NuSTAR data sets available in the archive listed in Table 3.
|( G)||(UT)||( erg s)||(d)||(erg)|
|SGR 05014516||1.9||2008-08-22 12:41:59||2a-d||PD||5.90.2||15.92.9||0.760.05|
|1E 1547.05408||3.2||2008-10-03 09:28:08||3a-d||PL||9.10.4||–||0.130.02|
|1E 1547.05408||3.2||2009-01-22 01:32:41||4a-e||PL||25.70.6||–||0.290.01|
|SGR 04185729||0.061||2009-06-05 20:40:48||5a-e||PD||6.10.4||42.911.6||1.990.30|
|SGR 18330832||1.8||2010-03-19 18:34:50||6a-b||PL||8.81.2||–||0.070.06|
|Swift J182216069||0.14||2011-07-14 12:47:47||7a-c||PD||7.20.3||11.20.9||1.250.02|
|Swift J1834.90846||1.4||2011-08-07 19:57:46||8a-c||PL||1.80.4||–||0.280.09|
Note. – X-ray outbursts after the Suzaku and Swift launches, i.e., outbursts from 1E 2259+586 in 2002, XTE J1810-197 in 2003, and 1E 1048.1-5937 in 2007 are not included. Further details of individual outbursts are listed in Ref., (1a) Krimm et al. (2006); (1b) Israel et al. (2007); (1c) Naik et al. (2008); (1d) Clark et al. (2005); (2a) Holland et al. (2008); (2b) Enoto et al. (2009); (2c) Rea et al. (2009); (2d) Aptekar et al. (2009); (3a) Krimm et al. (2008); (3b) Israel et al. (2010); (3c) Tiengo et al. (2010); (4a) Gronwall et al. (2009); (4b) Enoto et al. (2010b); (4c) Ng et al. (2011); (5a) van der Horst et al. (2009); (5b) van der Horst et al. (2010); (5c) Rea et al. (2010); (5d) Esposito et al. (2010); (5e) Güver et al. (2011); (5d) Rea et al. (2013a); (6a) Gelbord et al. (2010); (6b) Göǧüş et al. (2010); (6c) Esposito et al. (2011); (7a) Cummings et al. (2011); (7b) Rea et al. (2012b); (7c) Scholz et al. (2012); (8a) D’Elia et al. (2011); (8b) Kargaltsev et al. (2012); (8c) Esposito et al. (2013a);
The data were processed and filtered with the standard nupipeline and nuproducts softwares of HEASOFT version 6.16 and the NuSTAR CALDB version 20141020. The on-source spectra were extracted from a circular region of 1.0 radius centered on the target objects within which nearly 90% photons are collected. Since some AXPs are faint hard X-ray sources, we used the background modeling software nuskybkg (Wik et al., 2014) for accurate background subtraction. This tool generates a simulated background spectrum expected on the selected source region by fitting blank-sky spectra from the same focal plane. We selected, for the background spectral modeling, three annual regions with radii 2.0–5.0, 5.0–8.0, and 8.0–12.3 centered on the target sources for each telescope, and adjusted model parameters to explain the actual blank-sky data. The background spectrum was simulated from the best fit modeling parameters with a 100 times longer exposure to reduce statistical uncertainties. The accuracy of the simulated background spectrum was verified using blank sky data as described in Kitaguchi et al. (2014).
If there are simultaneous Swift coverage of during the NuSTAR observations, we also utilized the archived Swift/XRT data listed in Table 3, after the data processing as described in §2.3. If the observations were carried out in a sequential way during a month, we merged continuous data with different observation ID into one spectrum and response for our long-term and phase averaged analyses. Two series of observations of 1E 2259586 were performed in 2013 April and March, so we derived two spectra (Table 3). As an example, we show the background-subtracted X-ray spectra of 4U 0142+61 in Figure 6. The derived NuSTAR spectra are consistent with previous works by An et al. 2013a, Vogel et al. 2014, and Tendulkar et al. 2015.
2.3. Swift and RXTE Observations of Outbursts
Transient magnetars are characterized by sporadic X-ray outbursts, namely sudden increases of the persistent emission, which have recently provided a drastic increase of the number of this class (e.g., as early studies, Gavriil et al. 2002; Kouveliotou et al. 2003; Kaspi et al. 2003 and for a recent review, Rea & Esposito 2011). The onset of an outburst is usually noticed by a detection of short bursts by the Swift Burst Alert Telescope (BAT; Gehrels et al. 2004; Barthelmy et al. 2005), and then monitored with the Swift X-ray Telescope (XRT; Burrows et al. 2005) or with Rossi X-Ray Timing Explorer (RXTE; Bradt et al. 1993), as shown in Figure 7.
We conducted Suzaku ToO observations of some transients usually within a week after. The obtained Suzaku snap shots are also presented in Figure 7. We studied characteristics of outbursts of latest known 8 outbursts of 7 sources which occurred after the Suzaku launch, as listed in Table 4 (see also Figure 3). The onset of an outburst is defined as the first short bursts reported by Swift/BAT or Frermi/Gamma-ray Burst Monitor (GBM).
We uniformly processed all the public available XRT data of 8 outbursts via the standard procedure FTOOLS xrtpipeline with default filtering criteria. We used the latest available RMF matrix in CALDB v20140610, while generated the ARF files with the xrtmkarf tool. For the imaging Photon Counting (PC) mode, we extracted source photons from a circular region with a 48″(20 pixels) radius centered on the target, while collected background spectra from annular regions with the inner and outer radii of 167″(70 pixels) and 286″(120 pixels), respectively. When the PC-mode count rates exceed 0.5 count s, we excluded a central 8.0″(3.4 pixels) region following a standard procedure333http://www.swift.ac.uk/analysis/xrt/pileup.php. For the Windowed Timing (WT) mode with an one-dimensional information and 1.76 ms time resolution, we extracted source and background spectra from a strip of 94″width around the source and surrounding regions by 140″away from the target, respectively. When the count rate exceeds 100 cnt s, we excluded the central 14″strip to avoid the pile-up. After the above standard pipelines, we discarded observations with poor photon statistics if the total source count is smaller than 100 cnts per observation.
The non-imaging RXTE Proportional Counter Array (PCA; Jahoda et al. 2006) operates in the 2–60 keV energy band with a full width at half-maximum field of view of 1. Due to nearby sources, we only used the PCA data for SGR 05014516 and SGR 04185729. The data were processed via the standard procedure using FTOOLS rex, pcarsp, and recofmi tasks.
3. Analysis and Results
3.1. Spectral modeling of two X-ray components
We carried out unified spectral fitting of the Suzaku phase-average broad-band spectra. Phase-resolved spectroscopy, available only for bright and slowly rotating objects (e.g., 1RXS J18049.0400910), is beyond the scope of this paper. In order to avoid instrumental calibration uncertainties of the XIS, the 1.7–1.9 keV data were discarded, and a 2% systematic error was assigned to the XIS spectral bins. The XIS and HXD-PIN spectra were binned so that each bin has either 5 significance or 30 counts. The cross-normalization factor of HXD-PIN was fixed at 1.164 and 1.181 relative to XIS-FI in cases of the XIS- and HXD-nominal pointing positions (Maeda et al., 2008), respectively. The normalization of XIS-BI to XIS-FI was allowed to differ by up to 5%. For the simultaneous Swift and NuSTAR spectra (§2.2) the normalization was fixed to that of the Swift/XRT and the cross-normalization between the telescopes (FPMA and FPMB) was allowed by up to 5%.
|104859||2013-07||N/A||from Yang et al. (2015)|
A photo-absorption factor was multiplied to an intrinsic continuum spectral model of the SXC. We employed the phabs model (Balucinska-Church & McCammon, 1992) in XSPEC with the solar metallicity abundance angr (Anders & Grevesse, 1989) and cross-section bcmc; this combination has been widely used in the literature and allows us to compare with previous results. When the HXC is detected in the 15–60 keV band, it was expressed by an additional single power-law. We further added a plasma emission model when analyzing the 1E 1841045 and CXU J171405.74381031 data, to describe the surrounding supernova remnant (SNR) Kes 73 (Kumar et al., 2014) and CTB 37B (Sato et al., 2010), respectively, as described in Appendix A.
The intrinsic SXC spectrum is conventionally fitted by a model comprising two blackbody components (hereafter 2BB model), or a combination of a blackbody plus an additional soft power-law (BB+PL model), The second high-energy component of both models is considered to represent either a temperature anisotropy over the stellar surface, an up-scattering of soft photons in the magnetosphere, or effects of a magnetised neutron star atmosphere (e.g., Lyutikov & Gavriil 2006; Rea et al. 2008; Güver et al. 2011). These empirical 2BB and BB+PL models roughly explain the data, though only approximately sometimes. The low and high blackbody temperatures in the 2BB model, and , are known to follow a relation of (Nakagawa et al., 2009), thus the number of free spectral parameters is expected to be three rather than four of the 2BB or BB+PL models.
Since the SXC spectral modeling has not reached a consensus, we utilize an empirical blackbody shape with a Comptonization-like power-law tail (hereafter CBB model, Tiengo et al. 2005; Halpern et al. 2008; Enoto et al. 2010b, and Paper I). This CBB model is mathematically described by three parameters; the temperature , soft-tail power-law photon index , and normalization corresponding to the emission radius , and the model reproduces the soft-tail at 5 keV of the BB+PL model without a large that is needed by the 2BB.
We present the Suzaku CBB best-fit parameters in Table 5 and corresponding spectra in Figure 8. The NuSTAR fit results are given in Table 5 together with some examples in Figure 9. The NuSTAR shapes of bright AXPs, 4U 014261 and 1E 1841045, are consistent with those of Suzaku. The HXC of 1E 2259586 was detected with NuSTAR (Vogel et al., 2014), but not with Suzkau.
Note. – Pulsar timing information: spin period (s), period derivative s s), surface magnetic field G), and spin-down luminosity erg s, where g cm is the neutron star momentum of inertia.
Spectral information: The 1–60 keV luminosity of the SXC and HXC, , , and their toral . All the luminosities, , , , and are shown in an unit of erg s.
Hardness ratio (HR): Evaluated from absorbed fluxes of 15–60 keV and 1-10 keV () or luminosities () after correcting absorption.
3.2. Correlations among spectral parameters
3.2.1 Ratio of HXC to SXC vs. magnetic field
In Paper I, we proposed a broad-band spectral evolution of this class: i.e., i) the hardness ratio of the HXC to SXC is positively (or negatively) correlated to their (or ), and ii) the HXC photon index becomes harder toward the weaker sources (see also Kaspi & Boydstun 2010).
Based on our updated sample shown in Figure 8, we revised these correlations. Figure 10 top-left panel shows the ratio of absorbed fluxes, , as a function of , which is derived from the pulsar timing information independently from the spectroscopy. The Spearman’s rank-order test of this correlation gives a significantly high value, . The correlation is fitted as,
using the Bayesian method in Kelly (2007) (linmix package) to account for measurement errors and intrinsic scatter of the data. While the correlations is derived from the spectral analyses below 70 keV, the potential HXC cutoff does not strongly affect the correlation (Paper I). Due to limited photon statistics of several Suzaku sources, we can only study total emission. Deconvolution into pulsed and un-pulsed components (Kuiper et al., 2012) will be reported in future publications.
As shown in plots (Figure 8), the HXC largely contributed to the SXC band below 10 keV in stronger objects (e.g., SGR 180620, SGR 190014, and 1E 1547.05408). To remove this mixing, and to eliminate the effects of the photo-absorption, we also define the absorption-corrected luminosity ratio between the two components, (listed in Table 6), in the same way as Paper I. The Spearman’s rank-order significance becomes . The correlation slope of becomes steeper than those of as,
This is shown in the top-right panel of Figure 10. On these correlations, we revised timing information ( and ) from Paper I, referring to the McGill catalog (Olausen & Kaspi, 2013), and further added NuSTAR observations. Data points of canonical AXPs 4U 014261 and 1E 1841045 are consistent with those with Suzaku, and the new HXC detection from 1E 2259586 (Vogel et al., 2014) falls on the correlation. The Galactic center source SGR J174529, though not shown in Figure 10, is also expected to follow the relation since its wide-band spectrum resembles that of 1E 1547.05408 (Mori et al., 2013).
The above correlation to the directly measured quantity can be converted to correlations to and , although the additional two relations are not independent to Eq. (2) since and are estimated using combinations of the same and ; i.e., and . Furthermore, considering the clustering of rotational periods of magnetars in a narrow range (–11 s), Correlation of Eq. (2), (k0.72), gives and . These relations are shown in the middle and bottom panels in Figure 10, and same fitting procedures give,
The slopes of Eq. (5) and (6) are consistent with those from Paper I within error bars. The Suzaku upper limit for the second lowest -field source Swift J1822.31606 ( G, i.e., ) is also consistent with this picture. Thus we reconfirm, and reinforce, the evolution in and as reported in Paper I.
3.2.2 Photon index of HXC vs. magnetic field
The second prediction of Paper I is the HXC spectral hardening toward weaker- objects, as seen in representative spectra in Figure 11 (top). Figure 11 (bottom) also shows the HXC photon index as a function of , which is fitted as
The values are stable on a long-time scale for persistently bright sources such as 4U 0142+61, SGR 180620, and 1E 1841045, while some transients show slope change during the outbursts. This was also reported during the 400 days INTEGRAL monitoring of 1E 1547.05408 changing from to (Kuiper et al., 2012). This figure clearly indicates a peculiar trend that relatively weaker HXC intensity sources show harder spectral slope of the HXC.
3.2.3 Surface temperature of SXC vs.
The surface temperature of the SXC is plotted as a function of in Figure 12 where we also added of other isolated neutron stars from previous studies. This plot indicates 1) higher of magnetars than that of other isolated neutron stars, 2) a tendency of the positive correlation between and in the quiescent neutron star sample, and 3) increase of during transient magnetar outbursts. All these properties suggest that the values of reflect the effects of magnetic energy dissipation, which is an implicit but direct consequence of the magnetar hypothesis.
where and are the normalization and decay index, respectively. The solution is obtained as
with . This formula successfully explains the clustering of rotational period of SGRs and AXPs around 2–12 s (Colpi et al., 2000), and resolves the overestimation of in 1E 2259+586 when compared with the age derived from plasma diagnostics of the surrounding SNR CTB 109 (Nakano et al. 2015, but see also Suwa & Enoto 2014). Then, let us here assume that the surface temperature is determined by a balance between the radiative cooling and heating by the magnetic energy dissipation of in the crust. Following Pons et al. (2007), this is described as
where , , and are the surface area, crust thickness, and the Stefan-Boltzmann constant, respectively. Combining this with Eq. (8), we derive