THE X-RAY COUNTERPART OF THE HIGH-B PULSAR PSR J0726−2612

To look for X-ray pulsations, we first determined the frequency that maximized the power in a Z²₁ periodogram (Rayleigh statistic; Buccheri et al. 1983) at different multiples of the radio frequency. We found no obvious peak at the expected frequency of the pulsar (Z²₁ = 0.7), but a strong one (Z²₁ = 21.7) at roughly double the frequency, 0.290493 ± 0.000002 Hz (where the uncertainty was calculated following Ransom 2001). We found no evidence for significant power in higher harmonics (Z²₁ = 1.2 and 0.70 at the third and fourth harmonic, respectively). We folded our data on half our best-fit frequency to construct a binned light curve (with 16 phase bins, Figure 2). As expected from the lack of other harmonics, a sinusoid provided a good fit (χ² = 11.7 for 13 degrees of freedom, dof), with a pulsed fraction (semi-amplitude) of 27% ± 5%. The implied time of arrival (TOA), defined as the maximum of the sinusoid closest to the middle of the observation, is MJD 55727.6883125 ± 0.0000006. The ephemeris in the ATNF catalog (based on data from 2005 to 2006) predicts a frequency of 0.29049679119 ± 9.6 × 10⁻¹⁰ Hz at the epoch of our observation, which differs by ∼2σ from our measurement. Further radio observations would help determine whether this is due to chance or due to something intrinsic (a glitch or timing noise).

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In order to compare the phase of the radio and X-ray pulses, we retrieved an archived Parkes observation of PSR J0726 from 2005 March 26. The pulse profile, shown in Figure 2, was substantially noisier than that shown in Burgay et al. (2006), but still sufficed to determine a TOA. From the highest point in the profile, we find MJD 53455.29291874 ± 0.00000004, with the uncertainty being ±1 phase bins. With this TOA and the ATNF ephemeris, we infer a phase difference of ${\rm TOA}_{\rm radio}-{\rm TOA_{\rm X}}=0.07\pm 0.11$ cycles, where the uncertainty is dominated by uncertainties in the ephemeris (see Figure 2).

Spectral fitting was done in sherpa (Refsdal et al. 2009). For the fits, we only included events between 0.32 and 1.1 keV, as the response below 320 eV is not well understood. This leaves 1003 source and 267 background counts. We follow recommendations in modeling the low-energy background with a power law instead of subtracting it (although given that the expected background in the source area is less than 1 count, it does not influence the results). We binned the source counts such that each bin contained at least 25 counts and was at least 29 eV wide, so that χ² statistics are a good approximation, and we do not oversample the instrumental resolution of ∼100 eV.

We tried three main source models: a thermal blackbody, a non-thermal power law, and a simple neutron-star atmosphere (NSA) model (Pavlov et al. 1991; Zavlin et al. 1996), all modified by interstellar absorption (using xsphabs; the parameters changed only minutely with other choices, such as xstbabs and xswabs). We tried NSA models with and without a strong magnetic field; for both, we fixed the mass and radius of the neutron star at 1.4 M_☉ and 10 km, respectively. Our results are summarized in Table 1 (there and below, temperatures and radii refer to those measured by a distant observer).

Table 1. Results of X-Ray Fits to PSR J0726−2612

Model	NH	Γ or kT	A or R/da	Fabs b ×10−13	Funabs b ×10−13	χ2/dof
	(1020 cm−2)	(N/A or eV)	(10−5 s−1 cm−2 keV−1	(erg s−1 cm−2)	(erg s−1 cm−2)
			or km kpc−1)
Blackbody	$\phantom{0}8_{-3}^{+4}$	87 ± 5	5.7+2.6− 1.3	4.5	12.9	45.1/67
Blackbody	$\phantom{0}2_{\phantom{-}\phantom{0}}$	95 ± 2	3.5+0.3− 0.2	4.5	5.6	48.1/68
Blackbody	$21_{\phantom{-}\phantom{0}}$	74 ± 2	17.1+1.5− 1.4	3.6	33.8	55.0/68
NSA (B = 0)	14+9− 4	22 ± 3	307+370− 122	4.2	22.7	52.8/67
NSA (B = 1013 G)	12+4− 4	42 ± 4	$63_{-24}^{+39\phantom{.}}$	4.3	19.2	52.8/67
Power law (Γ free)	20+4− 4	6.4 ± 0.4	7.6+1.0− 0.8	4.2	60.6	76.9/67
Power law (Γ = 3)	$\phantom{0}\phantom{..}0^{+0.1}$	3	9.0+0.7− 0.2	3.2	3.2	195/66
Blackbody phase-resolved:
Minimac	$\phantom{0}9_{-4}^{+5}$	85 ± 6	5.8+2.7− 1.7	3.3	8.5	24.3/37
Maximac	$\phantom{0}9_{-4}^{+5}$	86 ± 6	7.1+3.5− 2.2	5.1	13.2	47.1/51

Notes. Quantities without uncertainties were held fixed during the fit. All uncertainties are for 1σ confidence, and all other parameters were allowed to vary during the calculation of the uncertainties. ^aFor the NSA models, the mass is fixed to 1.4 M_☉ and the radius is fixed at 10 km, so the uncertainties calculated for R/d are based on the best-fit distance. The normalization of the power-law model A is the photon rate at an energy of 1 keV. ^bThe fluxes are given in the 0.32–1.1 keV band and are given both as observed and corrected for absorption. ^cPhase-resolved spectroscopy using a blackbody model. The two phase bins each include 50% of the data and were fitted simultaneously with the same absorption.

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The NSA models gave reasonable fits, but implied implausibly small distances: 33⁺²²_{− 18} and 160⁺¹¹⁰_{− 60} pc for the B = 0 and B = 10¹³ G models, respectively. A power-law model gave a significantly worse fit than the thermal models (χ² = 76.9 versus 45.1 for 67 dof). We found that, similar to the INSs, a simple blackbody gave a good fit (Figure 3) and the most reasonable parameters.⁵ In what follows, we use that as our baseline model. We find there is significant covariance between the fitted parameters, which, within 1σ, leads to changes in absorption of 4 × 10²⁰ cm⁻² and in temperature of ∼ 5 eV. To explore the influence of the absorption column, we also tried fits where we held N_H fixed at 1 or 10 times the DM (70 cm⁻³ pc = 2.1 × 10²⁰ cm⁻²). These fits were somewhat worse than those with N_H free, but still had reduced χ² less than 1.

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To constrain any additional non-thermal emission, we tried adding a power law to the blackbody. We found that it had negligible effect on the parameters, and, assuming Γ = 3, we infer a 1σ upper limit of the photon rate of 7 × 10⁻⁶ s⁻¹ cm⁻² keV⁻¹ at 1 keV, corresponding to ≲  3% of the flux in the 0.32–1.1 keV band.

We also tried fitting the spectrum of PSR J0726 with a model that included an additive Gaussian line, in order to constrain the presence of absorption features similar to those seen for the INSs, which have equivalent widths of up to several 100 eV (Haberl 2007; van Kerkwijk & Kaplan 2007). We fixed the full width at half-maximum of the line to 0.1 keV, comparable to the energy resolution of the back-illuminated ACIS-S3 CCD, and varied the line energy between 0.3 keV and 1.1 keV, fitting only for its amplitude (allowing both positive and negative amplitudes). As expected from Figure 3, we did not find evidence for any absorption line. The largest improvement in the fit occurs near 0.6 keV, for an emission line with a height of 35%, but even this reduces χ² by only 4, which is not significant given our number of trials (based on simulations, we estimate a false alarm probability of ∼ 30%). We infer a 68% confidence upper limit of 50 eV to the equivalent width of any feature.

Finally, we looked for phase-resolved trends in two ways. First, we determined the median energy as a function of pulse phase (upper panel in Figure 2), finding little change except perhaps a hint of hardening at the maximum that is coincident with the radio peak, although given the current statistics this is not significant (the χ² for the median energy is 9 for 15 dof). Second, we separated the data into two bins: one containing the two maxima and one the two minima, each with 50% of the exposure time. From our fit (Table 1 and Figure 3), we find negligible difference in temperature between the maxima and minima, consistent with the lack of change seen in median energy. Thus, the pulsations appear to reflect mostly changes in emitting area.

To check for possible extended emission, e.g., from a pulsar wind nebula, we compared our observations with a simulated point-spread function (PSF), created using ChaRT (the Chandra Ray Tracer) and MARX (version 4.5.0), for a spectrum consistent with our best-fit blackbody. We find good agreement for radii ⩾2 pixels (1''), although with only ≈180 counts at these radii, the constraints are not strong. Oddly, the two bins at the smallest radii, 0–0.5 pixels and 0.5–1.0 pixels, had some deviations, with the model PSF underpredicting the counts in the first bin by about 6σ (30%) and overpredicting the second by about 4σ (26%). Since it is unlikely that the pulsar is more centrally concentrated than a point source, we probably are simply reaching the limits in the model (we experimented with the Chandra processing, turning off pixel position randomization, but found that this made little difference). We conclude that there is no evidence for extended emission on scales of ≳ 1''.

PSR J0726 was selected to be similar to the INSs in having a long spin-period, P > 3 s, and strong magnetic field, B = (1–3) × 10¹³ G. With a thermal spectrum with kT = 87 ± 5 eV and R ≈ 6 km (at the nominal distance of ∼1 kpc in the Gould Belt), its X-ray properties are similar as well (indeed, it would be classified as an INS based on these). Its spectrum has no evidence for absorption, unlike RX J1308.6+2127, which has strong absorption (Haberl et al. 2003) while having a very similar magnetic field and a slightly higher temperature (B = 3.4 × 10¹³ G, Kaplan & van Kerkwijk 2005b; kT = 102 eV, Schwope et al. 2007). However, RXJ0720.4−3125, another INS with a similar if slightly lower field (B = 2.4 × 10¹³ G; Kaplan & van Kerkwijk 2005a), had weak absorption, with an equivalent width of ∼5 eV, which we would not be able to detect, when its temperature was most similar to PSR J0726 (kT = 86 eV, Haberl et al. 2004). Intriguingly, this source changed, developing much stronger absorption while becoming hotter (kT = 94 eV, de Vries et al. 2004; Haberl et al. 2006; van Kerkwijk et al. 2007). Taking our inferred temperature at face value, it is thus possible that PSR J0726 emits identically to an INS of the same temperature and dipole magnetic field strength. If so, at higher sensitivity it may show weak absorption at ∼300 eV. (We caution, however, that the dependencies of absorption energy and strength on temperature and magnetic field strength remain puzzling for the INSs as a class; Kaplan & van Kerkwijk 2009a, 2009b.)

The inferred luminosity L_X = 1.5 × 10³²d²_kpc erg s⁻¹ (0.32–1.1 keV) is about half the rotational energy loss rate $\dot{E}=4\pi ^2I\dot{P}/P^3 = 2.8 \times 10^{32}\,{\rm erg\,s}^{-1}$ (for a moment of inertia I = 10⁴⁵ g cm²). This is on the low side of what is seen for the INSs ($L_{\rm X}\sim (0.5\ldots 100)\dot{E}$), possibly just a consequence of PSR J0726 having a shorter period for the same B (for dipole spin-down, $\dot{E}\propto B^2/P^4$). It is much larger than the non-thermal emission typically observed for rotation-powered pulsars ($L_{\rm X}\approx 10^{-3}\dot{E}$, Becker & Trümper 1997), although we cannot exclude that PSR J0726 has a similar non-thermal component: our 1σ upper limit of 3% of the 0.32–1.1 keV flux for the contribution of a power law with Γ = 3 (a value typical for pulsars) implies $L_{\rm PL}\lesssim 0.015d_{\rm kpc}^2\dot{E}$.

The pulse properties of PSR J0726 also echo those of the INSs, which show smooth profiles dominated by the fundamental or the first harmonic. The pulse fraction of 27% ± 5% is a little larger than the ∼1% to 18% seen for the INSs (Haberl 2007), but it is not dramatically different. We note that without the radio period, we might have actually identified the pulse period of PSR J0726 as half of the true value. The lack of temperature variation is somewhat strange (cf. up to 10% changes in kT over the pulse of RX J1308.6+2127, for example; Schwope et al. 2005) as, naively, it implies that we are seeing changes in projected area of large regions of similar temperature with anything in between so much colder that it does not contribute. It may be that instead the whole surface emits at more or less a uniform temperature, and that the pulsations reflect anisotropies in the emission, perhaps associated with the strong magnetic field. The same may hold for the INSs, which typically also show only modest changes in temperature with pulse phase.

A possible difference with the INSs is that PSR J0726 has an order-of-magnitude smaller characteristic age. This may again be a consequence of its shorter period for the same B (for dipole spin-down, τ∝(P/B)²), but might also point to an evolutionary difference (see below). Another characteristic of INSs is that they have faint optical counterparts, but with optical/UV fluxes a factor of 6–50 above the extrapolation of the X-rays. This is in contrast to middle-aged pulsars such as PSR B0656+14 and Geminga, which have ultraviolet fluxes that are more consistent with the X-ray extrapolations (Shibanov et al. 2005; Kargaltsev et al. 2005). It will be interesting to see whether PSR J0726 has an excess or not.

Of course, the most glaring difference between PSR J0726 and the INSs is the radio emission. Numerous searches have yet to find confirmed radio emission (coherent or bursty) from the INSs (Kondratiev et al. 2009, and references therein). This may be a result of their location near the pulsar "death line," or more simply a consequence of their narrow radio beams: the 50% width of the radio pulse from PSR J0726 is <1% of the pulse period (consistent with general trends for long-period pulsars) so the chance of missing the radio pulse is large.

Overall, we conclude that with the exceptions of its radio emission and characteristic age, the properties of PSR J0726 agree with those of the INSs. Based on the compilations of Kaplan & van Kerkwijk (2009b) and Zhu et al. (2011, references therein), it is the best pulsar analog to the INSs to date.

In order to look for evolutionary trends, we can compare PSR J0726 to sources with similar properties in the P−$\dot{P}$ diagram, as well as with the evolution expected from the work of Pons et al. (2009), which seems to explain the origins of the INSs (Figure 1). A first comparison is with INSs of similar field and temperature, RX J0720.4−3125 and RX J1308.6+2127. As mentioned, the main difference is that the characteristic age of PSR J0726 is 200 kyr, while those of the INSs are >2 Myr. This could imply that the true age of PSR J0726 is closer to its characteristic age than is the case for the INSs, and maybe that it has undergone less B decay. This is consistent with the models of Pons et al. (2009): 3 × 10¹³ G is near the dividing line where field decay becomes important, and the true age is expected to be no more than a factor two shorter than the characteristic age (see Figure 1). Taking the models at face value, one infers that PSR J0726 was born with a dipole field of just below 10¹⁴ G, while most INSs would have had a field about a factor two stronger.

As a second comparison, we can compare PSR J0726 with two X-ray-detected objects that have almost the same period: the modest-B INS RX J0420.0−5022 (1.0 × 10¹³ G, Kaplan & van Kerkwijk 2011) and the high-B pulsar PSR J1718−3817 (7.4 × 10¹³ G, Zhu et al. 2011). The former is very similar to PSR J0726, with the main difference being that it is cooler (kT ≈ 45 eV). From the evolutionary tracks, it seems most likely that RX J0420.0−5022 initially simply had even lower magnetic field strength, which decayed by a factor ∼2 or so, and that, like PSR J0726, its true age is at most a factor two shorter than its characteristic age of 2 Myr.

From the evolutionary tracks, PSR J1718−3817 would be a good candidate progenitor for INSs like RX J0720.4−3125, and indeed it has a largely thermal spectrum consistent with a blackbody with a significantly hotter temperature (kT ≈ 190 eV), suggestive of ongoing field decay. However, the emitting radius of ∼2 km and pulsed fraction of ∼50% differ from those found for the INSs (and PSR J0726), and are more reminiscent of even younger high-B pulsars like PSR J1119−6127 (Gonzalez et al. 2005), which also have high pulsed fractions and smaller radii (although distance and fitting uncertainties make the radii for all these objects poorly constrained). It may be that this reflects some combination of ongoing B decay and non-thermal heating; all these younger, strong-field objects have substantially larger spin-down energy losses. Alternatively, the stronger field may lead to more anisotropic emission.

Overall, it seems that the INSs and high-B pulsars form a single family (also see Kaspi 2010 for further discussion), with initial fields that were stronger than their current ones and that caused rapid initial spin-down. The long periods for the slower spinning objects also imply low rotational energy losses and thus weak non-thermal emission. Combined with some additional heating due to field decay, this makes the thermal emission stand out more than it would in normal pulsars.

A continuing puzzle, however, is the difference with the magnetars (Ng & Kaspi 2011), which occupy similar parts of the P−$\dot{P}$ diagram, but are clearly much more strongly affected by magnetic field decay. It may be that those were born with much stronger toroidal components to the field (which affect the spin-down only indirectly, via the more rapid field decay). In any case, there may be a smooth continuum, given objects like PSR J1846−0258 (B = 4.9 × 10¹³  G) which exhibited a sudden, magnetar-like X-ray outburst (Gavriil et al. 2008; Kumar & Safi-Harb 2008; Ng et al. 2008), the INS RX J0720.4−3125 that exhibited a possible magnetic reconfiguration (de Vries et al. 2004; van Kerkwijk et al. 2007), the transient magnetar XTE J1810−197 that was detected in outburst (Ibrahim et al. 2004) but in quiescence appears more like an INS (Bernardini et al. 2011), or the putative low-B magnetar SGR 0418+5729 (<8 × 10¹² G; Rea et al. 2010; Turolla et al. 2011).