Spin-down Measurement of PSR J1852+0040

# Spin-down Measurement of PSR J1852+0040 in Kesteven 79: Central Compact Objects as Anti-Magnetars

J. P. Halpern & E. V. Gotthelf Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027
###### Abstract

Using XMM-Newton and Chandra, we achieved phase-connected timing of the 105 ms X-ray pulsar PSR J18520040 that provides the first measurement of the spin-down rate of a member of the class of Central Compact Objects (CCOs) in supernova remnants. We measure , and find no evidence for timing noise or variations in X-ray flux over 4.8 yr. In the dipole spin-down formalism, this implies a surface magnetic field strength  G, the smallest ever measured for a young neutron star, and consistent with being a fossil field. In combination with upper limits on from other CCO pulsars, this is strong evidence in favor of the “anti-magnetar” explanation for their low luminosity and lack of magnetospheric activity or synchrotron nebulae. While this dipole field is small, it can prevent accretion of sufficient fall-back material so that the observed X-ray luminosity of  erg s must instead be residual cooling. The spin-down luminosity of PSR J18520040,  erg s, is an order-of-magnitude smaller than . Fitting of the X-ray spectrum to two blackbodies finds small emitting radii,  km and  km, for components of  keV and  keV, respectively. Such small, hot regions are ubiquitous among CCOs, and are not yet understood in the context of the anti-magnetar picture because anisotropic surface temperature is usually attributed to the effects of strong magnetic fields.

ISM: individual (Kes 79) — pulsars: individual (PSR J08214300, 1E 1207.45209, PSR J18520040) — stars: neutron
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## 1. Introduction

The class of relatively faint X-ray sources known as central compact objects (CCOs) in supernova remnants (SNRs) are apparently isolated neutron stars, which we define here by their steady flux, predominantly thermal X-ray emission, lack of optical or radio counterparts, and absence of a surrounding pulsar wind nebula (see reviews by Pavlov et al. 2004 and De Luca 2008). Table 1 lists basic data on the well-studied CCOs, as well as candidates whose qualifications are not well established. Of the seven most secure members, three are definitely pulsars with periods of 0.105, 0.112, and 0.424 s (Gotthelf et al., 2005; Gotthelf & Halpern, 2009; Zavlin et al., 2000). Until now, no spin-down was detected from a CCO, which is most simply interpreted as indicating a weak surface dipole magnetic field . In two cases, PSR J18520040 ( s) and 1E 1207.45209 ( s), the upper limits on from spin period measurements are  G and  G, respectively (Halpern et al., 2007; Gotthelf & Halpern, 2007), smaller than that of any other young neutron star. We also found  G from a pair of observations of PSR J08214300, the 0.112 s pulsar in Puppis A (Gotthelf & Halpern, 2009).

Important implications of these results are that the birth periods of the CCO pulsars are not significantly different from their present values, and that their spin-down luminosities are, and have always been, insufficient to generate significant non-thermal magnetospheric emission or synchrotron nebulae. A corollary is that the so-called “characteristic age” that is used to approximate the true age of pulsar has, for CCOs, no meaning, being at least millions of years for pulsars that are demonstrably in supernova remnants that are only a few thousand years old. It is also reasonable to suppose that some isolated radio pulsars with weak magnetic fields that have characteristic ages of millions of years may actually be former CCOs that are only moderately aged.

Most of the properties of the CCOs can thus be explained by an “anti-magnetar” model (Halpern et al., 2007; Gotthelf & Halpern, 2008), including the possibility that their weak magnetic fields are causally related to their slow rotation periods at birth through the turbulent dynamo (Thompson & Duncan, 1993) that generates the magnetic field. (See Spruit 2008 for a review of possible mechanisms for the origin of magnetic fields in neutron stars.) While CCOs are inconspicuous relative to ordinary young pulsars and magnetars, the fact that they are found in SNRs in comparable numbers to other classes of neutron stars implies that they must represent a significant fraction of neutron star births. Considering that the CCO in Cassiopeia A is the youngest known neutron star (330 yr), and postulating that a CCO in SN 1987A explains why its pulsar has not yet been detected, argues that anti-magnetars are potentially a populous class.

The compact X-ray source CXOU J185238.6004020 was discovered in the center of the SNR Kes 79 by Seward et al. (2003). In previous papers, we reported the discovery of 105 ms pulsations from that CCO, now named PSR J18520040 (Gotthelf et al., 2005, Paper 1), and the first few observations that established only an upper limit on its period derivative corresponding to  G (Halpern et al., 2007, Paper 2). Here, we present a dedicated series of timing observations of PSR J18520040 that constitute the first definite measurement of the spin-down rate of a CCO pulsar, confirming its unusually small dipole magnetic field and supporting the anti-magnetar model. The plan that was devised to obtain the needed series of time-constrained observations is described in Section 2. Analysis and results of the timing data are presented in Section 2.1, and the high-quality X-ray spectrum and pulse profile that were obtained from the summed observations are the subject of Section 2.2. Discussion of the anti-magnetar model, and possible explanations for the X-ray spectrum appear in Section 3, followed by the conclusions in Section 4.

In this paper, we adopt a distance of 7.1 kpc to Kes 79 from H i and OH absorption studies (Frail & Clifton, 1989; Green & Dewdney, 1992) updated using the Galactic rotation curve of Case & Bhattacharya (1998). We also assume the dynamical estimate of 5.4–7.5 kyr for the age of the SNR from Sun et al. (2004).

## 2. X-ray Observations

After the first four timing observations of PSR J18520040 in 2004 and 2006 (Paper 2), it was evident that the frequency derivative was too small to measure without obtaining a phase-coherent series of observations spanning several years. The most economical way to measure is to begin with a logarithmically spaced sequence of observations that maintains the absolute cycle count and measures the frequency with increasing accuracy, until the small quadratic term in the phase ephemeris

 ϕ(t)2π=f(t−t0)+12˙f(t−t0)2+...

begins to make a significant contribution to the phase. In this case, it was also deemed possible (Paper 2) that accretion from fall-back material could contribute timing irregularities known as torque noise, of a magnitude comparable to the existing upper limits on dipole spin-down. This made it all the more important to obtain a well-sampled ephemeris that could test for such effects.

Unfortunately, maintaining cycle count would require more observations classified as time-constrained than the Chandra X-ray Observatory allocates to any one project, while for XMM-Newton, semiannual visibility windows for this source are only 40 days long, not wide enough to securely bridge over the intervening 5 month gaps. It took until 2008 to implement a strategy that uses the two satellites in a coordinated fashion, filling two XMM-Newton visibility windows with six observations each of variable spacing, while requesting pairs of Chandra observations to bridge the gaps between and after the two XMM-Newton windows. In this manner, a phase-coherent timing solution spanning 1.7 yr could be achieved, which could also be extrapolated backward to incorporate the earlier observations. All but one of the approved observations in 2008–2009 were performed as planned. Due to a loss of contact with the XMM-Newton spacecraft, the last observation of 2008 was rescheduled to 2009, but this did not compromise the success of the program. We were thus able to obtain a fully coherent timing solution incorporating all of the observations listed in Table 2, including the earliest ones, spanning 4.8 yr in total.

All of the XMM-Newton observations used the pn detector of the European Photon Imaging Camera (EPIC-pn) in “small window” (SW) mode to achieve 5.7 ms time resolution, and an absolute uncertainty of  ms on the arrival time of any photon. We processed all EPIC data using the emchain and epchain scripts under Science Analysis System (SAS) version xmmsas_20060628_1801-7.0.0. The leap second at the end of 2008 was inserted manually. Simultaneous data were acquired with the EPIC MOS cameras, operated in “full frame” mode. Although not useful for timing purposes because of the 2.7 s readout, the location of the source at the center of the on-axis MOS CCDs allows a better background measurement to test for flux variability, an important indicator of accretion, than the EPIC-pn SW mode.

The Chandra observations used the Advanced Camera for Imaging and Spectroscopy (ACIS) in continuous-clocking (CC) mode to provide time resolution of 2.85 ms. This study uses data processed by the pipeline software revisions v7.6.9–v8.0. Reduction and analysis used the standard software package CIAO (v3.4) and CALDB (v3.4.2). The photon arrival times in CC mode are adjusted in the standard processing to account for the known position of the pulsar, spacecraft dither, and SIM offset. Absolute accuracy of the time assignment in Chandra CC-mode is limited by the uncertainty in the position of the pulsar, which was determined in Paper 2 from an ACIS image. The typical accuracy of pixel then corresponds to an uncertainty of  ms, which is similar to the XMM-Newton accuracy, and is 0.03 rotations in the case of PSR J18520040. We will show that the measured dispersion in pulse arrival times is comparable to this uncertainty.

### 2.1. Results of Timing Analysis

For each observation in Table 2 we transformed the photon arrival times to Barycentric Dynamical Time (TDB) using the pulsar coordinates determined in Paper 2 and reproduced in Table 3. Diffuse SNR emission is a significant source of background. To maximize the pulsar signal-to-noise ratio, we used a source extraction radius of for the XMM-Newton observations, and five columns () for the Chandra CC-mode data. An energy cut of  keV was found to maximize pulsed power. The pulse profile and value of the period in each observation was derived from a periodogram (Buccheri et al., 1983), a choice of harmonics that was found to minimize the uncertainties. The resulting profiles were cross-correlated, shifted, and summed to create a master pulse profile template. Individual profiles were then cross correlated with the template to determine the time of arrival (TOA) at each epoch.

Starting with the dense series of XMM-Newton observations in 2008 September, the TOAs were iteratively fitted using the TEMPO software. We fitted the three observations from September 19–23 to a linear ephemeris, and added TOAs one at a time using a quadratic ephemeris, finding that the new TOA would match to cycles the predicted phase derived from the previous set. After adding the final observation to the ephemeris, we then worked backward in time from 2008 September to 2004 October until all 23 observations had been included. The quadratic term contributes cycles of rotation over the 4.8 yr span of the ephemeris, which yields the small uncertainty in discussed below. The phases and errors were determined by cross-correlating with a final iterated template of co-added profiles produced from the best fitting ephemeris given in Table 3. Figure 1 shows the residuals of the individual observations from the best fit, which demonstrates the validity of the solution. The weighted rms of the phase residuals is 3.4 ms, or 0.032 pulse cycles, which is comparable to the individual measurement errors. There is no evidence of timing noise or higher derivatives in the residuals. The variation of (pulsed power) among the observations listed in Table 2 is also consistent with statistical expectations. Figure 2 shows the summed pulse profile from the 16 XMM-Newton observations, for which it is possible to measure a reasonably accurate background (unlike the Chandra CC-mode data).

The sensitivity of the results to and can be estimated analytically. If a pulsar is spinning down smoothly, then a coherent timing solution spanning time will have an uncertainty in frequency of , and will be sensitive to a period derivative of . This in turn will measure with fractional uncertainty

 δBsBs ≈ 1.0×1038 P3B2s T2
 = 0.05(Bs1010G)−2(T4.8 yr)−2(P0.105 s)3.

A coherent ephemeris for PSR J18520040 spanning 4.8 yr has an uncertainty on of , corresponding to a detection limit of  G. In comparison, the measured values  s and have fitted uncertainties consistent with these analytic estimates, and imply in the dipole spindown formalism a surface magnetic field strength  G, a spin-down luminosity  erg s, and characteristic age  Myr, all with negligible statistical error.

### 2.2. Flux and Spectral Analysis

In Papers 1 and 2 we presented several observations of PSR J18520040 that were consistent with steady flux and a blackbody spectrum of  keV. The luminosity of erg s corresponded to a blackbody radius of only  km. This is typical result for a CCO, and indicates a concentrated hot spot that remains to be understood. Using the methods described in Paper 1, we now combine all 16 XMM-Newton observations of PSR J18520040 into one spectrum in order to search for deviations from a blackbody that might indicate temperature variations on the surface, or cyclotron lines. EPIC pn and MOS spectra were fitted jointly. The accumulated exposure allows us to fit the spectrum over  keV, an increase in coverage over the  keV range used in the previous papers. While a single blackbody can still be fitted with a temperature of 0.46 keV, the high signal-to-noise ratio and expanded energy range of the summed spectrum reveal systematic deviations from the fit; the reduced for 240 degrees of freedom is unacceptable (see Figure 3 and Table 4). Similar to the results from other CCOs, we find that a fit to two blackbodies is significantly improved (), with temperatures of  keV and  keV, while the corresponding radii  km and  km still cover only a small fraction of the surface. Here we define radius using the phase-averaged luminosity regardless of the unknown emission geometry, which could be, for example, a concentric annulus. Adoption of the two-blackbody fit results in a higher bolometric luminosity than the single blackbody, erg s vs. erg s. We don’t combine the Chandra spectra here for an independent fit because of the increased background and other uncertainties involved in analyzing CC-mode data for this faint source.

Additional spectral models that were explored include the nonmagnetic neutron star hydrogen atmosphere of Zavlin et al. (1996), and a simplified Comptonized blackbody, as described by Halpern et al. (2008) for application to anomalous X-ray pulsars. Each of these models fits nearly as well as the two-blackbody model because they can eliminate the residual excess at high energy that is left by a single blackbody fit (see Figure 4 and Table 4). For the neutron star atmosphere (NSA), we fixed the parameters and  km (corresponding to  km), treating the effective temperature and distance as free parameters. As expected, the fitted temperature is smaller than those of the blackbody models, but the fitted distance of 23.7 kpc is a factor of 3.3 higher than the known value. This indicates that in the atmosphere model only of the surface is emitting. We are not motivated to search for an atmosphere model that fits to the full surface area, as was done for the Cas A CCO by Ho & Heinke (2009), because the larged pulsed fraction of PSR J18520040 clearly requires a small hot spot. The same interpretation attaches to the Comptonized blackbody model, in which the inferred blackbody radius is only  km.

The large intrinsic pulsed fraction, (defined as the fraction of counts above the minimum in the light-curve, corrected for background; see Figure 2) confirms that the emitting area must be small and far from the rotation axis, while the line of sight also makes a large angle to the rotation axis. The pulse shape does not appear to be a function of energy (Figure 5), which also suggests that the emitting area is small. The fitted column density from any model in Table 4 agrees reasonably well with the derived from fits to the SNR spectrum. Sun et al. (2004) find  cm from fitting a variety of equilibrium and non-equilibrium ionization models to ASCA and Chandra spectra of the SNR, while Giacani et al. (2009) find  cm from fitting a non-equilibrium ionization model to the XMM-Newton observations of 2004.

We then searched for any indication of variability by extracting and fitting the spectrum of each individual observation, fixing the spectral parameters (except for the total flux) to those of the summed spectrum. In order to minimize statistical and systematic errors in this comparison, we restricted the fitted energy range to  keV for the individual spectra. The resulting individual fluxes are shown in Figure 6, where they are seen to be constant within errors. The mean  keV flux is erg cm s. The typical uncertainty in each observation is , and the rms dispersion among the 23 observations is .

Unlike the unique case of 1E 1207.45209, there is no evidence for cyclotron absorption lines in the spectrum of PSR J18520040 or in any other CCO. 1E 1207.45209 has strong absorption features at 0.7 and 1.4 keV (Sanwal et al., 2002; Mereghetti et al., 2002) that can be attributed to the cyclotron fundamental energy and its first harmonic in a field of  G (Bignami et al., 2003), according to the relation  keV, where is the gravitational redshift. The spectrum of PSR J18520040 can now be understood in terms of its weaker surface -field. For  G, the cyclotron fundamental and first harmonic are at 0.27 keV and 0.54 keV, below the region accessible to X-ray spectroscopy (Figure 3), especially because of the larger intervening column density to PSR J18520040. The same explanation applied to other well-observed CCOs suggests that they also have weaker surface -fields than 1E 1207.45209.

## 3. Discussion

### 3.1. CCOs as Anti-Magnetars

The steady spin-down of PSR J18520040 is consistent with magnetic braking of an isolated neutron star with a weak magnetic field of  G. In this case, the derived characteristic age of 192 Myr is not meaningful because the pulsar was born spinning at its current period,  s, as was the case for the other CCO pulsars, 1E 1207.45209 and PSR J08214300, which have  s and  s, respectively. A recent population analysis of radio pulsars by Faucher-Giguère & Kaspi (2006) favors such a wide distribution of birth periods (Gaussian centered on  ms,  ms).

A -field of this magnitude could be just the fossil field left by flux conservation during the contraction of the core of the progenitor star, as originally hypothesized for neutron stars by Woltjer (1964). Under this hypothesis, CCOs could simply be those neutron stars in which no additional mechanism of -field amplification has been effective. As stronger fields can be generated by a turbulent dynamo whose strength depends on the rotation rate of the proto-neutron star (Thompson & Duncan, 1993), it is natural that pulsars born spinning slowly would have the weaker -fields. The model of Bonanno et al. (2006) supports this, in particular finding that the -field of a slowly rotating neutron star should be confined to small-scale regions, while a global dipole that would be responsible for spin-down is absent.

PSR J18520040 falls in a region of () parameter space (Figure 7) that is devoid of ordinary (non-recycled) radio pulsars (Manchester et al., 2005). It overlaps with recycled pulsars in this area. The spin parameters of PSR J18520040 are not beyond the empirical or theoretical radio pulsar death lines of Faucher-Giguère & Kaspi (2006) or Chen & Ruderman (1993), respectively. One possible explanation for the absence of radio emission from CCOs is low-level accretion of SN debris for thousands or even millions of years. However, the sample of CCOs is not yet large enough to know if they are intrinsically radio quiet.

Binary pulsars with similar spin parameters as PSR J18520040 are thought to have been partly spun up by accretion. It was also suggested by Deshpande et al. (1995) that most single pulsars in this region are recycled, the birth rate of pulsars with  G being too low in their estimation, perhaps one in  yr. To the contrary, Hartman et al. (1997) concluded that it is not possible to distinguish ordinary pulsars of from recycled ones, and that there is no reason to suppose that any such single pulsar is recycled. The measurements of spin parameters of CCOs certainly increases the inferred birth rate of neutron stars in this weak -field regime, a renewed warning not to assume that isolated radio pulsars with similar spin parameters are recycled. It should be expected that many of the radio pulsars with  G and  s in Figure 7 have characteristic ages that are meaningless, being hundreds of millions of years. They have not moved in the () diagram, and may be former CCOs whose SNRs dissipated only  yr ago. Once the SNR has disappeared and the neutron star has cooled, it is difficult to recognize and classify such an “orphan CCO” using X-rays unless it was first selected as a radio pulsar. Allowing for this observational handicap, CCOs having weak -fields may represent a channel of neutron star birth that is as common as any other.

This outcome is counter in its details to the long debated “injection” hypothesis. Using the “pulsar current” analysis proposed by Phinney & Blandford (1981), Vivekanand & Narayan (1981) and Narayan (1987) suggested that a large fraction of pulsars are injected with  s and (i.e., with large magnetic field), or that neutron stars do not turn on as radio pulsars until their decreases below a critical value of . This would require that they also cool rapidly in order not to be detected as thermal X-ray sources in SNRs. Later investigators (e.g., Lyne et al., 1985; Lorimer et al., 1993) argued that this interpretation suffers from substantial statistical uncertainties and selection effects in pulsar surveys, and that injection of a distinct population of pulsars is not necessary. While previous authors dismissed the possibility of injection of radio pulsars with weak -fields (e.g., Srinivasan et al., 1984), this appears to be exactly the origin of radio-quiet CCOs. The related problem of the missing pulsars in empty-shell SNRs (Gotthelf, 1998) has largely been solved in recent years through a variety of channels, as summarized by Kaspi & Helfand (2002), including the detection of radio-faint pulsars, pulsar wind nebulae in X-rays, and now, pulsations from CCOs.

The spin-down power erg s of PSR J18520040 is an order of magnitude smaller than its observed thermal X-ray luminosity, erg s, which argues that the latter is mostly residual cooling. Remaining questions presented by the X-ray properties of PSR J18520040 and other CCOs are focussed on the details of their X-ray spectra and pulse profiles, which require small heated areas. In the case of PSR J18520040, the spectrum is more complex than a single blackbody. In the two blackbody model, for example, the hotter component, of temperature  keV, has an area of only  km. The canonical open-field-line polar cap has area  km, which is comparable to the area of the hot spot, but polar cap heating by any magnetospheric accelerator must be negligible in this case, being much smaller than the spin-down power. Accretion may cover a wider area and generate more luminosity, but that process is also problematic for PSR J18520040, as discussed below. In the remainder of this section we discuss alternative hypotheses for the weak surface -fields and thermal hot spots of CCOs, involving internal magnetic fields, anisotropic conduction, and accretion of fall-back material. Although these theories have some attractive properties, they are speculative, and none yet offers a self-consistent explanation for all of the observed properties of CCOs.

### 3.2. Localized Heating by Magnetic Field Decay?

While the X-ray luminosity of PSR J18520040, erg s, is consistent with minimum neutron star cooling scenarios (Page et al., 2004, 2007) for the age of Kes 79 (5.4–7.5 kyr, Sun et al., 2004), the high temperatures and small surface areas fitted to the X-ray spectrum are difficult to understand without invoking either localized heating on the surface or strongly anisotropic conduction. We recall that the X-ray spectra and luminosities of CCOs are not very different from those of quiescent magnetars, another recently recognized class, being attributable largely to one or two surface thermal emission components (e.g., Halpern & Gotthelf, 2005). It is difficult to distinguish CCOs from quiescent magnetars without timing data or evidence about variability (Halpern & Gotthelf, 2009). Thus, it is tempting to hypothesize that the same magnetic field decay that is thought to be responsible for localized crustal heating in a magnetar can be operating in CCOs. However, in the case of CCOs, such -fields would need to have the same  G strengths as in magnetars to account for continuous X-ray luminosities of erg s, while having insignificant dipole moments that do not contribute to spin-down. One such configuration would be a small “sunspot” dipole on the rotational equator, to account for the large pulse modulation, while the rest of the star contributes dipole  G in order not to exceed the observed spin-down rate. While we cannot rule out this possibility, it would be remarkable if the magnetic field of a neutron star could be created or evolve into a configuration with such extreme contrast. Also, the conspicuous lack of X-ray variability from CCOs argues against invoking the same magnetic field strength and heating mechanism that is held responsible for magnetars, with their ubiquitous variability.

### 3.3. Anisotropic Conduction?

We next turn to the possibility that magnetic field confined entirely beneath the surface can be responsible for the nonuniformity of surface temperature. While a strong -field is a favored ingredient of models for anisotropic conduction, PSR J18520040 with its exceptionally weak dipole field would seem the least likely candidate for such an explanation. Nevertheless, it is possible that a strong toroidal field can exist under the surface, while only a weak external poloidal field contributes to spin-down. A toroidal field is expected to be the initial configuration generated by differential rotation in the proto-neutron star dynamo (Thompson & Duncan, 1993). The effects on the surface temperature distribution of an internal toroidal field were calculated by Pérez-Azorín et al. (2006), Geppert et al. (2006), and Page et al. (2007). One of the effects of crustal toroidal field is to insulate the magnetic equator from heat conduction, resulting in warm spots at the poles. It was even shown that the warm regions can be of different sizes due to the antisymmetry of the poloidal component of the field, which is reminiscent of the asymmetric opposing thermal regions in the Puppis A CCO (Gotthelf & Halpern, 2009).

In order to explain the large observed pulsed fraction of PSR J18520040, the axis of toroidal magnetic field must make a large angle with respect to the rotation axis of the neutron star. An orthogonal configuration was in fact adopted by Geppert et al. (2006) and Page et al. (2007). Even if the toroidal field component is initially parallel to the rotation axis, a toroidal field will deform the neutron star into a prolate shape, which tends toward orthogonality to the rotation axis as a minimum energy configuration (Braithwaite, 2009). The main problems with this mechanism are 1) anisotropic conduction is unlikely to produce a small hot region on PSR J18520040 that covers only of the surface area of the neutron star, and 2) it doesn’t explain why only one of the orthogonal poles is evidently hot.

Furthermore, to have a significant effect on the heat transport, the crustal toroidal field strength required in these models is  G, many orders of magnitude greater than the poloidal field if the latter is measured by the spin-down. Purely toroidal or poloidal fields are thought to be unstable (Tayler, 1973; Flowers & Ruderman, 1977), although the toroidal field may be stabilized by a poloidal field that is several orders of magnitude smaller (Braithwaite, 2009), so this may be a viable configuration for a CCO. On the other hand, twisting and breaking of the crust by such a large toroidal field is the basis of the magnetar model for soft gamma-ray repeaters and anomalous X-ray pulsars (Thompson et al., 2002), which also have large external dipole fields as measured by their rapid spin-down. In this picture, a CCO is a magnetar-in-waiting, a scenario that Pavlov & Luna (2009) found somewhat contrived, as do we. If any pulsar could be an incipient magnetar, it isn’t explained why CCOs have especially weak surface fields compared to ordinary pulsars.

### 3.4. Submergence of Magnetic Field by Hypercritical Accretion?

For as long as the SN explosion mechanism has been studied, it has been noted that a newly born neutron star may accrete large amounts of fall-back material in the hours to months after the SN. This could be submerge the initial magnetic field into the core (Geppert et al., 1999), and the surface field could be essentially zero if the accreted matter is not highly magnetized in a well-ordered fashion. After the accretion stops, the submerged field will diffuse back to the surface (Muslimov & Page, 1995), but this could take hundreds to millions of years (Geppert et al., 1999). In this picture, the CCOs could be those neutron stars that suffered the most fall-back accretion, while the normal pulsars with ages of a few thousand years must have accreted . In the model of Muslimov & Page (1995) with accretion of , the regrowth of the surface field is largely complete after  yr, so this would probably not explain the weak field of PSR J18520040. But if is accreted, then the diffusion time could be millions of years. Chevalier (1989) calculated that the neutron star in SN 1987A could have accreted of fallback material in the hours after the SN explosion, aided by a reverse shock from the helium layer of the progenitor. If so, it may never emerge as a radio pulsar. A more normal type II SN should accrete or less, which may delay the emergence of the magnetic field for tens of thousands of years, a timescale applicable to explaining the properties of CCOs.

Finally, it should be considered that a thermoelectric instability mechanism driven by the strong temperature gradient in the outer crust (Blandford et al., 1983) could regenerate the magnetic field submerged by accretion. However, the growth of the field via this mechanism could take  yr. CCOs could then be those neutron stars in which the thermoelectric instability is the dominant mechanism of generating magnetic field, perhaps because their initial rotation rates are slow.

The models discussed here have the effect of delaying the emergence of a normal magnetic field for times ranging from a thousand years to essentially forever. They are difficult to test using CCOs, for which it is impossible to measure the braking index, which could indicate field amplification. Furthermore, they don’t help to explain the small, hot surface areas seen in the X-ray spectra of CCOs. In order to achieve such a configuration, the magnetic field would have to be submerged everywhere except for one or two small regions, perhaps the magnetic poles of the neutron star, which could remain hot via conduction from the interior.

### 3.5. Continuing Accretion from a Fall-Back Disk?

We also consider ongoing accretion from a fall-back disk of supernova debris as a possible source of anisotropic surface heating. While variability is an indicator of accretion, we do not have evidence of any variations of PSR J18520040 at the 10% level among 23 observations spanning 4.8 yr, which would tend to eliminate accretion as a significant contributor to its X-ray luminosity. However, although accretion is widely considered to be an inherently unstable process, it is not clear that variability of X-ray binaries or AGNs can be extrapolated to accretion from a fossil disk at rates of only . Therefore, we also explore the possibility of accretion, constrained only by the steady spin-down rate of PSR J18520040, using the theory of propeller and accretion-disk torques.

The spin parameters of PSR J18520040 fall in a regime in which both dipole braking and accretion torques are conceivably significant. In Paper 2, we discussed the implications for of PSR J18520040 accreting and spinning down in the propeller regime, deriving

 ˙P≈2.2×10−16μ8/728˙M3/713(MM⊙)−2/7I−145(P0.105 s)
 ×(1−PPeq)

for the propeller effect. In this model, is the rate of mass expelled, which must be , which is the accretion rate onto the neutron star. We can therefore assume to calculate a lower limit on in the propeller accretion scenario. Assuming efficiency , g s is required. But if we were to adopt , where  G from assuming dipole spin-down, then the observed allows a negligible g s, which contradicts the accretion assumption.

If instead we use the measured as an upper limit on the propeller spindown rate, we can derive an upper limit on the required in the accretion scenario. Under these assumptions, G cm, or  G. However, this would marginally violate the conditions of the propeller model, because for such a small magnetic field, the magnetospheric radius is

 rm = 2.3×107μ4/726˙M−2/713(MM⊙)−1/7= 2.6×107 cm,

which is smaller than the corotation radius

 rco = (GM)1/3(P2π)2/3= 3.7×107 cm,

and the pulsar would be rotating near its equilibrium period. But there has not been enough time in the life of Kes 79 for a weakly accreting pulsar to come into equilibrium. To find PSR J18520040 in an equilibrium state would be a remarkable coincidence because its spin-down timescale,  yr, is orders of magnitude greater than its age. Therefore, it is more natural to conclude that the small of PSR J18520040 is due purely to dipole spin-down, and that it is not accreting. Absence of accretion would also argues against nonuniform surface composition as a cause of the temperature variations. Finally then, none of the possible mechanisms discussed here for hot spots on CCOs is entirely natural and self-consistent.

## 4. Conclusions and Further Work

Measurement of the spin-down rate of the 105 ms PSR J18520040 in Kes 79 was achieved using X-ray observations coordinated between XMM-Newton and Chandra. The resulting phase-connected ephemeris spanning 4.8 yr requires only the first derivatives of the spin frequency, with no measurable timing noise superposed. The straightforward interpretation of this result is dipole spin-down due to a weak surface magnetic field of  G, the smallest measured for any young neutron star. While this is the first measurement of the spin-down rate of a CCO, upper limits on the period derivatives of 1E 1207.45209 and PSR J08214300, as well as spectral features in those two, also indicate weak -fields. The properties of the CCO class were loosely defined in the past, but it is now evident that a weak -field is the physical reason that a large fraction of the neutron stars were so named. The body of evidence supports the “anti-magnetar” model for the origin of such CCOs: neutron stars born spinning “slowly” may as a result be endowed with only weak magnetic fields. PSR J18520040 falls in a region of () space that overlaps with moderately recycled pulsars. Single radio pulsars with similar spin parameters may therefore be former CCOs rather than recycled, and they may be much younger than their characteristic ages. X-ray observations of pulsars in this region may find evidence of their relative youth via surface thermal emission.

Ongoing timing studies of the CCOs 1E 1207.45209 and PSR J08214300 will able to measure their spin-down rates and can refine the correspondence between spectral features interpreted as electron cyclotron lines and surface -field. Those CCOs such as PSR J18520040, with no apparent absorption lines, may simply have weaker -fields than the others by a factor , so that the cyclotron resonance is below the soft X-ray band. As for CCOs that have not yet been seen to pulse, there is no reason to suppose that they are of a different physical class. Rather, their surface temperature distributions and/or viewing geometries may deliver only weak modulation that happens to fall below the sensitivity of existing data, while deeper observations may succeed in discovering their spins. It would be of great interest to discover pulsations from the CCO in Cas A, the youngest known neutron star, which in all respects is the prototype of the CCO class. At an age of 330 yr, it is an order of magnitude younger than the others, while having similar spectral properties (Pavlov & Luna, 2009). In our model, its spin parameters were fixed at birth, and should conform closely to those of the older CCOs. A recent Chandra observation of the Cas A CCO did not detect pulsations (see Appendix), but the High Resolution Camera (HRC) that was employed lacks energy resolution, a capability that may be crucial in the same way that it was for the XMM-Newton discovery of the pulsar in Puppis A (Gotthelf & Halpern, 2009).

A remaining theoretical puzzle about CCOs is the origin of their surface temperature anisotropies, in particular, the one or two warm/hot regions that are smaller than the full neutron star surface. The high signal-to-noise spectrum accumulated from PSR J18520040 reveals similar temperature structure as the other CCOs. The measured spin-down power of PSR J18520040 is too small by an order of magnitude to contribute to these excess emissions. We considered whether accretion of fall-back material can be responsible for this effect, but find it unlikely in the case of PSR J18520040 because of its slow, steady spin-down. If other CCOs are found to have similar spin-down properties, the same arguments would apply to them. Therefore, it is important to measure the spin-down rate of PSR J08214300, the CCO in Puppis A, and investigate further its apparent phase-dependent emission line at 0.8 keV (Gotthelf & Halpern, 2009), which may be indicative of accretion because it is in emission.

The small regions of high surface temperature are properties that CCOs share with magnetars, although most magnetars are hotter and more luminous. The total X-ray luminosities of CCOs are consistent with slow cooling scenarios, and there would be no need to hypothesize a mechanism of magnetic field amplification beyond simple flux freezing if it were not for their strongly anisotropic surface temperature distributions. Paradoxically, the explanations that have been considered for hot spots invoke strong magnetic fields just below the surface, which is exactly the basis of the magnetar model. In this sense, CCOs are potentially magnetars waiting to emerge, or maybe ordinary neutron stars in which the original field was submerged by especially massive fall-back of supernova debris. This is an unsatisfying picture, if only because the contrast between field strength in different regions must be a factor of or larger to affect the surface temperature distribution while maintaining the slow spin-down and allowing soft X-ray cyclotron lines. Resolving this essential mystery of the CCOs will undoubtedly generate new insight into the physics of neutron stars.

We thank Fernando Camilo for supplying Figure 5. This investigation is based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA, and Chandra. The opportunity to propose a large project that included coordinated observations between XMM-Newton and Chandra was crucial for the success of this long-term effort. Financial support was provided by NASA through XMM grant NNX08AX71G and Chandra Awards SAO GO8-9060X, SAO GO9-0058X, and SAO GO9-0080X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060.

## Appendix A Search for X-ray Pulsations from the Cas A CCO

In this Appendix we report on analysis of a recent Chandra observation designed to be the most sensitive yet to search for pulsations from CXOU J232327.9584842, the CCO in Cas A. But first we summarize the results of previous attempts. Murray et al. (2002) searched a 50 ks Chandra HRC observation and identified several candidate periods, but none was confirmed in a follow-up 50 ks observation (Ransom, 2002). Pavlov & Luna (2009) found from a Chandra ACIS observation taken in subarray mode for  s. That mode is limited by its sampling time of  s. ACIS in full-frame mode has a sampling time of 3.2 s, so is only sensitive to periods  s. For the 1 Ms of data taken in this mode (Huang et al., 2004) we searched the range  s and Hz s, corresponding to  yr. The resulting upper limit is at 99% confidence. Existing XMM-Newton data on CXOU J232327.9584842 are also limited in sensitivity and time resolution, and do not cover the full range of periods spanned by known CCO pulsars. Using an effective exposure of 9.2 ks in the EPIC pn taken in full-frame mode, Mereghetti et al. (2002) reported an upper limit of for  s, and for  s. However, these limits may have been underestimated by a factor of (see Pavlov & Luna, 2009). Our own analysis sets limits of for  s and for  s from this observation. Improvements in sensitivity and time resolution could be obtained with a longer XMM-Newton observation using the EPIC pn in SW mode, as was employed for the other CCO pulsars.

Recently, 487 ks of Chandra HRC timing data were obtained over a period of 11 days in 2009 March, of which 433 ks are in the public archive. We searched the public data for pulsations. A total of 11,486 counts were extracted from a circular aperture of radius , of which 6% are estimated to be background. We sampled () parameter space using the test, which is an optimal one for a source in which the light curve, presumed to arise from surface thermal emission, is expected to be weakly modulated and quasi-sinusoidal. We limited the search range to  Hz for  Hz s,  Hz for  Hz s, and  Hz for  Hz s, oversampling by a factor of in each parameter. This range covers the parameters of all the known CCO pulsars and magnetars. The largest values of found were . The theoretical distribution of noise power is exponential with a mean of 2, so the single trial probability that by chance is . Such a value is expected to arise randomly in the independent trials that were performed, so it is not significant. The expectation value of the intrinsic pulsed fraction is , where is the ratio of background to source counts, and is the total number of counts. In this case, a sinusoidal signal of would have a 50% probability of giving . However, taking into account the noise, which may either increase or decrease the total power, the 99% upper limit on the of a true signal in this case is 75 (Groth, 1975; Vaughan et al., 1994), corresponding to . On the other hand, these peak power values are somewhat overestimated because we oversampled Fourier space. Finally, then, we adopt an upper limit of for  ms in Table 1, which is the lowest limit yet obtained for Cas A over the range of periods that is spanned by the known CCO pulsars.

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