X-RAY VARIABILITY AND EVIDENCE FOR PULSATIONS FROM THE UNIQUE RADIO PULSAR/X-RAY BINARY TRANSITION OBJECT FIRST J102347.6+003841

We used xspec to fit each of several models to all EPIC imaging data sets from both epochs simultaneously. To verify that the data sets were compatible, we also fit different absorbed power laws to the two observations, obtaining compatible spectral indices and normalizations. For the MOS cameras, we restricted photons to the recommended energy range, namely, 0.2–10 keV, and for the PN camera we used the recommended lower limit of 0.13 keV but used the upper limit of 10 keV as there were not enough photons above this to provide any constraint. We grouped the photons to obtain at least 20 counts per spectral bin so as to have approximately Gaussian statistics.

We obtained an adequate fit to all imaging data sets with a power-law model including photoelectric absorption. We did not obtain adequate fits with an absorbed single blackbody (χ² = 1203.7 with 213 degrees of freedom, for a null hypothesis probability of ∼10⁻¹³⁸) or neutron-star atmosphere model (χ² = 1007.1 with 213 degrees of freedom, for a null hypothesis probability of ∼10⁻¹⁰³).

The simple power-law model, with a photon index of 1.26(4), already has a null hypothesis probability of 0.21, which is satisfactory from a statistical point of view. Although the statistics do not call for a thermal component, we may expect one on physical grounds (for example from the surface of the neutron star). We therefore also consider an absorbed neutron-star atmosphere plus power-law model to fit these data, as shown in Figure 1. This model, specified in xspec as phabs(nsa+pow), is based on Zavlin et al. (1996). During fitting we froze the neutron-star mass at 1.4 M_☉ and the radius at 10 km for the purposes of redshift and light bending; the smaller effective thermal emission radius suggests that the emission comes from a small "hot spot" on the surface. In light of the fact that the estimated B < 10⁸ G (Archibald et al. 2009), we also selected a model in which the magnetic field has negligible effects on the atmosphere, i.e., ≲10⁹ G.

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These two models are summarized in Table 1. Uncertainties given are 90% intervals returned by xspec's error command; luminosities are obtained by using the cflux model component to estimate unabsorbed and thermal fluxes in the 0.5–10 keV range and then using an assumed distance of 1.3 kpc to determine a luminosity. "Thermal fraction" is the fraction of this luminosity due to the thermal component of the spectrum, if any.

In both cases, fitting for photoelectric absorption in the model gave a very low upper bound on the neutral hydrogen column density, as noted in Homer et al. (2006). Such a low value is to be expected since the entire Galactic column density in this direction is estimated¹¹ to be only 1.9 × 10²⁰ cm⁻² (based on Kalberla et al. 2005).

Although both models are statistically adequate, the Akaike information criterion (Akaike 1974) suggests one should prefer the model containing a thermal component. The F test gives a null probability of 2 × 10⁻⁵ that the more complex model would produce such a large improvement in fit due to chance if the simple power-law model were correct. While there are concerns with using the F test in such a situation (Protassov et al. 2002, but see also Stewart 2009) it appears that the statistics do somewhat favor a model with a thermal component, although a purely nonthermal model cannot be excluded.

To test for orbital variability, we selected 0.2–12 keV source photons from the imaging-mode data sets in both our observations and those of Homer et al. (2006) and reduced them to the solar system barycenter. When combining data from multiple instruments, to take into account the different orbital coverages and sensitivities, we weighted bin values so that all average count rates match that observed in the MOS1 camera in the same observation. For the hardness ratio analysis, we omitted the PN data so that their different energy response and incomplete orbital coverage would not skew the results.

A weighted histogram of these counts is shown in Figure 2, along with a best-fit sinusoid based on a finely binned profile. We selected four sinusoids as this appears to give a good representation of the curve and a time resolution similar to the histogram. A Kuiper test (Paltani 2004) gives a probability of 1.3 × 10⁻¹⁹ (9.0σ) that photons drawn from a uniform distribution in orbital phase would be this non-uniform; the reduced χ² for a constant fit to the histogram is 11.3, with 11 degrees of freedom. While the evidence for variability is strong, with only ∼3 orbits covered by the two observations it is not certain that this variability is linked to orbital phase, although the fact that the minimum in the X-ray light curve occurs near orbital phase 0.25, when the companion passes closest to our line of sight to the pulsar, suggests a link. To test this, we plotted the photon arrival rates for each orbital period separately. Figure 3 shows that the flux during each individual orbit appears to be lower during phase 0–0.5 than during phase 0.5–1, which suggests that the variability is indeed orbital. Note that Homer et al. (2006) detected variability, but having only limited orbital coverage, could not determine whether it was orbital. We also computed a hardness ratio (Figure 2(b)), dividing the number of photons harder than 1 keV by the number of photons softer than 1 keV and comparing the eclipse versus non-eclipse regions (for this purpose we defined the "eclipse" region to be phases 0–0.5). The reduced χ² for a fit of these values to a constant hardness ratio is 8.76 for 1 degree of freedom, and the probability of such a reduced χ² arising if the hardness ratio were constant is 3.1 × 10⁻³ (2.7σ). Thus, we see marginally significant softening in the eclipse region.

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To test for pulsations, we extracted source and background photons from the PN camera using the energy range 0.25–2.5 keV, selected to give the most significant detection. We barycentered the photon arrival times and used the program tempo¹² and the contemporaneous radio ephemeris given in Archibald et al. (2009) to assign each photon a rotational phase (see Figure 4). We then tested these photons for uniform distribution in phase. The Kuiper test (Paltani 2004) gave a (single-trial) null hypothesis probability of 3.7 × 10⁻⁶ (4.5σ) and the H test (de Jager et al. 1989) gave a (single-trial) null hypothesis probability of 2.4 × 10⁻⁶ (4.6σ), using an optimal number of sinusoids (two). We confirmed that no significant pulsations were detected with the background photons or with an incorrect ephemeris. We also verified that the period predicted by the ephemeris is very close to the period at which the significance peaks (holding all other ephemeris parameters fixed).

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To estimate the degree to which the X-ray flux is modulated at the pulse period, one could simply take the lowest bin in the histogram as the background level and compute the fraction of photons above it; this yields a pulsed fraction of 0.27(9). However, this method is subject to large uncertainties, dependence on binning, and a large statistical upward bias due to the fact that we selected the bin in which signal plus noise is lowest, rather than that in which the (unknown) signal is lowest. To avoid these problems, we define a root-mean-squared pulsed flux by fitting a model F(x) with two sinusoids:

$$\begin{equation*} f_{{\rm RMS}} = \sqrt{\int _0^1 (F(x)-\bar{F})^2 \hbox{\mbox{\it d}}x}, \end{equation*}$$

where $\bar{F}$ is the model mean flux. This is in some sense a degree of modulation; if the signal consists of a constant background plus a variable emission process that drops to zero, this is not directly measuring the fraction of emission due to the variable process. (There is a conversion factor that depends on the exact shape of the pulse profile.) However, this quantity can be computed with substantially less uncertainty and bias. Computationally, we estimate the root-mean-squared amplitude in the Fourier domain, based on the amplitudes of the two complex Fourier coefficients (since higher-order Fourier coefficients are dominated by noise); since noise always contributes a positive power to Fourier coefficients, to reduce the bias we subtract the expected contribution of noise from the squared amplitude of each coefficient before taking the square root. We then convert this pulsed flux value to a pulsed fraction by dividing by the total background-subtracted flux from J1023.

For the energy range 0.25–2.5 keV, we estimate a root-mean-squared pulsed fraction of 0.11(2). In the two subbands 0.25–0.6 keV and 0.6–2.5 keV, we find root-mean-squared pulsed fractions of 0.17(5) and 0.14(3), respectively, with profiles that are broadly similar and in phase. Above 2.5 keV we find no evidence for pulsations, though a 3σ upper limit on the pulsed fraction is only 0.20.

In a review of X-ray emission from millisecond pulsars, Zavlin (2007) describes three primary sources of X-ray emission: emission from an intrabinary shock, emission from the neutron star itself, which is some combination of thermal and magnetospheric emission, and emission from a pulsar wind nebula outside the binary system. As all these mechanisms may be operating in J1023, we next consider their contributions, if any, to the observed X-rays from this system.

4.1.1. Emission from an Intrabinary Shock

J1023 likely has a strong pulsar wind, since the optical data suggest that the companion is being heated by a luminosity of ∼2 L_☉ from the pulsar (Thorstensen & Armstrong 2005). This is much greater than the X-ray luminosity of the system (∼0.03 L_☉), but well below the upper limit (∼80 L_☉) on the spin-down luminosity of the pulsar (Archibald et al. 2009). If material is leaving the companion, either through Roche-lobe overflow or a stellar wind, we should expect an intrabinary shock, where this flow meets the pulsar wind. Such a shock could readily produce power-law X-ray emission (Arons & Tavani 1993). If localized, it could easily account for the orbital modulation we observe in the X-ray emission. If the emission were due to Roche-lobe-overflowing material meeting the pulsar wind we might expect it to be localized at or near L1. Given the system geometry described in Archibald et al. (2009) (a 46° inclination angle, corresponding to a pulsar mass of 1.4 M_☉, and a Roche- lobe-filling companion; see Figure 5), the L1 point itself is eclipsed by the companion for 0.32 of the orbit, centered on orbital phase 0.25. We would expect spectral softening during this period, since the relatively hard power-law emission is blocked but the, presumably softer, emission from the neutron star is not. A larger X-ray-emitting region, due either to material streaming away from the L1 point or to a stellar wind shock, would result in a broader, shallower, and potentially asymmetric dip in the X-ray light curve.

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The possibility of a wind from the companion is interesting, since it is not clear how Roche-lobe overflow would provide the ionized material causing the radio eclipses, which occur well above the orbital plane, roughly centered on the companion's closest approach to our line of sight. Archibald et al. (2009) reported dispersion measure (DM) changes of ∼0.15 pc cm⁻³ above a cutoff frequency of ∼1 GHz at radio eclipse ingress and egress. Assuming that this is the plasma frequency implies an electron density of ∼10¹⁰ cm⁻³; combined with the excess DM measurement, this implies a layer of thickness ∼4 × 10⁷ cm, relatively thin compared to the orbital separation of 1.2 × 10¹¹ cm. This thin sheet of material could in principle arise as the shock front where the pulsar wind meets a wind from the companion, but it is difficult to explain the companion's wind being strong enough to support such a shock: given the line-of-sight geometry of the system, the material causing the radio eclipses must be about as far from the companion as it is from the pulsar. If we assume that the highly relativistic pulsar wind provides the ∼2 L_☉ required by the companion heating models of Thorstensen & Armstrong (2005), it seems difficult to explain how the companion could have a wind of comparable pressure anywhere along the line of sight. Thus, the radio eclipses remain a mystery, and Roche-lobe overflow seems a more likely explanation for the origin of the intrabinary shock.

4.1.2. Emission from the Neutron Star

4.1.3. Emission from a Pulsar Wind Nebula

Nebular emission from pulsars arises when the particle wind driven by the pulsar's magnetospheric activity flows out of the pulsar's immediate neighborhood and meets the surrounding medium; for reviews see Gaensler & Slane (2006) or Kaspi et al. (2006). Pulsars like J1023 whose wind is confined by the ambient interstellar medium exhibit nebular emission that generally takes a cometary form, with an arc-like bow shock preceding the pulsar and a "trail" of ejected material streaming back along the pulsar's track.

The angular size of bow shock emission depends on the pulsar's spin-down luminosity, its proper motion, and the local interstellar medium density. Kargaltsev & Pavlov (2008) give a formula for predicting the "stand-off" angle of the X-ray bow shock from the pulsar:

$$\begin{equation*} \theta = 5\farcs 4\;n_{0.1}^{-1/2}\mu _{19}^{-1}{\dot{E}_{35}}^{1/2}D_{1.3}^{-2}, \end{equation*}$$

where n_0.1 is the mean density of the interstellar medium divided by 0.1 cm⁻³, μ₁₉ is the proper motion divided by 19 mas yr⁻¹, $\dot{E}_{35}$ is the spin-down luminosity divided by 10³⁵ erg s⁻¹, and D_1.3 is the distance to J1023 divided by 1.3 kpc. We have supplied best-guess parameters for J1023 (Archibald et al. 2009), so that absent further information, we might expect a stand-off distance of ∼5'' for the X-ray bow shock. Thus, although nebular emission is not resolved in our XMM-Newton images, higher-resolution images with the Chandra X-ray Observatory, or in the Hα or radio bands, might yet resolve a bow shock.

Kargaltsev & Pavlov (2008) find that the ratio of neutron-star emission to nebular emission generally lies between ∼0.1 and 10, which suggests that nebular emission may produce some of the X-rays we observe. Moreover, Kargaltsev & Pavlov find that nebular emission from bow shocks has a power-law spectrum with photon indices 1 ≲ Γ ≲ 2 (Kargaltsev & Pavlov 2008), consistent with what we observe from J1023, though the latter is somewhat harder than most pulsar wind nebulae. The orbital variability, on the other hand, argues against that component of the emission arising from an extrabinary pulsar wind nebula.

In quiescence, most LMXBs have spectra that are dominated by thermal emission from the neutron star. This emission is typically consistent with a hydrogen atmosphere model with effective radius ∼10 km (Brown et al. 1998). Some LMXBs in quiescence also have a small power-law component of photon index 1 ≲ Γ ≲ 2 in their spectrum (Campana et al. 1998), while a few quiescent LMXBs have spectra completely dominated by this nonthermal component. For example, the quiescent LMXB SAX J1808.4 − 3658 has a spectrum that is a fairly hard power law with no detectable thermal emission (Heinke et al. 2009). J1023 resembles this latter category, although if a thermal component is present its effective radius appears to be substantially less than 10 km and the power-law spectral index is fairly hard. On the other hand, J1023's radio and possible X-ray pulsations distinguish it from all known quiescent LMXBs.

SAX J1808.4 − 3658 is of particular interest because it is the prototype and best-studied example of a class of LMXBs from which millisecond X-ray pulsations have been detected during active phases. Many authors have suggested that SAX J1808.4 − 3658 should turn on as a radio pulsar during quiescence (e.g., Wijnands & van der Klis 1998; Chakrabarty & Morgan 1998; Campana et al. 2004), but no radio pulsations have been detected in spite of thorough searches (e.g., Burgay et al. 2003; Iacolina et al. 2009). The non-detection of radio pulsations could be because SAX J1808.4 − 3658 is shrouded by previously ejected ionized material or it could simply be an issue of unfortunate beaming. In any case, it is natural to compare SAX J1808.4 − 3658 to J1023.

During its active phases, SAX J1808.4 − 3658 reaches a sustained luminosity of ∼4 × 10³⁶ erg s⁻¹ (Galloway & Cumming 2006), in sharp contrast to the upper limit of 2 × 10³⁴ erg s⁻¹, available for J1023 during its disk phase (Archibald et al. 2009). In its quiescent state, SAX J1808.4 − 3658 shows X-ray emission dominated by a hard power law (Γ = 1.74(11)), with a small (≲0.1) fraction of thermal emission, and a total X-ray luminosity of 7.9(7) × 10³¹ erg s⁻¹ (Heinke et al. 2009). This is somewhat similar to what we observe in J1023, which has a total luminosity of 9.9(5) × 10³¹ erg s⁻¹, although the spectral index of 1.26(4) is somewhat harder than that seen from SAX J1808.4 − 3658. If J1023 has a thermal component, its power law is substantially harder, with a spectral index of 0.99(11). The thermal component would have an effective radius of 0.7^+0.5_−0.1 km and supply 0.06(2) of the total luminosity. While the spectral index seen in J1023 is harder than that seen from SAX J1808.4 − 3658, it is in line with the hard spectral indices seen from other X-ray-detected radio millisecond pulsars (for example, 47 Tuc W, though PSR J1740-530 is softer; see below). Since SAX J1808.4 − 3658 is known to cool quickly, even thermal X-ray pulsations in quiescence would be evidence of magnetospheric activity heating its polar caps. Campana et al. (2002) searched for such X-ray pulsations from SAX J1808.4 − 3658 in quiescence, but were unable to conduct meaningful searches due to its faintness; SAX J1808.4 − 3658 is roughly 3.5 kpc away (Galloway & Cumming 2006) compared to the roughly 1.3 kpc we assume for J1023 (Archibald et al. 2009).

The similarity of the X-ray properties of SAX J1808.4 − 3658 in quiescence to those of J1023 suggests that SAX J1808.4 − 3658 may indeed harbor a radio millisecond pulsar in quiescence; conversely, the same similarity suggests that J1023 may undergo episodes of active accretion.

Among radio pulsars, the two best-studied examples which closely resemble J1023 are 47 Tuc W (Bogdanov et al. 2005) and PSR J1740 − 5430 (D'Amico et al. 2001). Both pulsars exhibit large, variable radio-frequency eclipses and both are thought to have somewhat massive unevolved companions (≳0.13 M_☉ and 0.19–0.8 M_☉, respectively). For comparison, J1023's companion is thought to be ∼0.2 M_☉ and shows a spectrum characteristic of a main-sequence star (Archibald et al. 2009; Thorstensen & Armstrong 2005). The radio eclipses are in all three cases evidence for material leaving the companion and presumably being expelled from the system, and in all three cases the companion appears to fill and perhaps overflow its Roche lobe (Bogdanov et al. 2005; Ferraro et al. 2001; Thorstensen & Armstrong 2005).

Bogdanov et al. (2005) studied 47 Tuc W and found an X-ray spectrum consisting of a dominant hard power law (Γ = 1.14(35), contributing ∼75% of the total flux) plus a thermal component. They also observed orbital variability, and in particular a substantial X-ray eclipse spanning phases¹³ 0.15–0.45 and centered slightly ahead of the optical minimum, at phase 0.2. This is accompanied by substantial softening of the X-ray spectrum during eclipse. Given these observations, Bogdanov et al. suggest that the power-law X-ray emission originates from a shocked region where material overflowing from the companion of 47 Tuc W meets the pulsar wind and is blown out of the system. Bogdanov et al. (2010) studied Chandra X-ray Observatory observations of PSR J1740 − 5430. Although limited by the scarcity of photons, they found a spectrum consistent with a power law of index Γ = 1.73(8) or with a somewhat harder power law plus a blackbody component. Their estimates of variability were limited by restricted orbital coverage as well as by a paucity of photons, but they found marginal evidence for orbital modulation, in particular a possible decrease in luminosity during the radio eclipses, possibly accompanied by a softening. Our observations of J1023 are more photon starved than those of Bogdanov et al. (2005) of 47 Tuc W, but we do see evidence for eclipses, and possibly for softening during eclipses. In the case of J1023, the possibility of overflowing gas is supported by the recent disk phase.

The similarity of the observational properties of these three millisecond pulsars suggests that their companions are all overflowing their Roche lobes, so that mass flows through the L1 point, where it encounters the pulsar wind and is swept away. On the other hand, the similarity also suggests the possibility that like J1023, 47 Tuc W or PSR J1740 − 5430 may undergo episodes in which the mass transfer rate from the companion increases and an accretion disc forms. Such episodes would presumably be signaled by optical changes, possibly by extinction of the radio pulsations, and presumably by modest X-ray brightening. All together, these observations suggest that as a system reaches the end of its life as an LMXB, its accretion rate drops and the millisecond pulsar becomes active. After this point, the wind from the pulsar generally prevents mass leaving the companion from forming an accretion disk or entering the pulsar magnetosphere. Temporary increases in the mass accretion rate may allow the occasional suppression of the wind and formation of an accretion disk, as was observed in J1023 in 2001.