Astron. Astrophys. 336, 545-552 (1998)

3. Discussion

The detection of pulsed X-ray emission from PSR J0218+4232 makes this the fourth ms-pulsar for which modulation at the pulse-period is observed. Of the three other ms-pulsars showing spin-modulated X-ray emission, namely PSR J0437-4715 (Becker & Trümper 1993; Halpern et al. 1996; Kawai et al. 1998), PSR B1821+24 (Danner et al. 1994, 1997; Saito et al. 1997; Rots et al. 1998; Becker & Trümper 1997) and PSR J2124-3358 (Becker & Trümper 1997), only PSR B1821-24 shows narrow pulses in its lightcurve similar to PSR J0218+4232. The other two ms-pulsars, PSR J0437-4715 and PSR J2124-3358, show both broad and smooth X-ray lightcurves. In addition, the latter have luminosities in the ROSAT 0.1-2.4 keV band about 3 orders of magnitude lower than the first two. Therefore we concentrate in the remainder of the discussion on the comparison of PSR J0218+4232 with PSR B1821-24, which have the smallest characteristic ages (), by 1-2 orders of magnitude, of the ms-pulsars detected at X-rays sofar.

PSR B1821-24 has been studied in detail by Saito et al. (1997) using ASCA data. They showed that the narrow ( 100µs) first pulse after subtraction of the DC-component has a very hard spectrum (photon index -1.2 between 0.7 and 10 keV), which has to be of magnetospheric origin. Interestingly, the phase separation or alternatively 0.556 (Rots et al. 1998) between the two pulses of PSR B1821-24 is very similar to the measured by us for PSR J0218+4232. In addition, the first pulse in the lightcurve of Figs. 4 and 5 can be intrinsically be narrower than 1 bin, which is also 100µs. Unfortunately, we cannot derive spectra from our ROSAT HRI observation, but the narrow pulses detected from PSR J0218+4232 make us belief that these are also of magnetospheric origin. The origin of the substantial unpulsed component (see Fig. 4) is less obvious. This could be thermal emission from the neutron star surface as well as of magnetospheric origin. However, this unpulsed component can also be assigned to extended emission from e.g. a compact nebula, as is shown in Sect. 2.4. This will be discussed below.

Most striking are the differences in the shapes of the radio pulses of the two ms-pulsars. Backer & Sallmen (1997) show for PSR B1821-24 two narrow pulses and one broader radio pulse (at 800 and 1395 MHz), very different from the extremely broad radio pulse of PSR J0218+4232 detected throughout the pulsar period (Fig. 7). As mentioned in the introduction, the broad radio-pulse from PSR J0218+4232 was explained with the geometry of an aligned rotator (Navarro et al. 1995), but the two narrow peaks with the indication of bridge emission between them as seen in the X-ray lightcurve (see Figs. 4,5), require at least a small angle between the magnetic - and rotation axis. Namely: Such double-peaked pulses with bridge emission are currently explained by models in which the high-energy emission is seen from one magnetic pole. In polar cap models (most recently: Sturner et al. 1995; Daugherty & Harding 1996) the non-thermal beam is a hollow cone centered on the magnetic pole. In outer gap models (most recently Romani 1996) the emission occurs in a wide fan beam that is formed by the surface of the last open field line in the outer magnetosphere. For both models a double-peaked pulse can only be observed when the rotator is not completely aligned and the edge of the cone is visible to the observer twice per rotation. Unfortunately, we cannot compare the radio and X-ray profiles of PSR J0218+4232 in absolute timing, nor is it possible to identify a common pulse for tentative more detailed discussions like has been done for PSR B1821-24 by Backer & Sallmen (1997). Saito et al. (1997) compared the physical parameters of PSR B1821-24 with those of the Crab pulsar to understand the production of hard emission in the magnetosphere of a ms-pulsar for which the magnetic field strength is orders of magnitude weaker than for normal rotational pulsars. They pointed out that in the magnetosphere near the light-cylinder radius (), the radius at which the magnetosphere, if corotating with the neutron star, will have a speed equal to the speed of light, the magnetic field strength ( with and the averaged magnetic field strength at the neutron star surface and the neutron star radius respectively) comes out to be very close to that for the Crab. In addition, of ms-pulsars is 1-2 orders of magnitude smaller than those of the young normal pulsars, increasing strongly the curvature of the magnetic field lines which enhances the production of non-thermal emission (see Ho 1989). With our firm detection of pulsed emission from PSR J0218+4232 with a lightcurve similar to those of the Crab pulsar and the isolated ms-pulsar PSR B1821-24 it is interesting to compare now the physical parameters of the two ms-pulsars in more detail (see Table 1). They have very similar periods, PSR J0218+4232 rotating a bit faster, but PSR B1821-24 is 15 times younger, has a rotational energy loss 9 times higher and a surface magnetic field strength 5 times stronger. This suggests that the X-ray luminosity of PSR B1821-24 will be higher, as is indeed the case. The pulsed X-ray luminosities in the ROSAT band (0.1-2.4 keV) differ at most a factor of , proportional to the difference in , but the total X-ray luminosities differ at most by a factor of 4.

Fig. 7. Radio-profile at 410 MHz of PSR J0218+4232 as shown in Navarro et al. (1995). The pulse shape is broad and complex. Notice that there is no flat baseline to the profile at any phase. The pulsed fraction is about 50%.

Table 1. Parameter comparison between PSR J0218+4232 and PSR B1821-24 (from Navarro et al. 1995, Saito et al. 1997 and this work)
Notes:
X-ray luminosity given by Danner et al. (1997)
X-ray luminosity given by Becker & Trümper (1997)
400 MHz radio luminosity given by Foster et al. (1991) multiplied by
Rees & Cudworth (1991)
The magnetic field strength at the surface calculated by us is a factor of 2 lower than the value given by Saito et al. (1997). The difference can be traced back to the use of a factor of by Saito et al. in the formula relating the magnetic dipole moment to and . Our factor of 1 is consistent with that widely used in the pulsar community (e.g. Taylor et al. 1993, Becker & Trümper 1997, Navarro et al. 1995).

The derived total radio luminosity of PSR J0218+4232 is about a factor of three higher, while the luminosities of the pulsed radio components are, within the uncertainties on the distance estimates, about the same. It is interesting to note that the magnetic field strength at the light-cylinder of PSR J0218+4232 is only a factor of smaller than that of PSR B1821-24 due to its smaller ( 110 km vs 146 km). More remarkably, of PSR J0218+4232 is only a factor of smaller than of the Crab pulsar, while differs in this case more than 4 orders of magnitude (see also Saito et al. 1997).

The main difference in characteristics is the remarkably large fraction of unpulsed emission of 60% in X-rays (see Fig. 4) and 50% in radio (see Fig.7; systematically over the range 400-1400 MHz, Navarro et al. 1995) for PSR J0218+4232. We showed above that this X-ray emission might be extended with angular scale of . Navarro et al. (1995) noted that it is possible that the observed unpulsed emission in the radio comes from a compact nebula close to the pulsar. This nebula would then have the same steep spectral index as the pulsed emission and the nebula would have to be smaller than the VLA beam size of . The latter constraint is consistent with the possible extent found here in X-rays. Navarro et al. (1995) preferred the explanation for which the unpulsed emission comes from the pulsar, however, given our results above, we prefer now the explanation that the unpulsed X-ray and radio emissions are both manifestations of a compact nebula around the pulsar.

Danner et al. (1997) report the detection of an extended source next to PSR B1821-24. The shape of this source is "identical" to the distribution shown in Fig. 1, with the same angular extent. Since the estimated distances are comparable, even the absolute extent is similar, 0.4 pc. The main difference is that Danner et al. (1997) determine a separation between the pulsar and the extended source of . PSR B1821-24 is located near the edge of the globular cluster M28. Since the extended source appeared to be only slightly offset from the centre of the cluster, Danner et al. (1997) preferred an interpretation as a collection of low-luminosity accreting X-ray binaries in the cluster, over the interpretation as a synchrotron nebula. They considered the synchrotron nebula to be powered by a recent (of the order of 200 years ago) outburst of an unknown source, inconsistent with the pulsar age. However, if the pulsar is powering the nebula it is doing this continuously and no outburst is required. Therefore the interpretation as a synchrotron nebula remains a viable option. The binary ms-pulsar PSR J0218+4232 is not located in a globular cluster. Of the two options mentioned above only the interpretation as a synchrotron nebula remains. Kawai & Tamura (1997) searched for diffuse sources in the vicinity of normal radio pulsars using ASCA X-ray data. They found such sources with high probability for many pulsars, leading to the suggestion that they exist universally for all the active pulsars, and that they are powered by the pulsars. The extended sources near PSR B1821-24 and PSR J0218+4232 add two more candidates, now concerning recycled ms-pulsars.

Wei et al. (1996) discuss the production processes of pulsed and unpulsed gamma-ray emission in ms-pulsars using the outer gap model. They assume that the unpulsed gamma-rays come from a compact region, a couple of light cylinder radii from the pulsar rather than from an extended nebula. This unpulsed non-thermal emission (up to TeV energies) is produced in the interaction of the primary electrons/positrons from one gap interacting with the low-energy photons from another gap, which one expects to cross over just beyond the light cylinder. If we assume that the unpulsed X-ray emission measured from PSR J0218+4232 is the low-energy end of the spectrum of this component, rather than from a small nebula, then one would expect the signature of a point source in our maps. This seems not to be the case. Furthermore, the observed and derived parameters of PSR J0218+4232 and PSR B1821-24 are very consistent. Therefore it is unlikely that the first can produce such a strong unpulsed point-like X-ray component at the pulsar position while there is no evidence for such a component for the second.

Wei et al. (1996) produced pulsed and unpulsed spectra showing that at high-energy gamma-rays the unpulsed component becomes particularly important. In our earlier paper (Verbunt et al. 1996) we noted that the EGRET source 2EG J0220+4228 (Thompson et al. 1995) can be the counterpart of PSR J0218+4232, and we found indications for variation at the pulse period, however, consistent with being pulsed. In fact, also PSR B1821-24 is located close to a possible EGRET source (Fierro 1995), but the identification is less certain, since PSR B1821-24 is just outside the location confidence contour.

At high-energy -rays progress can be expected from our scheduled 3 weeks CGRO EGRET exposure in summer 1998 aimed at confirming our indications for pulsed emission above 100 MeV from PSR J0218+4232.

As mentioned above, due to the lack of spectral resolving power of the ROSAT HRI we can not perform a spectral analysis for PSR J0218+4232. Spectral information on the pulsed and DC components can only be obtained by long exposures using ASCA, SAX LECS/MECS and the future AXAF and XMM X-ray observatories.

© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998
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