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Astron. Astrophys. 331, 821-828 (1998)

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3. Discussion and conclusions

We have shown that the X-ray spectra of the isolated NS 1E1207.4-5209  in the center of the SNR PKS 1209-52 observed with the ROSAT PSPC and HRI and ASCA SIS0, GIS2 and GIS3 can be interpreted as thermal radiation from the hydrogen-covered, uniformly heated surface of the NS. The proposed interpretation resolves all the inconsistencies which follow from the BB interpretation of radiation of this object.

First, the range of distances, [FORMULA]  kpc, inferred for the standard NS mass [FORMULA] and radius [FORMULA]  km, is within the (conservative) limits, 1.1-3.9 kpc, obtained from radio observations of the SNR. This range shifts to lower distances with decreasing R and M: e.g., [FORMULA]  kpc for [FORMULA], [FORMULA]  km. Thus, the assumption about hot spots on the NS surface, which is difficult to reconcile with the lack of pulsar activity in 1E1207.4-5209, is superfluous in our model.

Second, the effective temperature [FORMULA]  K ([FORMULA]  K), obtained from the fits with our hydrogen atmosphere models, matches well with a number of NS cooling models (see Fig. 5 and discussion below). On the contrary, it is difficult to reconcile the results of the BB interpretation with models of the NS cooling.

[FIGURE] Fig. 5. Comparison of the surface temperatures inferred from the BB (empty boxes) and hydrogen atmosphere (hatched boxes) fits of the spectra of 1E1207.4-5209 and the Vela pulsar with NS cooling curves for three EOS of the NS matter, two NS compositions, and different models for additional frictional heating. The cooling curves are taken from Van Riper et al. (1995), where more detailed explanations can be found.

Third, the inferred hydrogen column density towards the 1E1207.4-5209, [FORMULA] and 0.5-1.5 for high and low surface magnetic fields, respectively, agrees well with [FORMULA] obtained from fitting the spectra of the SNR shell. These estimates are consistent with the [FORMULA] values obtained by Kellett et al. (1987) from the EXOSAT observations of PKS 1209-52. Moreover, measurements of [FORMULA] from UV observations of several stars in the vicinity of 1E1207.4-5209 ([FORMULA], [FORMULA]) yield hydrogen column values in virtually the same range (Fruscione et al. 1994):  [FORMULA] for HD112244 ([FORMULA], [FORMULA], [FORMULA]  kpc), [FORMULA] for HD115842 ([FORMULA], [FORMULA], [FORMULA]  kpc) and HD111822 ([FORMULA], [FORMULA], [FORMULA]  kpc). On the contrary, the BB fit gives [FORMULA], clearly incompatible with all the other independent estimates.

The fact that 1E1207.4-5209 shows no pulsar activity can be explained, in addition to the trivial explanation of unfavorable orientation of its magnetic and rotational axes, by slow rotation or/and low magnetic field of the NS, so that it falls below the "death line" on the P - [FORMULA] diagram, [FORMULA]  s-3. For the simplest model of the magnetic dipole radiator, the pulsar period increases with time t as [FORMULA], where [FORMULA]  s, [FORMULA]  g cm2 is the moment of inertia of the NS and [FORMULA]. The condition that the NS is below the death line can be written as [FORMULA]  s-3, or [FORMULA]  s. Hence, if B is in the range of strong magnetic fields allowed by our fits, [FORMULA], we may expect that the NS rotates slowly, [FORMULA]  s. If faster pulsations are discovered in future X-ray observations of 1E1207.4-5209, it would indicate that B is in the other range compatible with our fits: [FORMULA]  G. It is worth noting that if the NS was born as a pulsar at an appreciable distance from the death line, only an enormous magnetic field, [FORMULA]  G at standard NS parameters, could decelerate its rotation so that the pulsar would "die" at the relatively young age, [FORMULA]  yr. Hence, discovery of slow pulsations would mean that the NS was born slowly rotating unless its magnetic field is superstrong.

Since we have estimated the effective temperature of the NS, it is interesting to compare it with what is predicted by various cooling models. Fig. 5 shows examples of NS cooling curves from Van Riper et al. (1995) for three equations of state (EOS), stiff (Pandharipande-Smith [PS]), intermediate (Friedman-Pandharipande [FP]) and soft (Baym-Pethick-Sutherland [BPS]), and two interior compositions resulting in slow and fast cooling (solid and dashed lines, respectively). Cooling curves without additional heating are depicted by thick lines, whereas thin lines show cooling curves for two models, proposed by Epstein & Baym (EB) and Alpar, Cheng & Pines (ACP), for pinning of the superfluid vortices to the crust lattice (see Van Riper et al. 1995 for references and detailed explanations). They correspond to strong and weak frictional heating associated with the dissipation of energy of differential rotation between the NS crust and superfluid interior (only the EB model is available for the BPS EOS). In the same picture we plot boxes corresponding to the inferred atmosphere and BB temperatures of 1E1207.4-5209, assuming its age in the range [FORMULA]  yr, and similar boxes for the Vela pulsar whose X-ray radiation was investigated in terms of the hydrogen atmosphere models by Page et al. (1996). We adopted [FORMULA]  yr for the Vela age, between the conventional characteristic age [FORMULA] and an upper limit estimated by Lyne et al. (1996). We see that the BB temperature of 1E1207.4-5209 is well above the values predicted by all these cooling models, whereas the BB temperature of the Vela pulsar is compatible only with the standard (slow) cooling model supplemented by strong heating for the stiff EOS. The effective temperature of 1E1207.4-5209 obtained with the atmosphere fits is compatible, given the poorly known age, with the slow cooling models for all the three EOS, at moderate or no heating. For the stiff EOS, it is also compatible with the fast (quark) cooling accompanied by strong frictional heating. However, the large NS radius for this EOS would mean a distance [FORMULA]  kpc (cf. Fig. 4), uncomfortably large in comparison with conventional estimates. The same cooling curve (fast cooling with the EB heating for the stiff EOS) is the only one which goes through both the 1E1207.4-5209 and Vela pulsar boxes obtained from the atmosphere fits. This, however, does not necessarily mean that slow cooling models or other EOS or other heating rates are excluded. First, the ROSAT PSPC spectrum of the Vela pulsar, used in both BB and atmosphere fits, was not observed directly because the pulsar was not resolved from a surrounding mini-nebula of [FORMULA] diameter, which makes the results of the spectral fits less certain. Second, one cannot exclude, in principle, that the NS of the Vela pulsar differs from 1E1207.4-5209 (e.g., the mass of the former may be greater, that could lead to an "exotic" interior composition associated with an enhanced neutrino luminosity and accelerated cooling). Finally, there exist many more cooling models than shown in Fig. 5, and some of them may satisfy both the 1E1207.4-5209 and Vela pulsar temperatures. For instance, a strong neutrino emission induced by the nucleon Cooper pair formation process (see Page 1997, and references therein), which was neglected in most of the previous NS cooling models, may result in great variety of cooling curves, depending on the (unknown) parameters of the nucleon pairing (Yakovlev 1997, private communication). For a more detailed comparison of the inferred temperatures with the cooling models, it would be very important to evaluate more accurately the distance to PKS 1209-52 (which would constrain the NS radius and hence the EOS) and the age of this object.

There exist a number of other radio silent isolated NS candidates whose observational manifestations are similar to those of 1E1207.4-5209. The most convincing example is 1E/RXJ0820-4247 in the SNR Puppis A, whose BB temperature, [FORMULA]  K, and radius, [FORMULA]  km (Petre et al. 1996), virtually coincide with those of 1E1207.4-5209. Another example with similar properties is RXJ0002+6246 in the SNR G117.7+0.6 (Hailey & Craig 1995), whose identification is, however, less certain because of its faintness (likely, due to a larger distance and greater [FORMULA]). We expect that applying the NS atmosphere models to the analysis of such objects will allow us to evaluate their radii and effective temperatures, and to constrain their magnetic fields.

One more radio-silent NS candidate, 1E1613-5055 in the center of the SNR RCW 103 (Tuohy & Garmire 1980), appears as a different kind of object - the BB fit of its spectrum yields a considerably higher temperature, [FORMULA]  K, at a few times smaller radius of the emitting region (Gotthelf et al. 1997). However, this object is deeply immersed in the remnant diffuse emission so that it is hard to separate its spectrum from that of the SNR, with the limited spatial resolution of ASCA. We expect that the forthcoming AXAF and XMM missions would resolve the point source and provide a spectrum suitable for the detailed analysis.

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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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