1 Introduction

PSR J0205+6449, a pulsating X-ray source, was discovered by Murray et al. (2002) in the supernova remnant 3C 58, which is most likely associated with the historical supernova SN 1181. It is thus one of the youngest neutron stars (NSs) observed. Recently, using Chandra observations Slane et al. (2002) inferred an upper limit on the effective surface temperature (redshifted for a distant observer): $T_{\rm s}^\infty < 1.08$ MK. They emphasized that this upper limit for a young NS is low, "suggesting the presence of some exotic cooling contribution in the interior''. In other words, it provides evidence for the powerful direct Urca process (Lattimer et al. 1991) in the NS inner core, or for similar processes of enhanced neutrino emission in pion-condensed, kaon-condensed, or quark core, as reviewed, e.g., by Pethick (1992).

Here we analyze this intriguing possibility in more detail using recent results of the NS cooling theory (Kaminker et al. 2001; Yakovlev et al. 2001b; Kaminker et al. 2002, hereafter KYG; Yakovlev et al. 2002, hereafter YGKP) and taking into account the observational data on thermal emission of other isolated middle-aged NSs.

The observational basis is shown in Figs. 1 and 2. They display the upper limit of  $T_{\rm s}^\infty$for PSR J0205+6449 with the age of SN 1181, and the observational values of  $T_{\rm s}^\infty$for eight middle-aged isolated NSs, the same as in KYG and YGKP. They are: RX J0822-43, 1E 1207-52, and RX J0002+62 (radio-quiet NSs in supernova remnants); Vela, PSR 0656+14, Geminga, and PSR 1055-52 (observed as radiopulsars); and RX J1856-3754 (also a radio-quiet NS). We do not analyze the less likely possibility that the age of J0205+6449 is given by the pulsar dynamical age $\approx$5400 yr, measured by Murray et al. (2002); that case could be easier explained by the cooling theory. The values of $T_{\rm s}^\infty$and t for other sources are the same as in KYG and YGKP, with the only exception of the age of RX J1856-3754, $t=5 \times 10^5$ yr, as revised recently by Walter & Lattimer (2002). Note also a too slow spindown rate of 1E 1207-52 measured by Pavlov et al. (2002) which may cast doubts on the correct determination of the age of this NS.

Figure 1: Observational limits on surface temperatures of nine NSs compared with cooling curves of NSs with several masses. The curves are calculated adopting proton superfluidity 1p and neutron superfluidity 2nt in the NS cores.

Figure 2: Same as in Fig. 1 but for model 3nt of neutron superfluidity instead of 2nt.

Figure 3: Density dependence of the critical temperatures of superfluidity of protons (model 1p) and neutrons (models 2nt and 3nt) in a NS core. Vertical dotted line shows direct Urca threshold, $\rho =\rho _{\rm D}$.