1 Introduction

3C 58 is a beautiful example of a filled-center (or plerionic) supernova remnant (SNR), probably associated with the historical supernova event in 1181 A.D. (Stephenson 1971). This object has always received much attention because, on the one hand, it shows some characteristics similar to the Crab SNR, while, on the other hand, it seems very different to the Crab itself. For instance, 3C 58 has a compact ( $10^\prime\times 6^\prime$) elliptical morphology with a very bright core (Reynolds & Aller 1988) and linear size similar to the Crab; Frail & Moffett (1993) have reported a wisp-like elongated structure at $2.6\hbox{$^{\prime\prime}$ }$ from the core, which has been observed also in the Crab and which is probably associated with the pulsar wind termination shock. However, unlike the Crab, there is no clear evidence of a pulsating point source located in the center, as would be expected, since the morphology strongly suggest that the nebula is powered by a spinning neutron star. Despite considerable effort, pulsations have not been detected so far in either radio (see e.g. Lorimer et al. 1998), nor in X-rays (Helfand et al. 1995, H95 hereafter). Moreover, the X-ray to radio flux ratio ( $f_{\rm X}/f_{\rm r}$) of 3C 58 is 100 times lower than that of the Crab (H95), its spectral break occurs at 50 GHz (300 times less than the break of the Crab, Green & Scheuer 1992) and its radio luminosity is increasing instead of decreasing as expected (Green 1987). These remarkable differences are also seen in other plerions, and Woltjer et al. (1997) have proposed the introduction of a new sub-class of plerions, the "non Crab-like plerions", of which 3C 58 can be considered the prototype. For these objects, a non-standard evolution of the pulsar can be invoked, but the details are not yet clear.

It is therefore very important to investigate the physical properties which render 3C 58 so peculiar, in order to put this object and its sub-class in the right perspective. In particular, the detection or non-detection of the central source is obviously a key point. Becker et al. (1982) reported the presence of a compact X-ray source in 3C 58 from their Einstein HRI observation, about 10 $^{\prime\prime}$ in extent, and contributing to 15% of the detected X-ray flux. Later, Helfand et al. (1995) revisited the X-ray emission of 3C 58 using ROSAT HRI data, confirming the compact source and favored a model in terms of hot polar caps to explain the emission. However, it has not been possible so far to take an X-ray spectrum of the source to study it, and to understand if it is really a point source or an enhancement of the pulsar nebula. Torii et al. (2000) have pointed out that the inclusion of a black-body component in the fit of the ASCA GIS+SIS data of 3C 58 yields an improvement of the $\chi ^2$. They claim that the best-fit black-body component is responsible for $\sim$7% of the unabsorbed flux in the 0.5-10 keV of the whole remnant, and that it is the spectral signature of the central source.

It is also very important to assess the presence of a shell around the pulsar nebula, for it may give compelling constraints on the age of the remnant, the shock velocity and the density of the environment. In the case of the $\sim$800 yr old 3C 58 (as other plerions as well), it is expected that the main shock will encounter the stellar ejecta and/or the interstellar medium (ISM) giving rise to a limb brightened shell. However, no sign of a shell has been detected at centimeter wavelengths at distances greater than $5\hbox{$^\prime$ }$ from the core (Reynolds & Aller 1985). However, Reynolds & Aller (1988) have imaged the faint outer emission of the nebula at a distance between 2$^\prime$ and $4\hbox{$^\prime$ }$and have noticed limb brightening at several locations. In this paper, we present a study of the XMM-Newton data of 3C 58 obtained during the Calibration and Performance Verification (Cal/PV) phase of the mission. We show that a stringent upper-limit can be imposed on the presence of thermal emission from a central point source, and we also find evidence for a thermal outer shell. The implications of these findings for current models of 3C 58 are also discussed.