4 Discussion

4.1 Projection model versus other models

Distinctions of the previous physical models for TXC from the projection model are noted below. 1) The model with strong cooling can be used within the frame of the radiative model of SNR; the presented model describes TXCs as SNRs in the adiabatic phase of their evolution. 2) In comparison with the projection model, the spectrum of the central region in the model with thermal conduction is softer due to reducing the temperature (Jones et al. 1998). 3) The models with thermal conduction or evaporation increase the density in the internal part of SNR. The projection model does not require such modification of internal density distribution; the density profiles in this model are similar to those in the Sedov (1959) solution. 4) A small-scale inhomogeneous ISM is required for the model with evaporation. Projected composites are a consequence of large-scale nonuniformity of the ISM with the scale-height of order < $10\ {\rm pc}$. 5) Other possibilities of creating a centrally-filled morphology, such as differential absorption or emission from ejecta, specifically modify the spectra of the object.

4.2 Magnetic field and density gradient orientations in molecular clouds

The projection model of TXCs assumes that an SNR evolves in a nonuniform medium with a different nature of nonuniformity and does not require the presence of a molecular cloud near SNR. However, since TXCs are mainly located near such clouds, we have considered here evolution of SNR at the edge of a cloud, as the most probable case. Magnetic field and ISM density gradient orientations are critical parameters for the proposed model. Therefore, let us find observations which reveal a close alignment between the density gradient and the magnetic field in molecular clouds. This might support the presented model since SNR is most clearly TXC under such an alignment.

Figure 4: a and b. Influence of h on the distribution of thermal X-ray surface brightness ( $\log S^{>0.1\ {\rm keV}}$) a) and spectral index ( $\alpha ^{5\ {\rm keV}}$) b). Curves are labelled with the model codes according to Table 1. Radii are normalized to unity

The observational techniques used to measure the orientation and strength of the magnetic field in molecular clouds are reviewed by Troland (1990) and Crutcher (1994). Zeeman effect observations give information about the strength of magnetic field component $B_{\rm los}$ parallel to the line of sight (Crutcher et al. 1993). To define the orientation of magnetic field component $B_{\rm pos}$ in the plane of the sky, polarization measurements of the radio, infrared and optical line emission are used. Polarization data maps reveal the clouds' magnetic field morphology in the plane of the sky but do not enable us to find the amplitude of $B_{\rm pos}$. Thus, we cannot obtain the actual three-dimensional orientation of the magnetic field from the observations because only one component of B can be measured directly.

It is also difficult to find out the density gradient direction in a cloud, especially in low density regions ($\sim$ $10\div 100\ {\rm cm^{-3}}$) which we are interested in. Column density maps yield a projected 2-D structure of a 3-D cloud. Since the density distribution along the line of sight in a cloud generally remains unknown, we cannot draw conclusions about a three-dimensional direction of the density gradient. Another complication is a mostly filamentary stucture of clouds which prevents us from seeing a large-scale gradient of density.

For our purpose, it is reasonable to look for clouds with $B_{\rm los}\approx 0$ when polarization directions show a morphology of total field B. There are 27 clouds with measurements of the Zeeman effect (Crutcher 1999). Crutcher et al. (1993) have reported 10 sensitive observations without any detections of the Zeeman splitting. Since Zeeman observations are only sensitive to $B_{\rm los},$ the authors assume that the magnetic fields in these clouds lie mostly in the plane of the sky. The cloud positions support this assumption, for looking at 9 of these clouds we are looking nearly perpendicularly at the local spiral arm, where the field is predominantly directed along the arm (Crutcher et al. 1993).

One of the most interesting cases of these observations is the nearby ($\sim$ $140\ {\rm pc}$) Taurus complex for which several polarization analyses have been made. There is additional support for $B_{\rm los}\approx 0$ in it (at least around the TMC-1C core): this is a high aspect ratio of the core flattening along $B_{\rm pos}$ (Troland et al. 1996). Thus, we may assume that the map of polarizations in the Taurus cloud (e.g. Moneti et al. 1984) gives us a large-scale direction of B. Denser regions in Taurus are filamentary in the plane of the sky, as the column density map shows (e.g. Wiseman & Adams 1994), but we expect that a large-scale ($\sim$ $10\ {\rm pc}$) gradient of density in the Taurus cloud should be nearly aligned with the direction of magnetic field. The cloud has a flattened structure which is belived to be the result of the collapse controlled by interstellar magnetic field (Heyer et al. 1987). In such a case, gas tends to collapse along magnetic field lines and this causes the minor axis of the cloud to be parallel to $B\approx B_{\rm pos}$. The direction of the density gradient should be along the minor axis of the collapsed object.

We would like to note that in a situation when we cannot have firm orientations of magnetic field and density gradient from observations, SNR itself may sometimes be considered as a test of these orientations because the radio morphology of SNR depends on the magnetic field and the thermal X-ray morphology - on the interstellar density.

4.3 Barrel-like TXCs

It is obvious that the projection model of TXCs does not require the density gradient to be strictly along the line of sight. When inclination angle $\delta$ changes from $90\hbox{$^\circ$ }$ to $0\hbox{$^\circ$ }$, the thermal X-ray peak moves from the center of the projection to an edge. Therefore, the boundary between SNRs which are either centrally-peaked or limb-brightened in X-rays is not quite clear from the point of view of the proposed model: the both cases are the same shell-like SNRs projected onto the plane of the sky in different ways.

Another interesting fact concerns a more crucial component of the model. The magnetic field component along the line of sight should be maximum among other components to provide a shell-like radio morphology. As it has been noted above, if the magnetic field is oriented primarily in the projection plane, we can observe a barrel-like morphology (Fig. 1). Such a situation suggests looking for remnants which have a barrel-like radio morphology ($\phi$ close to $90\hbox{$^\circ$ }$) coupled with a centrally-brightened thermal X-ray one. Such remnants yield additional support for the projection model of TXCs, since these SNRs are simply another case of the magnetic field orientation.

The list of 17 SNRs which are bilateral in the radio band is presented by Gaensler (1998). Unfortunately, X-ray observations are only known for 6 of them (Green 2000). Three of these 6 SNRs are of a shell-like type, both in radio and X-rays ($\gamma$ Cygni, G156.2+5.7 and SN 1006), two others (G296.5+10.0 and RCW89) have pulsars. Only VRO 42.05.01 is centrally-brightened in thermal X-rays (Burrows & Guo 1994; Guo & Burrows 1997). It, therefore, is a candidate for a "barrel-like TXC". The results of future X-ray observations will show whether there exist more such remnants.

4.4 $\mathsf{\gamma}$-rays from TXCs

Gamma-ray emission from SNRs is important because it allows us to draw conclusions about the cosmic ray acceleration on shocks.

Recent observations of nonthermal X-rays from the SN Tycho (Ammosov et al. 1994), SN 1006 (Koyama et al. 1995), Cas A (Allen et al. 1997), G347.3-0.5 (Koyama et al. 1997), IC 443 (Keohane et al. 1997), G266.2-1.2 (Slane et al. 2001) and TeV $\gamma$-rays from SN 1006 (Tanimori et al. 1998), and G347.3-0.5 (Muraishi et al. 2000) give firm experimental confirmations that Galaxy cosmic rays are accelerated on the shocks of SNRs up to the energies $10^{14}\ {\rm eV}$.

The third EGRET catalog (Hartman et al. 1999) lists 170 unidentified GeV $\gamma$-ray sources. 74 of them are located at $\vert b\vert<10\hbox{$^\circ$ }$ and 22 of these sources coinside with directions towards known SNRs (Romero et al. 1999). 6 SNRs from this list are TXCs (IC 443, MSH 11-61A, W28, W44, 3C 396, G359.1-0.5), 2 are Crab-like (CTB 87, G27.8+0.6) and 4 are of a shell-like type (Puppis A, Vela, G359.0-0.9, $\gamma$-Cygni). It is not clear which morphological class other SNRs belong to, because no X-ray observations of them have been reported (Green 2000).

Different emission mechanisms compete in the analysis of observed $\gamma$-ray spectra. Unfortunately, we still have no direct observational confirmations as to proton acceleration in SNRs. Only $\gamma$-rays from $\pi^{\rm o}$ meson decays created in proton-nucleon interactions allow us to look inside the cosmic ray nuclear component acceleration processes. To make proton origin $\gamma$-rays dominating in an SNR model, we need a high number density of target nuclei ($\sim$ $10^2{-}10^5\ {\rm cm^{-3}}$). Therefore, $\pi^{\rm o}$ decay $\gamma$-rays are expected from SNRs which interact with molecular clouds. The new model for TXCs strongly suggests: the thermal X-ray peak inside the radio shell of SNR testifies that one part of the SNR shock enters a denser medium than other parts of the shell. Thus, the proposed model of TXCs allows us to consider members of this class as prospective sources of $\pi^{\rm o}$ decay $\gamma$-emission.