4. The dynamics of Cas A
4.1. The discrepancy between the X-ray and radio measurements
Our measurement of the expansion age of Cas A is significantly shorter than the expansion age derived from proper motion measurements of compact radio features, although we should, as pointed out, beware of biases caused by the different morphologies of the radio and X-ray image. As put forward in the introduction, the advantage of an X-ray determination of the expansion rate over a measurement based on the compact radio features is that the bulk of the mass radiates in X-rays, whereas the compact radio features are associated with the magnetic fields and relativistic electrons. This does, however, not mean that we can easily discard the radio data for that reason, as the compact radio features, some of which show remarkable resemblance to bow shocks, can be comprehensively described as ejecta with a higher than average density and moving supersonically through diffuse X-ray emitting gas (Anderson et al. 1994, AR95). This means that it is expected that the diffuse gas is moving more slowly than these compact features. Clearly, our measurement is at odds with this interpretation. However, the kinematics of the Western region in the radio band do display phenomena that are not easily explained by a simple dynamical model. For instance, the compact radio features in the Western region show large deviations from a radially outward motion. Some features even display an inward motion (Anderson et al. 1994). Such deviations do bias the expansion rate of the radio features towards a longer timescale, but at the moment we lack a clear understanding of this phenomenon. Another peculiarity which is hard to understand from the point of view of the overall dynamics of Cas A is a small but significant net acceleration of the radio features towards the North. So our understanding of the compact radio features is still incomplete. The discrepancy between our expansion rate and the expansion rate based on the compact radio features certainly deserves serious future attention. We therefore concentrate on the implications of the shorter expansion timescale for the dynamics of Cas A derived from the analysis presented here.
4.2. The reverse-shock model
The explosion leading to Cas A probably took place in 1680, that is if one assumes that the 6th magnitude star observed by Flamsteed was indeed the supernova (Ashworth 1980). Although there are some problems with this identification, this explosion date is supported by the kinematics of the subset of fast moving optical knots which are probably least decelerated (Fesen et al. 1987). So we assume that in 1996, the year of the last RHRI observation of Cas A, the remnant was 316 yr old. Combining this with our overall expansion timescale of 501 yr we arrive at a deceleration parameter of (the ratio of the true age over the expansion age). The deceleration parameter equals the ratio of the current velocity over the average velocity. To put this value in a simple theoretical framework we refer to the self-similar hydrodynamical model of Chevalier (1982). The Chevalier model includes a blast-wave and a reverse-shock. The model assumes that the density profile of the unshocked gas is distributed as for the ejecta component and for the circumstellar medium with n and s as free parameters. Optical spectroscopy (Chevalier & Kirshner 1978, 1979) indicates that Cas A is expanding into the wind of its progenitor, which implies . For type II supernovae the density distribution of ejecta is probably rather steep, , but for more compact stars, such as the Wolf-Rayet star that was the progenitor of Cas A, the density distribution may be less steep.
The radius of the contact discontinuity between ejecta and circumstellar matter evolves in the Chevalier model as . The case corresponds to the Sedov (1959) evolution and does not correspond to any physical solution. The deceleration parameter for the Chevalier model is . So for and the observed value of we need which is very close to the Sedov solution. However, if taken literally it would mean that Cas A is blast-wave instead of reverse-shock dominated as generally believed. One can of course assume that is a reasonable but not quite good representation of the structure of the circumstellar medium around the progenitor. For example, gives , which gives a valid Chevalier model, but lacks the conceptual simplicity of a model. Another assumption of the Chevalier model that may not be valid is the power law density distribution of the ejecta. Only the outer layers of ejecta are thought to have a distribution well represented by a power law. If, however, a substantial fraction of the ejecta has already been shocked, then the evolution of Cas A has entered a phase for which the Chevalier model is not applicable anymore. The fact that for we arrive at a solution close to the Sedov model may indeed indicate that Cas A is in a transition phase from a reverse-shock dominated to a blast-wave dominated (Sedov) phase. A model in which most of the ejecta have already been shocked is in agreement with the mass ratio of the swept up and ejected mass proposed by Vink et al. (1996). Note that also the X-ray spectrum of Cas A cannot be well described by a Chevalier model because the model implies a much larger ratio between the reverse-shock and blast-wave temperatures than observed (Jansen et al. 1988, Vink et al. 1996). A Chevalier model provides a better fit to the X-ray spectrum, but has the drawback that we know that Cas A is moving through the wind of its progenitor.
Apart from the ejecta density distribution the circumstellar medium may also be more complicated than assumed by the Chevalier models. Indeed, two recent numerical models indicate that the the circumstellar medium may include a dense shell of material originating in the red supergiant phase of the progenitor and swept up by the fast wind of the Wolf-Rayet star (García-Segura et al. 1996 and Borkowski et al. 1996). The study by Borkowski et al. (1996) was made in order to reproduce the expansion rate of Cas A as observed in the radio (AR95) which, however, may not be the correct value as this study indicates. The possible existence and position of such a shell (it may also reside outside the current blast-wave) can provide valuable information about the detailed history and properties of the progenitor, as shown by García-Segura et al. (1996). However, the numerical models are too specific to see how our result would change their conclusions.
4.3. An encounter with a molecular cloud?
Both numerical models do not pay attention to inhomogeneities that may have led to a possible slower expansion of the Western region or to the differences in expansion velocities of the optical knots between the front and the back of the remnant (Reed et al. 1995). An explosion in an off-center bubble is a possibility (Reed et al. 1995). The asymmetry of the bubble may be caused by existing inhomogeneities in the interstellar medium. Another interesting and possibly related suggestion (Keohane et al. 1996, AR95) is that in the West Cas A is interacting with a molecular cloud seen in OH absorption towards Cas A (Bieging & Crutcher 1986). This is the same cloud that is probably responsible for the relative hardness of the Western region seen in Fig. 2. In the case of an interaction with a molecular cloud it is expected that the Western region would be relatively bright. This is in fact the case when the X-ray emission is corrected for the absorption towards Cas A (Keohane et al. 1996) which varies strongly over the remnant.
© European Southern Observatory (ESO) 1998
Online publication: September 30, 1998