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3 Dense clumps in the central part of SNR MSH15-52

We suggest that PSR B1509-58 and SNR MSH15-52 are the remnants of the SN explosion of a massive star (Gvaramadze 1999b). In this case, the structure of MSH15-52 could be determined by the interaction of the SN blast wave with the ambient medium reprocessed by the joint action of the ionizing emission and stellar wind of the SN progenitor star (McKee et al. 1984; Shull et al. 1985; Ciotti & D'Ercole 1989; Chevalier & Liang 1989; Franco et al. 1991; D'Ercole 1992; Gvaramadze 1999b,c, 2000a). The outer shell of the SNR could arise due to the abrupt deceleration of the SN blast wave after it encounters the density jump at the edge of the bubble created by the fast stellar wind during the main-sequence or the Wolf-Rayet (WR) stages. On the other hand, some structures in the central part of the SNR[*] could be attributed to the interaction of the SN blast wave with the circumstellar material lost during the late evolutionary stages of the SN progenitor star [this is the material that determines the appearance of young typeII SNRs, e.g. SN1987A (e.g. McCray 1993) or CasA (e.g. Garcia-Segura et al. 1996; Borkowski et al. 1996)]. During the red supergiant (RSG) stage a massive star loses a significant part (about two thirds) of its mass in the form of a slow, dense wind. This matter occupies a compact region with a characteristic radius of few parsecs (the high-pressure gas in the main-sequence bubble significantly affects the spreading of this region, Chevalier & Emmering 1989; D'Ercole 1992). Before the SN exploded, the progenitor star (of mass > $15-20 ~ M_{\odot}$) becomes for a short time a WR star (e.g. Vanbeveren et al. 1998). At this stage, the fast stellar wind sweeps up the slow RSG wind and creates a low-density cavity surrounded by a shell of swept-up circumstellar matter. The shell expands with a nearly constant velocity $v_{\rm sh} \simeq
(\dot{M} _{\rm WR} v_{\rm WR} ^2 v_{\rm RSG}/3\dot{M} _{\rm
RSG})^{1/3}$, where $\dot{M} _{\rm WR} , \dot{M} _{\rm RSG}$ and $v_{\rm WR}, v_{\rm RSG}$ are, correspondingly, the mass-loss rates and wind velocities during the WR and RSG stages (e.g. Dyson 1981), until it catches up the shell separating the RSG wind from the main-sequence bubble. For parameters typical for RSG and WR winds, one has $v_{\rm sh} \simeq 100{-}200 \, {\rm km}\,{\rm
s}^{-1}$. The interaction of two circumstellar shells results in Rayleigh-Taylor and other dynamical instabilities, whose development is accompanied by the formation of dense clumps moving with radial velocities of $\simeq$ $v_{\rm sh}$ (Garcia-Segura et al. 1996). The dense clumps could originate much closer to the SN progenitor star due to the stellar wind acceleration during the transition from the RSG to the WR stage (Brighenti & D'Ercole 1997). The number density of clumps is $\geq$10 $^5 \, {\rm cm}^{-3}$ provided they are not fully ionized and were able to cool to a temperature of $\leq$102 K (Brighenti & D'Ercole 1997). Direct evidence of the existence of high-density clumps close to the SN explosion sites follows from observations of young SNRs. For example, the optically emitting gas of quasi-stationary flocculi in CasA is characterized by a density of $\simeq$10 $^4 ~ {\rm cm}^{-3}$ and a temperature of $\geq$104 K (e.g. Lozinskaya 1992). Assuming that the optical emission of a floccule comes from an ionized "atmosphere" around the neutral core, one can estimate the density of the core to be $\geq$10 $^6 ~ {\rm cm}^{-3}$, provided that the temperature of the core is $\leq$102 K. Similar estimates could also be derived from observations of the optical ring around SN1987A, the inner ionized "skin" of which has nearly the same parameters (e.g. Plait et al. 1995) as the optically emitting gas of flocculi in CasA, or from observations of some other young SNRs (e.g. Chugai 1993; Chugai & Danziger 1994). The radial velocity of flocculi in CasA ranges from $\simeq$80 to $\simeq$ $400 \, {\rm km}\,{\rm s}^{-1}$(e.g. Lozinskaya 1992).

Initially, the new-born pulsar moves through the low-density cavity created by the fast wind of the presupernova star until it plunges into the first dense clump on its way. This happens at the moment $t \sim r_{\rm cav} /v_\ast$, where $r_{\rm cav} \simeq
1$-2 pc is the radius of the cavity, $v_\ast = v_{\rm p} - v_{\rm
cl}$, $v_{\rm p}$ and $v_{\rm cl}$ are respectively the velocities of the pulsar and the clump. For $v_{\rm p} \simeq 150 \, {\rm
km}\,{\rm s}^{-1}$ and $v_{\rm cl} \simeq 100 \, {\rm km}\,{\rm
s}^{-1}$, one has $t\simeq (2$- $4)\times 10^4$ years[*]. Let us assume that all matter captured inside the accretion radius $r_{\rm acc} =2GM_{\ast}
/v_{\ast} ^2$ ( $v_{\ast} \gg c_{\rm s}$, where $c_{\rm s}$ is the sound speed in the cold, dense circumstellar clump) of the pulsar moving through the clump penetrates into the region of the light cylinder, where it is accelerated to relativistic velocities and then leaves this region in the form of equatorial outflow (cf. Istomin 1994; King & Cominsky 1994). The rate at which the ambient medium arrives at the light cylinder could be estimated as

\dot{M} \, = \, \pi r_{\rm acc} ^2 n_{\rm cl} m_{\rm p} v_{\ast} ,
\end{displaymath} (2)

where $n_{\rm cl}$ is the number density of the clump, and $m_{\rm p}$ is the mass of a proton. If the pulsar braking is indeed mainly due to the acceleration of circumstellar protons arriving at the light surface, then one obtains from (1) and (2) that $n_{\rm cl} \simeq 3.8\times 10^6 \, v_{\ast ,50} ^2 \, {\rm cm}^{-3}$, where $v_{\ast ,50} =v_{\ast} /50 \, {\rm km}\,{\rm s}^{-1}$. The time it takes for PSR B1509-58 to cross the clump, $t' \,
\simeq \, l_{\rm cl} /v_{\ast}$, where $l_{\rm cl}$ is the characteristic size of clumps, should be larger than the time since the pulsar discovery, i.e. t' > 30 years. This requirement results in $l_{\rm cl} \geq 5\times 10^{15} v_{\ast ,50}$ cm and $M_{\rm cl} > 0.0002 v_{\ast ,50} ^3\;
M_{\odot}$, where $M_{\rm cl}$ is the characteristic mass of clumps. For the SN progenitor star of mass $\geq$15 $M_{\odot}$, the mass of the circumstellar gas (i.e. the matter lost during the RSG stage) is about $10~M_{\odot}$, and the number of clumps is < $5\times 10^4$. For the current radius of the region occupied by circumstellar matter of about 10 pc (Gvaramadze 1999b), one finds a covering factor of the clumpy circumstellar material (i.e. the fraction of the sphere occupied by clumps) $\simeq$10-4.

For accretion to occur, the standoff radius $r_{\rm s}$ of the bow shock (formed by the outflow of relativistic particles) should be less than $r_{\rm acc}$. For the spherically symmetric outflow, one has $r_{\rm s} =(\alpha \vert{\dot E}\vert/4\pi n_{\rm cl}m_{\rm p}
cv_{\ast}^2)^{1/2} < r_{\rm acc} =2GM_{\ast} /v_{\ast} ^2$, where we assume that only a fraction $\alpha < 1$ of the spin-down luminosity $\vert{\dot E}\vert$ is transferred to the ambient medium (cf. Kochanek 1993). This condition can be re-written as $\alpha <
(\gamma_{\rm p}/4)^{-1} v_{\ast} /c \simeq 10^{-3} \gamma_{\rm p}
^{-1} v_{\ast ,50}$ (cf. Kochanek 1993; Manchester et al. 1995), i.e. $\alpha$should be much smaller than the usually adopted value of $\simeq$1 (e.g. Kulkarni & Hester 1988; Cordes et al. 1993). Weak coupling ( $\alpha \ll 1$) of the pulsar wind with the ambient medium is consistent with an outflow composed of highly relativistic particles (e.g. Kochanek 1993 and references therein). Alternatively, if the outflow of relativistic particles is confined to the vicinity of the rotational equatorial plane, one can expect that the ambient matter accretes onto the pulsar's magnetosphere along the polar directions. Another possibility is that the ambient matter penetrates in the pulsar wind bubble through instabilities in the bow shock front. In the latter both cases $r_{\rm s}$ could be larger than $r_{\rm acc}$, and one can adopt $\alpha \simeq 1$(see next section).

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