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Astron. Astrophys. 335, 370-378 (1998)

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2. Introduction

One of the factors governing the blast wave dynamics is the non-stationarity of the background. This appears in various astrophysical situations. Let us outline some of them.

(1) For the first [FORMULA] years the expansion of a Type II supernova remnant occurs inside a rarefied cavity produced by the wind of pre-supernova. The pre-explosion gas expands within a cavity with deceleration (v) since the wind loses its energy to the shift of the outer layers of interstellar gas (Weaver et al. 1977). The dynamics of a blast wave inside a preexisting wind-driven cavity was studied numerically by Ciotti and D'Ercole (1989) and Chevalier and Liang (1989).

(2) The earlier stage of supernova explosion is free expansion of matter ejected from the interior of exploded star into a circumstellar and then interstellar space. Gandel'man and Frank-Kamenetskii (1956) and Sakurai (1960) showed that after the blowout of the power-law stellar atmosphere by the blast wave the postshock flow approaches a free homologous expansion v with the power-law distribution of density which in a spherical case takes the form [FORMULA] (Chevalier & Soker 1989). For the Type I supernovae it is adopted n (Colgate & McKee 1969), for the Type II supernovae n (Jones et al. 1981). According to the numerical simulations for SN 1987A n (Arnett 1989). Free expansion continues until the mass of swept-up ambient matter becomes of the order of the mass of ejecta.

(3) Free expansion of matter with a power-law density distribution behind the blast wave occurs not only after the blowout of a power-law atmosphere but also that of an exponential one (Raizer 1964; Grover & Hardy 1966). In astrophysical environment such a possibility is realized in case of sequential supernova explosions concentrated in OB associations (Bruhweiler et al. 1980). A large-scale cavity with a size comparable with the thickness of the galactic disk is then formed. The cavity expands primarily perpendicular to the disk plane in the direction of the density antigradient. Since the density drops with the distance over the plane of symmetry rapidly, approximately as an exponential or Gaussian law (the best fit is a composite law), the cavity stretches with acceleration and blows out the exponential (Gaussian) atmosphere in finite time throwing out matter to large heights into the gaseous galactic halo (Tomisaka & Ikeuchi 1986; MacLow & McCray 1988; Igumentshchev et al. 1990; Tenorio-Tagle et al. 1990). Such a phenomenon, termed the "galactic fountain", is thought to be one of the basic mechanisms providing matter and heat transport into the halo (Shapiro & Field 1976; Norman & Ikeuchi 1989).

(4) According to the explosive theory of galaxy formation (Ostriker & Cowie 1981; Ikeuchi 1981) the present structure of the universe is the result of sequence of large-scale explosions in the early epoch. Cosmological blast waves are driven into an unperturbed background which expands as v in case of the flat universe, for which the gravitational energy exactly compensates the kinetic energy, or v in case of the well-open universe with a negligible gravity. Although the observations from COBE do not count in favour of the explosive scenario (Levin et al. 1992) the developed theory (Ikeuchi et al. 1983; Bertschinger 1983) may be relevant to the description of individual explosive phenomena in the intergalactic medium.

Of the contexts listed above the cases of a freely expanding ambient medium into which astrophysical blast waves may propagate constitute a major portion. These are the cases of the post-blowout expansion and the case of a low-density universe with a negligible gravity. The blast wave dynamics in a freely expanding medium has been the subject of numerical (Hausman et al. 1983; Hoffman et al. 1983) and analytical self-similar (Ikeuchi et al. 1983; Bertschinger 1983) and approximate investigations (Ostriker & McKee 1988), mainly in the cosmological context. The distinctive property of the dynamics is that the blast wave gradually decelerates and asymptotically comoves with the expanding background.

In this paper we present an exact analytical solution for a blast wave dynamics in a freely expanding medium which is true in all, initial, intermediate and final state asymptotics. Sect. 3 presents the statement of the problem, the solution is developed in Sect. 4 and its astrophysical applications to interstellar matter physics and cosmology are discussed in Sect. 5.

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© European Southern Observatory (ESO) 1998

Online publication: June 12, 1998