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Astron. Astrophys. 354, 645-656 (2000)

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4. Physical nature of the bubble

Possible scenarios for the origin and evolution of the Cepheus Bubble have been proposed by KBT and Patel et al. (1998). In the following we discuss how the 3-dimensional expanding HI shell, described in the present work, fits into these scenarios.

Mass and energetics.

We determined the mass of the HI shell by summing up the column densities of the HI gas (Hartmann & Burton 1997) over the apparent area of the shell. In order to separate the emission related to the shell from foreground and background emissions we multiplied the measured [FORMULA] channel values by the corresponding factor weighting coefficients from factors 2, 3 and 5, obtained in Sect. 2.2. In this way we obtained a mass of [FORMULA], including a factor of 1.4 to account for the total mass to HI mass ratio (Brown et al. 1995). This value is close to the value of [FORMULA] obtained by Patel et al. (1998). Including the mass of molecular gas ([FORMULA], Patel et al. 1998) would not change significantly the total mass.

From the estimated mass and observed size of the shell we obtain an initial ambient density of [FORMULA] cm-3 for the interstellar medium in this region. The mass of the bubble, together with the effective expansion velocity derived in Sect. 2.3, provides an estimate of the total kinetic energy of [FORMULA] erg for the expanding shell. Following Weaver et al. (1977), we assume that about 20% of the total energy deposited into the ISM is converted into kinetic energy. With this assumption the total energy of the bubble is [FORMULA] erg.

The derived total energy is close to the canonical value of a supernova explosion of [FORMULA] erg, thus such an event is a possible origin of the expansion. In order to check if other sources were also able to provide the required energy of the expansion, we estimated the total contribution of stellar winds from some 20 O-type and early B-type members of Cep OB2a. The stars selected are located within a circle of 3o (the approximate angular diameter of the internal cavity) around HD 207198, and we assume that all are members of the associaton. The mechanical luminosity was calculated by estimating the mass loss from the spectral type and the luminosity vs. mass loss relation of Garmany et al. (1981) and from the analytical expression given by Kudritzki (1998). This gives [FORMULA] erg s-1 for the mechanical luminosity of the OB stars. Assuming that this luminosity was constant during the lifetime of Cep OB2a ([FORMULA] yrs, Sect. 1), the total power exerted amounts to [FORMULA] erg. This figure agrees within a factor of 2 with the total energy required for the expansion of the bubble. Considering the uncertainties in our computations, we conclude that the integrated stellar wind from the existing early-type stars in the interior of the bubble during a period of [FORMULA] yrs could also power the observed expansion.

Kinematics and age. Massive O-type stars affect their environments via UV radiation, stellar wind, and supernova explosion. UV photons ionize the interstellar gas and develop an HII region, as well as homogenize the surrounding medium by photoevaporating the nearby clouds and/or removing them via the `rocket effect' (McKee et al. 1984). This homogenization process enables us to describe the temporal evolution of the expansion by the analytical formulae of Weaver et al. (1977) and Chevalier (1974) (see also Tenorio-Tagle & Bodenheimer 1988). In both the stellar wind bubble (SWB) and supernova remnant (SNR) scenarios the evolution of the size is given by a power law of [FORMULA], where [FORMULA] in case of SNR in post-Sedov phase and [FORMULA] in the case of SWB. The expansion velocity of the radius of the ring pattern is given by the time derivative of [FORMULA], i.e. [FORMULA]. Division of [FORMULA] by [FORMULA] gives a simple equation for obtaining t, the age of the Bubble. We emphasize that none of the mechanical luminosity of the stellar wind, the explosion energy of the SN or the density of the ambient interstellar matter enters into the final expression of t, depending only on p, the observed size and expansion velocity of the shell. The ages obtained from this simple formula give therefore facing values of [FORMULA] yrs (SNR) and [FORMULA] yrs (SWB) for the expansion age of the Bubble.

The age derived for a SWB, however, is only 40% of the lifetime of Cep OB2a, and during this period the energy injected into the ISM via stellar wind is only [FORMULA] erg. This energy is significantly lower than the [FORMULA] erg required for the expansion of the bubble. It would also be difficult to explain why the creation of the SWB does not coincide with the birth of most of the early-type stars. From these arguments we think that a supernova explosion occurring about [FORMULA] yrs ago is a more straightforward explanation for the origin of the expansion. The derived expansion age of a SNR is also consistent with the kinematic age of the runaway star [FORMULA] Cep ([FORMULA] yrs, Stone 1979), which was proposed by KBT to be the former companion of the exploded star.

Evolution of the Cepheus Bubble.

As was discussed in the previous paragraph, the observed large scale expansion of the Cepheus Bubble is probably due to a relatively recent supernova explosion in the Cep OB2a association. The true age of the bubble, however, may be significantly larger, because the strong stellar wind and UV radiation from the progenitor of the supernova, along with other OB stars in Cep OB2a, is expected to create a large cavity already long before the supernova event. Both KBT and Patel et al. (1998) propose that the younger subgroup of the association Cep OB2b has been triggered by the older subgroup Cep OB2a. Since the age of the most massive star of the younger subgroup is about [FORMULA] yrs (Patel et al. 1998), an extended cavity/shell structure of approximately the present size was already present [FORMULA] yrs ago.

In this picture the supernova has exploded in an already existing low density cavity. It is likely that by the time of the supernova event the shell around the cavity was already fragmented and its expansion practically stopped (Patel et al. 1998). The expanding shock front of the supernova, however, revived the old shell by forcing its fragments into motion again. The shock front also interacted with those regions which existed before the explosion, such as IC 1396, and possibly S140, NGC 7129. This interaction can explain the relatively sharp and well-defined inner edge of the Cepheus Bubble (Figs. 1 and 6). The supernova shock might have also influenced the structure of the star forming regions all along the Cepheus Bubble and triggered the recent wave of star formation indicated by the IRAS measurements (Balázs & Kun 1989; Patel et al. 1998).

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© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000
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