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Astron. Astrophys. 322, 291-295 (1997)

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4. Discussion

Previous interferometric measurements of sizes of H2 O maser regions have been restricted to semiregular (SR-), Mira variables and M-Supergiants. OH 39.7+1.5 is the first OH/IR star for which such a measurement has been carried out. Based on the velocities displayed in single-dish spectra, Engels et al. (1986) predicted OH/IR stars to have intermediate sizes between those of the blue AGB variables and those of M-Supergiants. Indeed the outer shell radius of OH 39.7+1.5 of 3 [FORMULA] cm (200 AU) is about ten times greater than the typical radii of SR- or Mira variables with mass loss rates [FORMULA] [FORMULA] [FORMULA] /yr (Bowers & Johnston 1994), and somewhat smaller than in M-Supergiants (Johnston et al. 1985, Bowers et al. 1993, Yates & Cohen 1994). Therefore, in general, the sizes of the H2 O masing region increase with mass loss rate, expansion velocity and probably luminosity of the star.

The most redshifted H2 O maser velocities coincide with the reddest OH maser velocities implying that the final expansion velocity is already reached within the H2 O maser shell. Between the outer radius and the OH maser shell at 3 [FORMULA] cm (Van Langenvelde et al. 1990) little, if any acceleration of the outflowing gas occurs. Assuming a stellar radius of 2 [FORMULA] cm and adopting 3 [FORMULA] cm as the outer H2 O maser shell radius, the acceleration of the outflow is finished within 15 [FORMULA], followed by a constant expansion over at least 150 [FORMULA]. The confinement of the acceleration to the inner part of the shell seems to be a general characteristic of OH/IR stars, given the close coincidence of H2 O and OH maser velocity ranges for many of them (Engels et al. 1986; Engels & Lewis 1996). OH/IR stars show no evidence for large velocity gradients at large radial distances, like the one claimed to be present in the M-Supergiant VX Sgr (Chapman & Cohen 1986). The radial velocity curve is therefore in accordance with the usual theory of radiation pressure on dust, where constant dust opacity beyond the grain condensation radius is assumed (Goldreich & Scoville 1976).

The anticorrelation in the detectability of radial and tangential water masers from OH 39.7+1.5 and their variations is unique, although we have searched for other examples. It was not a singular event for OH 39.7+1.5 however, as a similar line was observed in the past. Apparently, the tangential masers are less stable than the radial ones. While the latter reappear again at the same velocity and position, the former do not. From four periods now covered by observations, tangential lines appeared only during the first (1984) and the third (1991) period, and not during the minima in 1987 (Engels & Lewis 1996) and 1995. Thus observable tangential emission occurs only occasionally.

It is often thought that radial and tangential maser lines are located in different parts of the shell. As small velocity gradients along radial paths are achieved only far away from the star, radial masers are expected to reside in the outer parts of the shell, while the tangential masers are expected preferentially in zones of high velocity gradients close to the star (Chapman & Cohen 1985). However, in the present case masing in the inner acceleration zone is quenched and the spatial position of the tangential line is incompatible with a position in this zone.

It is therefore more plausible to assume that tangential and radial masers come from about the same volume of gas, with tangential emission only possible, as long as radial maser emission is inhibited. During the bright phase of the star, the temperature in the maser shell suffices to collisionally excite the maser throughout the shell and excitation along radial paths will be preferred, because the velocity gradient is smallest in this direction. Pump events will be fully used up by the radial masers, inhibiting maser emission in other directions. When the stellar brightness decreases, the shell temperature decreases and falls eventually below a threshold, beyond which inversion of the maser levels cannot be maintained. The location of this threshold moves radially inward with decreasing shell temperature, shortening the radial maser paths until their lengths become comparable to those possible in other directions. The critical gain length might be estimated from the position and the width of the line profile (0.7 km s-1) of the tangential maser. At a distance of D = 3 [FORMULA] cm in a constant radially symmetric outflow with [FORMULA] = 17 km s-1, velocity coherence [FORMULA] v [FORMULA] km s-1 is achieved along a tangential line of sight over a length of D  [FORMULA] [FORMULA] [FORMULA] cm. Thus, as soon as the radial gain length approaches this size, the longest gain paths may occur in other directions than the radial one. As even modest asymmetry of the maser zone will produce substantial anisotropy in the outgoing radiation (Alcock & Ross 1985), a switch in beaming direction is possible. The tangential gain length increases until the stellar minimum is reached and decreases afterwards. The temperature variation should have reached a minimum by then, because otherwise the new beaming direction will be extinguished shortly afterwards as well.

Thus considerable fine tuning between the mass loss rate, expansion velocity and luminosity amplitude seems to be required, to make the switch of beaming directions observable. A favourable combination of these parameters may only occur during a short phase of the development of a circumstellar shell, which would explain, why the observation of mode switching is thus far peculiar to OH 39.7+1.5.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998