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Astron. Astrophys. 324, 211-220 (1997)

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4. Discussion

The results of the preceding section show that the model under consideration can explain the observed high brightnesses [FORMULA] of the [FORMULA] line. Combined observations of both the [FORMULA] and [FORMULA] lines constrain the physical parameters of the maser sources and their environment.

We realize that the results of this paper are subject to the uncertainties of modelling, and the list of physical processes influencing the pump efficiency is not complete in our study. For example, collisions with relatively hot electrons in preshock regions can provide additional excitation, i.e. increase the pump rate, etc. However, relevant modelling is impossible at present mainly because of the lack of data on transition probabilities, etc. Corresponding studies in basic molecular physics will greatly benefit the solution of this problem.

Anyhow, at present there is no known alternative to pumping through torsionally excited levels which can explain the observed high brightnesses of the strongest Class II methanol masers. This paper describes the basic features of that mechanism, which appear to have a general character independent of the quantitative details of the torsional pumping. For example, beaming increases the 6 and 12 GHz brightness temperatures, etc.

In order to account for the extremely high observed values of [FORMULA], [FORMULA] and [FORMULA] the masers governed by the described pumping mechanism should be beamed with the factor [FORMULA]. Lower beaming leads to decreased maser brightness because of dispersal of the pumping energy over a wider angle. Further, the 6 GHz methanol masers are quenched at hydrogen densities [FORMULA]. At the same time there should exist a lower limit for hydrogen number density. This value could be obtained through the relation

[EQUATION]

derived from the definition of specific column density. Here R is the source size in the tangential direction.

Satisfactory agreement with observations under the described pumping mechanism is obtained with values of [FORMULA] cm-3 s. Further, the relative abundance of methanol can not be greater than [FORMULA] and [FORMULA] can not exceed the thermal breadth ([FORMULA] cm [FORMULA]). So, we arrive at the estimate of the lower limit for density

[EQUATION]

Estimates of the source sizes depend greatly on the geometrical model. Assuming that the tangential dimensions of maser sources are equal to the observed sizes of maser spots ([FORMULA] cm, Menten et al. 1992) one finds that the hydrogen number density should exceed [FORMULA] cm-3. However, the actual lower limit is not so strict even in the case when maser sources are isolated clumps because the strongest methanol masers are saturated. So, observed sizes of maser spots correspond to the dimensions of the unsaturated core which is smaller than the maser source itself. Moreover, if the maser spots represent correlation paths in a turbulent medium (see below) the source size can be comparable to that of the ultracompact H II region ([FORMULA] cm). Under this assumption the densities in those portions of matter which contribute to the maser spot appearance can be as low as [FORMULA] cm-3.

In order to supply enough energy for pumping masers through the levels of torsionally excited states the ambient dust should be sufficiently warm. Observed values of [FORMULA] are achieved with [FORMULA] K. It should be noted that the field of maser radiation in the proposed model looks like a hedgehog. So, a reasonable amount of warm dust can account for the total flux of methanol masers.

The calculations show that for production of the strong masers the methanol abundance relative to molecular hydrogen should be high. The required values are up to [FORMULA] and could be realized within [FORMULA] yr after evaporation of grain mantles (see, e.g., Millar et al. 1991; Hartquist et al. 1995). Observations indicate that the methanol relative abundance can reach sufficiently high values, at least in hot cores and shocked regions (e.g., Plambeck & Menten 1990; Sobolev 1993). Studies of Orion by Jacq et al. (1993) and Saito et al. (1994) have shown that the relative abundance of deuterated and main species methanol strongly supports the grain evaporation mechanism for methanol abundance enhancement against other chemical processes.

Two possible origins of methanol maser sources with such parameters have been discussed in the current literature.

The first, denoted as the 'clump' hypothesis, was explicitly described in Paper I. In this hypothesis the maser sources are isolated elongated clumps influenced by the passage of shock waves. Such clumps could be formed as a result of the interaction of the shock with the interstellar cloud (see, e.g., results of calculations by Bedogni & Woodward 1990; Stone & Norman 1992), or alternatively could be primordial clumps. It is noteworthy that the shock can align the clumps and lead to formation of somewhat organized structures.

In the clump hypothesis the tangential dimensions of clumps should correspond to the observed sizes of maser spots. Under the constraints of the described pumping mechanism this implies that the clumps should have high densities and should be substantially elongated in the radial direction.

The weak point of this hypothesis is the need for low gas temperature in clumps with high methanol abundance. Sobolev & Deguchi suggested that the masering clump can undergo some efficient cooling process after the evaporation of grain mantles. In dense clumps the time-scale of chemical evolution is greater than the time-scale of cooling (Charnley et al. 1995). An alternative possibility is that methanol in dense clumps can be sputtered through grain-grain collisions without substantial heating of the gas. Such collisions can be initiated by the penetration of grains accelerated by a shock propagating in the less dense ambient medium. Rough estimates show that a considerable portion of the accelerated particles should be trapped in the dense clump. So, general considerations find no obvious contradictions, but more elaborate examination is necessary.

The second hypothesis, a protostellar disc, was proposed by Norris et al. (1993). This hypothesis is based on the fact that in some cases the maser spots lie along lines of an arc. In the protostellar disc the maser sources could be represented by actual clumps and by regions with correlated velocities. The latter possibility depends on the relation between systemic and chaotic motions in the disc.

Densities in the discs are quite high, so the gas temperature must be low in order not to quench the masers. Note that the temperatures in such formations are strongly controlled by the central emitting source, and cooling after the passage of a shock wave is less efficient than in the 'clump' hypothesis. The other possibility is that the masers could arise when the star has evaporated the grain mantles but has not yet heated up the gas. However, estimating these time-scales is not so easy and further careful examination is necessary.

According to present knowledge the following hypothesis of Class II methanol maser formation in the disc looks more plausible. The source has developed outflow (e.g., bipolar outflow). In the region of interaction between the outflow and the disc exists a layer of warm dust providing infrared photons for pumping the masers. Dust particles accelerated in the outflow region penetrate into the disc and initiate grain-grain collisions which lead to sputtering of methanol from grain mantles without substantial heating of the gas (the situation is similar to that described above in discussion of the 'clump' hypothesis). The temperature in the bulk of the disc can be low (see, e.g., Andre & Montmerle 1994). So, the above situation corresponds to conditions under which Class II methanol masers are created by the pumping mechanism described in the current paper. It should be noted that the above scenario is based on rough estimates and thorough examination involving fluid dynamics calculations is necessary.

For the 6 GHz masers in W3(OH), observational data suggests that the possible protostellar discs are small. Since our pumping mechanism requires [FORMULA] cm-3 such formations are not likely to have sufficient column densities.

The third hypothesis concerning formation of masers in a turbulent medium appeared when the results of this paper were under consideration (Sobolev, Wallin & Watson 1997, in preparation). In this hypothesis maser spots are formed as a result of radial velocity correlation in different parts of the source which have favourable conditions for population inversion. In such masers the sizes of the maser spots are determined by the spectrum of scales for turbulent formations. Since quite a high fraction of matter on the line of sight can contribute to the appearance of the maser, densities can be as low as [FORMULA] cm-3, while satisfying the relation between the lower limit of necessary values of specific column density and the source size. That substantially distinguishes the turbulent hypothesis from the others and eases up the explanation of the high [FORMULA] value in W3(OH). It is worth mentioning that in the low density regime the requirement of relatively low gas temperature is no longer necessary. Hence, the necessary thermodynamic conditions are created more easily. Moreover, portions of matter contributing significantly to maser brightness (i.e., those closer to the observer) may be situated quite far from the background ultracompact HII region. Such conditions are favourable for the pumping mechanism described in this paper. Further, additional calculations have shown that with lower densities the current pumping mechanism does not require a difference between the kinetic temperature in the source and the temperature of the pumping radiation. Such thermodynamical conditions are easier to create. Though substantial effort is necessary to prove the 'turbulent' nature of the strongest Class II methanol masers this hypothesis is very promising.

It is shown that the brightness of the 6 GHz [FORMULA] methanol line is strongly influenced by background emission. Observations indicate that many sources have an underlying ultracompact H II region which is bright in free-free radio continuum. This fact is supported by results of Menten et al. (1992) and recent observations of Ellingsen et al. (1996b) which have shown that sources of strong maser emission in the 6 GHz line often correlate with the peaks of continuum emission at corresponding frequencies. However, we would like to note that in sources with only the 2.7 K microwave background, values of [FORMULA] exceeding [FORMULA] K could be achieved.

The reported calculations show that H II region emission strongly influences the excitation of the saturated [FORMULA] transition, as well as providing a source of background radiation for amplification. To produce the ratio of intensities of the strongest Class II methanol maser lines observed in W3(OH) ([FORMULA] about 150), the H II region emission should be highly diluted ([FORMULA]). This implies that a considerable portion of the maser radiation is formed in regions situated rather far from the H II region (at least in W3(OH)). Conditions in those methanol masers are likely to be produced by a shock wave propagating closer to the observer, e.g., the one preceding the ionization front which forms the ultracompact H II region. However, it should be noted that the W3(OH) ratio is considerably larger than that seen in other methanol maser sources (Caswell et al. 1995b). Such ratios could be realized in sources with less diluted background emission.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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