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4 Conclusions and summary

For the maser model presented above we used the generally accepted picture for star formation in which a massive new born B/O type star is surrounded by a HII region and a large surrounding cloud of dust. According to [Bloemhof et al.] (1996) some of the OH masers have "proper motions" and are falling towards the star. In this picture water containing grains move with considerable velocities of some $\rm km\, s^{-1}$ - depending on the distance from the star - towards the central star.

We defined a "small grain border" between the HII region and the cold interstellar cloud by the region where the small grains are directly irradiated by the heat flux from the star. The life time of these grains is short which implies that the "small grain border" should move outwards with time. Because the larger grains live longer than the small grains, the larger grains remain inside this border and are evaporated by the heat flux from the star in the presence of VUV radiation. They are photolysed and relax by IR radiation to lower states. The competition between photodissociation and IR relaxation yields a characteristic distribution over the OH quantum states which is determined by the competition between IR relaxation and photodissociation and does not depend on the evaporation rate.

Inversion and gain is found between all levels in the $^2\Pi_{3/2}$ multiplet for which OH masers are observed near new born stars which implies that all these observed OH masers can be explained by the photodissociation of water in the first absorption band. It is interesting to note that the masers do not require a high photodissociation rate but operate over a wide range of $\gamma$'s. The gain for a given maser transition is the product of a specific gain and the evaporation rate for all OH quantum states. The specific gain results from the competition between the photodissociation rates and IR relaxation rates and is only a function of $\gamma$.

The specific gain is much larger for the ground state maser than for any of the excited state masers. Considerably large gains are obtained over a wide range of $\gamma$'s for the ground state and the gain increases with decreasing $\gamma$. This somewhat surprising result, i.e., that the inversion becomes large for small photodissociation rates, is due to the fact that the OH in the ground state is destroyed slowly for small $\gamma$'s which leads to a pile up of population in this state. Because of the large specific gain for the ground state relatively low evaporation rates are sufficient to obtain high gain. The evaporation of the $\rm 10-100\,\mu m$ grains close to the border of the HII region yields sufficiently high evaporation rates even at low temperatures around 120 K. The grains also last a long time, so that they may be replaced by the grains moving from beyond the small grain border to the star or the ground state masers move with the velocity of the expanding HII region. Therefore the ground state masers can last for a long time.

In contrast to the ground state masers, the masers in the excited states suffer large losses due to IR relaxation and consequently show a much smaller specific gain. However, the specific gain is larger for small photodissociation rates and decreases with increasing $\gamma$. Because of the much smaller specific gain much larger evaporation rates are required to explain the high gains observed for excited states. To explain a gain of $3\ 10^{-12}\,{\rm m}^{-1}$, as suggested by [Baudry & Diamond] (1998) for the j=7/2 maser, the evaporation rate must become as high as $\Gamma \approx 10^7\,{\rm m^{-3}\,s^{-
1}}$. This is only possible if many big "grains", like comets or small planets, that live long enough to penetrate deep inside the HII region acquire high temperatures around e.g. 250 K. Then massive evaporation of water will occur and yield high evaporation rates which will, however, last only for a limited time. Some of the j=7/2 maser spots observed by [Baudry & Diamond] (1998) et al. show indeed an intensity increase by a factor of more than 10 over a decade. The excited state masers are therefore expected to be transient phenomena during star formation.

There is much more work required to elucidate details of the present mechanism and there are other features of maser radiation that have to be explained, like line width,

velocity extent, variability or the fact that hyperfine lines appear sometimes in absorption and sometimes in emission. We believe that a deeper understanding of many of these features requires an extension of the present model, e.g. inclusion of FIR pumping and at very small $\gamma$'s collisional effects as well. Also, the situations near new born stars have to be compared in detail to analyse whether or not the predictions given here agree with observation.

Baudry & Diamond (1998) suspect that the central star is the "common source" of energy for the j=3/2, j=5/2 and j=7/2 OH masers observed in W3(OH). This is exactly what results from the present model: the common source of energy is the heat- and VUV- flux that causes grains to evaporate water which is photolysed subsequently to give an inversion that depends also on IR relaxation. This yields high gain for all OH maser transitions observed near new born stars.

Acknowledgements

Most of the referenced papers used to develop the presented maser model are obtained using the NASA Abstract Data System (ADS). We thank the NASA for this Service.


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