G G G G

WW^Q

Fig 15.13.

Maser amplification. In each frame, a molecule in the upper level of the maser transition is indicated by a large circle, and one in the lower level is indicated by a small circle. (a) All of the molecules are in the upper state, and a photon is incident from the left. (b) The photon stimulates emission from the first molecule, so there are now two photons, in phase. (c) These photons stimulate emission from the next two molecules, resulting in four photons. (d) The process continues with another doubling in the number of photons.

Shortly after the development of laboratory masers, an interstellar maser was discovered. It involved the molecule OH. Four emission lines of OH were observed, but their relative intensities were wrong for a molecule in equilibrium. As radio telescopes were developed with better angular resolution, the emission was observed to become stronger and stronger. This means that the emission is probably very intense, but coming from a very small area. This behavior was suggestive of an interstellar maser. The next maser discovered was in the water (H2O) molecule, at a wavelength of 1 cm. As observations with better resolution became possible, it was clear that the objects were giving off as much energy as a 1015 K blackbody over that narrow wavelength range in which the emission was taking place.

A small size for these sources was also deduced from rapid variations in their intensity. Suppose we have a sphere of radius R, as shown in Fig. 15.14. If the sphere were suddenly to become luminous, then the first photons to leave each point on the surface would not reach us simultaneously. The photons from the edge of the sphere have to travel a distance R farther than the photons from the nearest point. These photons will arrive a time At = R/c later than the first photons. Therefore, it will take this time for the light we see to rise from its initial low level to the final high value. A similar analysis holds for the time it would take for us to see the light turning off.

The above analysis tells us that an object's brightness cannot vary on a time scale faster than the size of the emitting region, divided by c. If we see variations in intensity over a time scale of a year, the source cannot be larger than a light year across. Interstellar masers were found to vary in intensity on an even shorter time scale, of the order of a month, indicating an even smaller size.

Example 15.7 Maser size

Estimate the maximum size of a maser that varies on the time scale of one month. What is the angular size of this object at a distance of 500 pc?

solution

The time scale for the variations is At = (24 h/day)(3600 s/h)(30 day)

This corresponds to a size of

The angular size (in arc seconds) is related to R (in AU), and the distance d (in pc) by (equation 2.16)

In fact, masers are even smaller than this size, and have angular extents much less than 1 arc second. This means that we need radio interferometers to study masers. Very long baseline inter-ferometry has been used to study masers.

When we try to understand interstellar masers we must explain both the pump and the path length for the gain. Many of the theories require very high densities. For example, we think that the presence of water masers suggests densities in excess of 108 cm~3. This is much denser than even the dense cores that we normally see in molecular clouds. We therefore think that masers are associated with objects collapsing to become protostars. We take the presence of H2O or OH masers in a region to indicate the possibility of ongoing star formation.

When we observe masers, we often see them in clusters, such as that depicted in Fig. 15.15. With radio interferometry, we can measure the positions of the masers very accurately. We can even measure their proper motions. We can use Doppler shifts to measure their radial velocities. However, we expect the motions of a cluster to be random, so the average radial velocity should

Expanding Gas Shell

Expanding Gas Shell

Fig 15.15.

equal the average transverse velocity vT. From equation (13.6) we see that the distance is related to the proper motion and transverse velocity by d(pc) = vT(km/s)/4.74^(arc sec/yr)

Therefore, an accurate study of the motions of masers allows us to determine the distance to a cluster of masers. It is hoped that this will develop into a very powerful distance measuring technique. This technique works equally well for random motions or for the masers being in an expanding shell. The only requirement is that the average velocity along the line of sight is the same as the average velocity perpendicular to the line of sight.

Maser emission is also observed in the molecule SiO (silicon monoxide). From the regions in which it is observed, it seems that SiO maser emission is associated with mass outflow from evolved red giant stars. Also, some OH masers are associated with similar regions.

15.6.3 Energetic Flows

A major recent discovery is that many regions of star formation seem to be characterized by strong outflows of material. One piece of evidence for such flows comes from the observation of very broad wings on the emission lines of CO (Fig. 15.16). The widths of these wings range from 10 to 200 km/s. The broad wings are usually seen only over a small region where the CO emission is strongest. A peculiar feature of this emission is that the red-shifted wing and blueshifted wing seem to be

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