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Astron. Astrophys. 364, 232-236 (2000)

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3. Discussion

In order to interpret reasonably the rapid time variability, the physical parameters in the masing region should be obtained. The brightness temperature of maser emission can be expressed as (Moran 1989)


where c is the speed of light, and k is Boltzmann's constant. [FORMULA][FORMULA]/[FORMULA] is the apparent angular size of the source as seen by the observer and a is the radius of maser spots which have the typical size of [FORMULA] cm (Reid & Moran 1981). F and [FORMULA] are the measured flux density at line center and observing frequency, respectively. The initial flux density of the -84.4 km [FORMULA] component in NGC 6334C was about 750 Jy. Eq. (1) indicates [FORMULA] to be about 3.2 [FORMULA] K. Similarly, for the -52.8 km [FORMULA] component in W3(OH), its lowest flux density was 685 Jy. It implies [FORMULA] = 4.6 [FORMULA] K. The total population in the [FORMULA] and [FORMULA] levels for the saturated water maser can be expressed as (Moran 1989)


where [FORMULA] and [FORMULA] are thee maser linewidths and observed source sizes. [FORMULA] is the pump efficiency, usually assumed to be 0.01, and A and [FORMULA] are the Einstein coefficients and the decay rate per molecule from the maser levels, respectively. For the 22 GHz H2O transition, A = 1.9 [FORMULA], and [FORMULA] is expected to be [FORMULA] 1 [FORMULA]. The total gas density, which is predominately molecular hydrogen, [FORMULA] can be estimated for an H2O maser by the equation (Moran 1989)


where [FORMULA] is the density of water molecules. For masers associated with star-forming regions, [FORMULA], and [FORMULA], therefore, the hydrogen density, [FORMULA], was decreasing from about 2.0 to 1.1 [FORMULA] for the -52.8 km [FORMULA]component in W3(OH) and increasing from about 0.8 to 2.4 [FORMULA] for the -84.4 km [FORMULA] component in NGC 6334C during our observations. In masing regions, changes in the density of gas can give rise to an effective change in pump rate. Interstellar H2O masers are too far from the central star to be radiatively pumped (Moran 1989). Kylafis & Norman (1991) discussed the pumping of H2O masers in star-forming regions by collisions with [FORMULA] molecules. According to their view, the number density of [FORMULA] molecules derived above is too low to produce such a high brightness temperature ([FORMULA] K).

Burke et al. (1978) studied an H2O maser flare in W3(OH) and obtained a good fit using a simple model in which energy was released very quickly inside a spherical maser cloud. This model could not work appropriately in our experiment, because it did not account for flickering behavior observed during the rise of the -81.2 km [FORMULA] flare in NGC 6334C and also did not explain why the flux density of the -52.8 km [FORMULA] component in W3(OH) decayed almost linearly unless the feature was undergoing an exponential decay, but was far down on the tail of the curve.

The rapid time variability of the observed water maser features could arise from a radiative instability of masers, interstellar scintillation and changes in the pump rate.

In partially saturated masers, a radiative instability can cause a periodic variation, but most of the models focus on OH masers with timescales of the order of hours (Scappaticci & Watson 1992).

The rapid time variations could also be due to interstellar propagation effects, such as diffractive or refractive scintillation. For the strongly diffractive scintillation, the correlation timescale is [FORMULA] [FORMULA] [FORMULA]/2[FORMULA] for a source of angular size [FORMULA], observing wavelength [FORMULA], and a relative transverse velocity [FORMULA] (Simonetti et al. 1993). For water masers in W3(OH), the typical diameter of maser spot [FORMULA] [FORMULA] 1 1013cm and [FORMULA] 20 km [FORMULA] (Alcolea et al. 1993), the diffractive timescale is about 50 s. The correlation timescale of refractive scintillation is [FORMULA] [FORMULA] [FORMULA]/[FORMULA], where [FORMULA] is the observed angular size. For the assumption [FORMULA] = [FORMULA], the refractive timescale is about 90 days. Obviously, the former is too short compared to our observing timescale while the latter is somewhat long. However, the true sizes of the water masers in the two regions are likely to be less than the typical estimate in diameter, and the refractive time scale might fit the fluctuation time observed in our experiment.

All water maser sources in both W3(OH) and NGC 6334C are located near ultra-compact HII regions. At the initial phases of star formation, a strong stellar wind is one of the main characteristics. This extremely fast wind, moving at velocities of several hundred km [FORMULA], may very well drive the molecular outflows. As the result of the influence of the energetic protostellar wind, the dense clumps are dispersed into space. Clumps either create shocks in the surrounding clouds or are themselves shock compressed. Masers within the compressed gas, with beamings perhaps perpendicular the clump's motions. Thier motions and superposition of their beamings may cause the variabilities of the masers. The variabilities of the observed masers require random gas movements of [FORMULA] 50 km [FORMULA] which are unreasonably large (Mattila et al. 1985).

Tarter & Welch (1986) suggested that if collisions take place among clumps at sufficient relative velocities, the powerful energy can excite H2O maser emission. The collision rapidly heats the gas to the temperature of the dust and thus quenches the pump. Because the energy is associated with the relative velocity v, the model requires a wide range of collision velocities among dense clumps. In order to obtain v, in the present paper, we assume that both collision clouds are the same. Some physical parameters in the masing region are [FORMULA] 2000 Jy, [FORMULA] 2 kpc, and [FORMULA] 50 kHz and the total luminosity of the maser, [FORMULA] 5 [FORMULA]. The apparent isotropic maser luminosity, [FORMULA](for a spherical maser, [FORMULA] = L), is given by the equation (Moran 1989)


where [FORMULA] is the rate of dissipation of kinetic energy, and [FORMULA] and [FORMULA] are the frequency of maser and pump frequency, respectively. If the pump operates at [FORMULA] 40 µm, then [FORMULA] 2 [FORMULA]. According to Reid & Moran (1988) and Tarter & Welch (1986)


where r, [FORMULA] and [FORMULA] are the size of the maser cloud, the number density of gas in the maser cloud, and the mass of a hydrogen molecule, respectively. In the present paper, [FORMULA] 4 [FORMULA] cm, and [FORMULA], hence, we obtain [FORMULA] 10 km[FORMULA]. VLBI observations indicated that the magnitude of proper motions of some masers in the W3(OH) region was quite different from that of other masers in the region. This implies that there was a wide range of velocities among dense clumps. Similarly, the large blue shift of the water masers in NGC 6334C suggests there were strong activities in the masing region, indicating a possible existence of a wide range of velocities among dense clumps. So, the relative velocity [FORMULA] 10 km[FORMULA] is common among these maser clouds. The collision among maser clouds naturally provides a explanation for the rapid time variations.

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Online publication: December 15, 2000