(l)Primary references can be found in Moran [1993], (2) SP = statistical parallax; M = model fit. (3) Number of maser features. (4) Outflow velocity in kms~!. In Orion and W49N there are additional higher velocity flows. (5) Systemic velocity. (6) Proper motion distance. (7) Distance from kinematic model: v = 220 kms'1, R0 = 7.8 kpc and random velocity = 4 kms'1. (8) Weighted residual. (9) Preliminary estimate. (10) No distance estimate can be made because the outflow is well collimated and nearly in the plane of the sky (see Figure 6).

Distances to seven H20 maser sources have been determined by these methods and the results are tabulated in Table 1. Because these masers originate from various places in the plane of our galaxy, the size of the galaxy can be estimated from a simple model of galactic rotation, i.e., constant circular motion at 220 kms-1. The distance from the Sun to the Galactic Center, R0, is estimated to be 7.8 ±0.6 kpc. See the review by Reid[ 1993] for a comprehensive discussion of the various measurements of R0.

A preliminary estimate has been made of the distance to the maser cluster in the nearby galaxy M33 with the method of statistical parallax [Greenhillet al., 1993], These measurements are difficult because with a typical velocity of 30 kms-1 and an expected distance of 700 kpc, the angular motions areonly about 9 ¿ias yr1 (see Eg 10).

5.2 Expanding Envelopes in Late-Type Stars

The OH masers at 1612 MHz arise preferentially from the parts of the spherical shell that are nearest to and farthest from the Earth (i.e., along the line of sight to the star). This happens because the OH is far enough from the star that the envelope has reached its terminal velocity and the velocity gradients along the line of sight are small, thus the amplification gain paths are large in these directions. The masers are pumped by infrared radiation from the star, which varies periodically. The flux densities of the maser features also vary periodically with the variations in stellar pump power. However, because of the light travel time, there will be a time lag, T, between the "light curve" from the back side maser and the "light curve" from the front side maser. This lag is 8-80 days, corresponding to shell diameters of 1016"17 cm. If the size of the maser shell, 6 (about 1 - 10"), is measured by interferometry, then the distance can be estimated by the simple relation, D = ct/0. Distances to about a dozen stars have been measured by this technique. The estimate of the size of the galaxy deduced from them gives R0 = 8.8 ± 0.9 kpc (see summary in [Moran, 1993]).

5.3 Rotating disks in AGN

It should be possible to measure the proper motions of the maser in molecular disks in active galactic nuclei. Measurements are underway for NGC4258, where the proper motions are expected to be 32 x (6.4Mpc/D) ¿uas yr1. However, a distance can also be estimated by comparing the centripetal accelerations of masers with the angular size and velocity of the disk. These accelerations manifest themselves as drifts in the line-of-sight velocities of spectral features with time as the systemic components on the near side of the disk move across the line of sight (see Figure 8) [Greenhill et al., 1995b]. For NGC4258 this distance is 6.4±0.9 Mpc {Miyoshi et al., 1995], Optically determined distances range from 3.5 to 7 Mpc. Because the maser-motion technique is based solely on trigonometric calculations, it offers a method of estimating distance that is independent of more traditional methods, which are affected by absorption and other effects.

6 Interstellar scattering

The angular sizes of most masers are intrinsically very small. Their images can be "blurred" because of wavefront phase perturbations induced on the radiation as it passes through the turbulent ionized interstellar medium [Rickett, 1990], The rms deviation in the index of refraction varies as X2 and hence the image size varies approximately as X2 (A,11'5 for Kolmogorov turbulence) and also about as the square root of the secant of the galactic latitude and the square root of the distance. The scattering of maser emission has been studied extensively by Gwinn et al. [1989] and others. Scattering is particularly intense in the direction of the Galactic Center and amounts to about 1 " at 18 cm wavelength. Recently, Frail et al. [1994b] have found that the images of OH masers at 18 cm wavelength are anisotropic in the vicinity of the Galactic Center. This anisotropy may be due to the effect the magnetic field has on aligning the turbulence.

I thank my colleagues of CfA involved in spectral line VLBI measurements for simulating discussions (A. Argon, L. Greenhill, J. Herrnstein, K. Menten, M. Reid, and A. Trotter).


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