Mathematics – Probability
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dda....31.1302p&link_type=abstract
American Astronomical Society, DDA meeting #31, #13.02
Mathematics
Probability
Scientific paper
The dependence of the analysis of detailed motions within our galaxy on the distribution of mass therein warrants the vigorous pursuit of a variety of observational techniques that constrain this distribution. Hardware and software developments have led to successful programs that have detected and cataloged more than 250 gravitational lensing events, involving stellar masses and called microlensing events for historical reasons, toward the center of the galaxy, and the data continues to accumulate at an ever increasing rate. This means that microlensing can be an effective probe of galactic structure and other properties in conjunction with other techniques when the data set is sufficiently large. The microlensing optical depth tau is the probability that a ray from a distant source will pass within the Einstein ring radius RE of an intervening star (lens) on its way to the observer. The optical depth as a function of the direction of the line of sight is very sensitive to the distribution of stars in the galaxy---especially that in a bar-like bulge. This is demonstrated for variations of a particular galaxy model. The time scale of an event is defined as tE=RE/v with v being the relative transverse velocity between the star being lensed (source) and the lens projected onto the lens plane, The distribution of time scale frequencies, the number of events per unit tE as a function of tE, depends on the mass function of the lenses, the distribution of both lenses and sources along the line of sight, and the circular velocities and velocity dispersions of the stars. Like the optical depth, the time scale frequency distributions are also sensitive to the line of sight directions. Both the optical depths and the time scale frequency distributions are routinely obtained from the growing data set. Although the dependence on so many parameters precludes definitive measures of any one galactic property by microlensing alone, constraint of some of these parameters with other techniques will allow powerful microlensing constraints on the distribution of stellar mass near the galactic plane. In particular, microlensing can detect late type dwarf stars that are invisible to all other techniques. In fact, the meager data set of about 50 events toward the galactic center that have so far been analyzed and published, imply far more M-type dwarfs than found in star counts. An empirical optical depth three times larger than that predicted from axisymmetric galactic models supports other evidence for a bar-like central bulge with the long axis pointing more or less toward the Sun. There may already be a sufficient number of events to constrain the distribution of stars in the galactic bar in considerably more detail. The variation of optical depth and time scale frequency distributions over an extensive range of parameter space defining galactic properties is demonstrated.
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