Numerical Study of Statistical Properties of the Galactic Center Distance Estimate from the Geometry of Spiral Arm Segments

The influence of various factors on the statistical properties of the Galactic center distance (R₀) estimate obtained by solving the general problem of determining the geometric parameters of a Galactic spiral arm from its segment with the inclusion of the distance to the spiral pole, i.e., R₀, in the set of parameters has been studied by the Monte Carlo method. Our numerical simulations have been performed for the model segments representing the Perseus and Scutum arms based on masers in high-mass star forming regions. We show that the uncertainty in the present-day parallax measurements for these objects systematically decreases (!) with increasing heliocentric distance, while the relative uncertainty in the parallaxes is, on average, approximately constant. This lucky circumstance increases significantly (by a factor of 1.4–1.7) the accuracy of estimating R₀ from the arm segment traced by masers. Our numerical experiments provide evidence for the consistency of the R₀ estimate from the spiral-segment geometry. The significant biases of the estimate detected only for the Scutum arm are caused mainly by the random parallax errors, the small angular extent of the segment, and the small number of objects representing it. The dispersion of the R₀ estimate depends most strongly on the angular extent of the segment and the parallax uncertainty if the latter, on average, does not depend on the distance. The remaining parameters, except for the pitch angle, exert an equally significant, but weaker influence on the statistical accuracy of the estimate. When the data on 3–8 segments are processed simultaneously, the predicted standard error of the final estimate is σR₀ ? 0.5?0.3 kpc, respectively. The accuracy can be improved by increasing the extent of the identified segments and the number of objects belonging to them. The method of determining R₀ from spiral segments has turned out to be operable for a wide set of possible parameters even when using an L-estimator (median). This makes the development of a more complex method based on an M-estimator, which allows one to properly take into account the measuring and natural dispersions of objects relative to the arm center line and, thus, to avoid the biases of the parameter estimates, meaningful.