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

Abstract

The influence of various factors on the statistical properties of the Galactic center distance ($R_0$) 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., $R_0$, 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 approximately constant. This lucky circumstance increases by a factor of 1.4-1.7 the accuracy of estimating $R_0$ from the arm segment traced by masers. Our numerical experiments provide evidence for the consistency of the $R_0$ 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 $R_0$ 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. When the data on 3-8 segments are processed simultaneously, the predicted standard error of the final estimate is $σ_{R_0} \simeq 0.5$-$0.3$ kpc, respectively. The accuracy can be improved by increasing the extent of the identified segments and the number of objects belonging to them. A more complex variant of the method taking into account the measuring and natural dispersions of objects relative to the arm center line will avoid the biases of the parameter estimates.