Numerical Study of Statistical Properties of the Galactic Center Distance Estimate from the Geometry of Spiral Arm Segments. (arXiv:1811.06886v1 [astro-ph.GA])

Numerical Study of Statistical Properties of the Galactic Center Distance Estimate from the Geometry of Spiral Arm Segments. (arXiv:1811.06886v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Nikiforov_I/0/1/0/all/0/1">I.I. Nikiforov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Veselova_A/0/1/0/all/0/1">A.V. Veselova</a>

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
$sigma_{R_0} simeq 0.5$-$0.3$ 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.

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
$sigma_{R_0} simeq 0.5$-$0.3$ 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.

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