Simulated Galactic methanol maser distribution to constrain Milky Way
  parameters
  Using trigonometric parallaxes and proper motions of masers associated with
massive young stars, the Bar and Spiral Structure Legacy (BeSSeL) survey has
reported the most accurate values of the Galactic parameters so far. The
determination of these parameters with high accuracy has a widespread impact on
Galactic and extragalactic measurements. This research is aimed at establishing
the confidence with which such parameters can be determined. This is relevant
for the data published in the context of the BeSSeL survey collaboration, but
also for future observations, in particular from the Southern Hemisphere. In
addition, some astrophysical properties of the masers can be constrained,
notably the luminosity function. We have simulated the population of
maser-bearing young stars associated with Galactic spiral structure, generating
several samples and comparing them with the observed samples used in the BeSSeL
survey. Consequently, we checked the determination of Galactic parameters for
observational biases introduced by the sample selection. Galactic parameters
obtained by the BeSSeL survey do not seem to be biased by the sample selection
used. In fact, the published error estimates appear to be conservative for most
of the parameters. We show that future BeSSeL data and future observations with
Southern arrays will improve the Galactic parameters estimates and smoothly
reduce their mutual correlation. Moreover, by modeling future parallax data
with larger distance and, thus, greater relative uncertainties for a larger
numbers of sources, we found that parallax-distance biasing is an important
issue. Hence, using fractional parallax uncertainty in the weighting of the
motion data is imperative. Finally, the luminosity function for 6.7 GHz
methanol masers was determined, allowing us to estimate the number of Galactic
methanol masers.
