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Register a new userKinematic Distances: A Monte Carlo Method
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Distances to high mass star forming regions (HMSFRs) in the Milky Way are a crucial constraint on the structure of the Galaxy. Only kinematic distances are available for a majority of the HMSFRs in the Milky Way. Here we compare the kinematic and parallax distances of 75 Galactic HMSFRs to assess the accuracy of kinematic distances. We derive the kinematic distances using three different methods: the traditional method using the Brand & Blitz (1993) rotation curve (Method A), the traditional method using the Reid et al. (2014) rotation curve and updated Solar motion parameters (Method B), and a Monte Carlo technique (Method C). Methods B and C produce kinematic distances closest to the parallax distances, with median differences of 13% (0.43 kpc) and 17% (0.42 kpc), respectively. Except in the vicinity of the tangent point, the kinematic distance uncertainties derived by Method C are smaller than those of Methods A and B. In a large region of the Galaxy, the Method C kinematic distances constrain both the distances and the Galactocentric positions of HMSFRs more accurately than parallax distances. Beyond the tangent point along longitude=30 degrees, for example, the Method C kinematic distance uncertainties reach a minimum of 10% of the parallax distance uncertainty at a distance of 14 kpc. We develop a prescription for deriving and applying the Method C kinematic distances and distance uncertainties. The code to generate the Method C kinematic distances is publicly available and may be utilized through an on-line tool.
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We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.
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