Volume 591, July 2016
|Number of page(s)||10|
|Section||Numerical methods and codes|
|Published online||24 June 2016|
Distance and luminosity probability distributions derived from parallax and flux with their measurement errors
With application to the millisecond pulsar PSR J0218+4232
Institute for Mathematics, Astrophysics and Particle Physics, Radboud
PO Box 9010,
e-mail: A.Igoshev@science.ru.nl; F.Verbunt@science.ru.nl; E.Cator@science.ru.nl
Received: 29 September 2015
Accepted: 27 April 2016
We use a Bayesian approach to derive the distance probability distribution for one object from its parallax with measurement uncertainty for two spatial distribution priors, a homogeneous spherical distribution and a galactocentric distribution – applicable for radio pulsars – observed from Earth. We investigate the dependence on measurement uncertainty, and show that a parallax measurement can underestimate or overestimate the actual distance, depending on the spatial distribution prior. We derive the probability distributions for distance and luminosity combined – and for each separately when a flux with measurement error for the object is also available – and demonstrate the necessity of and dependence on the luminosity function prior. We apply this to estimate the distance and the radio and gamma-ray luminosities of PSR J0218+4232. The use of realistic priors improves the quality of the estimates for distance and luminosity compared to those based on measurement only. Use of the wrong prior, for example a homogeneous spatial distribution without upper bound, may lead to very incorrect results.
Key words: methods: statistical / stars: luminosity function, mass function / pulsars: general / pulsars: individual: PSR J0218+4232
© ESO, 2016
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