Parent Distributions of the Periods and Magnetic Inclination Angles of Radio Pulsars

• Published in: Publications of the Astronomical Society of Japan 2003-04, Vol.55 (2), p.461-466
• Main Authors: Zhang, Li, Jiang, Ze-Jun, Mei, Dong-Cheng
• Format: Article
• Language: English
• ISSN: 0004-6264; 2053-051X
• DOI: 10.1093/pasj/55.2.461

We studied the parent distributions of pulsar periods and inclination angles by means of the Monte Carlo method. In our simulations, assuming that the parent period distribution satisfies a gamma function with two parameters, we tested a number of various parent distributions of the inclination angles ( $\alpha$ ), which are the inclination angles of the magnetic axis to the pulsar spin axis, and different relations between the beam angular radius ( $\rho$ ) and the pulsar period ( $P$ ) (i.e. $\rho \hbox{-} P$ relation). The simulated periods, pulse widths, and inclination angles were compared with the observed data using the Kolmogorov–Smirnov significance test. Our results indicate that: (i) the parent inclination angles could not be expressed by a flat function (a possible parent distribution is cosine-like or $\propto \{ 0.6/ \cosh[ 3.5 (\alpha-0.43) ] \} + \{ 0.15 / \cosh[ 4.0 (\alpha-1.6) ] \}$ ); (ii) the parent period distribution depends slightly on the $\rho \hbox{-} P$ relation, and is different from the observed period distribution (their differences can be expressed by different values of two parameters when the parent and observed period distributions can be described as gamma functions); and (iii) the average beaming fraction is about 0.12.