TY - JOUR

T1 - A method to deconvolve mass ratio distribution of binary stars

AU - Curé, Michel

AU - Rial, Diego F.

AU - Cassetti, Julia

AU - Christen, Alejandra

AU - Boffin, Henri M.J.

N1 - Publisher Copyright:
© 2014 ESO.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Aims. It is important to know the binary mass-ratio distribution to better understand the evolution of stars in binary systems and to constrain their formation. However, in most cases, that is, for single-lined spectroscopic binaries, the mass ratio cannot be measured directly, but can only be derived as the convolution of a function that depends on the mass ratio and on the unknown inclination angle of the orbit on the plane of the sky. Methods. We extend our previous method for deconvolving this inverse problem by obtaining the cumulative distribution function (CDF) for the mass-ratio distribution as an integral. Results. After a suitable transformation of variables, this problem becomes the same as the problem of rotational velocities vsini, allowing a close analytic formulation for the CDF. We here apply our method to two real datasets: a sample of Am star binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 association. Conclusions. We are able to reproduce previous results for the sample of Am stars. In addition, the mass-ratio distribution of massive stars shows an excess of systems with a low mass ratio, in contrast to what was claimed elsewhere. Our method proves to be very reliable and deconvolves the distribution from a sample in one single step.

AB - Aims. It is important to know the binary mass-ratio distribution to better understand the evolution of stars in binary systems and to constrain their formation. However, in most cases, that is, for single-lined spectroscopic binaries, the mass ratio cannot be measured directly, but can only be derived as the convolution of a function that depends on the mass ratio and on the unknown inclination angle of the orbit on the plane of the sky. Methods. We extend our previous method for deconvolving this inverse problem by obtaining the cumulative distribution function (CDF) for the mass-ratio distribution as an integral. Results. After a suitable transformation of variables, this problem becomes the same as the problem of rotational velocities vsini, allowing a close analytic formulation for the CDF. We here apply our method to two real datasets: a sample of Am star binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 association. Conclusions. We are able to reproduce previous results for the sample of Am stars. In addition, the mass-ratio distribution of massive stars shows an excess of systems with a low mass ratio, in contrast to what was claimed elsewhere. Our method proves to be very reliable and deconvolves the distribution from a sample in one single step.

KW - Binaries: general

KW - Methods: analytical

KW - Methods: data analysis

KW - Methods: numerical

KW - Methods: statistical

KW - Stars: fundamental parameters

UR - http://www.scopus.com/inward/record.url?scp=84919799002&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201424531

DO - 10.1051/0004-6361/201424531

M3 - Article

AN - SCOPUS:84919799002

SN - 0004-6361

VL - 573

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A86

ER -