Disk mass estimates in a binary system

E. Nagel

Instituto de Astronomía, Universidad Nacional Autónoma de México, Apdo. Postal 70–264, 04510 México, D. F., México (enagel@astroscu.unam.mx)

Received 2007 April 30
Accepted 2007 November 21

RESUMEN

Desde el punto de vista analítico, un asunto natural de estudio en un sistema binario en órbita circular es la consecuencia de la conservación de la constante de Jacobi (C_J). La implicación principal es que para cada partícula existen zonas permitidas y prohibidas. Este esquema es válido al incluir interacciones entre las partículas; esto únicamente significa que C_J y el espacio de configuración permitido–prohibido depende del tiempo. La formación y evolución inicial de un disco alrededor de una estrella aislada se interpreta de acuerdo con este marco. Extendemos este modelo para el caso en el cual se tiene una estrella secundaria pequeña. Las estimaciones observacionales de la razón entre las masas del disco circunprimario y circunbinario son congruentes con un conjunto de simulaciones SPH en el cual la razón entre la separación entre las estrellas y el radio del disco es el parámetro que cambia. Se usa GW Ori como ejemplo.

ABSTRACT

The consequences of the conservation of the Jacobi constant (C_J) are studied here analytically for a circular binary system. The main result is that for every particle there are prohibited and allowed zones. This scheme is valid with the inclusion of interactions between the particles in the orbital plane of the binary system; this means that C_J and the allowed–prohibited configuration space are time–dependent. The formation and initial evolution of a disk around an isolated star is interpreted according to this work. We extend this model for the case where there is a small secondary star and argue that observational estimates of the ratio between circumprimary and circumbinary disk masses are consistent with a set of SPH simulations in which the ratio between the separation of the stars and the disk radius is the parameter that varies. GW Ori is used as an example.

Key Words: accretion, accretion disks — binaries: general — circumstellar matter

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Acknowledgement

I thank Jorge Cantó for his continued support and advice. The assistance of William Lee in the numerical part of this research is gratefully acknowledged. I am in debt to the referee whose comments helped to clarify the subject of this paper. I also thank William Lee for a critical reading of the original version of the paper. The help of Stan Kurtz with the writing of the final version of the article is also acknowledged.

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