Abstract
Abstract Background The Roche lobe geometry is important to understand and study the properties of the mass-losing component in a semi-detached binary system. However it is not easy to calculate accurately, and existing tables usually do not include the parameters of the binary system under study, nor do they allow for non-synchronous rotation. Results A calculator for properties of the Roche lobe is presented in two formats. An easy-to-use Java version has a graphic interface, and a Fortran 90 version has a command line interface. The Fortran version allows for easy modifications by the user. Both versions have two basic output options: one provides values of a set of various quantities (such as the Lagrange points along the binary axis, and area and volume of the Roche lobe); the second provides $R(\theta,\phi)$ R ( θ , ϕ ) , the distance from the stellar center to the stellar surface for any specified polar angle. A single set of input parameters can be entered directly or a large set of input parameters can be specified in a text file. The calculator includes the options to have non-synchronous rotation of the star, or to have the star underfill its Roche lobe. It can be used to calculate Roche lobe properties for the case of elliptical orbits, with some restrictions. Conclusions We present a convenient software tool for quickly and accurately calculating Roche lobe properties for mass ratio in the range 0.01 to 100, for Roche lobe fill-out factor in the range 0.1 to 1.0, and for dimensionless rotation rate of the star in the range 0.1 to 2.0. This will allow anyone working with a binary star system to obtain the Roche lobe or stellar surface geometry for their system.
Highlights
The Roche lobe geometry is important to understand and study the properties of the mass-losing component in a semi-detached binary system
The purpose of the present work is to present an freely available software tool, written in two versions (Java and Fortran), which calculates radii of the Roche lobe
3.2 Fits to Roche lobe radii The Eggleton formula has been widely used to calculate volume equivalent radius of the Roche lobe for the case of synchronous rotation p = (here we note that the q we use is equivalent to /q used by Eggleton ( ))
Summary
To carry out the calculations of the Roche Lobe properties, a Java version with a graphic interface (see Additional file ), and a Fortran version, with a command line interface (see Additional file ), were created. 3.2 Fits to Roche lobe radii The Eggleton formula has been widely used to calculate volume equivalent radius of the Roche lobe for the case of synchronous rotation p = (here we note that the q we use is equivalent to /q used by Eggleton ( )). The results of the residuals of the cubic spline fits from accurate numerical values are shown in Figure , together with the residuals of the Eggleton formula from accurate numerical values
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