The Binary Broadening Function

Abstract

We propose an extended formalism for the spectral broadening function (BF) based on the multiplication rule of block matrices. The formalism, which we named the binary broadening function (BBF), can produce decomposed BFs for individual components of a binary star system by using two spectral templates. The decomposed BFs can be used to derive precise rotational profiles and radial velocities for individual components. We test the BBF on simulated spectra and actual observational spectra to show that the method is feasible on spectroscopic binaries, even when the spectral lines of two stellar components are heavily blended. To demonstrate the capability of the method, we conduct a simulation of `sketching' (imaging) a transiting circumbinary exoplanet using the BBF. We also discuss issues of implementation such as the variation of BBF with biased templates, the pros and cons of BBF, and cases when the method is not applicable.