Astrometric and Light-Travel Time Orbits to Detect Low-Mass Companions: A Case Study of the Eclipsing System R Canis Majoris

Abstract

We discuss a method to determine orbital properties and masses of low-mass bodies orbiting eclipsing binaries. The analysis combines long-term eclipse timing modulations (the light-travel time [LTT] effect) with short-term, high-accuracy astrometry. As an illustration of the method, the results of a comprehensive study of Hipparcos astrometry and over 100 years of eclipse timings of the Algol-type eclipsing binary R Canis Majoris are presented. A simultaneous solution of the astrometry and the LTTs yields an orbital period of P₁₂=92.8+/-1.3 yr, an LTT semiamplitude of 2574+/-57 s, an angular semimajor axis of a₁₂=117+/-5 mas, and values of the orbital eccentricity and inclination of e₁₂=0.49+/-0.05 and i₁₂=91.7d+/-4.7d, respectively. Adopting the total mass of R CMa of M₁₂=1.24+/-0.05 M_solar, the mass of the third body is M₃=0.34+/-0.02 M_solar, and the semimajor axis of its orbit is a₃=18.7+/-1.7 AU. From its mass, the third body is either a dM3-4 star or, more unlikely, a white dwarf. With the upcoming microarcsecond-level astrometric missions, the technique that we discuss can be successfully applied to detect and characterize long-period planetary-size objects and brown dwarfs around eclipsing binaries. Possibilities for extending the method to pulsating variables or stars with transiting planets are briefly addressed.