Astrometric and Light-travel Time Orbits to Detect Low-mass Companions: a Case Study of the Eclipsing System R Canis Majoris

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 (light-travel time or 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 a hundred 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 semi-major axis of a12 = 117±5 mas, and values of the orbital eccentricity and inclination of e12 = 0.49±0.05, and i12 = 91.7±4.7 deg, respectively. Adopting the total mass of R CMa of M12 = 1.24±0.05 M⊙, the mass of the third body is M3 = 0.34±0.02 M⊙ and the semi-major 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. Subject headings: stars: individual (R CMa) — astrometry — stars: fundamental parameters — binaries: eclipsing — stars: late-type