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 P_12=92.8+/-1.3 yr, an LTT semiamplitude of 2574+/-57 s, an angular semi-major axis of a_12=117+/-5 mas, and values of the orbital eccentricity and inclination of e_12=0.49+/-0.05, and i_12=91.7+/-4.7 deg, respectively. Adopting the total mass of R CMa of M_12=1.24+/-0.05 Mo, the mass of the third body is M_3=0.34+/-0.02 Mo and the semi-major axis of its orbit is a_3=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.