Local effects in astrometric binary orbits: perspective transformation and light-travel time

The next generation of astrometric instruments will reach accuracies deserving new treatments. In order to get astrometric parameters achieving the precision permitted by the measurements, it will be necessary to take into account effects that were neglected until the present time. Two effects concerning the orbital elements of binary stars are considered hereafter: the former is the local perspective (LP) effect, which is due to the variation of the distance and of the orientation of the orbital plane during the observation time-span; the equations describing this effect are derived for the first time. The latter effect is the light-travel time (LTT), which is also related to the orientation of the orbital plane, and which is as efficient as the preceding one. Taking these effects into account would allow to find the ascending nodes of the orbits, and lead to orbital elements more accurate than when they are ignored.
It is derived from simulations that, at a distance of 5 pc, and assuming velocities typical of Population I stars, the position of the right ascending node could be derived for a few simulated unresolved binaries when the astrometric measurements have errors around 1 μas. For the resolved brown dwarf binary 2MASS J07464256+2000321, it appears that ignoring the LP effect would result in underestimating the masses of the components by 14 per cent of the errors as soon as the astrometric errors are around 20 μas for each measurement. However, a 'degenerate LP solution', taking into account the variation of the semimajor axis when the distance is varying, should provide reliable masses when the measurement errors are larger than 1 or 2 μas. A few binaries in the Gaia program could deserve a degenerate LP solution, whereas a complete LP+LTT solution could be justified for resolved binaries observed with Space Interferometry Mission ( SIM ).