Constraining the Inclination of Binary System Orbits with the Astrometric Excess Noise from Gaia DR3

Abstract: Orbital inclination is crucial in determining the mass of the binary. The astrometric excess noise contain the orbital motion information, which can be used to constrain the inclination. We aim to constrain the orbital inclination of a binary system by combining radial velocity measurements with the astrometric excess noise from the Gaia DR3 solution. The astrometric excess noise is directly related to the orbital parameters. For a binary system with a radial velocity solution, it can be treated as a function of the orbital inclination. Using the Gaia nominal scanning law and the estimated centroid uncertainties, we simulate Gaia astrometric epoch observations to reproduce the expected excess noise. By sampling different inclinations and comparing the resulting simulated excess noise with the value reported in Gaia DR3, we can constrain the inclination to a specific interval. We have developed a method to constrain the orbital inclination within a specific range, enabling a more accurate determination of the binary mass, particularly for spectroscopic binaries. Internal and external validations demonstrate the robustness of the method, although certain limitations remain. It is most reliable for systems exhibiting a strong astrometric signal of binary motion, while caution is required when applying it to binaries with weak astrometric wobbles or poorly sampled orbits.