# What is the tidal radius of the Sirius system?

The Fomalhaut system is a trinary system, with Fomalhaut A (1.9 M), Fomalhaut B (0.7M) and Fomalhaut C (0.2M). Fomalhaut C is 2.5 light years from Fomalhaut A, and 3.2 light years away from Fomalhaut B. The tidal radius of the Fomalhaut system is 6.2 light years.

The Sirius system (Sirius A, 2M, Sirius B, 0.9M) is roughly 1.1x more massive than Fomalhaut A and B. What would be some ways to calculate a tidal radius of the Sirius sytem, to get an estimate of at what distance other stars could orbit the Sirius system?

• By "tidal radius", you mean the distance past which an object will no longer be gravitationally bound to the system? – Phiteros Dec 12 '16 at 18:38
• Yes, or, I came across the term in a paper on the Fomenhault system "We demonstrate that the astrometry, radial velocity, and photometric data for LP 876-10 are consistent with the star being a third, bound, stellar component to the Fomalhaut multiple system, despite the star lying nearly 6◦ away from Fomalhaut A in the sky. The 3D separation of LP 876-10 from Fomalhaut is only 0.77 ± 0.01 pc, and 0.987 ± 0.006 pc from TW PsA (Fomalhaut B), well within the estimated tidal radius of the Fomalhaut system (1.9 pc). " So basically, what they use it for. – memex Dec 12 '16 at 18:50

The tidal radius for a star or collection of stars near the Sun and on a circular orbit (matches Sirius reasonably well) is given by (e.g. Pinfield et al. 1998) $$R_T \simeq \left( \frac{GM}{2(A-B)^2} \right)^{1/3} ,$$ where $A$ and $B$ are the Oort constants and $M$ is the total mass.
Using the value of $A-B$ from Feast et al. (1997), this reduces to $$R_T = 1.43 \left( \frac{M}{M_{\odot}} \right)^{1/3}\ \ {\rm pc}.$$