# 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

## 1 Answer

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 $$R_T = 1.43 \left( \frac{M}{M_{\odot}} \right)^{1/3}\ \ {\rm pc}.$$

Using this formula, I get that the tidal radius for Fomalhaut is 2.01 pc (in reasonable agreement with whatever source you are using). As the mass of the Sirius system is only marginally larger then the tidal radius will be almost the same, since it depends on the cube root of mass.

• This would mean that the tidal radius of the Sun is 1.43 parsecs. Proxima would then be located within the tidal radius of the Sun rendering Sun and Alpha Centauri a physical system. Very obvious not a very realistic scenario. If the tidal radius of a stellar object is defined by gravitational forces cancelled out by surrounding objects then the outer rim of the postulated Oort cloud with 100,000 AU would be more appropriate. For other bodies with different mass this would then be the outer radius of a corresponding fictive "Oort" cloud – Wilfried Knapp Nov 27 '19 at 16:43
• @WilfriedKnapp The tidal radius is defined as where the difference in gravitational force caused by an external potential exceeds the gravitational force of the object itself. That is 1.43 pc for the Sun. That is, objects closer than 1.43pc to the Sun have the possibility of being bound to the Sun. That does not mean that they are. Obviously Alpha Cen, Prox Cen etc. are not, because they have a very significant velocity wrt the Sun. I have demonstrated where the quoted numbers come from and how they scale with mass. – ProfRob Nov 27 '19 at 20:56