Hello. I am interested in tidal interactions due to close encounters between stars in clusters.
As described in Press&Teukolsky 1977 (PT77) the energy deposited into a star following a close encounter can be encapsulated by a “tidal coupling constant” (really a function of the encounter distance and stellar model). I am currently working on tabulating tidal coupling constants for a broad range of stellar models (see the github repository here).
For each star the process is: (a) construct a MESA model (b) calculate the spectrum of normal modes with GYRE (c) calculate the overlap integrals for each mode. The overlap integral for a particular mode is
$Q= \int_0^1 r^2 \rho \ell r^{\ell1} [ \xi^R + (\ell+1) \xi^H] dr$,
where rho is the stellar density, and xi^R (xi^H) are the radial (tangential) components of the mode (renormalized following PT77). Computing the tidal coupling constants involves a summation over different modes. So far I just have the quadrupole order (l=2) coupling constants. (Apologies I could not figure out how to render the above equation inline)
I am using MESA v. 9793, GYRE v. 5.0. I have attached sample inlists for both.
Hopefully these tables will eventually be incorporated into the FEWBODY code!
I would appreciate any feedback on this project, particularly on the following two points.
(1) As I mention in the README here the overlap integrals of massive stars do not vary smoothly between consecutive, high order gmodes. I have tried playing with some of numerical parameters in the MESA/GYRE inlists (e.g. grid resolution), but this does not change the result. The experiments are described in the linked repo. Overall, the behavior of the overlap integrals for high order gmodes looks fish to me. But maybe it is physical? Do you have any insight on this?
(2) We would be interested in doing this for red giants also. I was wondering if any pitfalls are immediately apparent. (A collaborator expressed a concern that calculating the tidal coupling constants for red giants would be difficult to do robustly due to dense oscillation frequencies and small amplitudes).
Apologies if the above is somewhat openended...
Tidal coupling constants with MESA/GYRE

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 Joined: Wed Aug 01, 2018 11:04 am
Tidal coupling constants with MESA/GYRE
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Re: Tidal coupling constants with MESA/GYRE
Hi, Aleksey?
Calculating the overlap integral Q_nl directly from the displacement eigenfunctions will inevitably suffer from the numerical inaccuracies, especially for
high order gmodes. One way to circumvent the problem is to directly use the Eulerian perturbation of gravitation potential (see eq. 9 in Burkart et al 2012, MNRAS, 421, 983), this is is also one of the outputs that GYRE can offer, without adopting the Cowling approximation of course.
Hope it helps.
best regards,
Zhao
Calculating the overlap integral Q_nl directly from the displacement eigenfunctions will inevitably suffer from the numerical inaccuracies, especially for
high order gmodes. One way to circumvent the problem is to directly use the Eulerian perturbation of gravitation potential (see eq. 9 in Burkart et al 2012, MNRAS, 421, 983), this is is also one of the outputs that GYRE can offer, without adopting the Cowling approximation of course.
Hope it helps.
best regards,
Zhao

 Posts: 2
 Joined: Wed Aug 01, 2018 11:04 am
Re: Tidal coupling constants with MESA/GYRE
This is very helpful. Thank you! It is definitely a more straightforward way to get the overlap integrals. Although, the results are similar to what I get using the displacement eigenfunction directly. The exception is high order pmodes in low mass stars.
l=2 , 20 Msun l=2, 0.3 Msun
l=2 , 20 Msun l=2, 0.3 Msun