Higher-order perturbations to (high-frequency) rotation

[warrick]

I'm currently collaborating on a fairly rapidly-rotating δ Sct pulsator (think ω/ωcrit ≈ 0.2-0.4). If the mode identification we're using is correct (and I think it is), then there appears to be an asymmetry in the rotational splittings. We thought'd we try to model the pulsations with MESA & GYRE but I don't know of a built-in way to get asymmetric mode splittings in these low-order p-modes (n≈1-10, ℓ≤3), since we're outside the regime covered by the TAR.

I'm about to dig into the literature but wondered if any GYRE users could offer any tips of suggestions where to look. My starting point is to assume one can somehow go to second (or higher) order in the rotation rate using data in the eigenfunctions, which looks like the way I'm headed with Saio 1981, which I arrived at via Kjeldsen et al. (1998).

[rhtownsend]

Hi Warrick --

Quoting from Section 3.8.6 of Asteroseismolog (Aerts, JCD & Kurtz):

In rapidly rotating stars terms quadratic and of higher order in Ω can no longer be ignored. This also includes the distortion of the star by rotation (see Section 3.2.4.2). For moderate rotation a perturbation expansion includ- ing terms of order Ω2 can be carried out. This was initially discussed by Simon (1969) and further developed, e.g., by Chlebowski (1978), Saio (1981), Gough & Thompson (1990) and Dziembowski & Goode (1992).32 The treatment was extended to third order in Ω by Soufi et al. (1998; see also Karami 2008). An interesting analysis to O(Ω2) was carried out by Sobouti (1980), consid- ering also an expansion around the convectively neutral state. Christensen- Dalsgaard & Dziembowski (2000) summarized the main aspects of the pertur- bation treatment of rapid rotation; the present section draws heavily on their presentation. For simplicity we assume uniform rotation in the following.

cheers,

Rich