Table 1.
Comparison of rotational frequency shifts, magnetic frequency shifts in the non-rotating case, and magnetic frequency shifts in presence of rotation.
| n | ℓ | m | fn, ℓ, m | fn, ℓ | fshift (a) | fshift (b) (c) | fshift (b) (c) | Sc (b) (c) | ℐ (b) | fshift |
|---|---|---|---|---|---|---|---|---|---|---|
| rot. | no rot. | rot. | 26.1 kG | 82.4 kG | (G−2) | mag./rot. | ||||
| −11 | 1 | −1 | 0.6867 | 0.8187 | 0.1320 | 5.2442 × 10−5 | 5.2270 × 10−4 | 9.4030 × 10−14 | 1.9334 × 104 | 1.0268 × 10−5 |
| −10 | 1 | −1 | 0.7573 | 0.8979 | 0.1406 | 5.6099 × 10−5 | 5.5915 × 10−4 | 9.1720 × 10−14 | 2.2684 × 104 | 1.1100 × 10−5 |
| −9 | 1 | −1 | 0.8381 | 0.9923 | 0.1542 | 9.6437 × 10−5 | 9.6120 × 10−4 | 1.4267 × 10−13 | 4.3094 × 104 | 1.7750 × 10−5 |
| −15 | 2 | −1 | 0.8720 | 1.0462 | 0.1742 | 4.4627 × 10−4 | 4.4481 × 10−3 | 6.2618 × 10−13 | 2.2076 × 105 | 2.9489 × 10−4 |
| −8 | 1 | −1 | 0.9222 | 1.0933 | 0.1712 | 2.1844 × 10−4 | 2.1772 × 10−3 | 2.9329 × 10−13 | 1.0754 × 105 | 4.8303 × 10−5 |
| −7 | 1 | −1 | 1.0037 | 1.1943 | 0.1905 | 1.2655 × 10−4 | 1.2613 × 10−3 | 1.5555 × 10−13 | 6.8059 × 104 | 5.3927 × 10−5 |
| −11 | 2 | −1 | 1.1268 | 1.4108 | 0.2839 | 2.8547 × 10−5 | 2.8453 × 10−4 | 2.9705 × 10−14 | 1.9044 × 104 | 1.1579 × 10−5 |
| −6 | 1 | −1 | 1.1483 | 1.3708 | 0.2225 | 2.5492 × 10−5 | 2.5408 × 10−4 | 2.7300 × 10−14 | 1.5736 × 104 | 1.0588 × 10−5 |
| −10 | 2 | −1 | 1.2198 | 1.5454 | 0.3256 | 3.0370 × 10−5 | 3.0270 × 10−4 | 2.8847 × 10−14 | 2.2191 × 104 | 1.1646 × 10−5 |
| −9 | 2 | −1 | 1.3337 | 1.7058 | 0.3721 | 5.1999 × 10−5 | 5.1829 × 10−4 | 4.4749 × 10−14 | 4.1940 × 104 | 1.7241 × 10−5 |
| −5 | 1 | −1 | 1.3775 | 1.6455 | 0.2680 | 8.9291 × 10−6 | 8.8998 × 10−5 | 7.9658 × 10−15 | 6.6164 × 103 | 2.5934 × 10−6 |
| −4 | 1 | −1 | 1.7358 | 2.0601 | 0.3244 | 4.4448 × 10−6 | 4.4302 × 10−5 | 3.1672 × 10−15 | 4.1234 × 103 | 1.0487 × 10−6 |
| −6 | 2 | −1 | 1.8191 | 2.3408 | 0.5217 | 1.2792 × 10−5 | 1.2750 × 10−4 | 8.0223 × 10−15 | 1.4158 × 104 | 8.9695 × 10−6 |
| −2 | 1 | −1 | 3.4811 | 3.9638 | 0.4826 | 5.1817 × 10−6 | 5.1647 × 10−5 | 1.9191 × 10−15 | 9.2493 × 103 | 3.7177 × 10−7 |
| −6 | 2 | 2 | 4.3408 | 2.3408 | 2.0000 | 7.9952 × 10−6 | 7.9690 × 10−5 | 5.0140 × 10−15 | 1.4158 × 104 | 3.1559 × 10−6 |
| −1 | 1 | −1 | 4.9948 | 6.1084 | 1.1135 | 1.7332 × 10−4 | 1.7275 × 10−3 | 4.1653 × 10−14 | 4.7676 × 105 | 1.4840 × 10−7 |
Notes. For each identified frequency in the spectrum of HD 43317 are given the radial order n, the angular degree ℓ, the azimuthal order m, the theoretical frequency computed with GYRE, the corresponding frequency at zero rotation, the rotational frequency shift, magnetic frequency shifts computed in the non-rotating case with two different values of the magnetic field, the magnetic splitting coefficient Sc defined in Eq. (15), the quantity ℐ defined in Eq. (16), and the magnetic frequency shift in the TAR computed using the formalism developed in the present paper. Frequencies are given in d−1.
In contrast with Buysschaert et al. (2018), where rotational frequency shifts were computed for the corresponding zonal (m = 0) mode, we simply compute them here as the difference between the frequency in the rotating case and the frequency in the non-rotating case.
These quantities were incorrectly computed in Buysschaert et al. (2018) (see text).
In Hasan et al. (2005), the same notation Sc is used indiscriminately for the coefficient used to compute magnetic frequency shifts (in Sect. 2) and for the coefficient used to compute magnetic splittings between modes of different azimuthal orders (in Sect. 3). Here we use the former definition, and the magnetic frequency shifts are computed accordingly.
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