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Table D.1

Parameters, χ2 statistics, and derived quantities of the slow-rotation model for all possible oscillation modes up to degree l = 7.

Parameters Derived quantities
l m k (0) Posc = 2π/ω φ osc,ref φ rot,ref Ω /ω νsin(ir) i r a sph ω (0) Ω /ω(0) η M R ⋆ Prot = 2π/ Ω log (g (cm s-2))
(days) (km s-1) (°) (R⊙) (days-1) (M⊙) (R⊙) (days) (dex)
5 + 1 0.792 1.3818 0.4963 0.5323 0.0576 16.07 1.96 44.2 4.3 0.2688 4.5429 0.0577 0.0042 7.3 10.9 23.9801 3.22
6 + 1 0.676 1.3818 0.5009 0.5472 0.0671 16.28 2.15 39.7 5.3 0.2938 4.5435 0.0672 0.0067 5.3 10.4 20.5795 3.13
7 + 1 1.233 1.3884 0.5391 0.5624 0.0771 15.27 1.29 36.7 5.4 0.1774 4.5224 0.0771 0.0048 6.4 9.1 18.0159 3.33
4 −1 1.536 1.3839 0.7075 0.4535 0.0776 16.07 1.53 40.8 6.0 0.2099 4.5492 0.0774 0.0039 7.1 8.7 17.8413 3.41
3 −1 1.142 1.3851 0.1256 0.6720 0.0964 18.16 1.48 35.5 6.1 0.2030 4.5545 0.0960 0.0081 5.6 8.9 14.3632 3.29
1 + 1 0.909 1.3813 0.9207 0.4446 0.0768 18.03 3.94 36.4 6.1 0.5389 4.4614 0.0783 0.0067 7.8 10.8 17.9848 3.26
7 −3 0.819 1.3823 0.1565 0.4628 0.0769 19.41 1.37 43.1 6.1 0.1873 4.5549 0.0767 0.0072 5.9 10.1 17.9838 3.20
7 + 2 1.207 1.3870 0.6614 0.5348 0.0771 15.80 1.12 35.1 6.2 0.1534 4.5238 0.0772 0.0049 7.9 9.8 17.9975 3.35
5 −2 1.317 1.3814 0.1746 0.5724 0.0576 14.91 1.76 50.7 6.3 0.2407 4.5571 0.0575 0.0025 7.1 9.1 23.9694 3.37
5 + 2 0.769 1.3803 0.6947 0.5746 0.0586 16.46 2.01 44.3 6.3 0.2747 4.5431 0.0587 0.0045 7.1 11.0 23.5749 3.21
6 −4 0.909 1.3832 0.7240 0.5129 0.0659 19.42 1.24 48.8 6.5 0.1699 4.5567 0.0657 0.0048 7.9 10.7 20.9742 3.27
4 + 1 1.234 1.3811 0.9872 0.5926 0.0689 16.22 1.96 42.0 6.6 0.2685 4.5415 0.0691 0.0039 7.6 9.6 20.0320 3.36
4 + 2 1.321 1.3897 0.7807 0.6111 0.0686 15.06 1.38 44.4 6.6 0.1900 4.5059 0.0688 0.0036 5.9 8.6 20.2708 3.33
2 + 0 0.545 1.3813 0.8712 0.4993 0.0746 16.78 3.76 34.1 6.6 0.5147 4.5487 0.0746 0.0102 5.0 11.0 18.5110 3.06
2 −2 0.539 1.3957 0.5391 0.3711 0.0739 19.12 2.85 40.4 6.7 0.3944 4.5571 0.0730 0.0099 5.1 11.0 18.8904 3.06
4 −3 1.140 1.3975 0.7082 0.6050 0.0743 17.75 0.98 49.8 6.8 0.1363 4.5211 0.0739 0.0048 5.1 8.6 18.8158 3.27
6 −3 0.899 1.3833 0.0071 0.5219 0.0673 18.87 1.36 49.5 6.9 0.1862 4.5532 0.0672 0.0050 6.5 10.1 20.5470 3.24
6 −6 0.751 1.3937 0.4611 0.4594 0.0658 19.11 1.28 48.5 6.9 0.1760 4.5295 0.0655 0.0057 6.4 10.7 21.1718 3.19
6 + 0 0.919 1.3834 0.3775 0.5611 0.0673 16.23 2.37 38.4 6.9 0.3254 4.5420 0.0673 0.0049 7.7 10.6 20.5663 3.27
4 + 4 0.690 1.3962 0.7106 0.2175 0.0702 18.47 1.33 42.5 6.9 0.1844 4.4687 0.0707 0.0072 5.8 10.7 19.8864 3.14
5 + 5 0.688 1.3808 0.2273 0.4272 0.0545 19.47 0.58 73.9 6.9 0.0792 4.5297 0.0547 0.0044 5.0 10.1 25.3432 3.13
2 + 2 1.093 1.3942 0.8837 0.5255 0.0746 18.81 1.88 42.9 7.0 0.2594 4.4506 0.0755 0.0052 7.8 10.2 18.6906 3.31
7 −2 0.975 1.3817 0.4457 0.4625 0.0768 17.76 1.21 44.3 7.0 0.1662 4.5537 0.0767 0.0060 5.1 9.0 17.9843 3.23
5 + 4 0.713 1.3807 0.2725 0.5985 0.0581 18.93 0.95 54.2 7.0 0.1295 4.5330 0.0583 0.0048 6.6 11.0 23.7633 3.18
7 + 0 1.096 1.3883 0.3865 0.5701 0.0771 17.02 1.29 38.3 7.0 0.1774 4.5257 0.0771 0.0054 7.1 9.8 18.0165 3.31
6 −5 1.071 1.3847 0.4185 0.5136 0.0659 19.04 0.92 52.1 7.1 0.1260 4.5554 0.0656 0.0040 7.6 10.0 21.0169 3.32
4 + 0 1.403 1.3838 0.9448 0.4823 0.0766 16.52 1.92 40.1 7.1 0.2627 4.5405 0.0766 0.0042 7.6 9.2 18.0720 3.39
5 −1 0.815 1.3838 0.2473 0.6037 0.0586 17.20 1.96 46.9 7.1 0.2684 4.5449 0.0585 0.0042 7.6 11.0 23.6274 3.24
6 −2 1.030 1.3841 0.2414 0.5387 0.0673 16.95 1.49 48.2 7.1 0.2044 4.5469 0.0672 0.0044 5.7 9.2 20.5577 3.26
2 −1 0.979 1.3952 0.7438 0.3904 0.0718 19.42 2.71 52.6 7.3 0.3745 4.5304 0.0714 0.0052 5.7 9.4 19.4333 3.25
5 −4 1.069 1.3812 0.4125 0.3427 0.0576 19.35 1.08 78.0 7.4 0.1474 4.5665 0.0574 0.0031 6.2 9.4 23.9732 3.29
6 + 3 0.573 1.3855 0.2597 0.5681 0.0674 17.07 2.10 39.4 7.4 0.2876 4.5240 0.0676 0.0080 5.2 10.9 20.5540 3.08
3 + 1 1.623 1.3831 0.6094 0.5803 0.0796 16.88 1.19 49.1 7.5 0.1624 4.5277 0.0798 0.0039 5.1 7.7 17.3795 3.38
5 + 0 0.940 1.3832 0.3577 0.5768 0.0586 16.82 1.78 53.8 7.5 0.2442 4.5426 0.0586 0.0036 6.1 9.7 23.6226 3.25
6 + 6 1.039 1.3862 0.9538 0.9418 0.0670 18.04 1.32 54.6 7.5 0.1815 4.5111 0.0673 0.0044 5.3 9.0 20.6847 3.25
7 + 6 1.102 1.3819 0.3203 0.6680 0.0804 19.89 1.05 49.9 7.5 0.1441 4.5272 0.0807 0.0059 5.3 8.8 17.1895 3.27
5 −3 0.923 1.3853 0.2485 0.4441 0.0576 19.21 1.30 58.9 7.5 0.1790 4.5487 0.0574 0.0036 7.9 10.7 24.0647 3.28
7 −1 1.136 1.3800 0.2391 0.4212 0.0759 16.77 0.98 44.3 7.5 0.1342 4.5560 0.0758 0.0051 5.2 8.6 18.1923 3.28
4 −2 1.375 1.3888 0.5970 0.6288 0.0743 17.42 1.50 53.1 7.6 0.2058 4.5410 0.0740 0.0040 5.0 8.0 18.6890 3.33
7 + 7 1.139 1.3840 0.3603 0.8341 0.0911 19.86 1.13 40.9 7.6 0.1545 4.5139 0.0916 0.0074 6.0 9.1 15.1984 3.29
4 + 3 0.558 1.3875 0.4925 0.6222 0.0701 18.01 1.29 39.8 7.7 0.1777 4.5047 0.0705 0.0089 5.1 11.0 19.7801 3.06
7 −5 0.753 1.3875 0.0735 0.3664 0.0826 19.26 1.54 35.8 7.9 0.2115 4.5453 0.0823 0.0090 6.9 10.9 16.8068 3.20
6 + 5 0.904 1.3939 0.0170 0.5899 0.0674 18.82 1.04 53.7 7.9 0.1436 4.4894 0.0677 0.0051 5.4 9.5 20.6841 3.21
1 + 0 0.552 1.3812 0.9277 0.5236 0.0750 17.69 3.44 36.0 7.9 0.4712 4.5492 0.0750 0.0102 5.1 11.0 18.4167 3.07
7 + 3 1.147 1.3867 0.1874 0.5493 0.0771 16.04 1.12 35.0 8.0 0.1532 4.5217 0.0772 0.0052 7.9 9.9 17.9944 3.34
3 −2 0.545 1.3894 0.1333 0.5666 0.0896 17.92 1.96 30.0 8.0 0.2698 4.5561 0.0889 0.0145 5.1 11.0 15.5149 3.06
7 −4 0.731 1.3806 0.1750 0.3787 0.0769 19.51 1.39 39.5 8.1 0.1902 4.5637 0.0767 0.0080 6.7 10.9 17.9570 3.19
7 −7 0.947 1.3972 0.9249 0.3570 0.0904 19.58 1.46 40.5 8.1 0.2021 4.5224 0.0898 0.0085 5.2 9.2 15.4635 3.22
7 −6 0.822 1.3977 0.9766 0.3665 0.0825 19.81 1.27 38.7 8.2 0.1762 4.5152 0.0821 0.0082 6.8 10.6 16.9496 3.22
5 + 3 0.834 1.3814 0.5376 0.5662 0.0586 17.86 1.98 56.2 8.3 0.2712 4.5350 0.0587 0.0041 5.9 10.0 23.5851 3.20
6 −1 0.764 1.3840 0.3804 0.5393 0.0673 17.66 1.59 42.7 8.5 0.2173 4.5436 0.0672 0.0059 6.4 10.6 20.5764 3.19
3 + 0 2.644 1.3850 0.3184 0.6185 0.0807 17.05 0.61 56.3 8.6 0.0831 4.5365 0.0807 0.0025 6.2 6.9 17.1702 3.55
2 + 1 1.150 1.3860 0.9319 0.5183 0.0746 16.70 1.68 38.0 8.7 0.2309 4.5051 0.0751 0.0049 7.9 10.0 18.5693 3.34
1 −1 1.192 1.3833 0.7813 0.5990 0.0741 18.35 2.13 44.4 9.0 0.2921 4.6263 0.0727 0.0044 7.9 9.7 18.6732 3.36
3 −3 0.686 1.3836 0.8712 0.4988 0.0897 17.83 1.69 32.5 9.0 0.2319 4.5921 0.0887 0.0115 5.1 10.1 15.4178 3.13
5 −5 0.771 1.3836 0.4334 0.3416 0.0580 17.42 0.71 53.4 9.1 0.0979 4.5631 0.0577 0.0043 5.9 10.2 23.8619 3.19
7 + 5 0.691 1.3865 0.4376 0.6696 0.0731 19.06 1.32 42.0 9.4 0.1815 4.5168 0.0733 0.0078 5.8 10.7 18.9664 3.15
6 + 4 0.531 1.3927 0.2685 0.5754 0.0673 17.34 1.75 39.8 9.5 0.2420 4.4970 0.0675 0.0086 5.0 11.1 20.6960 3.05
0 + 0 0.808 1.3835 0.7017 0.7845 0.0827 17.52 2.50 32.4 9.5 0.3420 4.5416 0.0827 0.0085 7.1 10.8 16.7291 3.22
6 + 2 0.684 1.3805 0.4750 0.5388 0.0672 15.54 1.61 36.2 9.5 0.2199 4.5440 0.0673 0.0066 5.8 10.7 20.5323 3.15
4 −4 0.585 1.3938 0.5172 0.6031 0.0746 18.14 1.18 38.2 9.7 0.1632 4.5416 0.0741 0.0094 5.2 10.8 18.6808 3.09
3 + 3 0.950 1.3818 0.5339 0.5900 0.0780 16.88 0.85 34.3 9.9 0.1165 4.5028 0.0787 0.0065 7.6 10.5 17.7242 3.28
7 + 4 0.866 1.3868 0.3483 0.5457 0.0761 17.47 1.36 40.4 9.9 0.1863 4.5183 0.0763 0.0067 5.5 9.7 18.2232 3.20
3 + 2 1.109 1.3809 0.7472 0.6237 0.0781 16.62 0.48 41.8 10.2 0.0655 4.5205 0.0786 0.0056 5.1 8.7 17.6865 3.26

Notes. The rugged χ2 landscape and the model’s extreme sensitivity to tiny changes in several of the oscillation parameters, means that the numerical χ2 minimization normally fails to find the global best fit; the results shown here are probably just good fits instead of the best fit. The quantity η is the ratio of the centrifugal force to the gravitational force at the equator of the star (see Eq. (30) in Schrijvers et al. 1997). The table is sorted in ascending order by the reduced χ2.

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