1. Takashi Sekii Division of Solar and Plasma Astrophysics and Hinode Science Center NAOJ Rotation of KIC 11145123

2. …in collaboration with Don Kurtz Hideyuki Saio Masao Takata Hiromoto Shibahashi & Simon Murphy Kurtz et al. (2014)

3. The talk is about  Asteroseismic inference on rotation of a terminal-age main-sequence star KIC11145123  The star exhibits both p-mode oscillations and g-mode oscillations  The star is almost a rigid rotator  The envelope however is rotating slightly faster HELAS VI@Göttingen 4 Sep 2014

4. KIC11145123  A late A star  Kepler magnitude K p =13  Huber et al. (2014) Effective temperature: T eff = 8050±200 K Surface gravity: log g = 4.0±0.2 (g in cgs) HELAS VI@Göttingen 4 Sep 2014

5. Oscillations of KIC11145123  Kepler quarters 0-16, long cadence, 1340-day long HELAS VI@Göttingen 4 Sep 2014 Amplitude spectrum

6. Oscillations of KIC11145123  Kepler quarters 0-16, long cadence, 1340-day long HELAS VI@Göttingen 4 Sep 2014 P-mode rangeG-mode range

7.  It is a δ Sct-γ Dor hybrid  From the numerous peaks the following modes were selected for modelling 5 p modes (1 singlet, 2 triplets & 2 quintuplets)  The singlet is of the highest amplitude 15 g-mode triplets  High overtones with the mean period spacing Oscillations of KIC11145123 HELAS VI@Göttingen 4 Sep 2014 ΔP g =0.0024 d ν 1 =17.964 d -1

8. Modelling KIC 11145123  The low value of ΔP g indicates that the star is in an advanced stage of evolution HELAS VI@Göttingen 4 Sep 2014

9. Modelling KIC 11145123  The strategy Match ΔP g and then match ν 1 Then see how well the other modes fit HELAS VI@Göttingen 4 Sep 2014

10. Modelling KIC 11145123  The best model M=1.46M  Has a convective core (r 〜 0.05R) Z=0.01, Y=0.36  Helium abandunce high  Too faint and too cool for the KIC parameters HELAS VI@Göttingen 4 Sep 2014

11. Rotational shift of frequencies HELAS VI@Göttingen 4 Sep 2014

12. Nearly a rigid rotator  The g-mode splittings show very small scattering Δf g =0.0047562±0.0000023 d -1 (average) Implies a rigid rate of about 0.0095 d -1 (in rotational frequency)  C nl →1/2 for dipole g modes  The p-mode shifts are more or less consistent with this rate too  C nl →0 for p modes  However… HELAS VI@Göttingen 4 Sep 2014

13. Rotational shift of frequencies HELAS VI@Göttingen 4 Sep 2014

14.  The envelope seems to be rotating slightly faster since… Δf g =0.0047562±0.0000023 d -1 (average) Δf p =1.0101560±0.0000025 d -1 (l=1, n=3) Δf p -2Δf g >0  Note that Ω p /2π ＞ Δf p (lower bound) Ω g /2π<2Δf g (upper bound) HELAS VI@Göttingen 4 Sep 2014 Core vs envelope

15. Two-zone modelling  Fitting the following form  …not even to individual splittings, but to the p- and g-averaged splittings HELAS VI@Göttingen 4 Sep 2014

16. Two-zone modelling HELAS VI@Göttingen 4 Sep 2014 Solid: g-mode kernel Dotted: p-mode kernel Step functions: two-zone models Good separation between regions sampled by two kernels

17. Two-zone modelling  Averaging kernel (r b =0.3R) HELAS VI@Göttingen 4 Sep 2014 Solid: avg krn for Ω 1 Dotted: avg krn for Ω 2 ‘Localization’ fairly good and small dips do not affect the conclusion

18. Discussions (2/1)  The modelling uncertainty does worry us, but it does NOT affect the main inferences on the rotation  The nearly rigid rotation suggests a strong angular momentum transport It is UNLIKELY that the star is strongly magnetic HELAS VI@Göttingen 4 Sep 2014

19. Discussions (2/2)  If the envelope as a whole is rotating faster, why? Angular transport by waves? A viscosity-type mechanism cannot spin the outside up over the internal rate Mass accretion?  Also to explain the high He abandunce  One unexplored issue: what is the least exotic 2-d rotation profile consistent with data? HELAS VI@Göttingen 4 Sep 2014

20. Summary  A terminal-age main-sequence A star KIC11145123 exhibit both p-mode oscillations and g-mode oscillations  This permits us to examine the core rotation and the envelope rotation separately The star is almost a rigid rotator The envelope however is rotating slightly faster ‘on average’  There are implications on angular momentum transport mechanism HELAS VI@Göttingen 4 Sep 2014