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

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

The talk is about  Asteroseismic inference on rotation of a terminal-age main-sequence star KIC  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 4 Sep 2014

KIC  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 4 Sep 2014

Oscillations of KIC  Kepler quarters 0-16, long cadence, 1340-day long HELAS 4 Sep 2014 Amplitude spectrum

Oscillations of KIC  Kepler quarters 0-16, long cadence, 1340-day long HELAS 4 Sep 2014 P-mode rangeG-mode range

 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 KIC HELAS 4 Sep 2014 ΔP g = d ν 1 = d -1

Modelling KIC  The low value of ΔP g indicates that the star is in an advanced stage of evolution HELAS 4 Sep 2014

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

Modelling KIC  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 4 Sep 2014

Rotational shift of frequencies HELAS 4 Sep 2014

Nearly a rigid rotator  The g-mode splittings show very small scattering Δf g = ± d -1 (average) Implies a rigid rate of about 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 4 Sep 2014

Rotational shift of frequencies HELAS 4 Sep 2014

 The envelope seems to be rotating slightly faster since… Δf g = ± d -1 (average) Δf p = ± 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 4 Sep 2014 Core vs envelope

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

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

Two-zone modelling  Averaging kernel (r b =0.3R) HELAS 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

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 4 Sep 2014

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 4 Sep 2014

Summary  A terminal-age main-sequence A star KIC 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 4 Sep 2014