Rotation of KIC 11145123
Takashi Sekii
Division of Solar and Plasma Astrophysics
and
Hinode Science Center
NAOJ
…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
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
KIC11145123
 A late A star
 Kepler magnitude Kp=13
 Huber et al. (2014)
 Effective temperature: Teff = 8050±200 K
 Surface gravity: log g = 4.0±0.2 (g in cgs)
HELAS VI@Göttingen 4 Sep 2014
Oscillations of KIC11145123
 Kepler quarters 0-16, long cadence,
1340-day long
des (g modes)
metric data for
m the surface
e stars known
veral hundred
g its four-year
first success,
arise some baf adiabatic osd by the three
er, the spheriAmplitude
se indices
repspectrum
adial displacesurface nodes,
gitude, respecradial, dipolar
HELAS VI@Göttingen 4 Sep 2014
gative) m designates prograde (retrograde) modes with
otation in the inertial frame. The radial order n is asth the structure in the radial direction (Takata 2012).
arly follow Takata (2006) for the radial order of dipolar
gative values of n denote the radial orders of g modes.
Oscillations of KIC11145123
 Kepler quarters 0-16, long cadence,
123 has a Kepler1340-day
magnitude K p = 13, andlong
is a late A
RVATIONS AND FREQUENCY ANALYSIS
the Kepler Input Catalogue (KIC) revised photometry
l. 2014), its effective temperature is 8050 ± 200 K and
gravity is log g = 4.0 ± 0.2 (cgs units), showing it to be
uence A star. The data used for the analysis in this paper
ler quarters 0 to 16 (Q0 – Q16) long cadence (LC) data.
an orbital period about the Sun of 372.4536 d, hence
are just over 93 d. We used the multi-scale, maximum
(msMAP) pipeline data; information on the reduction
n be found in the data release notes 211 . To optimise
for exoplanet transit signals, the msMAP data pipeline
trophysical signals with frequencies less than 0.1 d− 1
greater than 10 d). None of the pulsation frequencies
in this paper are near to that lower limit, but if the star
rotational signal, e.g. from starspots, that will have been
he pipeline. Since, as we show, the rotation period is near
y data reduction technique will struggle to find a direct
s period because of its similarity to the time span or the
Figure 1. Top panel: An amplitude spectrum for the Q0-16 Kepler long
terly rolls.P-mode
This has no range
effect on our analysis.
G-mode range
cadence data up to the Nyquist frequency for KIC 11145123, showing the
p panel of Fig. 1 shows a full amplitude spectrum out
presence of both g modes and p modes that are clearly separated. The midist frequency for KIC 11145123 for the nearly continudle and bottom panels show expanded looks in the p-mode and g-mode
HELAS
4 Sep 2014
Q0-16 LC data spanning 1340 d (3.7 y). There are
pul- VI@Göttingen
frequency ranges, respectively.
oth the g-mode and p-mode frequency regions, which
Oscillations of KIC11145123
 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
ν1=17.964 d-1
 15 g-mode triplets
 High overtones with the mean period spacing
ΔPg=0.0024 d
HELAS VI@Göttingen 4 Sep 2014
Modelling KIC 11145123
 The low value of ΔPg indicates that the
star is in an advanced stage of evolution
HELAS VI@Göttingen 4 Sep 2014
Modelling KIC 11145123
 The strategy
 Match ΔPg and then match ν1
 Then see how well the other modes fit
HELAS VI@Göttingen 4 Sep 2014
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
Rotational shift of frequencies
dwnlm = m(1- Cnl ) ò Knl (r)W(r)dr
HELAS VI@Göttingen 4 Sep 2014
Nearly a rigid rotator
 The g-mode splittings show very small
scattering
 Δfg=0.0047562±0.0000023 d-1 (average)
 Implies a rigid rate of about 0.0095 d-1 (in
rotational frequency)
 Cnl→1/2 for dipole g modes
 The p-mode shifts are more or less
consistent with this rate too
 Cnl→0 for p modes
 However…
HELAS VI@Göttingen 4 Sep 2014
Rotational shift of frequencies
HELAS VI@Göttingen 4 Sep 2014
Core vs envelope
 The envelope seems to be rotating
slightly faster since…
 Δfg=0.0047562±0.0000023 d-1 (average)
 Δfp=1.0101560±0.0000025 d-1 (l=1, n=3)
 Δfp-2Δfg>0
 Note that
 Ωp/2π＞Δfp (lower bound)
 Ωg/2π<2Δfg (upper bound)
HELAS VI@Göttingen 4 Sep 2014
Two-zone modelling
 Fitting the following form
ìï W
1
W(r) = í
ïî W2
(0 £ r £ rb )
(rb £ r £ R)
 …not even to individual splittings, but to
the p- and g-averaged splittings
HELAS VI@Göttingen 4 Sep 2014
Two-zone modelling
Solid: g-mode kernel
Dotted: p-mode kernel
Step functions:
two-zone models
Good separation between
regions sampled by two
kernels
HELAS VI@Göttingen 4 Sep 2014
Two-zone modelling
 Averaging kernel (rb=0.3R)
Solid: avg krn for Ω1
Dotted: avg krn for Ω2
‘Localization’ fairly good
and small dips do not
affect the conclusion
HELAS VI@Göttingen 4 Sep 2014
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
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
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