J/A+A/568/L12 Rotational frequency splitting in Sun-like stars (Nielsen+, 2014)
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Rotational splitting as a function of mode frequency for six Sun-like stars.
Nielsen, M. B., Gizon, L., Schunker, H., Schou, J.
=2014A&A...568L..12N
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ADC_Keywords: Stars, dwarfs ; Stars, late-type ; Rotational velocities ;
Space observations
Keywords: Asteroseismology - Stars: rotation - Stars: Solar-type -
Methods: data analysis
Abstract:
Asteroseismology offers the prospect of constraining differential
rotation in Sun-like stars. Here we have identified six high
signal-to-noise main-sequence Sun-like stars in the Kepler field,
which all have visible signs of rotational splitting of their p-mode
frequencies. For each star, we extract the rotational frequency
splitting and inclination angle from separate mode sets (adjacent
modes with l=2, 0, and 1) spanning the p-mode envelope. We use a
Markov chain Monte Carlo method to obtain the best fit and errors
associated with each parameter. We are able to make independent
measurements of rotational splittings of ~8 radial orders for each
star. For all six stars, the measured splittings are consistent with
uniform rotation, allowing us to exclude large radial differential
rotation. This work opens the possibility of constraining internal
rotation of Sun-like stars.
Description:
We used short-cadence (~58s) white light observations from the NASA
Kepler mission from March 2009 until the end of the mission in early
2013. The data were obtained from the Mikulski Archive for Space
Telescopes.
We fit the power spectrum with a model consisting of a constant noise
level, two frequency-dependent Harvey-like noise terms (see Eq. (1) in
Aigrain et al. 2004A&A...414.1139A), in addition to the individual
oscillation modes. We model these as a sum of Lorentzian profiles as
per Eq. (10) in Handberg & Campante (2011A&A...527A..56H), each
consisting of mode power, frequency, and linewidth.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table1.dat 78 6 Variance weighted mean rotational splittings
<{delta}{nu}>, inclination *, and rotation
period {Omega}/{Omega}_{sun}_ for the six
Sun-like stars.
table2.dat 126 277 Best-fit parameters for six Kepler stars
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Description of file: table2.dat
Values of table 2 are obtained from the posterior distributions of
each fit parameter, when fitting the model (described in the text) to
the observed spectrum of six stars in the Kepler field. The first
column contains the parameter name with the subsequent columns
specifying the values for each star as indicated by the Kepler Input
Catalogue (KIC) numbers given in the first row. The suffix '*_50th'
indicates the median of the posterior distribution, and '*_16th' and
'*_84th' are the 16th and 84th percentile values indicating the lower
and upper error of a given value.
The table first lists the Harvey-like terms used to fit the background
model which was done independently, before fitting the mode sets.
These are Harvey_1* and Harvey_2* (see Aigrain et al.
2004A&A...414.1139A), each with a characteristic power, frequency and
exponent. We also include an asymmetric Gaussian to account for the
contribution from the p-mode envelope, where 'Gaussian_frequency*' and
'Gaussian_power*' are the central frequency and height of the
Gaussian. The parameters 'Gaussian_width_b*' and 'Gaussian_width_r*'
are the Full Width at Half Maximum of the Gaussian on the right and
left side of 'Gaussian_frequency*. The final term in the background
model is a constant describing the high-frequency shotnoise
(Shotnoise_power*).
Following this is a list of the fit parameters for each mode set.
These are labeled with the prefix 'MS#_' indicating the mode set. The
mode frequency and height are additionally labeled according to the
angular degree (l2, l0, and l1). The list of mode sets continues up to
MS9, however, some stars have less mode sets and so the values for the
corresponding parameters have been set to -9999.
In all cases, frequencies, splittings, and widths are in units of
{mu}Hz. Power and height are given in units of ppm^2^/{mu}Hz, while
inclinations are given in units of degrees. The exponents of the
background terms are unitless.
See also:
V/133 : Kepler Input Catalog (Kepler Mission Team, 2009)
J/ApJS/211/24 : Rotation periods of Kepler MS stars (McQuillan+, 2014)
J/ApJS/211/2 : Stellar properties of Q1-16 Kepler targets (Huber+, 2014)
J/ApJS/210/1 : Asteroseismic study of solar-type stars (Chaplin+, 2014)
J/A+A/551/L8 : Chromospheric activity of field stars (Pace, 2013)
J/PASP/124/1279 : Q3 Kepler's combined photometry (Christiansen+, 2012)
J/ApJS/199/30 : Eff. temperature scale for KIC stars (Pinsonneault+, 2012)
J/ApJ/749/152 : Asteroseismic analysis of 22 solar-type stars (Mathur+, 2012)
J/MNRAS/423/122 : Abundances of 93 solar-type Kepler targets (Bruntt+, 2012)
J/AJ/144/24 : The Kepler-INT survey (Greiss+, 2012)
J/A+A/529/A89 : Kepler satellite variability study (Debosscher+, 2011)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 3 A3 --- --- [KIC]
5- 12 I8 --- KIC KIC number
14- 17 I4 K Teff [5669/6097] Effective temperature
19- 21 I3 K e_Teff Teff uncertainty
23- 26 F4.2 [cm/s2] logg [4/4.4] Surface gravity
28- 31 F4.2 [cm/s2] e_logg logg uncertainty
33- 36 I4 uHz lFit [1157/1760] lower fit frequency interval (1)
37 A1 --- --- [-]
38- 41 I4 uHz uFit [1662/2609] upper fit frequency interval (1)
43- 47 F5.3 uHz dnu [0.4/0.81] Variance weighted mean rotational
splitting <{delta}{nu}> (2)
49- 53 F5.3 uHz e_dnu [0.03/0.08] dnu uncertainty
55- 59 F5.3 uHz dvsini Variance weighted mean {delta}{nu}sini
61- 65 F5.3 uHz e_dvsini dvsini uncertainty
67- 68 I2 deg inc Unweighted mean of Inclination ** (2)
70- 73 F4.2 Sun Omega Stellar rotation rate relative to the solar
value {Omega}/{Omega}_{sun}_
(with {Omega}_{sun}_=0.424uHz)
75- 78 F4.2 --- e_Omega Omega uncertainty
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Note (1): Frequency intervals considered for each star, where each interval
is divided into segments of length approximately equal to the large
frequency separation.
Note (2): The variance weighted mean splittings <{delta}{nu}> are shown as
dashed lines in Fig. 2, where the listed errors are the standard
deviations of the weighted mean values. We note that the posterior
distributions for the {delta}{nu} are only approximately Gaussian.
The posterior distributions of inclination measurements cannot be
approximated as a Gaussian and so we only show the unweighted mean of
the inclinations where typical errors are ~20{deg}. The reader should
not use the mean values and associated errors reported here, but
should refer to the online material for more accurate values for each
mode set.
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 30 A30 --- Param Parameter names (explained in the
"Description of file" section above)
31- 46 F16.3 --- 4914923 ?=-9999 Best-fit values for 4914923
47- 62 F16.3 --- 5184732 ?=-9999 Best-fit values for 5184732
63- 78 F16.3 --- 6106415 ?=-9999 Best-fit values for 6106415
79- 94 F16.3 --- 6116048 ?=-9999 Best-fit values for 6116048
95-110 F16.3 --- 6933899 ?=-9999 Best-fit values for 6933899
111-126 F16.3 --- 10963065 ?=-9999 Best-fit values for 10963065
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Acknowledgements:
Martin Bo Nielsen, nielsenm (at) mps.mpg.de
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(End) Martin Bo Nielsen [IAG, Goettingen], Emmanuelle Perret [CDS] 14-Aug-2014
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