Stellar Parameters through Analysis of the Kepler Oscillation Data

Chen Jiang & Biwei JiangDepartment of AstronomyBeijing Normal University2 April 2010

Kepler Mission : A search for habitable planets

SUCCESSFULLY LAUNCHED:On 7 March 2009 at 03:50 Universal Time (6 March at 10:50 p.m. local time at Kennedy Space Center)

The Extended Solar Neighborhood

Kepler mission will not only be able to search for planets around other stars, but also yield new insights into the parent stars themselves.

How old are stars? How do they evolve? Is the Sun a typical star? How does matter behave under the extreme conditions in stars?

Stellar Parameters Determination

Objects: red giants Data : red giant oscillation data from Kepler

project Code: Yale Stellar Evolution Code (YREC7) Parameters to determine: mass and Z Comparison: L, Teff, and Δν

Solar-like Oscillation in Red Giants

Solar-like oscillations are caused by turbulent convective motions. They are stochastically excited and have very small amplitudes.

Solar-like oscillations are predicted for low-mass main sequence stars and stars located the red edge of the classical instability strip with mass about 1.6Msun, as well as in red giants.

Data Analysis

Purpose: to identify the frequency of maximum power (νmax )

and the large separation of the oscillations (Δ ) from the ν

power spectrum;

Method: Fourier transform to obtain νmax , Δ ;ν

Data: 50 low-luminosity stars (νmax > 100 μHz, L 30L ), long-

cadence(29.4-min sampling), A total of 1639 integrations ( 14

bad ones), 34 days (T. R. Bedding, D. Huber, et al. 2010)

νmax = 100.988 μHz

Δ = 9.8205ν μHz

Light curve and power spectrum of a star in the Kepler Data

The relation between Δ and ν νmax

0.778 0.027max max( / )

Known:

R/R , Teff , log(G) , [Fe/H]

(Z/X) = 0.0245

( Grevesse & Noels, 1993)(Z/X)=0.031

To know: Z , mixing length , age ,

mass

[ / ] log( / ) log( / )sFe H Z X Z X

Estimate the mass:

Kjeldsen & Bedding (1995)

,Toutain & Fröhlich (1992)

Preliminary estimation:

3 2/ ( / ) ( / )M M R R

/ 4.301, 15.2065 0.4 HzR R

134.92 Hz

/ 1.01 0.06M M

Grid of evolutionary tracks:

For the sets of the modelling parameters that agree with the observational constraints, we used a fine resolution,

0.95 1.07 , 0.02

1.8

0.017 0.022,0.54 0.70, 0.001

M M M M M

Z X Z

0.0002Z

Modelling parameters:

/ 1.05,0.017 0.022,0.54 0.70, 0.001M M Z X Z

Observational constraints

0.031

0.98583.6933

0.6336

15.2065

Modelling inputs

M1 M2 M3 M4 M5 M6 M7

0.95 0.97 0.99 1.01 1.03 1.05 1.07

0.0179 0.0180 0.0182 0.0183 0.0184 0.0186 0.0187

0.577 0.580 0.587 0.590 0.593 0.600 0.603

ModelCharacteristics

0.031 0.031 0.031 0.031 0.031 0.031 0.031

0.9845 0.9860 0.9856 0.9867 0.9856 0.9854 0.9865

3.6936 3.6932 3.6925 3.6929 3.6932 3.6928 3.6932

0.6283 0.6299 0.6311 0.6309 0.6297 0.6304 0.6302

5.2890 5.1692 5.0556 4.8624 4.6478 4.6304 4.4580

15.2169 15.2902 15.3838 15.5521 15.7737 15.8887 16.0515

/

log /

log

log /

[ Hz]

Z X

L L

T

R R

Models that agree with the observational constraints

/M M

Z

X

/

log /

log

log /

age[Gyr]

[ Hz]

Z X

L L

T

R R

Way to Go…

Use a criterion to choose the best fitted models, χ2 minimization maybe.

Add to constrain the age of the model.δν Consider the to be a input parameter.α

Thanks!