1. Stellar Parameters through Analysis of the Kepler Oscillation Data Chen Jiang & Biwei Jiang Department of Astronomy Beijing Normal University 2 April 2010

2. 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

3. 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?

4. 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, T eff, and Δν

5. 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 1.6M sun, as well as in red giants.

6. Data Analysis  Purpose: to identify the frequency of maximum power (ν max ) and the large separation of the oscillations (Δν) from the power spectrum;  Method: Fourier transform to obtain ν max, Δν;  Data: 50 low-luminosity stars (ν max > 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)

7. ν max = 100.988 μHz Δν = 9.8205 μHz Light curve and power spectrum of a star in the Kepler Data

8. The relation between Δν and ν max

9.  Known: R/R , T eff, log(G), [Fe/H] (Z/X)  = 0.0245 ( Grevesse & Noels, 1993) (Z/X)=0.031  To know: Z, mixing length, age, mass

10.  Estimate the mass: Kjeldsen & Bedding (1995),Toutain & Fröhlich (1992) Preliminary estimation:

11.  Grid of evolutionary tracks:  For the sets of the modelling parameters that agree with the observational constraints, we used a fine resolution,

12. Modelling parameters:

13. Observational constraints 0.031 0.9858 3.6933 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 Model Characteristics 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 Models that agree with the observational constraints

14. Way to Go…  Use a criterion to choose the best fitted models, χ 2 minimization maybe.  Add δν to constrain the age of the model.  Consider the α to be a input parameter.

15. Thanks!