Detecting stellar differential rotation

1. Detecting stellar differential rotation NORDITA – Solar and stellar dynamo cycles Thomas Hackman, 5.10.2009 Thomas Hackman: Stellar differential rotation

2. Detecting stellar differential rotation from photometry and spectroscopy • Contents: • Effects of differential rotation on photometry and spectroscopy • Time series analysis of photometry • Doppler imaging • Combining spectroscopy and photometry Thomas Hackman: Stellar differential rotation

3. 1. Observing the solar differential rotation • Quantification of the surface differential rotation: • Surface differential rotation was first observed by tracing sunspots: • The angular velocity vs. the radial distance from the solar core was retrieved by helioseismology Thomas Hackman: Stellar differential rotation

4. 1. Sun spot latitudes vs. angular velocity • Observations of 36708 sunspot groups (Howard 1994) Thomas Hackman: Stellar differential rotation

5. 2. Estimating stellar differential rotation • Some available methods: • Study changes in the rotation periods derived from UBV-photometry or Ca II H&K:n fluxes • Modelling of star spots using photometry • The profile of photospheric absorption lines • Doppler-imaging • Combining Doppler-imaging and photometric time series analysis Thomas Hackman: Stellar differential rotation

6. 3. Differential rotation and photometry • Spots determine the photometric rotation period Pphot of active late-type stars • Surface differential rotation => Pphot will depend on the spot latitude y • Changes in the latitudinal location of the main spot(group) will be seen as changes in the period Pphot Thomas Hackman: Stellar differential rotation

7. 3.1 Time series analysis of photometry • TSPA = Three stage period analysis (Jetsu & Pelt, 1999, A&AS 139, 629) • Model: • Results: Period (P), amplitude (A), mean magnitude (M), photometric minimum fmin Thomas Hackman: Stellar differential rotation

8. 3.2 Differential rotation from photometry • From the variations in Pphot we can derive a lower limit for the differential rotation Z: where PW is the weighted mean of the periods and DPW their standard deviation • Assuming a solar differential rotation curve we can estimate a from: Thomas Hackman: Stellar differential rotation

9. 3.3 Estimate of the differential rotation of a FK Comae type star • HD199178 (Jetsu et al., 1999, A&A 351, 212): • => larger a than expected for rapid rotator Thomas Hackman: Stellar differential rotation

10. 3.4 Estimate of the differential rotation of a young solar analogue • HD 116956 (Lehtinen, 2009): • Again: Larger a than expected Thomas Hackman: Stellar differential rotation

11. 3.5 Is a varying period really a proof of differential rotation? • Problem: Any period analysis will give a scatter in Pphot , even if the real period is constant • … but this scatter can be estimated and is in general much smaller than the measured DPW • Signs of differential rotation: • A (cor)relation between Pphot and the amplitude A of the photometric light curve • Drifts in the photometric minimum (obtained with constant Pphot) Thomas Hackman: Stellar differential rotation

12. 3.6 Drifting minimum phases • Latitudinal migration of spot activity + differential rotation => drifts in the photometric minimum phases Wobbling of the minima in LQ Hya (Berdyugina et al. 2002) Thomas Hackman: Stellar differential rotation

13. 3.6 Drifting minimum phases • Minimum phases of HD 199178 (Jetsu et al. 1999) Thomas Hackman: Stellar differential rotation

14. 3.7 Spot modelling of stellar light curves Croll et al. 2006 • Using star spot models one can retrieve spot latitudes and rotation rates from photometry • Ex. MOST satellite observations (Croll et al. 2006, Walker et al. 2007) • Problem: Non-uniqueness of the solution Thomas Hackman: Stellar differential rotation

15. 4. Differential rotation and line profiles • Surface differential rotation will alter the rotationally broadened profile of photospheric absorption lines (Bruning 1981): • a > 0 => a ”sharper” line profile • a < 0 => a more ”flat-bottomed” line • Fourier transform can be used to detect differential rotation (Gray 1977, Reiners & Schmitt 2003) • … but spots will complicate the analysis Thomas Hackman: Stellar differential rotation

16. 4. Differential rotation from line profiles • HD 67483 (Reiners & Schmitt 2003) Thomas Hackman: Stellar differential rotation

17. 5. Differential rotation from Doppler images • Locate spots from time separated Doppler images and study if their longitudinal migration dependence on their latitudes • Cross-correlate consecutive Doppler images and solve the differential rotation curve • Include differential rotation as a parameter in the Doppler imaging solution Thomas Hackman: Stellar differential rotation

18. 5.1 The problem of artefacts • Doppler images always include artefacts • ”Shadows” of appearing at some longitudes but lower latitudes of the real features • Longitudinal ”stripes” • High contrast alternating cool and hot features, often ”arches” or ”ovals” • High contrast small features • Axisymmetric artefacts: Latitudinal bands • Latitudinal shifts of real features • Including artefacts in the analysis => usually nearly rigid body rotation Thomas Hackman: Stellar differential rotation

19. 5.1.1 Doppler images of HD155555 DI:s of HD 155555 (Dunstone et al. 2008): Spots and radial magnetic field Thomas Hackman: Stellar differential rotation

20. 5.1.2 Doppler images of HD199178 • Low latitude “shadows” of high latitude spots (Hackman 2004) Thomas Hackman: Stellar differential rotation

21. 6. Combining photometry and spectrometry • The spot latitudes from Doppler imaging • The corresponding spot rotation period from time series analysis of photometry • Differential rotation can be included as a stellar parameter in the Doppler imaging inversion • To correct the rotation profile … • … but not necessarily to correct the surface shear, because we only need to track the main spot Thomas Hackman: Stellar differential rotation

22. 6.1. Observations • Spectrometry: • Nordic Optical Telescope + SOFIN Échelle spectrograph • Photometry: • Different APT:s Thomas Hackman: Stellar differential rotation

23. 6.2 Estimate of differential rotation of HD 199178 (Hackman 2004) • Spot latitude y (= b) vs. Pphot yields • … but the range in y is very limited and is this negative a physically possible? • Best fit with the “solar” differenential rotation curve to line profiles yields Thomas Hackman: Stellar differential rotation

24. 6.3 Estimate of differential rotation of FK Comae • Average spot latitudes vs. W yield nearly rigid body rotation (Korhonen et al. 2007): • …but again not very convincing Thomas Hackman: Stellar differential rotation

25. 7. Conclusions • Time series analysis of photometry often gives a higher a than expected from theoretical models • Doppler imaging combined with photometric time series analysis should be the best method to estimate differential rotation • … but more data is needed (same old story) Thomas Hackman: Stellar differential rotation

26. Acknowledgements • Thanks to prof. Ilkka Tuominen, without whom I would probably not be here today! Thomas Hackman: Stellar differential rotation

27. 1.2 Solar differential rotation in depth • Angular velocity as a function of r/Rsol (R. Howe / GONG/ NOAO) Thomas Hackman: Stellar differential rotation