1. Spatially resolved evolution of stellar active regions Outline  Unveiling the stellar surface  Introduction to Doppler imaging  Short term changes of active regions: differential rotation  Long term evolution: spotcycles  Future prospects Potsdam im Oktober 2003, M. Weber http://www.aip.de/groups/activity Thanks to: K.G. Strassmeier J. Rice AIP - activity group

2. Sunspots & differential rotation  Equator rotates faster than the pole  “Rigidity” changes throughout the solar cycle and between Odd & Even cycles  Equatorial rotation faster in ONSC

3.  Stars exhibit periodic light variations (often rotationally modulated)  Activity-related features found in starspots are present in stellar spectra (e.g. CaII H&K)  Chromospheric emission lines very strong in such stars Starspots

4. Direct imaging of starspots 'direct' image of Betelgeuse Gilliland & Dupree 1996, ApJ  Faint Object Camera of HST  Interferometric techniques  Only very large & very near objects observable

5. Photometric spot models e.g. HK Lac: Oláh et al. 1997  Positions and sizes of spots are optimized  Several bandpasses (V,R,I,..) are used for inversion  Only simple spot configurations can be retrieved  Some assumptions have to be made

6. Principle of Doppler imaging Missing flux (in case of a dark spot) leaves a characteristc bump in spectral line profile.

7. Doppler imaging 1  Missing flux from spots produce line profile deformations  'bumps' move from blue to red wing of the profile due to the 'Doppler' effect.  Position of spots correspond to spot longitudes

8. Doppler imaging 2  Speed of spots give indication of the latitude (more uncertain than the longitude)  'bumps' from high latitude spots start out somewhere in the middle of the line wing, low latitude spots at the shoulder

9. Short term variations: differential rotation  Note the sign convention for  (the solar case is positive)  [  ]=degr/day (x 0.202 = µrad/s)  B & C not independent or:  Artificial star (see Rice & Strassmeier 2000)   = -0.05, P  7days

10. Simulating differential rotation  line profiles corresponding to 2 rotations of the model star  Using seven consecutive line profiles to reconstruct one image  Simulation of a medium-long (7 day) period star (II Peg)

11. a. Reconstructing differential rotation by cross-correlation  Artifical maps created using  =0.05 and P=6.72 days  Shown is original differential rotation, cross correlation measurements, and fit to cross-correlation  Fit coresponds to  =0.06 and P=6.6 days  Introduced for AB Dor by Donati & Collier Cameron (1997)  Observations for two consecutive images needed  Spot/active region lifetimes?

12. b. “Sheared-image method”  Donati et al. 2000 for RX J1508,6- 4423  Using  in inversion process  evaluating  2 for different periods and differential rotation values  Darkest value corresponds to best fit  aka “  2 Landscape” method  One image is enough  But longer timeline is an advantage as long as it is smaller than the spot lifetimes

13. c. Direct tracing of spots AB Dor; Collier Cameron et al. 2002 Combining LSD and matched-filter analysis  =0.0046 (P eq =0.5132 days)

14. IM Peg  K2III, V max =5.8, vsini=27  70 nights of observations  24.65 days rotation period (SB1)  Two consecutive stellar rotations well covered  Anti-solar differential rotation found (   -0.04)

15. IM Peg, cont’d Doppler images with 24 days time separation

16. IM Peg, cont’d  Cross correlation of the two average images  Monte-Carlo style calculation of 50 image- pairs & cross-correlations to estimate the error.  Best fit (red line) corresponds to  =  1 /  0 =0.58/14.39 = -0.04

17. IM Peg, cont’d  Including  in the inversion procedure “sheared image method”  Parameter variation to find the best fit.  Average value for the four calculations  =  1 /  0 = -0.04  Variation of both P and  :  =  1 /  0 = -0.02 ±0.01, P= 24.4 ±0.2

18. IM Peg, cont’d  2D-cross correlation reveals meridional flows  Sum of horizontal flow yields the differential rotation pattern  meridional flow appears to be pole-wards

19. More stars  HD 218153 (K0III, V=7.6)  HD 31993 (K2III, V=7.48)  LQ Hya (K0III, V=7.5)  II Peg (K2IV, V=6.9)  HD 208472, IL Hya, HK Lac

20. HD 218153  Differential rotation and meridional flow detected  Weber & Strassmeier 2001   =0.09 to 0.34 (lower/upper limit)

21. HD 31993  Differential rotation detected  Strassmeier et al. 2003   = -0.15

22. LQ Hya Donati et al. (in press) ; Kovari et al. (submitted)  P=1.59 days,  ≤ 0.05

23. II Peg  P=6.72days  5 consecutive Doppler images    -0.05

24. II Peg cont’d  Using  in the inversion leads to a non-zero value for some data sets only.  Dataset for one map spans more than one stellar rotation   and period needs to be varied at the same time  P=6.62±0.05 days,  = -0.05 ±0.02 Variation of  and Period (“  2 -Landscape method”)

25. Long term changes / Activity cycles  Solar  11yr activity cycle  Mt. Wilson survey found many cycles of solar-type stars  Tracing starspots over one activity cycle is a challenging task (not-only observing) time wise

26. IM Peg / long term  Active longitudes (Berdyugina et al. 2000)  Probable activity cycle of 6.5yrs  Photometric activity cycles are 29.8 and 10.4 years (Ribarik et al 2003)

27. II Peg / long term  Long-term variations of spots on II Peg (P  9.5yr)  Active longitudes and “flip- flop”; 4.65yr halfcycle  Berdyugina et al. 1999

28. Variable differential rotation?  Donati et al. (in press)  Differential rotation is different for V and I and for different epochs  Compare to yesterday’s talk by Lanza & Rodonò  Is there a link to activity cycles?

29. Summary  5 differential rotation measurements  Single star (HD 218153) has  > 0, other single star <0  Kitchatinov & Rüdiger 1999:  P rot, meridional flow, larger  for giants

30. Outlook  The availability of several robotic telescope facilities will make long-term studies much easier.  In addition, stars not observable (e.g. P=1day) from one spot cat be observed from several facilities concurrently.