Using Transiting Exoplanets to Study Starspots with Kepler

1. Using Transiting Exoplanets to Study Starspots with Kepler James R. A. Davenport (Western Washington University) @jradavenport — NSF Postdoctoral Fellow Leslie Hebb (Hobart and William Smith Colleges) Suzanne L. Hawley (University of Washington)
2. Strassmeier (1999) • Tracing activity (& cycles, minima, …) • Info. about surface B field • Tracing rotation • Tracing differential rotation • Some info. about stellar age Starspots No introduction needed for this crowd SDO Carroll (2012)
3. Phase / Longitude Flux • Get rotation period, approx. starspot sizes • Map back to surface features (at least longitudes)
 e.g. Roettenbacher (2013) Brightness Variations from Starspots No Transit
4. (4 days) GJ 1243 - M4 Prot=0.5926 days Poster #13.46 Flux Time Brightness Variations from Starspots & flares! Davenport et al. (2014) Hawley et al. (2014) No Transit
5. 0 360 180 -180 0 540 Longitude (deg) Time (days) No Transit Davenport et al. (2015)
6. 0 360 180 -180 0 540 Phase—Flux Map Longitude (deg) Time (days) No Transit Davenport et al. (2015)
7. Longitude (deg) 360 180 -180 0 540 Time (days) Differential Rotation “Equator-Lap-Pole” times of ~1500 days 10x slower than on Sun! Spot lifetimes:150-500 days for 2nd spot many years for 1st spot No Transit Davenport et al. (2015)
8. Reiners (2006) Collier Cameron (2007) Küker & Rüdiger (2011) GJ 1245 B GJ 1245 A GJ 1243 Diff. Rot. rate No Transit Davenport et al. (2015) Lurie et al. (2014)
9. Limits to phase-tracking flux modulations • very hard to constrain latitude of starspots • can only track 2 (maybe 3) starspots • rapid rotators preferred • can only track very slow evolution • limited differential rotation recovery • how dark (cool) vs how big are the spots? Transits help with many of these problems! No Transit
10. Out-of-transit modulation like for GJ 1243 The physical scenario: many spots on surface In-transit full of details!
11. “Bumps” very informative! darker (cooler) spots spot size
12. darker (cooler) spots 70-80% Agrees with solar umbra!
13. Want to recover: • starspot positions on surface • differential rotation law • starspot evolution timescales First: Test our spot-fitting code using simulated data
14. Light curve model from Llama (2012), based on “butterfly pattern” Time (years) Latitude (deg) Flux Time (years) Plus solar-like differential rotation, spot evolution, migration, diffusion…
15. Then add eclipsing planet (hot Jupiter like) Time (years) Flux
16. A “Kepler” light curve based on Llama (2012) Time Flux • 4 years of data • 5 min samples • 10 day rotation (equator) • 2 day planet orbit • rp/rs = 0.1
17. Use MCMC to fit every starspot (longitude, latitude, radius) x nspots planet orbit & stellar rotation fixed Flux Time sampler based on Hebb+ 2015 in prep
18. Repeat for every time window Flux Time
19. Longitude (deg) slower than mean period faster spot lifetime Time (days) rotating @ mean period Goal: measure differential rotation & spot evolution trace starspot longitudes with time
20. Longitude (deg) Time (days) Each set of points = full static MCMC solution! Point color & size = radius
21. Longitude (deg) Time (days) Colors = cluster grey points = no cluster Use Python sklearn “DBSCAN” to cluster DBSCAN = Density-based spatial clustering of applications with noise Each cluster represents 1 starspot moving in longitude over time
22. Time (days) Max slope = highest lat spot Recovers simulated differential rotation law coefficient, k=1 Longitude (deg)
23. Now some real data!
24. Kepler 17 - G2 (same as our Sun!) Prot= 12.1 days (faster than Sun) Porb= 1.5 days (super fast) Mass = 2.5 MJ Rp/Rs = 0.13 Kepler 17b Désert et al. (2011) Properties very similar to the simulated system!
25. Long Cadence Short Cadence Short Cadence Time (days) Flux
26. Use MCMC to fit every starspot (longitude, latitude, radius) x 8 spots Flux Time
27. Results from Kepler 17 Reminder: do this for every time window!
28. Longitude (deg) Time (days) Starspot evolution with time: more complicated! Point color & size = radius slower faster mean period
29. Longitude (deg) Time (days) For Kepler 17 find k=0.8 Compare with solar value of k=0.2
30. Trace starspot decay profiles Time (days) Largest sunspots Work in Progress solar decay m odel Area sunspot decay Hathaway (2008)
31. Starspot lifetimes versus Size* Starspot Lifetime (days) Starspot Lifetime (days) Max Spot Radius (Gnevyshev-Waldmeier rule) Work in Progress *as traced by the planet
32. Summary • Kepler 17 starspot contrasts similar to sunspots • With transits, can track evolution of at least 100 starspot groups over 4 years • Estimate differential rotation law! • Spot decay/lifetime may constrain diffusion timescale info Time Longitude @jradavenport