1. Ragozzine - ESSII Inclination Distribution of Exoplanetary Systems Extreme Solar Systems II Presentation 06.03 September 13, 2011 Darin Ragozzine (Harvard ITC Fellow), Kepler TTV/Multiples Working Group, & The Kepler Team

2. Ragozzine - ESSII Architecture of Kepler's Candidate Multiple Transiting Systems (Lissauer, Ragozzine, et al. 2011b) Accepted paper on arXiv (v4, many minor updates)

3. Ragozzine - ESSII Multiple Transiting Systems [none pre-Kepler]

4. Ragozzine - ESSII Multiple Candidate Systems!!! Borucki et al. 2011, Lissuaer et al. 2011b, Ragozine & Holman 2010

5. Ragozzine - ESSII Multiple Candidate Systems!!! Borucki et al. 2011, Lissuaer et al. 2011b, Ragozine & Holman 2010

6. Ragozzine - ESSII #B11 NewB11 Acceptable 1791~965471 211521871 3457320 48251 5181 6120 Triples/Doubles Detected B11 = 0.39 Triples/Doubles Accetpable B11 = 0.28 Triples/Doubles Detected NEW = 0.37 Triples/Doubles Acceptable NEW = ??? Quads/Triples Detected B11 = 0.18 Quad/Triples Accetable B11 = 0.05 Quads/Triples Detected NEW = 0.34 Detected Triples/Doubles Ratio stays about the same but Quads/Triples and Quints/Quads increased significantly

7. Ragozzine - ESSII Inclinations ↔ Formation/Evolution Protoplanetary disk is flattened by angular momentum which is transferred to the planets (Bitsch & Kley 2011) Collisions reduce/minimize inclinations Migration after inclination-resonance capture can excite inclinations (Lee & Thommes 2009) Scattering increases inclinations Forcing by external inclined object can enhance as well

8. Ragozzine - ESSII True Mutual Inclinations Nearly impossible from current RV, astrometry, or direct imaging except in special cases Systems with Multiple Transiting Planets - Do not reveal true mutual inclination automatically Multi-Transiting Systems have 4 unique new ways 1) Statistically (multiplicity discovery fractions, etc.) 2) TTV/TDV limits on individual systems 3) Multi-Rossiter-McLaughlin (rarely possible) 4) Exoplanet Mutual Events (O(1) detectable / yr)

9. Ragozzine - ESSII Inclination Distribution Statistically Inclination = True Mutual Inclination (Coplanarity) Critical for planet formation/evolution theories Compare frequency of different numbers of detected and non-detected planets Correlated with multiplicity (# planets / star) - Itself interesting - Needed to convert average number of planets per star to fraction of star with planets (Youdin 2011) Assume the majority can be described by particular multiplicity and inclination distribution functions

10. Ragozzine - ESSII Methods Forward Model, match to Kepler observations Alternative method by Tremaine & Dong 2011 1.5 < R < 6 R E, 3 < P < 125 days, ~all Kepler stars (red = sim)

11. Ragozzine - ESSII Results 2-3 planets with large inclinations 4-5 coplanar planets 3-4 nearly coplanar planets

12. Ragozzine - ESSII Results 2-3 planets with large inclinations 4-5 coplanar planets 3-4 nearly coplanar planets

13. Ragozzine - ESSII Caveats Nature of assumed multiplicity and inclination distribution functions can shift these numbers Kepler's completeness in the B11 sample (on which this is based) was limited; completeness possibly a function of multiplicity - New multiplicities not substantially different Also somewhat subject to errors in the KIC estimated stellar parameters

14. Ragozzine - ESSII Results Some caveats/assumptions (see L11b) Sample appears to contain two populations 1) nearly coplanar systems of 3-5 planets 2) either systems with 1 planet and/or multiple highly inclined planets Other “populations” we've seen: single hot Jupiters, solar system analogs, warm eccentric Jupiters, cold distant Neptunes - These may or may not be distinct populations

15. Ragozzine - ESSII Results Some caveats/assumptions (see L11b) Combining with other L11b results, we find: A few+ percent of stars have multiple (3-5), similar-sized, and nearly-coplanar 1.5-6 R E planets with periods between 3 and 125 days and period ratios that have a minor tendency to be just wide of resonance. FSWP = NPS / Multiplicity (approx 0.05 = 0.2/4) With the enhancement in Kepler detections reported yesterday, this goes up to ~5%.

16. Ragozzine - ESSII Radial Velocity Surveys Insensitive to inclination dispersion Good for measuring true multiplicity Also good at measuring density distribution (Howard et al. 2011, Gaidos et al. 2011, Wolfgang & Laughlin 2011) Ideally done with a model savvy to inclinations and multiplicities

17. Ragozzine - ESSII More Results from HARPS (Mayor et al. 2011) ~50% of stars host at least 1 planet < 30 M E and Periods < 100 days 70% of these are multiple!!! Among the 10 most sampled stars are 29 planets! Confirms that there is a prevalent population of multiple small-planet systems Calculating RVs from my model shows that RV observations are independent of inclination but strongly dependent on true multiplicities

18. Ragozzine - ESSII HARPS vs. Kepler When accounting for multiplicity, there is approximately an order of magnitude difference in the fraction of stars with planets measured by HARPS (~50%) and Kepler (~5%) Possible contributors to this discrepancy Residual Kepler incompleteness Overestimated HARPS result (with errors, 50 +/- 17%) KIC stellar parameters are inaccurate and/or biased Fundamentally different kinds of stars...

19. Ragozzine - ESSII HARPS vs. Kepler Possible contributors to this discrepancy Statistical issues with binning/comparison... since the frequency increases so rapidly at the small end, small differences can lead to large apparent discrepancies Imprecise or miscommunicated comparisons (e.g., Darin is confused/wrong) Small planets generally have high densities (see Wolfgang & Laughlin, Gaidos et al. Posters, Howard et al. 2011). - Estimating the sin i correction and assigning all planets a density of 1 g/cc, then Kepler would find all of them - If all planets had a density of 5.5 g/cc, then the expected detectability for Kepler goes to ~25%

20. Ragozzine - ESSII Conclusions Multi-transiting systems are awesome Significant population of planetary systems with 3-5 nearly-coplanar planets - Inclination limits from Kepler frequencies Disagreement between occurrence of systems between Kepler (~~5%) and HARPS (~~50%) Treatment of multiplicity-inclination distribution in joint RV/transit survey will help break degeneracies and measure densities

21. Ragozzine - ESSII Radial Velocity Surveys Best-fit model of Lissuaer et al. 2011B Calculate RV amplitude, K, for all planets Call planets with K < K_detect, “detectable” Results Inclination distributions are inconsequential for RV detection Absolute rates change as a function of N_p Relative rates (2 vs. 1 detected) change as a function of N_p Large difference between K_detect of 5 m/s and 2 m/s At 1-2 m/s, more multiples than singles

22. Ragozzine - ESSII Coplanarity Boost Use the presence of 2+ confirmed planets to place reasonable constraints on both the central plane of the planetary system and the dispersion about that plane Can be done in a way that is relatively insensitive to assumed inclination dispersion, though the assumption that planets and candidates have the same dispersion is hard to avoid Calculate the increased probability of other planets transiting in such a planetary system compared to random orientations Especially powerful for longest period planets in systems