Update on SysSim: Determining the Distribution of Exoplanetary Architectures

Transcription

1 Update on SysSim: Determining the Distribution of Exoplanetary Architectures Darin Ragozzine (UF / Florida Tech), Eric Ford (UF / Penn State) ExoStats 2014 CMU June 19, 2014

2 Invitation to Join BayCEP Bayesian Characterization of Exoplanet Populations Biweekly telecons Monday afternoons BayCEP?

3 I figuring out tricky tractable problems

4 Multi-Transiting Systems Transiting Planets Allow for physical characterization Radius, Density, Atmosphere (Interior, Composition, Habitability) Multiplanet systems Determine orbital architecture Use tools of planetary dynamics theory Multi-transiting systems are the most information-rich exoplanetary systems, combining the value of physical characterization with orbital architecture. Ragozzine & Holman 2010

5 Systems with Multiple Transiting Planets

6 10 11 But how are these planets distributed? What are their planetary systems like? How did these systems form? Use Information-Rich Multi-Transiting Systems Tens of billions of potentially habitable planets in the Milky Way with reasonable assumptions based on Kepler results (Dressing & Charbonneau 2013, Morton & Swift 2013, Kopparapu 2013). These are primarily in M dwarf Systems with Tightly-packed Inner Planets.

7 Kepler Big Picture Results Frequency and properties of different populations of planetary systems Hot Jupiters Circumbinary planets Systems with Tightly-packed Inner Planets (STIPs) Inner Solar System analogs Warm eccentric Jupiters (as seen in Rvs) Without multi-transit probability, cannot debias the observations to understand intrinsic populations Apply MTS Geometry to these systems Periods too long

8 Kepler Big Picture Results Frequency and properties of different populations of planetary systems Hot Jupiters Circumbinary planets Systems with Tightly-packed Inner Planets (STIPs) Inner Solar System analogs Warm eccentric Jupiters (as seen in Rvs) Need to understand geometric probability of multiple transiting planets or we cannot debias information-rich Kepler multis to understand intrinsic populations

9 Need Multi-Transiting Geometry Depends on inclination between orbits Celestial Sphere Ragozzine & Holman 2010

10 Debias Systems, not Planets Determining the frequencies of different types of planetary systems is complicated Use multi-transiting geometry to our advantage Preserve information on orbital architecture Can investigate an enormous number of questions

11 Multi-Transiting Geometry CORBITS: new fast N-planet semi-analytic solution (Brakensiek & Ragozzine, in prep.) For example, solar system has maximum of 3 planets in transit for any distant observer Publicly available (on Github)

12 Period Ratio Distribution CORBITS can be used to determine the debiased period ratio distribution: approximately lognormal

13 Radius Ratio of Neighbors Funded by NASA Origins PI Ragozzine/Ford SysGen

14 SysGen: Making Exoplanetary Systems SysGen is a component of SysSim that generates a synthetic catalog of exoplanetary systems that represents the true actual underlying population of exoplanetary systems What makes an exoplanetary system? N, the number of planets For each planet: Period/Semi-major axis Eccentricity (and geometric angle) Inclination (and geometric angle) Radius/Mass But, we also need to include correlations between planets Period Ratio Note that we re starting simple and working up to more complex problems

15 SysGen: Making Exoplanetary Systems From other debiasing methods, we already have a good sense of the underlying period distribution and the underlying period ratio distribution Let s APPROXIMATE the ~debiased distribution as our first guess for the true population of SysGen Doubly- broken Pareto with edges Truncated log normal

16 Matching Period and Period Ratio Dists Easy! Just draw Pinner from the P dist and Pouter/ Pinner from the Period Ratio Dist UH OH! Then the Pouter distribution doesn t look like the targeted period distribution Issues with to Kepler debiased Pinner distribution Doubly- broken Pareto with edges Truncated log normal

17 Matching Period and Period Ratio Dists Best naïve method: pick period p1 and pick a period ratio (PR). Use a weighted coin flip to decide whether P2=P1*PR or P2=P1/PR. (PR defined > 1) Weight comes from relative probability of P2 values from the target Period Distribution

18 Descent into Mathematics Integral Equations Fredholm Equation of the first kind Nystrom Method Singular Value Expansion Copulas Go to the board!

19

20 Easiest Answer Tweak the P1 distribution power law indices to compensate Can a better, more explicit, tweak be found?

21 Conclusions Multi-transiting systems contain a huge wealth of important science Modeling them with SysSim is a tricky tractable problem with many components Descent into mathematics helped to draw from semi-dependent distributions