SysSim

Background

We live in a time where even the populace ponders one of the biggest questions in science: is there life beyond Earth? In hopes of answering this question, NASA's Kepler Space Telescope (“Kepler”) was launched in spring 2009 and returned four years of photometric (brightness) measurements for over 100,000 stars. As a result, Kepler has discovered thousands of exoplanet candidates that cross in front of (“transit”) their parent stars by detecting the repeated dimmings. For all transiting planets, it is possible to estimate the orbital period and planetary radius, but if the system contains multiple transiting planets—known as “multi-transiting systems” (MTSs) — additional information can be extracted about the orbital properties. MTSs combine the determination of physical properties (like planetary radius) with the power of orbital dynamics possible in multi-planet systems, making them the most information-rich planetary systems outside our own solar system. In addition, approximately 20% of planets in MTSs have additional information in the Kepler data due to the dynamical interaction between the planets. Because these interactions cause normally periodic planets to transit early or late, they are known as “Transit Timing Variations” or TTVs. When Kepler MTSs have TTVs, then all the major physical and orbital characteristics can be determined or constrained: planetary mass, planetary radius, orbital period, eccentricity, and orbit orientation angles. Masses and radii can be combined to determine densities from which composition and formation history can be inferred.

Motivation

Science questions that benefit most from Kepler data and the proposed development of SysSim include:
1) What fraction of stars have planets?
2) Are there different populations of planetary systems? 
3) What are their frequencies and architectures? 
4) What fraction of stars have inner solar system analogs?
5) How do planetary systems change as a function of stellar properties?
6) What fraction of stars have potentially habitable planets?
7) What is the expected yield of future NASA exoplanet missions?
8) Is planet formation theory “X” consistent with the most powerful exoplanet data?
9) What is the planetary system environment of potentially habitable planets?
The ability to answer such a wide variety of important scientific questions is due to the
combination of the unprecedented Kepler data, the information-rich nature of multi-transiting
systems, a versatile debiasing model (SysSim), and the unique expertise of PIs Darin Ragozzine and Eric Ford.
It seems likely that most of these science questions will eventually be addressed by various
authors seeking to interpret Kepler data. However, in order to maximally leverage the powerful
new Kepler dataset correctly, completely, and self-consistently in a single coherent model, SysSim is being expanded and applied to the growing Kepler dataset to significantly
increase our understanding of the population of exoplanetary systems with critical
implications for quantitative validation of planet formation theories.

My Contribution

My job is to calculate the probability of detecting the simulated planet orbiting the simulated star. To do this, I am using KeplerPORTs (see Burke et al 2016) with some slight modifications. Since thousands and thousands of planets will be produced, the calcualtions for this probability must be quick, so unfortunately, we cannot call KeplerPORTS inside the iterations. Instead, I am precomputing a table of the signal to noise ratios for a 1 R_E planet as a function of period and transit duration for every Kepler star subject to the restraints mentioned in Burke et al 2016 (GK dwarfs with enough data available). This will be interpolated for the individual period and transit duration, and will be corrected for different radii (since we precomputed for R = 1R_E), inclinations, and impact parameters, since KeplerPORTs deals with central transits only. KeplerPORTs computes the detection probability of whether the telescope will observe enough transits with high enough S/N, so this will be combined with the geometric probability of detection calculated by CORBITs (Brakensiek and Ragozzine, accepted) to get the total probability.