1. Transit Analysis Package Zach Gazak John Tonry John Johnson

2. Extrasolar Planets 1992: First discovered (pulsar timing variations) 1995: First orbiting Main Sequence star (radial velocity) 1999: First photometric transit light curve: (Charbonneau et al. 2000)

3. Transiting Extrasolar Planets ~80 transiting exoplanets Transits give us access to the geometry of the system (Charbonneau et al. 2000) NASA

4. Modeling Transit Photometry Analytic light curve of (Mandel & Agol 2002) Period, Inclination, Rp, a, Rs, e, ω, T mid, limb darkening Inclination, Rp/Rs, a/Rs:

5. Parameter Statistics: MCMC Markov Chain Monte Carlo Gives access to Bayesian probability distribution model x 0 trial state x ’ Likelihood: –– ‾ 2 ~exp [ ] ℒ’ℒ’ If z ≤ then x 1 = x ’ ℒ’ℒ’ ℒ0ℒ0 0≤z≤1 (random uniform) otherwise, x 1 = x 0 More likely states always selected, but MCMC can explore.

6. Parameter Statistics: MCMC Markov Chain Monte Carlo Gives access to Bayesian probability distribution model x 0 trial state x ’ Likelihood: –– ‾ 2 ~exp [ ] ℒ’ℒ’ ℒ’ℒ’ ℒ0ℒ0 meets Jump probability?

7. Parameter Statistics: MCMC Markov Chain Monte Carlo Gives access to Bayesian probability distribution model x 0 trial state x ’ More likely states always selected, but MCMC can explore.... xNxN

8. MCMC Bayesian Distributions 15.1%

9. MCMC Bayesian Distributions

11. Testing the MCMC Algorithm Generate and Analyze Synthetic Transits WASP 10bHAT 12b

12. Testing the MCMC Algorithm Transits of varying precision must agree:

13. Where is Transit Science Going?

14. Is the “Classic” MCMC Enough? Most light curves show correlated “red” noise: But “classic” MCMC is not able to compensate.

15. Wavelet Processing “Fourier Like” but sensitive to frequency and scale. Daubechies 4th order

16. Wavelet Processing “Fourier Like” but sensitive to frequency and scale. Daubechies 4th order

17. Red Noise Filtering How “Likely” is the noise described by a (σ white, σ red ) pair? (Carter & Winn 2009) Maximize that “Wavelet Likelihood”:

18. Wavelet Basis MCMC Wavelet decompose residuals (data - model fit) Use wavelet likelihood instead of “Classic”

19. Wavelet Basis MCMC For contaminated data, “Classic” MCMC is insufficient! Severely underestimates probability distributions. “True” value Classic Wavelet

20. TrES-3b

23. TAP in Action

24. Transit Analysis Package Zach Gazak John Tonry John Johnson