Transit Analysis Package Zach Gazak John Tonry John Johnson

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)

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

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:

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.

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?

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

MCMC Bayesian Distributions 15.1%

MCMC Bayesian Distributions

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

Testing the MCMC Algorithm Transits of varying precision must agree:

Where is Transit Science Going?

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

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

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

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

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

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

TrES-3b

TAP in Action

Transit Analysis Package Zach Gazak John Tonry John Johnson