transit analysis package zach gazak john tonry john johnson
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Transit Analysis Package
Zach Gazak
John Tonry
John Johnson
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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, Tmid, limb darkening
Inclination, Rp/Rs, a/Rs:
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Parameter Statistics: MCMC
Markov Chain Monte Carlo
Gives access to Bayesian probability distribution
model x0
trial state x’
Likelihood: –χ
‾2~exp[ ]
ℒ’
ℒ’
ℒ0
⎯
meets Jump probability?
Parameter Statistics: MCMC
Markov Chain Monte Carlo
Gives access to Bayesian probability distribution
model x0trial state x’
More likely states always selected, but MCMC can explore.
. . . xN
MCMC Bayesian Distributions
15.1%
MCMC Bayesian Distributions
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MCMC Bayesian Distributions
Testing the MCMC Algorithm
Generate and Analyze Synthetic Transits
WASP 10b HAT 12b
Testing the MCMC Algorithm
Transits of varying precision must agree:
Where is Transit Science Going?
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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 FilteringHow “Likely” is the noise described by a (σwhite, σred) 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
TrES-3b
TrES-3b
TAP in Action
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Transit Analysis Package
Zach Gazak
John Tonry
John Johnson
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