The Theoretical Modeling of Transit Light Curves of Exoplanets

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The Theoretical Modeling of Transit Light
Curvesof Exoplanets
Shu-Chin Chen Institute of Astronomy, National
Tsing-Hua University, Hsinchu, Taiwan And
Ing-Guey Jiang Institute of Astronomy, National
Tsing-Hua University Hsinchu, Taiwan
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Outline

• Introduction
• general background
• detection methods
• Our goal
• The procedure
• theoretical model
• theoretical flux
• observational data fitting
• Future work

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Introduction

• An extra-solar planet, or exoplanet, is a planet
  beyond the Solar System.
• The first confirmed detections were made in the
  1990s since 2000, more than 15 have been
  discovered every year, and the most in 2007 so
  far.
• The first milestone in the discovery of
  extra-solar planets was in 1992, when Wolszczan
  and Frail published results in the journal Nature
  indicating that pulsar planets existed around
  PSR B125712.

• Doppler Spectroscopy
• First planet discovered by radial velocity
  method is 51 Pegasi b in 1995
• Transit Method
• First planet discovered by transit method is
  OGLE-TR-56 b in 2000

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Our Goal

• To develop an efficient method to calculate the
  flux and fit the data.
• To get better orbital solutions when new data is
  available
• To calculate the confidence level of each
  solution
• To explore the possibility of different
  eccentricity
• To be ready for our own observational data

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Procedure

• To calculate the theoretical flux
• Search the most likely orbit from the data
• Fold the observational data
• Do chi-square fitting

• Get the best fit physical parameters of the
  planetary system, such as rp, i, e, T
• Draw the confidence level

p90
(ti,fi) N data points, I 1,.N
p60
fi observed flux fc theoretical flux p
dependent variables N the number of data
points s flux uncertainties.
p the percentage of probability
Confidence level can show us the possible
parameters distribution.
What we have done
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The Limb-Darkening Effect
observer
?
r
1
No limb darkening For a uniform source, I(r) is
a constant.
With limb darkening, I(r) is a function of r.
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The Method to Calculate the Flux
Un-obscured
covers the limb of the stellar disk
Sepgt1p
star
Sep-p
p
p
Sep-p
p rp/ rs the planet size ratio Sep
the normalized separation
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The Method to Calculate the Flux
entirely within the stellar disk
0ltSepltp
Sep0
star
star
p
Sep-p
p
p-Sep
Sep
Sep p
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HD189377 facts
The Example
Un-obscured
The planet covers the limb of the stellar disk
The planet lies entirely inside the stellar disk
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I
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The Orbital Model of HD189733
3D pictures demonstrate the planet position . 2D
pictures show the planet crosses the stellar
disk.
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The Parameters
The effect of planetary size. The effect
of inclination.
The effect of planetary size. The
effect of inclination.
The effect of planetary size. The
effect of inclination.
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OGLE-TR-10 System
The folded data from OGLE. The curves is
theoretical flux.
The folded data from OGLE. The curves is
theoretical flux.
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The Original Data From OGLE
tigt2.45392HJDcontains 219 data points
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Folded Data

period 3.1 days

• The two parameters we choose are planetary
  size and inclined angle
• We found the best-fit planetary size
• is 1.2 RJ and the inclination is 85 deg

The original data from OGLE.
The original data from OGLE
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Confidence Region
??2 minimum (1.2, 85)
p68
p90
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Conclusions

• Limb-darkening effect cannot be ignored.
• Different parameters have different effects on
  light curves.
• In our study, the best-fit planetary size is 1.2
  RJ ,
• and the inclination we found is 85.0 deg.
• Parameters obtained in published paper, the
  planetary is 1.26 ( 0.07) RJ, and the
  inclination is 84.5 ( 0.6) deg.

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Future Work

• We hope to use Levenberg-Marquardt Method to
  determine best-fit parameters, and find the most
  likely orbit.
• In addition to the transit data, we will also use
  the data of stars radial velocity to do the
  fitting, to find even better orbits.
• We will use our own observational data to find
  other extra-solar planets.

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Thank you for your listening!