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Simultaneous Spectroscopic & Photometric
Observations of a Transit of TrES-1b
Norio Narita
(UT, JSPS Fellow)
Collaborators
K. Enya (JAXA), B. Sato (Okayama, NAOJ), Y. Ohta,
A. Taruya, Y. Suto (UT), J. Winn (MIT), E. Turner (Princeton),
M. Tamura, T. Yamada, W. Aoki (NAOJ), Y. Yoshii (UT)
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Contents
Motivation and Our Project
Analysis Method
Preliminary Results
Radial Velocities and a Light Curve
(e, ω), (V sin Is, λ) contours
Transit Center (Tc) and Timing Variation
Summary
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Observations of Transiting Systems
give us various clues to learn more about exoplanets
Examples of observable parameters:
Spectroscopy (out of transit):
RV amplitude K, Minimum Mass MP sin i
Eccentricity and Longitude of periastron (e, ω)
Period P, Semi-major Axis a, Stellar Rotation Velocity V sin IS
Photometry (transit light curve):
Inclination i, Radii Ratio RP /RS, Planet Radius RP,
True Mass MP, Density ρ, Stellar Limb Darkening Parameter u
RM effect (RV anomaly during transit):
Angle between Stellar-Spin and Planetary-Orbit Axes λ
observable only for transiting systems !
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Our Project
Simultaneous observations of planetary transits:
Radial velocity measurements
with Subaru 8m Telescope
at Mauna Kea, Hawaii.
V band photometry with
MUGNUM 2m Telescope
at Haleakala, Maui.
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Target and Purpose
Target: TrES-1 (V = 11.8)
Photometry: precisely observed (Winn et al. 2006)
Secondary eclipse: detected (Charbonneau et al. 2005)
RVs: poorly measured (only ~10 samples so far)
Purpose: characterize this system more precisely
measure RVs around transit phase (~20 samples)
detect the RM effect
put constrains for (e, ω) and (V sin Is, λ)
determine precise Tc
Observations: conducted on UT June 21, 2006
predicted as 238th transit (E = 238 in ephemeris)
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Analysis Method
χ2 minimization by the amoeba algorithm (Press et al.)
Radial Velocities:
computed with the algorithm by Sato et al. (2002)
errors are typically 10-15 m/s
public data by Alonso et al. (2004) and Laughlin et al (2005)
parameters: |K, e, ω, V sin IS, λ|, (i, u), [a, P, RS, RP/RS]
free
fixed
Light Curve:
parameters: |Tc(238), i, u|, (e, ω), [a, P, RS, RP/RS]
free
fixed
||: free parameters
(): fixed to the best-fit values of the other dataset
[]: fixed to values of Alonso et al. (2004) and Winn et al. (2006)
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Radial Velocity Fitting
All of 31 RV samples
best-fit with the RM effect
Using χ2 contours, we computed uncertainties of parameters:
K = 113.2 ± 4.0 m/s (cf. 115.2 ± 6.2 m/s: Alonso et al. 2004)
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Contours : (e, ω) solution
● 1σ
● 2σ
2 local minima exist:
(0.040, 274.4°)
χ2 = 16.34, dof = 25
(0.011, 222.9°)
χ2 = 15.71, dof = 25
The blue contours are
our (e, ω) solutions.
The region 90°< ω < 270°,
e > 0.003 does not allowed
(Charbonneau et al. 2005)
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Contours : (VsinIs, λ) solution
● 1σ
Best fit values: (2360, 42°)
● 2σ
1σ confidence level:
λ: 0° ~ 60° (prograde)
V sin IS: 1300 ~ 3600 m/s
Our result has fairly large
uncertainty..
V sin IS constraint (Laughlin et al. 2005)
It is still tentative,
further observations
would be required.
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Light Curve Fitting
P, RS, RP/RS are fixed to the values in Winn et al. 2006
MAGNUM Photometry
band: V
Relative Flux
1.01
total: 184 samples
1
photometric accuracy: 0.13%
0.99
best-fit rms: 0.21%
0.98
0.97
-0.2
cadence: 60 sec
-0.1
0
HJD - 2453908
0.1
exposure time: 40 or 60 sec
Our best-fit values and 1σ uncertainty
Tc (238) = 2453907.96400 ± 0.00023 (~20 sec)
u = 0.58 ± 0.03, i = 88.4 ± 0.1
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Possible Sign of Timing Variation
Transit Ephemeris:
Winn et al. 2006
Tc (E) = Tc (0) + E × P
our result
Tc (0) =
2453186.80603 ± 0.00028
P = 3.0300737 ± 0.0000026
(Winn et al. 2006)
Our result Tc(238) is slightly off from the prediction.
Observed – Calculated residuals of Tc may indicate TTV.
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Summary
We observed a transit of TrES-1b
Subaru spectroscopy
obtained 20 RV samples with 10~15 m/s uncertainty
put constraints on K, (e, ω), (VsinIS, λ)
proved a prograde orbital motion of TrES-1b
MAGNUM photometry
achieved ~2 mmag accuracy
determined Tc(238) to within ~20 seconds
found an interesting residual in transit timing
Details will be reported in Narita et al. in prep.