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What stellar properties can be learnt from planetary transits. Adriana Válio Roque da Silva CRAAM/Mackenzie. Sumary. Star: Atmospheric structure Spots: size, temperature, latitude of occurrence Mass Radius Planet: Radius Distance to the star Orbit inclination angle Orbital period - PowerPoint PPT Presentation
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What stellar properties can be learnt from planetary transits
Adriana Válio Roque da SilvaCRAAM/Mackenzie
Sumary Star:
– Atmospheric structure– Spots: size, temperature, latitude of occurrence– Mass– Radius
Planet:– Radius– Distance to the star– Orbit inclination angle– Orbital period
Simple test: secondary is a planet or a star?
Mercury transits
Mercury transit on November 15, 1999, that lasted about 1 hour.
Vênus transit – 8 June 2004
Exoplanets
133 planets detected by radial velocities
4 planets first detected by transits
Data:– HD 209458: high resolution data from HST– OGLE: over a hundred candidates, 4
confirmed by radial velocities (56,111,113,132)
Model Star white light image
of the Sun Planet opaque disk of
radius r/Rs
Transit: at each time the planet is centered at a given position in its orbit (aorb/Rs and i) calculate the integrated flux
Search in parameter space for the best values of r, aorb, and i (minimum 2)
Transit Simulation
Property 1: Limb darkening(Atmosphere)
Atmospheric profile
HST data for HD209458 (Brown et al. 2001) not well fit by the solar limb darkening, which is a linear function of =cos.instead it is best described by a quadratic function of ;
HD 209458
linear
quadratic
221 )1()1(1
)1(
)( ww
I
I
Limb darkening
Temperature gradient not as steep as in the solar photosphere
quadratic
linear
Property 2: Spots – size, temperature, and latitude
(indicator of stellar activity)
Silva ApJLetters, 585, 147, 2004
Sunspots
Regions of high concentration of magnetic fields; Indicators of magnetic activity cycle; Understanding of solar activity:
– solar flares, coronal mass ejections, etc; Currently it is not possible to detect, let alone
monitor the behavior of solar like spots on other stars due to their very small sizes.
Solar Transit Simulation
transit
sunspots
A white light image of the Sun is used to simulate the transit of a planet in front of a group of sunspots, that is, an active region. Two simulations are performed: one for an Earth sized planet and another the size of HD 209458b (1,347 RJup).
Simulation results
sunspot eclipse
Small variations in the lightcurve during the planetary transit can be seen when the planet occults dark regions on the solar disk, i.e., sunspots.
Model star Star represented by a
quadratic limb darkening with w1=0.2925 and w2=0.3475 (Brown et al. 2001).
Spot modeled by three parameters:– Intensity, as a function
of stellar intensity at disk center (max);
– Size, as a function of planet radius;
– Position, as a distance to the transit line in units of planet radius.
The Model
Planet in a circular orbit around HD 209458 with a period of 3.5247 days, major semi-axis of 0.0467 AU, and inclination angle, i=86,68.
Planet radius = 1.347 RJup, and stellar radius = 1.146 RSun.
The planet is represented by an opaque disk that crosses the stellar disk at 30.45° latitude (corresponding to i=86,68).
The planet position is calculated every two minutes.
Lightcurve intensity at every two minutes is the sum of all the pixels values in the image.
Data
Two observations with “bumps” in the light curve were used: Deeg et al. (2001) Brown et al. (2001) -
HST
HD209458 (Deeg et al. 2001)
Transit with spots without spots
HD209458 (Brown et al. 2001)
Transit with spots without spots
Results
Starspot temperature, T0, estimated from blackbody emission, where Te is the stellar surface temperature assumed to be 6000+50 K (Mazeh et al. 2000):
Starspot temperatures between 4900-5000 K.
SPOTS 26-jul-2000 25-apr-2000
Radius (Rp) 0.4-0.6 0.3-0.4
Intensity (Istar) 0.4-0.6 0.5-0.7
Distance to transit line (Rp)
0.5-0.8 0.7-0.9
Rp=9.4 104 km
1exp
1exp
o
e
e
o
KTh
KTh
I
I
Conclusions
This method enables us to estimate the starspots physical parameters.
From modeling HD208458 data, we obtained the starspots characteristics:
sizes of 3-6 104 km, being larger than regular sunspots, usually of the order of 11000 km (probably a group of starspots, similar to solar active regions).
temperatures of 4900 - 5500 K, being hotter than regular sunspots (3800-4400K), however the surface temperature of HD 209458, 6000K, is also hotter than that of the Sun (5770K).
Property 3: Mass and Radius (distinguish between planetary
and stellar companions)
OLGE transits
Data from OGLE project
Orbital period taken as the published value
Fit to the data yields:– r/Rs (planet radius)
– Aorb/Rs (orbit radius – assumed circular)
– i (inclination angle)
Lightcurve: planet radius
Planets with larger radius have deeper transits.
For Jupiter size planets, r=RJ, 2% decrease in intensity for a star with 1 solar radius
r
Lightcurve: orbital radius
Circular orbitLarger
orbital radius shorter transit phase interval
aorb
Lightcurve: orbit inclination
Orbit inclination angle close to 90o (a transit is seen)
Smaller inclination angle shorter transit phase interval
i
Orbit
For circular orbits:
Determine aorb/Rs from best fit of transit phase interval (f) from the data
aorb
ft
P
R
a
s
orb
1
2
2
Kepler’s 3rd lawAssuming that the secondary is a planet:
Mp << Ms
The ratio Ms1/3/Rs is determined once
aorb/Rs has been obtained.Determine Ms supposing the relation for
main sequence stars (Mihalas 1980):
3
1
2
2
4
PGM
a sorb
7.0
Sun
s
Sun
s
M
M
R
R
Stellar Mass and Radius
From fit to the data obtain:– aorb//Rs (orbit radius – assumed
circular)Period is knownFrom Kepler’s law and mass-radius
relationship:1.1
1
3
2
2 )/(4
sorbs Ra
PGM
Simple test: Planet?
Compare stellar mass obtained from the data fit, Mfit=Ms+Mp, with mass from direct observation of star, Ms
If Mfit>>Ms it is NOT a planet In this case the mass is actually the
sum of the mass of both stars, or the mass-radius relationship is not valid
Results
OGLE Ms (Msun) r (RJ) a (A.U.) I (o)
3 (*) 2.50 2.40 0.030 89.5
1.00 1.4 0.025 90
10 1.10 1.29 0.043 88.1
1.22+0.045
1.52 0.04 87-90
33 (*) 2.00 2.31 0.038 90.0
56 0.90 0.94 0.021 85.4
1.04+0.05 1.23+0.16 0.0225+0.0004
86.5-90
111 0.91 1.13 0.048 89.3
0.82+0.15 1.00+0.13 0.047+0.001
113 0.70 1.07 0.022 88.0
0.77+0.06 1.08+0.07 0.0228+0.0006
85+1
Radial velocitytransit
Conclusions
From transit observation of secondary objects in front of a star, it is possible to measure:– Ratio of companion to star radii: r/Rs;– Orbital radius (assuming circular orbit) in units
of star radius: aorb/Rs;– Orbital inclination angle, i, and period, P.
Combining Kepler’s 3rd law with a mass-radius relationship (RM0.7) it is possible to infer the mass and radius of the star.
Test: comparing this mass with stellar mass obtained from other observations can infer if companion is a PLANET or not.