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.