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  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 : 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/R s  Transit: at each time the planet is centered at a given position in its orbit (a orb /R s and i)  calculate the integrated flux  Search in parameter space for the best values of r, a orb, and i (minimum  2)

Transit Simulation

Property 1: Limb darkening (Atmosphere)

Atmospheric profile  HST data for HD (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 linear quadratic

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 b (1,347 R Jup ).

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= and w2= (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 with a period of days, major semi-axis of AU, and inclination angle, i=86,68.  Planet radius = R Jup, and stellar radius = R Sun.  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

HD (Deeg et al. 2001) Transit with spots without spots

HD (Brown et al. 2001) Transit with spots without spots

Results  Starspot temperature, T 0, estimated from blackbody emission, where T e is the stellar surface temperature assumed to be K (Mazeh et al. 2000):  Starspot temperatures between K. SPOTS 26-jul apr-2000 Radius (R p ) Intensity (I star ) Distance to transit line (R p ) R p = km

Conclusions  This method enables us to estimate the starspots physical parameters.  From modeling HD data, we obtained the starspots characteristics:  sizes of km, being larger than regular sunspots, usually of the order of km (probably a group of starspots, similar to solar active regions).  temperatures of K, being hotter than regular sunspots ( K), however the surface temperature of HD , 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/R s (planet radius) –A orb /R s (orbit radius – assumed circular) –i (inclination angle)

Lightcurve: planet radius  Planets with larger radius have deeper transits.  For Jupiter size planets, r=R J,  2% decrease in intensity for a star with 1 solar radius r

Lightcurve: orbital radius  Circular orbit  Larger orbital radius  shorter transit phase interval a orb

Lightcurve: orbit inclination  Orbit inclination angle close to 90 o (a transit is seen)  Smaller inclination angle  shorter transit phase interval i

Orbit  For circular orbits:  Determine a orb /R s from best fit of transit phase interval (  f) from the data a orb

Kepler’s 3rd law  Assuming that the secondary is a planet: M p << M s  The ratio M s 1/3 /R s is determined once a orb /R s has been obtained.  Determine M s supposing the relation for main sequence stars (Mihalas 1980):

Stellar Mass and Radius  From fit to the data obtain: –a orb/ /R s (orbit radius – assumed circular)  Period is known  From Kepler’s law and mass-radius relationship:

Simple test: Planet?  Compare stellar mass obtained from the data fit, M fit =M s +M p, with mass from direct observation of star, M s  If M fit >>M s  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 OGLEM s (M sun) r (R J) a (A.U.)I ( o ) 3 (*) (*) Radial velocity transit

Conclusions  From transit observation of secondary objects in front of a star, it is possible to measure: –Ratio of companion to star radii: r/R s ; –Orbital radius (assuming circular orbit) in units of star radius: a orb /R s ; –Orbital inclination angle, i, and period, P.  Combining Kepler’s 3 rd law with a mass-radius relationship (R  M 0.7 ) 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.