Download What stellar properties can be learnt from planetary transits?

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 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
HD 209458
linear
quadratic
 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
I ( )
 1  w (1   )  w (1   )
quadratic function of ;
I (1)
2
1
2
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
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).
transit
sunspots
Simulation results
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.
sunspot
eclipse
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
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
 Starspot temperature, T0, estimated from blackbody emission,
where Te is the stellar surface temperature assumed to be
6000+50 K (Mazeh et al. 2000):
 h 
 Starspot temperatures between 4900-5000 K.
Io

Ie
  1
exp 
KT
 e
 h 
  1
exp 
KT
 o
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
aorb
Circular orbit
Larger orbital
radius 
shorter transit
phase interval
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:
2 aorb P
1


2 Rs
t f
Determine aorb/Rs from best fit of
transit phase interval (f) from the
data
aorb
Kepler’s 3rd law
 Assuming that the secondary is a planet:
Mp << Ms
1
 GM s P
aorb  
2
 4
2
3


 The ratio Ms1/3/Rs is determined once aorb/Rs
has been obtained.
 Determine Ms supposing the relation for main
sequence stars (Mihalas 1980):
 Ms 
Rs

 
RSun  M Sun 
0 .7
Stellar Mass and Radius
From fit to the data obtain:
– aorb//Rs (orbit radius – assumed circular)
Period is known
From Kepler’s law and mass-radius
relationship:
2
 G

P

M s   2
3 
 4 (aorb / Rs ) 
1
1.1
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
transit
OGLE
3 (*)
Radial velocity
Ms (Msun)
r (RJ)
a (A.U.)
I (o)
2.50
2.40
0.030
89.5
1.00
1.4
0.025
90
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
0.91
1.13
0.048
89.3
0.82+0.15
1.00+0.13
0.047+0.001
0.70
1.07
0.022
88.0
0.77+0.06
1.08+0.07
0.0228+0.0006
85+1
10
111
113
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 (RM0.7) 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.