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Transiting Exoplanets
Artie Hatzes
Email: [email protected]→Lehre→Vorlesungen→Jena
Tentative Schedule
19. Oct: Introduction, Background, and Course overview
26. Oct: The Solar System, Basic Tools, Photometric technique
02. Nov: Sources of Noise and their Removal
09. Nov: Searching for transit signals in your data (Philipp Eigmüller)
16. Nov: Confirming the Nature of Transiting Planets
23. Nov: Modeling the Transit Curve (Szilard Czismadia)
30. Nov: Ground-based Surveys (Philipp Eigmüller)
07. Dec Results from the CoRoT Mission (Eike Guenther)
14. Dec: Results from the Kepler Mission
21. Dec: Spectroscopic Transits: Rossiter-McClaughlin Effect
04. Jan: Atmospheres of Transiting Planets
11. Jan Determination of Stellar Parameters (Matthias Ammler-von-Eiff)
18. Jan: Transit Timing Variations (Szilard Czismadia)
25. Jan: Space Missions: PLATO and TESS
01. Feb: Tidal Evolution of Close-in Planets (Martin Pätzold)
• Radial Velocities
• Astrometry
• Microlensing
• Transits
• Imaging
• Host Stars
• Brown Dwarfs and Free floating
• Formation and Evolution
• Interiors and Atmospheres
• The Solar System
• Our Solar System from Afar
(overview of detection methods)
• Exoplanet discoveries by the transit
• What the transit light curve tells us
• The Exoplanet population
• Transmission spectroscopy and the
Rossiter-McLaughlin effect
• Host Stars
• Secondary Eclipses and phase
• Transit timing variations and orbital
• Brave new worlds
By Carole Haswell
• Radial Velocities
• Exoplanet Transits and Occultations
• Microlensing
• Direct Imaging
• Astrometric Detections
• Planets Around Pulsars
• Statistical Distribution of Exoplanets
• Non-Keplerian Dynamics of Exoplanets
• Tidal Evolution of Exoplanets
• Protoplanetary and Debris Disks
• Terrestrial Planet Formation
• Planet Migration
• Terrestrial Planet Interiors
• Giant Planet Interior Structure and Thermal
• Giant Planet Atmospheres
• Terrestrial Planet Atmospheres and Biosignatures
• Atmospheric Circulation of Exoplanets
The Extrasolar Planet Encyclopaedia (Jean
Schneider): (note sends you to the Geneva Planet
Search Program)
• In 7 languages
• Tutorials
• Interactive catalog (radial velocity, transits, etc)
• On line histrograms and correlation plots
• Download data
The Nebraska Astronomy Applet: An Online Laboratory for
Pertinent to Exoplanets:
1. Influence of Planets on the Sun
2. Radial Velocity Graph
3. Transit Simulator
4. Extrasolar Planet Radial Velocity Simulator
5. Doppler Shift Simulator
6. Pulsar Period simulator
7. Hammer thrower comparison
Exoplanets is a fast moving field, the best
literature is the journals
NASA Astronomical Data Systems Abstract Service:
„Astronomy and Astrophysics Search“
Astro-ph preprint service:
Rate of Transiting Exoplanet Discoveries
HD 209458b
Methods of Detecting Exoplanets
1. Doppler wobble - Velocity reflex motion of the star
due to the planet: 459 planets
2. Transit Method - photometric eclipse due to
planet: 184 planets
3. Astrometry - spatial reflex motion of star due to
planet: 0 discoveries, 6 detections of known
4. Direct Imaging: 25 planets
5. Microlensing – gravitational perturbation by light:
13 planets
6. Timing variations – changes in the arrival of
pulses (pulsars), oscillation frequencies, or time of
eclipses (no transit timing variations): 12 planets
Discovery Space for Exoplanets
Historical Context of Transiting Planets (Venus)
Transits (in this case Venus) have played an important role in the
history of research of our solar system. Kepler‘s law could give us the
relative distance of the planets from the sun in astronomical units, but
one had to determine the AU in order to get absolute distances. This
could be done by observing Venus transits from two different places on
the Earth and using triangulation. This would fix the distance between
the Earth and Venus.
Historical Context of Transiting Planets (Venus)
From wikipedia
Jeremiah Horrocks was the first to attempt to observe a transit of
Venus. Kepler predicted a transit in 1631, but Horrocks re-calculated
the date as 1639. Made a good guess as to the size of Venus and
estimated the Astronomical Unit to be 0.64 AU, smaller than the
current value but better than the value at the time.
Transits of Venus occur in pairs separated by 8 years and these
were the first international efforts to measure these events.
Le Gentil‘s
One of these expeditions was by Guilaume Le Gentil who set out to the French colony of Pondicherry in
India to observe the 1761 transit. He set out in March and reached Mauritius (Ile de France) in July 1760.
But war broke out between France and England so he decided to take a ship to the Coromandel Coast.
Before arriving the ship learned that the English had taken Pondicherry and the ship had to return to Ile
de France. The sky was clear but he could not make measurements due to the motion of the ship.
Coming this far he decided to just wait for the next transit in 8 years.
He then mapped the eastern coast of Madagascar and decided to observe the second transit from
Manilla in the Philippines. The Spanish authorities there were hostile so he decided to return to
Pondicherry where he built and observatory and patiently waited. The month before was entirely clear,
but the day of the transit was cloudy – Le Gentil saw nothing. This misfortune almost drove him crazy, but
he recovered enough to return to France. The return trip was delayed by dysentry, the ship was caught in
a storm and he was dropped off on the Ile de Bourbon where he waited for another ship. He returned to
Paris in 1771 eleven years after he started only to find that he had been declared dead, been replaced in
the Royal Academy of Sciences, his wife had remarried, and his relatives plundered his estate. The king
finally intervened and he regained his academy seat, remarried, and lived happily for another 21 years.
Historical Context of Transiting Planets (Venus)
From wikipedia
Mikhail Lomonosov predicted the existence of an atmosphere on Venus from his
observations of the transit. Lomonosov detected the refraction of solar rays while
observing the transit and inferred that only refraction through an atmosphere could
explain the appearance of a light ring around the part of Venus that had not yet come
into contact with the Sun's disk during the initial phase of transit.
Venus limb
What can we learn about Planetary Transits?
1. The radius of the planet
2. The orbital inclination and the mass when
combined with radial velocity measurements
3. The Albedo from reflected light
4. The temperature from radiated light
5. Atmospheric spectral features
In other words, we can begin to characterize
The Planet Radius
The drop in intensity is give by the ratio of the cross-section areas:
DI = (Rp /R*)2 = (0.1Rsun/1 Rsun)2 = 0.01 for Jupiter
Ground-based measurements can usually get a
precision of about 0.01 mag
The Planet Mass
The radial velocity amplitude is often called the K-amplitude
In general from Kepler‘s law:
2pG ⅓ Mp sin i
Ms ⅔
For circular orbits (often the
case for transiting Planets):
28.4 Mp sin i
(1 – e2)½
Mp = mass of planet
Ms = mass of star
P = orbital period
Where Mp is in Jupiter masses, P is
in years, and Ms is in solar masses
Two important comments:
1) In the previous expressions I have made the approximation
that Ms » Mp, otherwise replace Ms with (Mp + Ms)
2) For radial velocities we only measure the component
of the orbital motion along the line-of-sight. Therefore
we only can derive Mp x sin i, where i is the orbital
inclination. But for transiting planets we know i. Thus
transiting planets allow us to derive the true mass of the
Because you measure the radial
component of the velocity you
cannot be sure you are detecting a
low mass object viewed almost in
the orbital plane, or a high mass
object viewed perpendicular to
the orbital plane
We only measure MPlanet x sin i
The Planet Atmosphere
Two ways to characterize an exoplanet‘s atmosphere:
Spectra during primary
eclipse: Chemical composition,
scattering properties
Spectra during secondary
eclipse: Chemical composition,
temperature structure
Useful Numbers: Transit Probability
i = 90o+q
Rs = stellar radius
a = semi-major-axis
sin q = Rs/a = |cos i|
Porb =  2p sin i di / 4p =
–0.5 cos (90+q) + 0.5 cos(90–q) = sin q
= Rs/a for small angles
Note that for large planets you must replace Rs + Rp. If a =10 Rs for a
Jupiter radius planet this changes the probability from 0.1 to 0.11. These
would of course be a grazing transits.
Useful Numbers: The Transit Duration
t = 2(R* +Rp)/v
where v is the orbital velocity and i = 90 (transit across disk center)
For circular orbits
From Keplers Law’s:
2 (a + a )3
P2 =
G(ms + mp)
v = 2pa/P
a = (P2 M*G/4p2)1/3
2R* P (4p2)1/3
2p P2/3 M*1/3G1/3
t 1.82 P1/3 R* /M*1/3 (hours)
In solar units, P in days
For more accurate times need to take into account the
orbital inclination and the fact that you have a finite radius planet
for i  90o need to replace R* with R:
R2 + d2cos2i = R*2
d cos i
R = (R*2 – d2 cos2i)1/2
Transit Numbers from our Solar System
t (hrs)
1.2 x 10-5
7.5 x 10-5
8.3 x 10-5
2.3 x 10-5
9.6 x 10-4
2.8 x 10-4
1.5 x 10-4
7.7 x 10-5
4.9 x 10-4
51 Peg b
N is the number of stars you would have to observe to see a transit, if all stars had such a
Useful Numbers: The Stellar Radius
One can solve transit duration for the stellar radius:
0.55 t M1/3
R in solar radii
M in solar masses
P in days
t in hours
Clearly the best estimate of the stellar radius comes from
spectroscopy. However, the transit duration can be used
1) as a first estimate that you are dealing with a dwarf star
and 2) a check on the spectroscopically derived stellar
Useful Numbers: The Stellar Density
2R* P (4p2)1/3
2p P2/3 M*1/3G1/3
t 1.09 G–⅓ P⅓ R* /M*⅓
t3 1.3 G P R*3 /M*
t3  C P (rmean)–1
Where rmean is the mean stellar density and is called the „transit stellar
density“. This can be used as a „sanity check“ to compare with values
determined from a formal spectral analysis. It also gives you the first hint on
the evolutionary status of the star.
The Stellar Radius
Radius as a function of Spectral
Type for Main Sequence Stars
A planet has a maximum radius ~ 0.15 Rsun. This means that a star can
have a maximum radius of 1.5 Rsun to produce a transit depth consistent
with a planet.
Along the Main Sequence
Spectral Type
Spectral Type
Stellar Mass (Msun)
Stellar Mass (Msun)
The photometric transit depth for a 1 RJup planet
Planet Radius (RJup)
Along the Main Sequence
1 REarth
Stellar Mass (Msun)
Assuming a 1% photometric precision this is the minimum planet radius as a
function of stellar radius (spectral type) that can be detected
Probability of detecting a transit Ptran:
Ptran = Porb x fplanets x fstars x DT/P
Porb = probability that orbit has correct orientation
fplanets = fraction of stars with planets
fstars = fraction of suitable stars (Spectral Type later than F5)
DT/P = fraction of orbital period spent in transit
Estimating the Parameters for 51 Peg systems: P ~ 4 d
This depends on where you look (galactic plane,
clusters, etc.) but typically about 30-40% of the stars
in the field will have radii (spectral type) suitable for
transit searches.
You also have to worry about late-type giant stars
A KIII Star can have R ~ 10 RSun
DI = 0.01 = (Rp/10)2
→ Rp = 1 RSun!
Unfortunately, background giant stars are
everywhere. In the CoRoT fields, 25% of the stars
are giant stars
Giant stars are relatively few, but they are bright and can be seen to
large distances. In a brightness limited sample you will see many
distant giant stars.
Estimating the Parameters for 51 Peg systems
Fraction of the time in transit
Porbit ≈ 4 days
Transit duration ≈ 3 hours
DT/P  0.08
For each test orbital period you have to observe enough to get the
probability that you would have observed the transit (Pvis) close to
For each field you have to observe enough to ensure that the
probability is close to 1 that you would observe
Estimating the Parameters for 51 Peg systems
Period ≈ 4 days → a = 0.05 AU = 10 R‫סּ‬
Porb  0.1
Although the fraction of giant planet hosting stars is
5-10%, the fraction of short period planets is
smaller, or about 0.5–1%
E.g. a field of 10.000 Stars the number of expected transits is:
Ntransits = (10.000)(0.1)(0.01)(0.3) = 3
Probability of a right orbital orientation
Frequency of Hot Jupiters
Fraction of stars with suitable radii
So roughly 1 out of 3000 stars will show a transit event due to a
planet. And that is if you have full phase coverage!
CoRoT: looks at 10,000-12,000 stars per field and is finding on
average 3 Hot Jupiters per field. Similar results for Kepler
Note: Ground-based transit searches are finding hot Jupiters 1 out
of 30,000 – 50,000 stars.
Catching a transiting planet is thus like playing
Lotto. To win in LOTTO you have to
1. Buy lots of tickets → Look at lots of stars
2. Play often → observe as often as you can
The obvious method is to use CCD photometry
(two dimensional detectors) that cover a large
Large-field Searches from the Ground
OGLE (Optical Gravitational Lensing Experiment)
• Started in 2001 with one a 1.3m telescope at Las Campanas
• Originally a microlensing experiment
• 35 x 35 arcmin2 field of view → look at galactic bulge
• 5 million stars monitored → 52 000 with photometry better
than 1.5% → 46 transits detected in first field
• Typical magnitude V = 15-17
• 9 planets discovered including first transiting planet
discovered with photometry
The first planet found with the transit method
Until OGLE-TR-56 the shortest period planet that was
found by the radial velocity method was 3 days.
Konacki et al.
Large-field Searches from the Ground
HAT/HATNet (Hungarian Automated Telescope)
• Started in 2003 with one telescope
• Currently 6 automated telescopes 4 at Whipple Observatory
in Arizona and two in Mauno Kea
• 2000 x 2000 pixels CCD with an 8 degree field of view
• Precision 3-10 millimags at I = 8 – 11
• 32 planets discovered (2 shared with WASP)
Large-field Searches from the Ground
TRES (Trans-Atlantic Exoplanet Survey)
• Started in 2000 with STARE (found first transiting exoplanet)
• Three 0.1m telescopes (Arizona, California, Canary Islands)
• CCD : 6 degree field of view
• < 2 millimags for bright stars, 10 mmag for R ~ 12.5
• 5 planets discovered
HD 209458b
• Mass = 0.63 MJupiter
• Radius = 1.35 RJupiter
• Density = 0.38 g cm–3
Large-field Searches from the Ground
WASP/SuperWASP (Wide Angle Search for Planets)
• Started in 2004 as WASP, 2006 as SuperWASP
• Each telescope uses eight 2k x 2k CCDs with a mosaic of
15 deg x 30 deg
• First run observed 6.7 million objects
• 4 mmag @V=9.5, [email protected]=12
• 65 planets discovered (2 shared with HAT)
Rate: 50 million stars
observed and 65 planets →
1 planet for every 1 000 000
Large-field Searches from the Ground
• Started in 2003
• Aims at bright stars
• Two 0.11m telescopes
• 1k x 1k CCDs with a mosaic of 7 deg x 7 deg
• First year of operation observed 7% of the sky and 100 000
• 10 mmag @V < 12
• 5 planets discovered
Rate: 5 planets for every
100 000 stars
1 planet for every 20 000
Other Searches from the Ground
• Started in 2008
• Aims finding planets around 2000 M dwarf stars (stellar
mass = 0.1 – 0.35 M‫)סּ‬
• Eight 0.4 m telesccopes
• Observe stars one at a time
• 10 mmag @V < 12
• 1 planet discovered
Rate: 1 planet for every 2 000
stars (M dwarfs)
Other Searches from the Ground
Open Clusters
• NGC 6791 (Mochjeska et al. 2005)
• No Planets found but only 1.5 expected
Globular Cluster
• 47 Tuc (Gilliland et al. 2000)
• Hubble Space Telescope
• No Planets found
Large-field Searches from Space
CoRoT (COnvection ROtation and Transits)
• 27 cm telescope in a Polar Orbit
• 2.8 x 1.4 square degree field
• Exoplanet and Asteroseismology
• Launched in December 2006
• Observe a field for up to 150 days
• ~ 150 000 stars observed
• 24 planets found so far
Rate: 1 planet for every 3000-6000
Large-field Searches from Space
• 0.95 cm telescope in a Earth Trailing orbit
• 105 square degree field
• 100 000 stars observed for 3.5 years
• Launched in March 2009
• 24 planets found so far
Rate: 1 planet for every 4 000 stars
Stellar Magnitude distribution of Exoplanet
V- magnitude