Transcript ppt

The Transit Method
1. Photometric
2. Spectroscopic (next time)
Detection and Properties of Planetary Systems
18 Apr: Introduction and Background:
25 Apr: The Radial Velocity Method
02 May: Results from Radial Velocity Searches
09 May: Astrometry
16 May: The Transit Method
23 May: Planets in other Environments (Eike Guenther)
30 May: Transit Results: Ground-based
06 Jun: Transit Results: Space-based
13 Jun: Exoplanet Atmospheres
20 Jun: Direct Imaging
27 Jun: Microlensing
04 Jul: No Class
11 Jul: Planets in Extreme Environments: Planets around evolved stars
18 Jul: Habitable Planets: Where are the other Earths?
Literature
Contents:
• Our Solar System from Afar
(overview of detection methods)
• Exoplanet discoveries by the transit
method
• What the transit light curve tells us
• The Exoplanet population
• Transmission spectroscopy and the
Rossiter-McLaughlin effect
• Host Stars
• Secondary Eclipses and phase
variations
• Transit timing variations and orbital
dynamics
• Brave new worlds
By Carole Haswell
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
observatory
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 an 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 transit im June 2012!
On 6. June 2012 the
second transit of the 8year pairs takes place.
Venus limb
solar
What are Transits and why are they important?
R*
DI
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
Radial Velocity measurements => Mp (we know sin i !)
=> density of planet
→ Transits allows us to measure the physical properties of the
planets
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. Density → first hints of structure
4. The Albedo from reflected light
5. The temperature from radiated light
6. Atmospheric spectral features
In other words, we can begin to characterize
exoplanets
Comparison of the Giant Planets
1.24
0.62
1.25
1.6
Mean density (gm/cm3)
http://www.freewebs.com/mdreyes3/chaptersix.htm
r (gm/cm3)
10
7
Earth
Mercury
5
4
3
Venus
Mars
Moon
The radius, mass, and
density are the first clues
about the internal structure
2
From Diana Valencia
1
0.2
0.4
0.6
0.8
1
1.2
Radius (REarth)
1.4
1.6
1.8
2
Earth
Venus
Earth and Venus have a core that is ~80% iron extending out
to a radius of 0.3 to 0.5 of the planet
Moon
Mercury
1.
2.
3.
The moon has a very small
core, but a large mantle
(≈70%)
Crust: 100 km
Silicate Mantle (25%)
Nickel-Iron Core (75%)
Mercury has a very large iron
core and thus a high density
for its small size
Transit Probability
i = 90o+q
q
R*
a
sin q = R*/a = |cos i|
a is orbital semi-major axis, and i is the
orbital inclination1
90+q
Porb =  2p sin i di / 4p =
90-q
–0.5 cos (90+q) + 0.5 cos(90–q) = sin q
= R*/a for small angles
1by
definition i = 90 deg is
looking in the orbital plane
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:
2R* P (4p2)1/3
t
2p P2/3 M*1/3G1/3
v = 2pa/P
a = (P2 M*G/4p2)1/3
t 1.82 P1/3 R* /M*1/3 (hours)
In solar units, P in days
Note t3 ~ (rmean)–1 i.e. it is related to the mean density of the star
Transit Duration
Note: The transit duration gives you an estimate of the stellar radius
Rstar =
0.55 t M1/3
P1/3
R in solar radii
M in solar masses
P in days
Most Stars have
masses of 0.1 – 4
solar masses.
t in hours
M⅓ = 0.46 – 1.6
For more accurate times need to take into account the
orbital inclination
for i  90o need to replace R* with R:
R2 + d2cos2i = R*2
d cos i
R*
R = (R*2 – d2 cos2i)1/2
R
Making contact:
1.
2.
3.
4.
First contact with star
Planet fully on star
Planet starts to exit
Last contact with star
Note: for grazing transits there is
no 2nd and 3rd contact
1
4
2
3
DI/I
Prob.
N
t (hrs)
forbit
Mercury
1.2 x 10-5
0.012
83
8
0.0038
Venus
7.5 x 10-5
0.0065
154
11
0.002
Earth
8.3 x 10-5
0.0047
212
13
0.0015
Mars
2.3 x 10-5
0.0031
322
16
9.6 x 10-4
Jupiter
0.01
0.0009
1100
29
2.8 x 10-4
Saturn
0.007
0.00049
2027
40
1.5 x 10-4
Uranus
0.0012
0.000245
4080
57
7.7 x 10-5
Neptune
0.0013
0.000156
6400
71
4.9 x 10-4
51 Peg b
0.01
0.094
11
3
0.03
Planet
Moon
6.2 x10-6
Ganymede
1.3 x 10-5
Titan
1.2 x 10-5
N is the number of stars you would have to observe to see a transit, if all stars had
such a planet. This is for our solar system observed from a distant star.
Note the closer a planet is to the star:
1. The more likely that you have a favorable orbit
for a transit
2. The shorter the transit duration
3.
Higher frequency of transits
→ The transit method is best suited for short period planets.
Prior to 51 Peg it was not really considered a viable detection
method.
Shape of Transit Curves
2
tflat
tflat
ttotal
=
[R* – Rp]2 – d2 cos2i
[R* + Rp]2 – d2 cos2i
ttotal
Note that when i = 90o tflat/ttotal = (R* – Rp)/( R* + Rp)
Shape of Transit Curves
HST light curve of HD 209458b
A real transit light curve is not flat
Shape of Transit Curves
Effects of Limb Darkening (or why the curve is not flat).
Bottom of photosphere
q2
q1
dz
Temperature
Temperature profile
of photosphere
10000
8000
6000
4000
z=0
tn =1 surface
Top of photosphere
z
z increases going
into the star
To probe limb
darkening in other
stars..
..you can use
transiting planets
No limb darkening
transit shape
At the limb the star has less flux than is expected, thus the planet blocks less light
At different
wavelengths in Ang.
Report that the transit duration
is increasing with time, i.e. the
inclination is changing:
However, Kepler shows no change
in the inclination!
To model the transit light curve and derive the true radius of
the planet you have to have an accurate limb darkening law.
Problem: Limb darkening is only known very well for one
star – the Sun!
Why Worry about Limb Darkening?
Suppose someone observes a
transit in the optical. The
„diameter“ of the stellar disk
is determined by the limb
darkening
Years later you observe the
transit at 10000 Ang. The star
has less limb darkening, it
thus has a larger „apparent
diameter. You calculate a
longer duration transit
because you do not take into
account the different limb
darkening
And your wrong conclusion:
More limb darkening →
short transit duration
Less limb darkening in red
→ longer transit duration
→ orbital inclination has
changed!
Effects of limb
darkening on
the transit
curve
Shape of Transit Curves
Grazing eclipses/transits
These produce a „V-shaped“
transit curve that are more
shallow
Planet hunters like to see a flat part on the bottom of the transit
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
Porb
Period ≈ 4 days → a = 0.05 AU = 10 R‫סּ‬
Porb  0.1
fplanets
Although the fraction of giant planet hosting stars is
5-10%, the fraction of short period planets is
smaller, or about 0.5–1%
Estimating the Parameters for 51 Peg systems
fstars
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.
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 → one must know the type of star you are observing!
Take 1% as the limiting depth that you can detect a transit from
the ground and assume you have a planet with 1 RJ = 0.1 Rsun
Example:
B8 Star: R=3.8 RSun
DI = (0.1/3.8)2 = 0.0007
Suppose you detect a transit event with a depth of 0.01. This
corresponds to a radius of 50 RJupiter = 0.5 Rsun
Additional problem: It is difficult to get radial velocity
confirmation on transits around early-type stars
Transit searches on Early type, hot stars are not effective
You also have to worry about late-type giant stars
Example:
A K III 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.
Along the Main Sequence
Spectral Type
DI/I
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
Estimating the Parameters for 51 Peg systems
Fraction of the time in transit
Porbit ≈ 4 days
Transit duration ≈ 3 hours
DT/P  0.08
Thus the probability of detecting a transit of a planet in a single
night is 0.00004.
For each test orbital period you have to observe enough
to get the probability that you would have observed the
transit (Pvis) close to unity.
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 right orbit inclination
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 → less efficient than space-based searches
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
field. You simultaneously record the image of
thousands of stars and measure the light
variations in each.
Confirming Transit Candidates
A transit candidate found by photometry is only a candidate
until confirmed by spectroscopic measurement (radial
velocity)
Any 10–30 cm telescope can find transits. To confirm these
requires a 2–10 m diameter telescope with a high resolution
spectrograph. This is the bottleneck.
Current programs are finding transit candidates faster than
they can be confirmed.
Light curve for HD 209458
Transit Curve: 10 cm telescope
Radial Velocity Curve for HD 209458
Transit
phase = 0
Period = 3.5 days
Msini = 0.63 MJup
Radial Velocity Curve: 2-10 m telescopes
Confirming Transit Candidates
Spectroscopic measurements are important to:
1. False positives
2. Derive the mass of the planet
3. Determine the stellar parameters
False Positives
It looks like a planet, it smells like a planet, but it is not a planet
1. Grazing eclipse by a main sequence star:
One should be able to distinguish
these from the light curve shape and
secondary eclipses, but this is often
difficult with low signal to noise
These are easy to exclude with Radial
Velocity measurements as the
amplitudes should be tens km/s
(2–3 observations)
This turned out to be an eclipsing binary
2. Giant Star eclipsed by main sequence star:
G star
Giant stars have radii of 10–100 R‫ סּ‬which translates
into photometric depths of 0.0001 – 0.01 for a
companion like the sun
These can easily be excluded using one spectrum to
establish spectral and luminosity class. In principle no
radial velocity measurements are required.
Often a giant star can be known from the transit time.
These are typically several days long!
e.g. giant star with R = 10 Rsun and M = Msun
and we find a transit by a companion with a
period of 10 days:
The transit duriation t would be 1.3 days!
Probably not detectable from ground-based observations
A transiting planet around a solar-type star with a 4 day
period should have a transit duration of ~ 3 hours. If the
transit time is significantly longer then this it is a giant or
an early type star.
Low resolution spectra can easily distinguish between a giant and main
sequence star for the host.
Green: model
Black: data
CoRoT: LRa02_E2_2249
Spectral Classification:
K0 III (Giant, spectroscopy)
Period: 27.9 d
Transit duration: 11.7 hrs → implies Giant,
but long period!
Mass ≈ 0.2 MSun
CoRoT: LRa02_E1_5015
Spectral Classification:
K0 III ?
Period: 13.7 d
Transit duration: 10.1 hrs → Giant?
Mass ≈ 0.2 MSun
3. Eclipsing Binary as a background (foreground) star:
Fainter binary
system in
background or
foreground
Total = 17% depth
Light from bright
star
Light curve of
eclipsing
system. 50%
depth
Difficult case. This results in no radial velocity variations as the fainter binary
probably has too little flux to be measured by high resolution spectrographs.
Large amounts of telescope time can be wasted with no conclusion. High
resolution imaging may help to see faint background star.
If you see a nearby companion you can do „on-transit“ and „off-transit“ with
high resolution imaging to confirm the right star is eclipsing
4. Eclipsing binary in orbit around a bright star (hierarchical
triple systems)
Another difficult case. Radial Velocity Measurements of the bright
star will show either long term linear trend no variations if the orbital
period of the eclipsing system around the primary is long. This is
essentialy the same as case 3) but with a bound system
If the binary is are low mass stars they
may be active:
Short period M dwarfs are very active and we would have seen Ca II
emission from the binary stars and X-ray emission
Spectral Classification:
K1 V (spectroscopy)
Period: 7.4 d
Transit duration: 12.68 hrs
Depth : 0.56%
CoRoT: LRa02_E1_5184
Radial Velocity (km/s)
Radial Velocity
Photometric Phase
Bisector
The Bisector variations correlate
with the RV → the spectra from the
binary companion is contaminating
the spectrum of the target star.
5. Unsuitable transits for Radial Velocity measurements
Transiting planet orbits an early type star with rapid rotation
which makes it impossible to measure the RV variations or
you need lots and lots of measurements.
Depending on the rotational velocity RV measurements are
only possible for stars later than about F3
Period =
Companion may be a
planet, but RV
measurements are
impossible
Period: 4.8 d
Transit duration: 5 hrs
Depth : 0.67%
No spectral line seen in this star. This is a
hot star for which RV measurements are
difficult
6. Sometimes you do not get a final answer
Period: 9.75
Transit duration: 4.43 hrs
Depth : 0.2%
V = 13.9
Spectral Type: G0IV (1.27 Rsun)
Planet Radius: 5.6 REarth
Photometry: On Target
CoRoT: LRc02_E1_0591
The Radial Velocity
measurements are
inconclusive. So, how do we
know if this is really a planet.
Note: We have over 30 RV
measurements of this star: 10 Keck
HIRES, 18 HARPS, 3 SOPHIE. In spite
of these, even for V = 13.9 we still do
not have a firm RV detection. This
underlines the difficulty of confirmation
measurements on faint stars.
LRa01_E2_0286 turns out to be a binary
that could still have a planet
But nothing is seen in the residuals
Results from the CoRoT Initial Run Field
26 Transit candidates:
Grazing Eclipsing Binaries: 9
Background Eclipsing Binaries: 8
Unsuitable Host Star: 3
Unclear (no result): 4
Planets: 2
→ for every „quality“ transiting planet found there are 10
false positive detections. These still must be followed-up
with spectral observations
Search Strategies
Look at fields where there is a high density of stars.
Strategy 1:
Look in galactic plane with a small (10-20 cm) wide field (> 1 deg2)
telescope
Pros: stars with 6 < V < 15
Cons: Not as many stars
WASP
• WASP: Wide Angle Search For Planets (http://www.superwasp.org). Also
known as SuperWASP
• Array of 8 Wide Field Cameras
• Field of View: 7.8o x 7.8o
• 13.7 arcseconds/pixel
• Typical magnitude: V = 9-13
Search Strategies
Strategy 2:
Look at the galactic bulge with a large (1-2m) telescope
Pros: Potentially many stars
Cons: V-mag > 14 faint!
OGLE
• OGLE: Optical Gravitational Lens Experiment
(http://www.astrouw.edu.pl/~ogle/)
• 1.3m telescope looking into the galactic bulge
• Mosaic of 8 CCDs: 35‘ x 35‘ field
• Typical magnitude: V = 15-19
• Designed for Gravitational Microlensing
• First planet discovered with the transit method
Search Strategies
Strategy 3:
Look at a clusters
Pros: Potentially many stars (depending on cluster)
Cons: V-mag > 14 faint! Often not enough stars, most open
clusters do not have 3000-10000 stars
A dense open cluster: M 67
Stars of interest have
magnitudes of 14 or
greater
A not so dense open cluster:
Pleiades
h and c Persei double cluster
A dense globular cluster: M 92
Stars of interest have
magnitudes of 17 or
greater
• 8.3 days of Hubble Space Telescope Time
• Expected 17 transits
• None found
• This is a statistically significant result.
[Fe/H] = –0.7
Search Strategies
Strategy 4:
One star at a time!
The MEarth project
(http://www.cfa.harvard.edu/~zberta/mearth/)
uses 8 identical 40 cm telescopes to search
for terrestrial planets around M dwarfs one
after the other
A transiting planet candidate is
only a candidate until it is
confirmed with Radial Velocity
measurements!
Radial Velocity Follow-up for a Hot Jupiter
The problem is not in finding the transits, the problem
(bottleneck) is in confirming these with RVs which requires
high resolution spectrographs.
Telescope
Easy
Challenging
Impossible
2m
V<9
V=10-12
V >13
4m
V < 10–11 V=12-14
V >15
8–10m
V< 12–14
V >17
V=14–16
It takes approximately 8-10 hours of telescope time on a
large telescope to confirm one transit candidate
CoRoT-1b
As a rule of thumb: if you have an RV precision less than onehalf of the RV amplitude you need 8 measurements equally
spaced in phase to detect the planet signal.
SOPHIE
V
0.5MJup
MNep
8
HARPS
Superearth
(7 ME)
V
16
8
0.5MJup
MNep
Superearth
(7 ME)
9
10
40
9
1
2
10
25
100
10
1
5
11
64
250
11
4
15
600
12
8
30
12
3
150
13
4
400
13
20
80
14
6
1000
14
50
200
15
24
15
0.5
125
500
16
54
16
3
300
17
136
17
8
800
Time in hours required (on Target!) for the confirmation of a
transiting planet in a 4 day orbit as a function of V-magnitude. RV
measurement groups like bright stars!
Stellar Magnitude distribution of Exoplanet
Discoveries
35,00%
Percent
30,00%
25,00%
20,00%
Transits
RV
15,00%
10,00%
5,00%
0,00%
0.5
4,50
8,50
12,50
V- magnitude
16,50
Two Final Comments
1. In modeling a transit light curve one only derives
the ratio of the planet radius to the stellar radius:
k = Rp/Rstar
2. In measuring the planet mass with radial velocities
you only derive the mass function:
3(1 – e2)3/2
P
K
3
(mp sin i)
=
f(m) =
2
(mp + ms)
2pG
The planet radius, mass, and thus density depends on
the stellar mass and radius. For high precision data the
uncertainty in the stellar parameters is the largest error
Summary
1. The Transit Method is an efficient way to find
short period planets.
2. Combined with radial velocity measurements it
gives you the mass, radius and thus density of
planets
3. Roughly 1 in 3000 stars will have a transiting hot
Jupiter → need to look at lots of stars (in galactic
plane or clusters)
4. Radial Velocity measurements are essential to
confirm planetary nature
5. Anyone with a small telescope can do transit work
(i.e even amateurs)