The Transit Method 1. Photometric 2.Spectroscopic (next time)

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 Method02 May: Results from Radial Velocity Searches09 May: Astrometry16 May: The Transit Method23 May: Planets in other Environments (Eike Guenther)30 May: Transit Results: Ground-based06 Jun: Transit Results: Space-based13 Jun: Exoplanet Atmospheres20 Jun: Direct Imaging27 Jun: Microlensing04 Jul: No Class11 Jul: Planets in Extreme Environments: Planets around evolved stars18 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 worldsBy Carole Haswell

Discovery Space for Exoplanets

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)

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.

From wikipedia


Transits of Venus occur in pairs separated by 8 years and these were the first international efforts to measure these events.

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.

Le Gentil‘s observatory

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.

From wikipedia


Venus transit im June 2012!

On 6. June 2012 the second transit of the 8-year pairs takes place.

Venus limb

solar

R*

I

The drop in intensity is give by the ratio of the cross-section areas:I = (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 are Transits and why are they important?

What can we learn about Planetary Transits?

1. The radius of the planet2. The orbital inclination and the mass when

combined with radial velocity measurements3. Density → first hints of structure4. The Albedo from reflected light5. The temperature from radiated light6. Atmospheric spectral features

In other words, we can begin to characterize exoplanets

http://www.freewebs.com/mdreyes3/chaptersix.htm

Comparison of the Giant Planets

1.24 0.62 1.25 1.6

Mean density (gm/cm3)

Mercury

MarsVenus

Earth

Moon

1

2

3

4

5

7

10

0.2 0.4

Radius (REarth)

(g

m/c

m3)

0.6 0.8 1 1.2 1.4 1.6 1.8 2

No iron

Earth-likeIron enriched

From Diana Valencia

The radius, mass, and density are the first clues about the internal structure

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

The moon has a very small core, but a large mantle (≈70%)

Moon Mercury

Mercury has a very large iron core and thus a high density for its small size

1. Crust: 100 km2. Silicate Mantle (25%)3. Nickel-Iron Core (75%)

R*

a

i = 90o+

sin = R*/a = |cos i|

Porb = 2 sin i di / 4 = 90-

90+

–0.5 cos (90+) + 0.5 cos(90–) = sin

= R*/a for small angles

Transit Probability

a is orbital semi-major axis, and i is the

orbital inclination1

1by definition i = 90 deg is looking in the orbital plane

Transit Duration

= 2(R* +Rp)/v

where v is the orbital velocity and i = 90 (transit across disk center)

For circular orbits v = 2a/P

From Keplers Law’s: a = (P2 M*G/42)1/3

1.82 P1/3 R* /M*1/3 (hours)2R* P (42)1/3

2 P2/3 M*1/3G1/3

In solar units, P in days

Note 3 ~ (mean)–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 M1/3

P1/3

R in solar radii

M in solar masses

P in days

in hours

Most Stars have masses of 0.1 – 4 solar masses.

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

R = (R*2 – d2 cos2i)1/2

d cos i R*

R

1. First contact with star2. Planet fully on star3. Planet starts to exit4. Last contact with star

Note: for grazing transits there is no 2nd and 3rd contact

Making contact:

1

2 3

4

Planet I/I Prob. N (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

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.

tflat

ttotal

tflat

ttotal

2[R* – Rp]2 – d2 cos2i

[R* + Rp]2 – d2 cos2i=

Note that when i = 90o tflat/ttotal = (R* – Rp)/( R* + Rp)

Shape of Transit Curves


A real transit light curve is not flat

HST light curve of HD 209458b

Shape of Transit Curves Effects of Limb Darkening (or why the curve is not flat).

2

1 dz

=1 surface

Top of photosphere

Bottom of photosphere

Temperature profile of photosphere

100008000

6000

4000

z=0

Tem

pera

ture

z

z increases going into the star

To probe limb darkening in other stars..

..you can use transiting planets

At the limb the star has less flux than is expected, thus the planet blocks less light

No limb darkening transit shape

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

More limb darkening → short transit duration

Less limb darkening in red → longer transit duration → orbital inclination has changed!

And your wrong conclusion:

Effects of limb darkening on the transit curve

Grazing eclipses/transitsThese 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 T/P

Porb = probability that orbit has correct orientation

fplanets = fraction of stars with planets

fstars = fraction of suitable stars (Spectral Type later than F5)

T/P = fraction of orbital period spent in transit

Estimating the Parameters for 51 Peg systems

Porb

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%

Period ≈ 4 days → a = 0.05 AU = 10 Rּס


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

I = (0.1/3.8)2 = 0.0007

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

Suppose you detect a transit event with a depth of 0.01. This corresponds to a radius of 50 RJupiter = 0.5 Rsun

You also have to worry about late-type giant stars

Example:

A K III Star can have R ~ 10 RSun

I = 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.

Spectral Type

I/I

Spectral Type

Stellar Mass (Msun) Stellar Mass (Msun)

Along the Main Sequence

The photometric transit depth for a 1 RJup planet

Stellar Mass (Msun)

Pla

net R

adiu

s (

RJu

p)

1 REarth

Along the Main Sequence

Assuming a 1% photometric precision this is the minimum planet radius as a function of stellar radius (spectral type) that can be detected


Fraction of the time in transit

T/P 0.08

Porbit ≈ 4 days

Transit duration ≈ 3 hours

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.

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.

Confirming Transit Candidates

Light curve for HD 209458

Transit Curve: 10 cm telescope

Radial Velocity Curve for HD 209458

Period = 3.5 days

Msini = 0.63 MJup

Transit phase = 0

Radial Velocity Curve: 2-10 m telescopes

Spectroscopic measurements are important to:

1. False positives

2. Derive the mass of the planet

3. Determine the stellar parameters

Confirming Transit Candidates

False Positives

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)

It looks like a planet, it smells like a planet, but it is not a planet

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 Rּס which 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 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.

Green: model

Black: data

Low resolution spectra can easily distinguish between a giant and main sequence star for the host.

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

Mass ≈ 0.2 MSun

Spectral Classification: K0 III ?

Period: 13.7 d

Transit duration: 10.1 hrs → Giant?

3. Eclipsing Binary as a background (foreground) star:

Fainter binary system in background or foreground

Light curve of eclipsing system. 50% depth

Light from bright star

Total = 17% 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

Short period M dwarfs are very active and we would have seen Ca II emission from the binary stars and X-ray emission

If the binary is are low mass stars they may be active:

CoRoT: LRa02_E1_5184Spectral Classification: K1 V (spectroscopy)

Period: 7.4 d

Transit duration: 12.68 hrs

Depth : 0.56%

Photometric Phase

Rad

ial V

eloc

ity

(km

/s)

Radial Velocity

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 =

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

Companion may be a planet, but RV measurements are impossible

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

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.

CoRoT: LRc02_E1_0591

6. Sometimes you do not get a final answer

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 A not so dense open cluster: Pleiades

Stars of interest have magnitudes of 14 or greater

h and 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

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=14–16 V >17

It takes approximately 8-10 hours of telescope time on a large telescope to confirm one transit candidate

The problem is not in finding the transits, the problem (bottleneck) is in confirming these with RVs which requires high resolution spectrographs.

As a rule of thumb: if you have an RV precision less than one-half of the RV amplitude you need 8 measurements equally spaced in phase to detect the planet signal.

CoRoT-1b

V 0.5MJup MNep Superearth (7 ME)

8 16

9 10 40

10 25 100

11 64 250

12 3 150 600

13 4 400

14 6 1000

15 24

16 54

17 136

SOPHIE

V 0.5MJup MNep Superearth (7 ME)

8

9 1 2

10 1 5

11 4 15

12 8 30

13 20 80

14 50 200

15 0.5 125 500

16 3 300

17 8 800

HARPS

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!

V- magnitude

Per

cen

t

Stellar Magnitude distribution of Exoplanet Discoveries

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

30,00%

35,00%

0.5 4,50 8,50 12,50 16,50

Transits

RV

Two Final Comments

1. In modeling a transit light curve one only derives the ratio of the planet radius to the stellar radius:

f(m) = (mp sin i)3

(mp + ms)2=

P

2G

K3(1 – e2)3/2

k = Rp/Rstar

2. In measuring the planet mass with radial velocities you only derive the mass function:

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

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)

Summary

Documents

The Transit Method 1. Photometric 2.Spectroscopic (next time)