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

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 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 Historical Context of Transiting Planets (Venus)

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 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 Historical Context of Transiting Planets (Venus)

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

Venus limb solar

R*R* II The drop in intensity is give by the ratio of the cross-section areas:  I = (R p /R * ) 2 = (0.1R sun /1 R sun ) 2 = 0.01 for Jupiter Radial Velocity measurements => M p (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 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 Mean density (gm/cm 3 )

Mercury Mars Venus Earth Moon Radius (R Earth )  (gm/cm 3 ) No iron Earth-like Iron enriched From Diana Valencia The radius, mass, and density are the first clues about the internal structure

EarthVenus 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%) MoonMercury Mercury has a very large iron core and thus a high density for its small size 1.Crust: 100 km 2.Silicate Mantle (25%) 3.Nickel-Iron Core (75%)

R*R* a  i = 90 o +  sin  = R * /a = |cos i| P orb =  2  sin i di / 4  = 90-  90+  – 0.5 cos (90+  ) cos(90 –  ) = sin  = R * /a for small angles Transit Probability a is orbital semi-major axis, and i is the orbital inclination 1 1 by definition i = 90 deg is looking in the orbital plane

Transit Duration  = 2(R * +R p )/v where v is the orbital velocity and i = 90 (transit across disk center) For circular orbits v = 2  a/P From Keplers Law’s: a = (P 2 M * G/4  2 ) 1/3   1.82 P 1/3 R * /M * 1/3 (hours) 2R * P (4  2 ) 1/3 2  P 2/3 M * 1/3 G 1/3    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 R star = 0.55  M 1/3 P 1/3 R in solar radii M in solar masses P in days  in hours Most Stars have masses of 0.1 – 4 solar masses. M ⅓ = 0.46 – 1.6

For more accurate times need to take into account the orbital inclination for i  90 o need to replace R * with R: R 2 + d 2 cos 2 i = R * 2 R = (R * 2 – d 2 cos 2 i) 1/2 d cos iR*R* R

1.First contact with star 2.Planet fully on star 3. Planet starts to exit 4. Last contact with star Note: for grazing transits there is no 2nd and 3rd contact Making contact:

Planet  I/I Prob.N  (hrs) f orbit Mercury1.2 x Venus7.5 x Earth8.3 x Mars2.3 x x Jupiter x Saturn x Uranus x Neptune x Peg b Moon6.2 x10 -6 Ganymede1.3 x Titan1.2 x 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.

t flat t total t flat t total 2 [R * – R p ] 2 – d 2 cos 2 i [R * + R p ] 2 – d 2 cos 2 i = Note that when i = 90 o t flat /t total = (R * – R p )/( R * + R p ) Shape of Transit Curves

A real transit light curve is not flat HST light curve of HD b

Shape of Transit Curves Effects of Limb Darkening (or why the curve is not flat). 22 11 dz  =1 surface Top of photosphere Bottom of photosphere Temperature profile of photosphere z=0 Temperature 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 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/transits These produce a „V-shaped“ transit curve that are more shallow Shape of Transit Curves Planet hunters like to see a flat part on the bottom of the transit

Probability of detecting a transit P tran : P tran = P orb x f planets x f stars x  T/P P orb = probability that orbit has correct orientation f planets = fraction of stars with planets f stars = 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 P orb P orb  0.1 f planets 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 R סּ

Estimating the Parameters for 51 Peg systems f stars 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 R sun. This means that a star can have a maximum radius of 1.5 R sun 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 R J = 0.1 R sun Example: B8 Star: R=3.8 R Sun  I = (0.1/3.8) 2 = 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 This corresponds to a radius of 50 R Jupiter = 0.5 R sun

You also have to worry about late-type giant stars Example: A K III Star can have R ~ 10 R Sun  I = 0.01 = (R p /10) 2 → R p = 1 R Sun ! 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 (M sun ) Along the Main Sequence The photometric transit depth for a 1 R Jup planet

Stellar Mass (M sun ) Planet Radius (R Jup ) 1 R Earth 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

Estimating the Parameters for 51 Peg systems Fraction of the time in transit  T/P  0.08 P orbit ≈ 4 days Transit duration ≈ 3 hours Thus the probability of detecting a transit of a planet in a single night is

For each test orbital period you have to observe enough to get the probability that you would have observed the transit (P vis ) close to unity.

E.g. a field of Stars the number of expected transits is: N transits = (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 Transit Curve: 10 cm telescope

Radial Velocity Curve for HD Period = 3.5 days Msini = 0.63 M Jup 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 R סּ which translates into photometric depths of – 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 R sun and M = M sun 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 M Sun

CoRoT: LRa02_E1_5015 Mass ≈ 0.2 M Sun 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_5184 Spectral Classification: K1 V (spectroscopy) Period: 7.4 d Transit duration: hrs Depth : 0.56%

Photometric Phase Radial Velocity (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 R sun ) Planet Radius: 5.6 R Earth 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_ 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 deg 2 ) telescope Pros: stars with 6 < V < 15 Cons: Not as many stars

WASP WASP: Wide Angle Search For Planets ( Also known as SuperWASP Array of 8 Wide Field Cameras Field of View: 7.8 o x 7.8 o 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 ( 1.3m telescope looking into the galactic bulge Mosaic of 8 CCDs: 35‘ x 35‘ field Typical magnitude: V = 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 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 ( 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 TelescopeEasyChallengingImpossible 2mV < 9V=10-12V >13 4m V < 10 – 11 V=12-14V >15 8–10m V< 12 – 14 V=14–16V >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

V0.5M Jup M Nep Superearth (7 M E ) SOPHIE V0.5M Jup M Nep Superearth (7 M E ) 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 Percent Stellar Magnitude distribution of Exoplanet Discoveries

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) = (m p sin i) 3 (m p + m s ) 2 = P 2G2G K 3 (1 – e 2 ) 3/2 k = R p /R star 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