Transit Searches: Techniques

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 Why are Transits Important?

Also in transit spectroscopy. As starlight passes through the atmosphere of the planet, part of it is absorbed.

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

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 = 0.55  M 1/3 P 1/3 R in solar radii M in solar masses P in days  in hours

For more accurate times need to take into account the orbital inclination and the fact that you have a finite radius planet 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

The Full Duration of the transit is including inclination is given by: D = P  arcsin { R*R* a sin i √ ( 1 + RpRp R*R* ( 2 ( a cos i R*R* ) 2 – { a is the semi-major axis

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.Nt (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

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 ) For main sequence stars we can use the mass radius relationship to eliminate either the mass or the radius from expression for transit time. 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

Limb darkening in other stars 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

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:

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.

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 is 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 KIII Star can have R ~ 10 R Sun DI = 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.

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 a transiting Hot Jupiter 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 field.

CCD Photometry 1. Aperture photometry 2. PSF photometry 3. Difference imaging CCD Imaging photometry is at the heart of any transit search program

Get data (star) counts Magnitude = constant –2.5 x log [Σ(data – sky)/(exposure time)] Instrumental magnitude can be converted to real magnitude by looking at standard stars Aperture Photometry Get sky counts

And to remind you what a magnitude is. If two stars have brightness B 1 and B 2, their brightness ratio is: B 1 /B 2 =  m 5 Magnitudes is a factor of 100 in brightness, larger values of m means fainter stars.

Aperture photometry is useless for crowded fields

Term: Point Spread Function PSF: Image produced by the instrument + atmosphere = point spread function Camera Atmosphere Most photometric reduction programs require modeling of the PSF Note: PSF is the two dimensional version of the Instrumental Profile (IP)

Crowded field Photometry: DAOPHOT Computer program developed to obtain accurate photometry of blended images (Stetson 1987, Publications of the Astronomical Society of the Pacific, 99, 191) DAOPHOT software is part of the IRAF (Image Reduction and Analysis Facility) IRAF can be dowloaded from (Windows, Mac) or (mostly Linux) In iraf: load packages: noao -> digiphot -> daophot Users manuals:

1. Choose several stars as „psf“ stars 2. Fit psf 3. Subtract neighbors 4. Refit PSF 5. Iterate 6. Stop after 2-3 iterations In DAOPHOT modeling of the PSF is done through an iterative process:

Original DataData minus stars found in first star list Data minus stars found in second determination of star list

Image Subtraction If you are only interested in changes in the brightness (differential photometry) of an object one can use image subtraction (Alard, Astronomy and Astrophysics Suppl. Ser. 144, 363, 2000)

Image subtraction: Basic Technique Get a reference image R. This is either a synthetic image (point sources) or a real data frame taken under good seeing conditions (usually your best frame). Find a convolution Kernal, K, that will transform R to fit your observed image, I. Your fit image is R * I where * is the convolution (i.e. smoothing) Solve in a least squares manner the Kernal that will minimize the sum: ([R * K](x i,y i ) – I(x i,y i )) 2 S i Kernal is usually taken to be a Gaussian whose width can vary across the frame.

Observation Smooth your reference profile with your Kernel function. This should look like your observation Reference profile: e.g. Observation taken under excellent conditions In a perfect world if you subtract the two you get zero, except for differences due to star variabiltiy In pictures:

These techniques are fine, but what happens when some light clouds pass by covering some stars, but not others, or the atmospheric transparency changes across the CCD? You need to find a reference star with which you divide the flux from your target star. But what if this star is variable? In practice each star is divided by the sum of all the other stars in the field, i.e. each star is referenced to all other stars in the field. T A B C T: Target, Red: Reference Stars T/A = Constant T/B = Constant T/C = variations C is a variable star

Sources of Errors Sources of photometric noise: 1. Photon noise: error = √N s (N s = photons from source) Signal to noise ratio = N s / √ N s = √N s Root mean scatter (rms) in brightness = 1/(S/N)

Sources of Errors 2. Sky: Sky is bright, adds noise, best not to observe under full moon or in downtown Jena. N data = counts from star N sky = background Error = (N data + N sky ) 1/2 S/N = (N data )/(N data + N sky ) 1/2 rms scatter = 1/(S/N)

N data rms N sky = 0 N sky = 10 N sky = 100 N sky = 1000

3. Dark Counts and Readout Noise: Dark: Electrons dislodged by thermal noise, typically a few per hour. This can be neglected unless you are looking at very faint sources Sources of Errors Typical CCDs have readout noise counts of 3–11 e –1 (photons) Readout Noise: Noise introduced in reading out the CCD:

Sources of Errors 4. Scintillation Noise: Amplitude variations due to Earth‘s atmosphere  ~ [ (kD 2 /4L) 7/6 ] –1 D is the telescope diameter L is the length scale of the atmospheric turbulence

Star looks fainterStar looks brighter

For larger telescopes the diameter of the telescope is much larger than the length scale of the turbulence. This reduces the scintillation noise.

Sources of Errors 5. Atmospheric Extinction Atmospheric Extinction can affect colors of stars and photometric precision of differential photometry since observations are done at different air masses Rayleigh scattering: cross section  per molecule ∝ –4 Major sources of extinction:

Absorption by gases Aerosol Extinction

A-star K-star Atmospheric extinction can also affect differential photometry because reference stars are not always the same spectral type. Atmospheric extinction (e.g. Rayleigh scattering) will affect the A star more than the K star because it has more flux at shorter wavelength where the extinction is greater Wavelength (Å) Intensity

Atmospheric extinction could produce false detections: Time Intensity Drop due to atmospheric extinction Transit detection algorithms would detect these as a transit

Sources of Errors 6. Stellar Variability: Signal that is noise for our purposes Stellar activity, oscillations, and other forms of variability can hinder one‘s ability to detect transit events due to planets. e.g. sunspots can cause a variations of about 0.1-1% Fortunately, most of these phenomena have time scales different from the transit periods.

Light Curves from Tautenburg taken with BEST Step 1: Observe a field of stars, plot up the photometry and make sure that it is consistent with what you expect from noise sources

Saturated bright stars A not-so-nice looking curve from an open cluster

CCD Counts t t Saturation Saturation + non- linearity

Finding Transits in the Data 1. Produce a time series light curve of your observations using your favorite technique (aperture, psf, or difference imaging photometry)

Finding Transits in the Data 2. Remove the bumps and wiggles due to instrumental effects and stellar variability using low pass filters

Finding Transits in the Data 3. Phase fold the data using a trial period

Finding Transits in the Data 3. Perform a least squares fit using a box (BLS = box least squares) w d Find the best fit box of width, w, and depth d. Define a frequency spectrum of residuals (parameter of best fit) as a function of trial periods. Peaks occur at most likely values of transit periods. The BLS is the most commonly used transit algorithm

Kovaks, Zucker, & Mazeh, A&A, 391, 369, 2002 The quantity SR is defined as such that when one has low residuals (i.e. good fit), SR has a maximum value.

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

Radial Velocity Curve for HD Period = 3.5 days Msini = 0.63 M Jup Transit phase = 0

Radial Velocity measurements are essential for confirming the nature (i.e. get the mass) of the companion, and to exclude so- called false postives. 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

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 with R = 10 R sun and M = M sun and a transit period of 10 days:  ≈ 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.

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.

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

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

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 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! Image in galactic bulge

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 with a large (1-2m) telescope 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

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 4mV < 10–11V=12-14V >15 8–10mV< 12–14V=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.

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

Tautenburg Exoplanet Search Telescope: a 30 cm “Amateur” Telescope

A proud amateur and his light curve of the new hot transiting Saturn