Confirming the Nature of Transiting Candidates

Spectroscopic observations are essential for transit searches:

1. Eliminate False positives

2. Derive stellar parameters essential for planet mass and radius (S/N > 100)

3. Derive the planet mass through Radial Velocity Variations (S/N > 10-20)

Transit candidates without spectroscopic observations are of very limited use.

Doppler measurements are required to get the true mass of the transiting planet and thus the density

28.4P1/3Ms

2/3

Mp sin iK = m/s

In general from Kepler‘s law:

For circular orbits (often the case for transiting Planets):

K = 2G

P

Mp sin i(

(⅓Ms

⅔

1

(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

Radial Velocity Amplitude of Planets at Different aR

adia

l Vel

ocity

(m

/s)

G2 V star

Rad

ial V

eloc

ity (

m/s

)A0 V star

M2 V starR

adia

l Vel

ocity

(m

/s)

collimator

Echelle Spectrographs

slit

camera

detector

corrector

From telescope

Cross disperser

Echelle grating

y ∞ 2

y

m-2

m-1

m

m+2

m+3

Free Spectral Range m

Grating cross-dispersed echelle spectrographs

An echelle spectrum of the Sun

What does the radial velocity precision depend on?

1. The spectral resolution (≡ )

2. The Signal to Noise Ratio (S/N) of your data.

3. Your wavelength coverage: the more spectral lines the more radial velocity measurements you have

4. The type of star you are looking at

Spectral Resolution

d

1 2

Consider two monochromatic beams

They will just be resolved when they have a wavelength separation of d

Resolving power:

d = full width of half maximum of calibration lamp emission lines

R = d

← 2 detector pixels

For Doppler confirmation of planets you need R = 50000 - 100000

How does the radial velocity precision depend on all parameters?

(m/s) = Constant × (S/N)–1 R–3/2 ()–1/2

: errorR: spectral resolving powerS/N: signal to noise ratio : wavelength coverage of spectrograph in Angstroms

For R=110.000, S/N=150, =2000 Å, = 2 m/s

C ≈ 2.4 × 1011

For a given instrument you can take its actual performance with real observations and scale accordingly

A7 star

K0 star

Early-type stars have few spectral lines (high effective temperatures) and high rotation rates.

Including dependence on stellar parameters

v sin i : projected rotational velocity of star in km/s

f(Teff) = factor taking into account line density

f(Teff) ≈ 1 for solar type star

f(Teff) ≈ 3 for A-type star

f(Teff) ≈ 0.5 for M-type star

(m/s) ≈ Constant ×(S/N)–1 R–3/2 v sin i( 2 ) f(Teff)()–1/2

For RV work the useful wavelength coverage is no more than 1000-2000 Å

For planet detection with radial velocity measurements you need a stable spectrograph. The traditional way of doing wavelength calibrations introduces instrumental errors. You need special tricks

Observe your star→

Then your calibration source→

The classic method should work for RV amplitudes of more than 100 m/s

Because the calibration source is observed at a different time from your star you can have instrumental shifts

... Short term shifts of the spectrograph can limit precision to several hunrdreds of m/s

Method 1: Observe your calibration source (Th-Ar) simultaneously to your data:

Spectrographs: CORALIE, ELODIE, HARPS

Stellar spectrum

Thorium-Argon calibration

The iodine cell used at the CES spectrograph at La Silla

Method 2: Iodine cell

Spectrum of Iodine

Spectrum of Iodine + Star

Telescope Instrument Wavelength Reference

1-m MJUO Hercules Th-Ar

1.2-m Euler Telescope CORALIE Th-Ar

1.8-m BOAO BOES Iodine Cell

1.88-m Okayama Obs, HIDES Iodine Cell

1.88-m OHP SOPHIE Th-Ar

2-m TLS Coude Echelle Iodine Cell

2.2m ESO/MPI La Silla FEROS Th-Ar

2.5m NOT FIES Th-Ar

2.7m McDonald Obs. 2dcoude Iodine cell

3-m Lick Observatory Hamilton Echelle Iodine cell

3.8-m TNG SARG Iodine Cell

3.9-m AAT UCLES Iodine cell

3.6-m ESO La Silla HARPS Th-Ar

8.2-m Subaru Telescope HDS Iodine Cell

8.2-m VLT UVES Iodine cell

9-m Hobby-Eberly HRS Iodine cell

10-m Keck HiRes Iodine cell

Transit Discoveries

HAT: 31 exoplanets V=8.7-13.2

WASP: 66 exoplanets V=8.3-12.6

Kepler: 24 exoplanets V=11-14

CoRoT: 24 exoplanets V=11.7-16

OGLE: 8 exoplanets V=14-15.8 Last discovery: 2007

Is doubtful that any more spectroscopic observations follow-up observations will be made of OGLE candidates because they are too faint. Groups will either observe Kepler/CoRoT targets (best possible light curves) or WASP/HAT candidates (bright)

Period (days)

RV

Err

or/A

mpl

itud

e

V-magnitude

RV error SOPHIE

RV error HARPS and HIRES

RV error ESPRESSO (VLT)

Jupiter

Neptune

Superearth 7 (MEarth)

In an ideal world with only photon noise:

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!

HD 166435

Rad

ial V

elo

city

(m

/s)

10

-10

0 0.2

0.4

0.6

0.8

Rotation Phase

Stellar activity can decrease your measurement precision !!!

Radial velocity variations due entirely to spots

Saar & Donahue (1996):

ARV (m/s) = 6.5 f0.9 vsini

Hatzes (2001):ARV (m/s) = (8.6 vsini – 1.6) f0.9

f is filling factor (photometric amplitude) in percent)

vsini (V in figure) is rotational velocity in km/s

f=0.5%, vsini=2 km/s → ARV = 7 m/s

f=0.5%, vsini=2 km/s → ARV = 8.3 m/s

Two expressions agree to within 20%

Stellar Activity can be the dominant noise source

Comparison of HARPS predicted RV error as a function of activity for a 10th magnitude star

Quiet Sun-Like

Modest Activity (vsini=2 k/s, f=2%)

Active

(vsin=10, f=3%)

Active

(vsin=30, f=5%)

1 m/s 4 m/s 25 m/s 175 m/s 800 m/s

In some cases it is possible to use „tricks“ to reduce the noise due to activity. See CoRoT-7b at end of lecture.

If you are looking at young active stars your RV precision will be signficantly worse and these will require more telescope resources

Bisectors can measure the line shapes and tell you about the nature of the RV variations:

What can change bisectors :• Spots• Blends• Pulsations

Span

Curvature

A Tool for confirming planets: Bisectors

Correlation of bisector span with radial velocity for HD 166435: Spot

Spectroscopic binaries can also produce line profile changes

The Cross-Correlation Function (CCF) is a common way to measure the Radial Velocity of a Star:

1. The CCF of your observation can be taken with a template of a standard star, a mask (0 values in the continuum and 1 in spectral lines) or with one observation of your star (relative velocities).

2. The centroid of the CCF gives you the Radial Velocity

3. An assymetric CCF → blend

4. The CCF represents the mean shape of your spectral lines. Measuring the bisector of the CCF can reveal line shape variations

In IRAF: rv package → fxcor

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

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

1. Grazing Eclipse by stellar companion

2. Giant Star eclipsed by a main sequence star

3. Background Eclipsing Binary (BEB)

4. Hiearchical Triple System

5. Star not suitable for radial velocity measurements

6. Unsolved cases

Before you start: Use what you know about transits!

If it is really a transiting/eclipsing body, then you expect the radial velocity to be zero at photometric (transit= phase zero, minimum at phase 0.25 and maximum at phase 0.75. RV variations must be in phase with the light curve.

Transit phase = 0

OGLE-TR-3 is NOT a transiting planet. You know this immediately because the RV is not in phase with the transit

1. Grazing eclipse by a main sequence star:

The shape of the light curve is the first indication of a binary star

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 Rsun. This results in an eclipse depth of 0.0001– 0.01 for a companion like the sun

This scenario can be resolved with relatively little cost in telescope resources:

1. A longer than expected transit duration is the first hint that you have a large star. For example a transiting planet in a 10 day orbit will have a duration of 4 hrs. Around a 10 Rsun star (planet still outside of the star) the duration will be 39 hrs

2. A low resolution spectrum will establish the luminosity class of the star

3. Two radial velocity measurements taken at minimum and maximum will establish binarity

This star was originally classified as a K0 main sequence star with photometry

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 (subgiant, photometry)

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.

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

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)

= 42 m/s

Error: 20-30 m/s

Radial VelocityBisector

The Bisector variations correlate withthe RV → this is a blend

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

5. 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

BLENDER Analysis: Confirming planets without RV measurements

1. Generate the brightness variations of an eclipsing binary

2. Include limb darkening, gravity darkening, reflection, oblateness, etc.

3. Use stellar isochrones to get stellar parameters (effective temperature, size, etc).

4. Search in parameter space

5. Assign probabilities to the best „blend scenario“ solution.

Star 2Star 1

Planet candidate Star 3

You have a good estimate of mass, luminosity of Star 1

Take possible masses, luminosity, etc for the binary components

Move them to different distances

If they are too close, you will see them in a spectrum

If they are too far, they will not contribute enough light

Star 2 and 3 are the test binary

The light curve shows a nice transit. There are RV variations consistent with a brown dwarf, but the CCF bisector shows variations

1)

2)

Map of possible binary masses that can reproduce the light curve of OGLE-TR-33:

1) Star 1 is the bright star in the binary

2) Star 2 is the „secondary“ in the binary

Fit to the light curve using the blended binary scenario

With TODCOR one can measure both components of the binary

The luminosity ration of the binary stars from the RV curve is consistent with the BLENDER analysis

Kepler-9b

Note: Primary is the main star, secondary is the brighter component of the binary, tertiary the fainter componentRed line is the best fit binary blend model (not good)

Kepler-9c

The blend model is indistinguishable from the planet model. One can then use probabilty arguments to promote the planet hypothesis

The „Sherlock Holmes Method“ of Confirming the Nature of Transiting Planets

Or

How to Confirm Planets Without a Radial Velocity Curve

„When you have excluded the impossible, whatever remains, however improbable, must be the truth“

– Sherlock Holmes (Sir Arthur Conan Doyle)

Case Study: CoRoT-7b

44

Can we prove that CoRoT-7b is a Planet without a RV curve?

R = 1.58 REarth

P = 0.85 d

Hypothesis #1: The transit is caused by a contaminant

On-off photometry established that nearby stars could not account for transit depth of CoRoT-7

Hypothesis #2: The star is really a giant star

No, it is a G8 Main Sequence Star

Hypothesis #3: There is a faint very nearby background eclipsing binary star that causes the eclipse

Adaptive Optics Imaging shows no very close companions

Hypothesis #4: A Hiearchical Triple system with 2 eclipsing M-dwarfs,

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

Hypothesis #5:The transit is caused by a background (or binary companion) M dwarf with a transiting Hot Jupiter

1. Giant planets to M dwarfs are rare

2 The M dwarf is bright in the Infrared. High resolution infrared spectral

observations show no evidence for an M dwarf companion.

There are only two astronomical bodies that have a radius ~ 1.5 REarth:

1. White Dwarf

2. A terrestrial planet

White Dwarfs have a mass of ~ 1 Solar Mass, so the radial velocity amplitude should be ~ 100s km/s. This is excluded by low precision radial velocity measurements.

Also photometry can exclude the white dwarf scenario

Modified From H. Rauer

CoRoT-3b : Radius = Jupiter, Mass = 21.6 Jupiter

CoRoT-1b : Radius = 1.5 Jupiter, Mass = 1 Jupiter

OGLE-TR-133b: Radius = 1.33 Jupiter, Mass = 85 Jupiter

CoRoT-1b

CoRoT-3b

OGLE-TR-133b

For companions that are the size of Jupiter you can have a planet, brown dwarf, or star.

44

The Challenge: Dealing with the Activity Signal

Prot = 23 d

Expected activity related RV variations:

flux ≈ 1.6% (spots)

Rotational veloctiy = 1.8 km/s

Saar & Donahue: 18 km/s

Hatzes: 22 m/s

Can We Get the Mass of CoRoT-7b?

44

RV

(m

/s)

JD

HARPS RVs for CoRoT-7b: 104 Measurements!

RV spot „jitter“ ≈ 20 m/s

Amplitude of transting planet ≈ 5 m/s

Mass Determinations for CoRoT-7b

Is it 3.5 ± 0.6 MEarth (Queloz et al. 2009)? → Harmonic Filtering

Is it 6.9 ± 1.43 MEarth (Hatzes et al. 2010)? → Fourier Pre-whitening

Is it 8.0 ± 1.2 MEarth (Ferraz-Melo al. 2010)? → High pass filtering

Is it 5.65 ± 1.6 MEarth (Boisse al. 2010)? → Harmonic Filtering

Is it 2.26 ± 1.83 MEarth (Pont al. 2010)? → Activity modeling

The mass you get depends on how you filter out the activity signal.

Pont et al. Using activity models:

Spots, long period planets, systematic errors

Orbital Phase

Rad

ial V

eloc

ity (

m/s

) K = 5 m/s

Try K = 2 m/s

Poor fit at phase 0.8-0.1

Orbital Phase

Rad

ial V

eloc

ity (

m/s

)

Try K = 8 m/s

Poor fit at phase 0-0.4

Orbital Phase

Rad

ial V

eloc

ity (

m/s

)

Two simple and reasonable assumptions:

1) A 0.85 d period is present in the RV data

Reasonable given Leger, Rouan, Schneider et al. (2009)

2) RV Variations from other phenomena (activity, other planets, systematic errors) over T < 4 hours is small.

rot = 0.01, RV < 0.5 m/s

RVplanets = 0 ± 0.9 m/s

Trick: Exploit the fact that the RV period from the planet is much shorter than the period expected from spots and stellar rotation

Use a Subset of the 106 HARPS RV measurements (Less is More!)

• 10 Nights with 3 measurements T=4 hours (orbit = 0.2)

• 17 Nights with 2 measurements T=2 hours (orbit = 0.1)

• Total 66 Measurements

• Consider each night an „independent“ data set that has its own zero point offset caused by the contribution of activity jitter that should be constant for that night

• Find the best fit sine curve with P = 0.85 d

Zero point offsets and phase are the only free parameters. The RV phase agrees with transit phase to within 0.01 phase

O–C = 1.7 m/s

RV = 1.8 m/s

K = 5.15 ± 0.94 m/s

M = 7.29 ± 1.35 MEarth

Best fit circular orbit:

Top: the RV amplitude as a function of the number of points used. The dashed line is the final amplitude using all data. Note that the correct RV amplitude can be measured with only 15 measurements over 5 nights.

Bottom: simulations of a fake orbit with „input“ amplitude versus the amplitude found by the method

Sanity Check: Periodogram of the nightly offsets

rot (P=23 d)

Amplitude of variations ≈ 10 m/s

Mstar = 0.895 ± 0.06 Msun

Rstar = 1.056 ±0.02 Rsun

MPl = 4.56 ±1.23 MEarth

RPl = 1.416 ±0.025 REarth

Pl = 8.8 ±2.5 cgs

Mstar = 0.91 ±0.03 Msun

Rstar = 0.82 ±0.04 Rsun

MPl = 7.29 ±1.35 MEarth

RPl = 1.58 ±0.10 REarth

Pl = 10.2 ±2.7 cgs

red2 = 4.3 red

2 = 1.5 = 3.07 m/s = 1.68 m/s

Kepler-10b versus CoRoT-7b: Inactive versus Active

Inactive Active

Strategy for confirming Transit Candidates around Faint Stars (V>10)

1. Make sure that your star is on target and that another star in the aperture is not causing the transit.

2. Do you see a secondary eclipse? Ellipsoidal variations? → Binary

3. Use low resolution spectra to get the spectral type of the star and to be sure it is not a spectroscopic binary

4. Use a blender-like analysis to establish what kind of binary stars can reproduce the observed transit.

5. Use low precision RV measurements to exclude a binary companion

6. Use adaptive optics/high resolution imaging to exclude a close background/foreground object

7. Get Infrared spectral observations to exclude an M-dwarf companion

8. Ask your RV friends to observe this star