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
In general from Kepler‘s law:
(
(
K=
2pG ⅓ Mp sin i
P
Ms ⅔
1
(1 – e2)½
For circular orbits (often the case for transiting
Planets):
K=
28.4 Mp sin i
P1/3Ms2/3
m/s
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 a
Radial Velocity (m/s)
G2 V star
Radial Velocity (m/s)
A0 V star
Radial Velocity (m/s)
M2 V star
Echelle Spectrographs
camera
detector
corrector
Cross disperser
From telescope
slit
collimator
Echelle grating
dl
Free Spectral Range Dl = l/m
m-2
m-1
m
m+2
m+3
y
Dy ∞ l2
Grating cross-dispersed echelle spectrographs
An echelle spectrum of the Sun
What does the radial velocity precision depend on?
1.
The spectral resolution (≡ l/dl)
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
← 2 detector pixels
dl
Consider two monochromatic
beams
They will just be resolved when they
have a wavelength separation of dl
Resolving power:
l
R=
dl
l1
l2
dl = full width of half
maximum of calibration
lamp emission lines
For Doppler confirmation of planets you
need R = 50000 - 100000
How does the radial velocity precision depend on all
parameters?
s (m/s) = Constant × (S/N)–1 R–3/2 (Dl)–1/2
s: error
R: spectral resolving power
S/N: signal to noise ratio
Dl : wavelength coverage of spectrograph in Angstroms
For R=110.000, S/N=150, Dl=2000 Å, s = 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
s (m/s) ≈ Constant ×(S/N)–1 R–3/2(Dl)–1/2 (
v sin i
f(Teff)
)
2
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
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:
Stellar
spectrum
Thorium-Argon
calibration
Spectrographs: CORALIE, ELODIE, HARPS
The iodine cell used at the CES spectrograph at La Silla
Method 2: Iodine cell
Spectrum of Iodine
Spectrum of Iodine + Star
Telescope
1-m MJUO
1.2-m Euler Telescope
1.8-m BOAO
1.88-m Okayama Obs,
1.88-m OHP
2-m TLS
2.2m ESO/MPI La Silla
2.5m NOT
2.7m McDonald Obs.
3-m Lick Observatory
3.8-m TNG
3.9-m AAT
3.6-m ESO La Silla
8.2-m Subaru Telescope
8.2-m VLT
9-m Hobby-Eberly
10-m Keck
Instrument
Hercules
CORALIE
BOES
HIDES
SOPHIE
Coude Echelle
FEROS
FIES
2dcoude
Hamilton Echelle
SARG
UCLES
HARPS
HDS
UVES
HRS
HiRes
Wavelength Reference
Th-Ar
Th-Ar
Iodine Cell
Iodine Cell
Th-Ar
Iodine Cell
Th-Ar
Th-Ar
Iodine cell
Iodine cell
Iodine Cell
Iodine cell
Th-Ar
Iodine Cell
Iodine cell
Iodine cell
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)
In an ideal world with only photon noise:
RV error SOPHIE
Period (days)
RV Error/Amplitude
Jupiter
Neptune
RV error HARPS
and HIRES
RV error ESPRESSO (VLT)
V-magnitude
Superearth 7 (MEarth)
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 activity can decrease your measurement precision !!!
Radial Velocity (m/s)
HD 166435
10
-10
0
Radial velocity variations due
entirely to spots
0
0
0
.
.
. Rotation
Phase
4
6
2
0
.
8
Stellar Activity can be the dominant noise source
f is filling factor
(photometric
amplitude) in
percent)
vsini (V in figure) is
rotational velocity
in km/s
Saar & Donahue (1996):
ARV (m/s) = 6.5 f0.9 vsini
f=0.5%, vsini=2 km/s → ARV = 7 m/s
Hatzes (2001):
ARV (m/s) = (8.6 vsini – 1.6) f0.9
Two expressions agree to within 20%
f=0.5%, vsini=2 km/s → ARV = 8.3 m/s
Comparison of HARPS predicted RV error as a function of
activity for a 10th magnitude star
Quiet
SunLike
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
If you are looking at young active stars your RV precision will be
signficantly worse and these will require more telescope resources
In some cases it is possible to use „tricks“ to reduce the noise due
to activity. See CoRoT-7b at end of lecture.
A Tool for confirming planets: Bisectors
Bisectors can measure the line shapes and tell you about
the nature of the RV variations:
Curvature
Span
What can change bisectors :
• Spots
• Blends
• Pulsations
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
Confirming Transit Candidates
Radial Velocity measurements are essential for confirming the
nature (i.e. get the mass) of the companion, and to exclude socalled false postives:
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!
Transit
phase = 0
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.
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
Low resolution spectra can easily distinguish between a giant and main
sequence star for the host.
This star was originally
classified as a K0 main
sequence star with
photometry
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 (subgiant, photometry)
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.
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
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
Bisector
Photometric Phase
s = 42 m/s
Error: 20-30 m/s
The Bisector variations correlate
withthe RV → this is a blend
5. Companion may be a planet,
but RV measurements are
impossible
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
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
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.
You have a good estimate of
mass, luminosity of Star 1
Star 1
Planet
candidate
Star 2
Star 3
Star 2 and 3
are the test
binary
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
2)
1)
The light curve shows a nice transit. There are RV variations
consistent with a brown dwarf, but the CCF bisector shows
variations
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
Red line is the best fit binary blend model (not good)
Note: Primary is the main star,
secondary is the brighter component
of the binary, tertiary the fainter
component
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
Can we prove that CoRoT-7b is a Planet without a
RV curve?
R = 1.58 REarth
P = 0.85 d
44
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
CoRoT-1b
OGLE-TR-133b
CoRoT-3b
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
For companions that are the size of Jupiter you can have a
planet, brown dwarf, or star.
Modified From H. Rauer
Can We Get the Mass of CoRoT-7b?
The Challenge: Dealing with the Activity Signal
Prot = 23 d
Expected activity related RV variations:
Dflux ≈ 1.6% (spots)
Saar & Donahue: 18 km/s
Hatzes: 22 m/s
Rotational veloctiy = 1.8 km/s
44
RV (m/s)
HARPS RVs for CoRoT-7b: 104 Measurements!
JD
RV spot „jitter“ ≈ 20 m/s
Amplitude of transting planet ≈ 5 m/s
44
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:
Radial Velocity (m/s)
Spots, long period planets,
systematic errors
K = 5 m/s
Orbital Phase
Radial Velocity (m/s)
Try K = 2 m/s
Orbital Phase
Poor fit at phase 0.8-0.1
Radial Velocity (m/s)
Try K = 8 m/s
Orbital Phase
Poor fit at phase 0-0.4
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 DT < 4 hours
is small.
 Dfrot = 0.01, DRV < 0.5 m/s
 DRVplanets = 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 DT=4 hours (Dforbit = 0.2)
• 17 Nights with 2 measurements DT=2 hours (Dforbit = 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
Best fit circular orbit:
sO–C = 1.7 m/s
sRV = 1.8 m/s
K = 5.15 ± 0.94 m/s
M = 7.29 ± 1.35
MEarth
Zero point offsets and phase are the only free parameters. The RV
phase agrees with transit phase to within 0.01 phase
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
nrot (P=23 d)
Amplitude of variations ≈ 10 m/s
Kepler-10b versus CoRoT-7b: Inactive versus Active
Inactive
Active
s = 3.07 m/s
s = 1.68 m/s
cred2 = 4.3
cred2 = 1.5
Mstar = 0.895 ± 0.06 Msun
Rstar = 1.056 ±0.02 Rsun
MPl = 4.56 ±1.23 MEarth
RPl = 1.416 ±0.025 REarth
rPl = 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
rPl = 10.2 ±2.7 cgs
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