Exoplanet Detection Techniques I
GUASA 12/10/2013
Prof. Sara Seager MIT
Exoplanet Detection Techniques I
•
•
•
•
Introduction
Planet Definition
List of Planet Detection Techniques
Planet Detection Techniques in More Detail
– Radial Velocity
– Transits
• Lecture I Summary
Fraction of stars with planets (P < 50 days)
Planet Occurrence from Kepler
Planet size (relative to Earth)
Howard, 2013
Fraction of stars with planets (P < 50 days)
Planet Occurrence from
Ground-Based RV
Planet mass (relative to Earth)
Howard, 2013
Known Planets 2013
Based on data compiled by J. Schneider
http://eyes.jpl.nasa.gov/exoplanets/index.html
Exoplanet Detection Techniques I
•
•
•
•
Introduction
Planet Definition
List of Planet Detection Techniques
Planet Detection Techniques in More Detail
– Radial Velocity
– Transits
• Lecture I Summary
What is a Planet?
?
What is a Planet?
Planet sizes are to scale. Separations are not.
Characterizing extrasolar planets: very different from solar system planets,
yet solar system planets are their local analogues
What is a Planet?
• No satisfactory definition.
• There is an official definition, that was socially
engineered
What is a Planet?
• The IAU members gathered at the 2006 General Assembly
agreed that a "planet" is defined as a celestial body that
– (a) is in orbit around the Sun,
– (b) has sufficient mass for its self-gravity to overcome rigid body
forces so that it assumes a hydrostatic equilibrium (nearly round)
shape, and
– (c) has cleared the neighbourhood around its orbit.
Official definition
precipitated by
“new Plutos”, the
so-called dwarf
planets
For an interesting
discussion see
http://www.gps.
caltech.edu/~m
brown/eightpla
nets/
http://www.gps.
caltech.edu/~m
brown/dwarfpla
nets/
and links therein.
Figure credit M. Brown
What is an Exoplanet?
• The IAU WGESP has agreed to the following statements (subject to change):
•
1) Objects with true masses below the limiting mass for thermonuclear fusion of
deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity)
that orbit stars or stellar remnants are "planets" (no matter how they formed). The
minimum mass/size required for an extrasolar object to be considered a planet should be
the same as that used in our Solar System.
•
2) Substellar objects with true masses above the limiting mass for thermonuclear fusion
of deuterium are "brown dwarfs", no matter how they formed nor where they are
located.
•
3) Free-floating objects in young star clusters with masses below the limiting mass for
thermonuclear fusion of deuterium are not "planets", but are "sub-brown dwarfs" (or
whatever name is most appropriate).
What is an Exoplanet?
• A planet outside of our solar system
Who Can Name Exoplanets?
•
•
•
In 2009, the Organizing Committee of IAU Commission 53 Extrasolar Planets (WGESP) on
exoplanets discussed the possibility of giving popular names to exoplanets in addition to
their existing catalogue designation (for instance HD 85512 b). Although no consensus
was reached, the majority was not in favour of this possibility at the time.
However, considering the ever increasing interest of the general public in being involved
in the discovery and understanding of the Universe, the IAU decided in 2013 to restart
the discussion of the naming procedure for exoplanets and assess the need to have
popular names as well. In 2013 the members of Commission 53 will be consulted in this
respect and the result of this will be made public on this page.
The nomenclature for exoplanets is indeed a difficult matter that deserves careful
attention in many aspects. Such a system must take into account that discoveries are
often tentative, later to be confirmed or rejected, possibly by several different methods,
and that several planets belonging to the same star may eventually be discovered, again
possibly by different means. Thus, considerable care and experience are required in its
design.
•
http://www.iau.org/public/themes/naming/#exoplanets
•
http://www.iau.org/static/public/naming/planets_and_satellites.pdf
Exoplanet Detection Techniques I
•
•
•
•
Introduction
Planet Definition
List of Planet Detection Techniques
Planet Detection Techniques in More Detail
– Radial Velocity
– Transits
• Lecture I Summary
Wikipedia List
• 1 Established detection methods
•
1.1 Radial velocity
•
1.2 Transit method
•
1.3 Orbital light variations (direct non-resolved detection)
•
1.4 Light variations due to Relativistic Beaming
•
1.5 Light variations due to ellipsoidal variations
•
1.6 Timing variations
•
1.6.1 Pulsar timing
•
1.6.2 Pulsation frequency (variable star timing)
•
1.6.3 Transit timing variation method (TTV)
•
1.6.4 Transit duration variation method (TDV)
•
1.6.5 Eclipsing binary minima timing
•
1.7 Gravitational microlensing
•
1.8 Direct imaging
•
1.8.1 Early discoveries
Wow! Way too many
•
1.8.2 Imaging instruments
concepts.
•
1.9 Polarimetry
•
1.10 Astrometry
Wikipedia List
• 1 Established detection methods
•
1.1 Radial velocity
•
1.2 Transit method
•
1.3 Orbital light variations (direct non-resolved detection)
•
1.4 Light variations due to Relativistic Beaming
•
1.5 Light variations due to ellipsoidal variations
•
1.6 Timing variations
•
1.6.1 Pulsar timing
•
1.6.2 Pulsation frequency (variable star timing)
•
1.6.3 Transit timing variation method (TTV)
•
1.6.4 Transit duration variation method (TDV)
•
1.6.5 Eclipsing binary minima timing
•
1.7 Gravitational microlensing
•
1.8 Direct imaging
•
1.8.1 Early discoveries
•
1.8.2 Imaging instruments
•
1.9 Polarimetry
•
1.10 Astrometry
Known Planets 2013
Based on data compiled by J. Schneider
The points show the masses versus
semimajor axis in units of the snow line
distance for the exoplanets that have
been discovered by various methods as
of Dec. 2011. See the Extrasolar Planets
Encyclopedia (http://exoplanet.eu/) and
the Exoplanet Data Explorer
(http://exoplanets.org/). Here we have
taken the snow line distance to be asl =
2.7 AU(M∗/M⊙). Radial velocity
detections (here what is actually plotted
is Mp sin i) are indicated by red circles
(blue for those also known to be
transiting), transit detections are
indicated by blue triangles if detected
from the ground and as purple
diamonds if detected from space,
microlensing detections are indicated
by green pentagons, direct detections
are indicated by magenta squares, and
detections from pulsar timing are
indicated by yellow stars. The letters
indicate the locations of the Solar
System planets. The shaded regions
show rough estimates of the sensitivity
of various surveys using various
methods, demonstrating their
complementarity.
Wright and Gaudi 2012, arXiv:1210.2471
Ideally we would learn how to
write down all of these equations.
But this would be a whole week of
classes
Exoplanet Detection Techniques I
•
•
•
•
Introduction
Planet Definition
List of Planet Detection Techniques
Planet Detection Techniques in More Detail
– Radial Velocity
– Transits
• Lecture I Summary
Radial Velocity Preview
K
Mayor and Queloz 1995
Today we will estimate exoplanet mass from radial
velocity data sets
RV Lecture Contents
•
•
•
•
•
Radial Velocity Definition
Planet Mass Derivation
Tour of Radial Velocity Curves
Measuring Planet Masses
Controversial RV Planet Detections
“Radial Velocity” Definition
• Radial velocity is the velocity of an object in
the direction of the line of sight
• In other words, the object’s speed straight
towards you, or straight away from you
“Radial Velocity” Definition
Radial Velocity in Context
• How fast is 10 m/s? 1m/s?
• What RV amplitude is required to detect a Jupiter-twin? An Earth twin?
• Vote for
–
–
–
–
–
10 m/s
1 m/s
0.1 m/s
0.01 m/s
0.001 m/s
Mayor and Queloz 1995
Radial Velocity Derivation
• Today we will derive the star’s line-of-sight
velocity, caused by the star’s motion about
planet-star common center of mass
• We will assume zero eccentricity, and an edgeon orbit (i=90 and sin i = 1)
Animation
• http://astro.unl.edu/classaction/animations/li
ght/radialvelocitydemo.html
• http://astro.unl.edu/classaction/animations/e
xtrasolarplanets/radialvelocitysimulator.html
RV Lecture Contents
•
•
•
•
•
Radial Velocity Definition
Planet Mass Derivation
Tour of Radial Velocity Curves
Measuring Planet Masses
Controversial RV Planet Detections
Planet Mass Derivation
2p a*
K º v* =
P
• We start with an equation for the line-of-sight velocity of
the star--the observable
• K is called the radial velocity amplitude
• The planet and star are orbiting their common center of
mass
Center of Mass
m1r1 = m2r2
http://csep10.phys.utk.edu/astr162/lect/
binaries/astrometric.html
Planet Mass Derivation
Star velocity
K the variable arbitrarily
assigned to the star
velocity
2p
K=
a*
P
Center of mass
m* a* = m p a p
Definition
a* + a p = a
Kepler’s Third Law
a3
P 2G
=
2
( m* + m p ) 4p
How many equations and how many unknown variables?
Assume the period is known from the observations
Planet Mass Derivation
• From last page
æm + m ö
p
a = a* çç *
÷÷
è mp ø
(m + m )
( m +m )
3
• Sub above into
Kepler’s Third Law
a*3
• Sub above into
v = K = 2a/P
mp
1
1/ 3
K = 1/ 3 (2pG)
2/3
P
( m* + m p )
• Algebra to get mp
using mp << m*
p
*
*
p
P 2G
=
4p 2
æ P ö1/ 3 2 / 3
m p = Kç
÷ m*
è 2pG ø
Planet Mass Derivation
æ P ö
2/3
m p » Kç
m
÷
*
è 2pG ø
1/ 3
æ P ö1/ 3 2 / 3
2
m p sini » K ç
÷ m* 1- e
è 2pG ø
• Here is the planet mass formula for a planet on an
eccentric orbit with an orbital inclination away
from edge-on.
Minimum Mass Concept
• Minimum mass concept
• http://www.daviddarling.info/encyclopedia/R/
radial_velocity_method.html
RV Lecture Contents
•
•
•
•
•
Radial Velocity Definition
Planet Mass Derivation
Tour of Radial Velocity Curves
Measuring Planet Masses
Controversial RV Planet Detections
Example 1
Courtesy G. Torres
Example 1
• M dwarf star eclipsing
another star
• Period = 3.80 days
Courtesy G. Torres
Example 2
Lopez-Morales 2005
Example 2
• Eclipsing binary star
• Each star is
M* ~ 0.6 Msun
• P = 0.488 days
http://www.sumanasinc.com/webcontent/anisamples/RadialVelocityCurve.html
Lopez-Morales 2005
Example 3
Rivera et al. ApJ, 2005
Example 3
• GJ876 b and c
• Notice the “glitches”
• The planets are
interacting and one
has changing orbital
parameters
Rivera et al. ApJ, 2005
www.exoplanets.org
Example 4
Rivera et al. ApJ, 2005
Example 4
• GJ 876d a 7.5 M planet
• Discovered after GJ 876b and c
• A three-planet system; one we
modeled during the first class
• Shown are the three planets
from examples 3 and 4
Rivera et al. ApJ, 2005
Example 5
Butler et al. 1996
Example 6
Butler et al. 2996
Examples 5 and 6
• Ups And
• A 3-planet system
• One we modeled for
the first class
Butler et al. 1996
Example 7
Example 7
P = 1.95 days
Mp = 12.6 MJ
Rp = 2.1 RJ
But… turned out to be a spurious signal!
Example 8
Pepe et al. 2002
Example 8
• Planet on an eccentric
orbit
• e = 0.498
• P = 10.9 days
• a = 0.104
• M* = 1.22 Msun
• Mp = 0.4 MJ
Pepe et al. 2002
Example 9
Naef et al. 200
Example 9
• Planet on a very
eccentric orbit!
• e = 0.927 +/- 0.012
• P = 112 days
• a = 0.469
• M* = 1.1 Msun
• Mp = 3.9 MJ
Naef et al. 200
RV Lecture Contents
•
•
•
•
•
Radial Velocity Definition
Planet Mass Derivation
Tour of Radial Velocity Curves
Measuring Planet Masses
Controversial RV Planets
Let’s Try It!
æ P ö
2/3
m p sini » K ç
÷ m*
è 2pG ø
1/ 3
• Measure the minimum planet mass in the 51 Peg
example
• K = 50 m/s; m* = 1.1 msun, P = 4.23 days
• G = 6.67300 × 10-11 m3 kg-1 s-2
• msun = 1.9891 × 1030 kg, mJ ~ 0.001 Msun
Example 1
K
P = 4.23077 d
a = 0.052
M* = 1.1 Msun
Mayor and Queloz 1995
Example 2
P = 5.3683 d
a = 0.041
M* = 0.31 Msun
0
0.25
0.5
0.75
1
Orbital Phase
Udry et al. 2007
Radial Velocity for Jupiter
• Find a scaling
æ P ö1/ 3 2 / 3
m p sini » K ç
÷ m*
relationship from the
è 2pG ø
previous Example 1.
æ 2pG ö1/ 3 æ 1 ö
K = m p siniç
÷ ç 2/3 ÷
• m* ~ 1 Msun
è P ø è m* ø
• K ~ 50 m/s
2/3
1/ 3
• mp sin i ~ 0.5
æ
ö
æ 4 ö
m*
K p [m /s] » 100m p [mJ ]ç
÷ ç
÷
• P ~4 d
è P[d]ø è msun ø
Radial Velocity for Earth
• Find a scaling
æ P ö1/ 3 2 / 3
m p sini » K ç
÷ m*
relationship from the
è 2pG ø
previous Example 1.
æ 2pG ö1/ 3 æ 1 ö
K = m p siniç
÷ ç 2/3 ÷
• m* ~ 1 Msun
è P ø è m* ø
• K ~ 50 m/s
2/3
1/ 3
æ 4 ö æ m* ö
• mp sin i ~ 0.5
K p [m /s] » 100m p [mJ ]ç
÷ ç
÷
è P[d]ø è msun ø
• P ~4 d
• 320 MEarth ~ 1 MJ
Exoplanet Equations
• The great thing about exoplanets is many
concepts are accessible for undergraduate
math and physics
• Radial velocity is the only example we will
work out in detail, but most of the other
methods are equally accessible
• I encourage you to work things out on your
own
RV Lecture Contents
•
•
•
•
•
Radial Velocity Definition
Planet Mass Derivation
Tour of Radial Velocity Curves
Measuring Planet Masses
Controversial RV Planet Detections
GJ 581 g
• THE LICK–CARNEGIE EXOPLANET
SURVEY: A 3.1 M⊕ PLANET IN
THE HABITABLE ZONE OF THE
NEARBY M3V STAR GLIESE 581
• Vogt et al., ApJ, 2010
• 11 years of HIRES precision radial
velocities (RVs) of the nearby
M3V star Gliese 581
• The authors removed each
planet, in order of signal strength,
assuming a circular orbit
• Concern is that signals were
accidentally introduced
• Followup observations by other
teams have not validated GJ 581
g, yet the original authors claim
the planet is still present
Alpha Cen B b
• An Earth-mass planet orbiting
Alpha Cen B
• Dumusque et al Nature, 2012
• P = 3.236 d, a = 0.04 AU,
• The authors removed many
signals: instrumental noise, stellar
oscillation modes, granulation,
rotational activity signal,
long0term activity signal (i.e.,
solar cycle), binary orbital
motion, binary light
contamination
• Concern is that so many elements
have to be fit and removed fro
the data that a planet signal may
have accidentally been
introduced
a = a* çç
è
÷÷
ø
mp
( mRV+ mLecture
) = P G Summary
( m +m ) 4p
3
a*3
p
*
2
2
*
p
mp
1
1/ 3
• Radial
K = velocity
2pG)(RV) definition
2/3
1/ 3 (
P
( m* + m p )
• Planet mass
æ P ö1/ 3 2 / 3
m p = Kç
÷ m*
è 2pG ø
• Key features in RV curves
• Radial velocity fitting
Exoplanet Detection Techniques I
•
•
•
•
Introduction
Planet Definition
List of Planet Detection Techniques
Planet Detection Techniques in More Detail
– Radial Velocity
– Transits
• Lecture I Summary
Transits
• Transits were and are being covered by Dr.
Martin Still
• The following slides are you to read through at
your convenience
• I will go over some of the slides in detail
Transit Lecture Contents
•
•
•
•
What is a Transiting Planet?
Tour of Transit Light Curves
Transit Observables and Planet/Star Properties
Beyond an Ideal Transit
– Noise
– Limb Darkening
Which Images are Real?
Which Images are Real?
Venus. Trace Satellite. June 8 2004.
Schneider and Pasachoff.
Mercury. Trace Satellite. November 1999.
HD209458b. November 1999.
Lynnette Cook.
Some Terminology
• Transit: passage of a smaller celestial body or its
shadow across a larger celestial body.
• Occultation: the temporary apparent disappearance
from view of a celestial body as another body passes
across the line of sight.
• Eclipse: the partial or complete obscuring, relative to
a designated observer, of one celestial body by
another.
Anatomy of a Transit
Transit Animation
• http://www.youtube.com/watch?v=a4M4Es3a
Q7Mhttp://astro.unl.edu/naap/esp/animation
s/transitSimulator.html
Flux Ratio
• Measurable: planet-to-star flux ratio
• Outcome: planet-to-star area ratio
Rp
Fno.transit - Ftransit
=
R*
Fno.transit
Drop in star brightness
as measured from
graph
Transit Lecture Contents
•
•
•
•
What is a Transiting Planet?
Tour of Transit Light Curves
Transit Observables and Planet/Star Properties
Beyond an Ideal Transit
– Noise
– Limb Darkening
HD 209458b: Rplanet=1.35 RJup, Rstar=1.2 Rsun
Hubble Space Telescope
Brown et al. 2001
HD 189733b: Rplanet=0.8 RJup, Rstar=1.15 Rsun
Hubble Space Telescope
Pont et al. 2007
starspots!
HD 209458b: Rplanet=1.35
RJup, Rstar=1.2 Rsun
Spitzer
24 microns
Richardson et al. 2006
GJ 436b:
Rplanet=4.3 REarth, Rstar=0.42
Rsun
Spitzer
8 microns
Deming et al. 2007
TrES-1:
Rplanet=1.08 RJup, Rstar=0.82
Rsun
Hubble Space Telescope
(picture courtesy of oklo.org)
TrES-3: Rplanet=1.295 RJup, Rstar=0.802 Rsun
Ground based telescopes
O’Donovan et al. 2007
HD 149026b: Rplanet=0.755 RJup, Rstar=1.457 Rsun
Spitzer -- 8 microns
Nutzman et al. 2008
Synthetic transits around
sun:
A = close-in Earth
B = variable star
C = Jupiter
D = “Neptune” (5 RE)
E = "SuperEarth” (10 RE)
F=binary star
All images: Rstar=1.0 Rsun
HD 209458b: Rplanet=1.35 RJup, Rstar=1.2 Rsun
First-ever amateur observation of an exoplanet
http://www.ursa.fi/sirius/HD209458/HD209458_eng.html
(Torres et al.
2008)
Transit Lecture Contents
•
•
•
•
What is a Transiting Planet?
Tour of Transit Light Curves
Transit Observables and Planet/Star Properties
Beyond an Ideal Transit
– Noise
– Limb Darkening
Anatomy of a Transit
Note the flat bottom of the transit light curve when the planet is fully
superimposed on the stellar disk
Note 1st, 2nd, 3rd, 4th contacts
Transit Light Curve Derivation
• We can solve for the planet mass, planet
radius, star mass, star radius, and inclination
from the equations and solutions for a
transiting planet.
• We will investigate the case for a central
transit (inclination = 0)
Flux Ratio
• Measurable: planet-to-star flux ratio
• Outcome: planet-to-star area ratio
Rp
Fno.transit - Ftransit
=
R*
Fno.transit
Drop in star brightness
as measured from
graph
Transit Duration
• The transit duration is set by the fraction of the
total orbit for which a planet eclipses the stellar
disk.
• For a central transit and for Rp << R* << a
2R* PR*
tT = P
=
2pa pa
Sackett 1998
Transit Duration
• Measurable: P, tT
• Rewrite the transit formula with measurables on
the right hand side
PR*
tT =
pa
R* ptT
=
a
P
Transit Duration
• For a non-central transit is left for you to work
out on your own
Sackett 1998
PR*
tT =
pa
æ Rp ö2 æ acosi ö2
ç1+ ÷ - ç
÷
è R* ø è R* ø
Kepler’s Third Law
• Period is measurable, and we use the equation for
Kepler’s Third Law
4p a
P=
GM*
2 3
M* 4 p
= 2
3
a
PG
2
Stellar Mass-Radius Relation
x
é R* ù
M*
= kê
ú
M sun
ë Rsun û
Assume the stellar-mass radius relationship is known
x ~ 0.8 for sun-like stars
x = k = 1 for lower mass stars
Putting the Equations Together
1.
2.
3.
R* ptT
=
a
P
M* 4 p 2
= 2
3
a
PG
x
4.
é R* ù
M*
= kê
ú
M sun
ë Rsun û
• Four equations
• Four unknowns Rp, a, R*,
M*.
• Measured from the transit
light curve: tT, Fno transit,
Ftransit,
• Given P, x, k
• Conclusion: from the
transit we may learn
about the planet size and
orbit and star mass and
radius
Let’s Try It!
•
•
•
•
P = 3.941534
x = 1, k = 1/0.928
tT = ?
F = ?
• Then find Rp and a
Holman et al. 2006
P = 3.941534
tT = ?
x = 1, k = 1/0.928
F = ?
Then find Rp and a
Hint: use algebra
before plugging in
numbers
Path to the Estimate
• Use equations (2) and (3) to find an
expression for R*
• Use equation (4) to find a second
expression for R*
• Take the above two equations and
solve for R*
• Use equation (2) to find a
• Use equation (1) to find Rp
• F ~ 0.02, tT ~ 0.11
R* =
M sun pGtT 3
Rsun 4P
M*
R* =
RSun 0.928
M Sun
P 1
a=
ptT R*
Answer From a Full Fit
•
•
•
•
•
•
Rp/R* = 0.13102
R* = 0.928
M* = 1.0
Rp = 1.184 RJ
a = 0.05 AU
(i = 89.31 degrees)
Holman et al. 2006
McCullough et al. 2006
Transit Lecture Contents
•
•
•
•
What is a Transiting Planet?
Tour of Transit Light Curves
Transit Observables and Planet/Star Properties
Beyond an Ideal Transit
– Noise
– Limb Darkening
Transit Light Curves
• Hubble Space
Telescope
• HD209458b
Brown et al. ApJ 2001
Limb Darkening
Knutson et al. 2006
Limb Darkening
• At the edges of the star
we can only see the
cooler, darker, outer layers
• At the center of the star
we can see the hotter,
brighter inner layers
• At an intermediate
distance between star
center and edge we can
see warm layers, for the
same path length
Wikipedia
Limb Darkening
• Limb darkening: the
diminishing of intensity in a
star image from the center to
the edge or “limb” of an image
• Stars look a different size at
different wavelengths
• At blue wavelengths we see an
inner, hotter shell of the star
• Vice-versa at red wavelengths
Knutson et al. 2006
Limb Darkening
Limb Darkening
Why is Limb Darkening a Problem?
• No limb darkening: planet
transit light curve has a
flat bottom
• Limb darkening: curvature
in the transit light curve
Torres 2007
– Harder to tell where ingress
and egress start and end,
hence simple parameter
derivation used in class
does not work
– Curvature in light curve can
be confused with grazing
binary stars
Drake and Cook 2004
Why is Noise a Problem?
• Increased noise reduces
the accuracy of
parameters (mass, radius,
etc) derived from the
transit light curve
McCullough et al. 2006
Transit Lecture Summary
• Definition of a Transiting Planet
• Transit Light Curve Observables Derivation
– Estimated transit duration, depth, time
– Derived M*, R*, Rp, a for a central transit
• Real Transit Light Curves
– Noise
– Limb Darkening
Lecture I Summary
Exoplanets come in all masses, sizes,
orbit parameters
Many different exoplanet discovery
techniques are known
Radial velocity and transit finding are
the most successful to date
Based on data compiled by J. Schneider