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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.

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Exoplanet Detection Techniques I

GUASA 12/10/2013

Prof. Sara Seager MIT


Exoplanet detection techniques i
Exoplanet Detection Techniques I

  • Introduction

  • Planet Definition

  • List of Planet Detection Techniques

  • Planet Detection Techniques in More Detail

    • Radial Velocity

    • Transits

  • Lecture I Summary


Planet occurrence from kepler
Planet Occurrence from Kepler

Fraction of stars with planets (P < 50 days)

Planet size (relative to Earth)

Howard, 2013


Planet occurrence from ground based rv
Planet Occurrence from Ground-Based RV

Fraction of stars with planets (P < 50 days)

Planet mass (relative to Earth)

Howard, 2013


Known planets 2013
Known Planets 2013

Based on data compiled by J. Schneider



Exoplanet detection techniques i1
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 planet1
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 planet2
What is a Planet?

  • No satisfactory definition.

  • There is an official definition, that was socially engineered


What is a planet3
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/~mbrown/eightplanets/

  • http://www.gps.caltech.edu/~mbrown/dwarfplanets/

    and links therein.

Figure credit M. Brown


What is an exoplanet
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 exoplanet1
What is an Exoplanet?

  • A planet outside of our solar system


Who can name exoplanets
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 i2
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
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 Pulsartiming

  • 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

Wow! Way too many concepts.


Wikipedia list1
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 Pulsartiming

  • 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 20131
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 i3
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
Radial Velocity Preview

K

Mayor and Queloz 1995

Today we will estimate exoplanet mass from radial velocity data sets


Rv lecture contents
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” 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 definition1
Radial Velocity” Definition


Radial velocity in context
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
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 edge-on orbit (i=90 and sin i = 1)


Animation
Animation

  • http://astro.unl.edu/classaction/animations/light/radialvelocitydemo.html

  • http://astro.unl.edu/classaction/animations/extrasolarplanets/radialvelocitysimulator.html


Rv lecture contents1
RV Lecture Contents

  • Radial Velocity Definition

  • Planet Mass Derivation

  • Tour of Radial Velocity Curves

  • Measuring Planet Masses

  • Controversial RV Planet Detections


Planet mass derivation
Planet Mass Derivation

  • 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
Center of Mass

m1r1 = m2r2

http://csep10.phys.utk.edu/astr162/lect/binaries/astrometric.html


Planet mass derivation1
Planet Mass Derivation

Star velocity

K the variable arbitrarily assigned to the star velocity

Center of mass

Definition

Kepler’s Third Law

How many equations and how many unknown variables?

Assume the period is known from the observations


Planet mass derivation2
Planet Mass Derivation

  • From last page

  • Sub above into Kepler’s Third Law

  • Sub above into

    v = K =2a/P

  • Algebra to get mp using mp << m*


Planet mass derivation3
Planet Mass Derivation

  • 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

  • Minimum mass concept

  • http://www.daviddarling.info/encyclopedia/R/radial_velocity_method.html


Rv lecture contents2
RV Lecture Contents

  • Radial Velocity Definition

  • Planet Mass Derivation

  • Tour of Radial Velocity Curves

  • Measuring Planet Masses

  • Controversial RV Planet Detections


Example 1
Example 1

Courtesy G. Torres


Example 11
Example 1

  • M dwarf star eclipsing another star

  • Period = 3.80 days

Courtesy G. Torres


Example 2
Example 2

Lopez-Morales 2005


Example 21
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
Example 3

Rivera et al. ApJ, 2005


Example 31
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
Example 4

Rivera et al. ApJ, 2005


Example 41
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
Example 5

Butler et al. 1996


Example 6
Example 6

Butler et al. 2996


Examples 5 and 6
Examples 5 and 6

  • Ups And

  • A 3-planet system

  • One we modeled for the first class

Butler et al. 1996



Example 71

P = 1.95 days

Mp = 12.6 MJ

Rp = 2.1 RJ

But… turned out to be a spurious signal!

Example 7


Example 8
Example 8

Pepe et al. 2002


Example 81
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
Example 9

Naef et al. 200


Example 91
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 contents3
RV Lecture Contents

  • Radial Velocity Definition

  • Planet Mass Derivation

  • Tour of Radial Velocity Curves

  • Measuring Planet Masses

  • Controversial RV Planets


Let s try it
Let’s Try It!

  • 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 × 1030kg, mJ ~ 0.001 Msun


Example 12
Example 1

K

P = 4.23077 d

a = 0.052

M* = 1.1 Msun

Mayor and Queloz 1995


Example 22
Example 2

0 0.25 0.5 0.75 1

P = 5.3683 d

a = 0.041

M* = 0.31 Msun

Orbital Phase

Udry et al. 2007


Radial velocity for jupiter
Radial Velocity for Jupiter

  • Find a scaling relationship from the previous Example 1.

  • m* ~ 1 Msun

  • K ~ 50 m/s

  • mp sin i ~ 0.5

  • P ~4 d


Radial velocity for earth
Radial Velocity for Earth

  • Find a scaling relationship from the previous Example 1.

  • m* ~ 1 Msun

  • K ~ 50 m/s

  • mp sin i ~ 0.5

  • P ~4 d

  • 320 MEarth ~ 1 MJ


Exoplanet equations
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 contents4
RV Lecture Contents

  • Radial Velocity Definition

  • Planet Mass Derivation

  • Tour of Radial Velocity Curves

  • Measuring Planet Masses

  • Controversial RV Planet Detections


Gj 581 g
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
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


Rv lecture summary
RV Lecture Summary

  • Radial velocity (RV) definition

  • Planet mass

  • Key features in RV curves

  • Radial velocity fitting


Exoplanet detection techniques i4
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

  • 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
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 real1
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
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.



Transit animation
Transit Animation

  • http://www.youtube.com/watch?v=a4M4Es3aQ7Mhttp://astro.unl.edu/naap/esp/animations/transitSimulator.html


Flux ratio
Flux Ratio

  • Measurable: planet-to-star flux ratio

  • Outcome: planet-to-star area ratio

Drop in star brightness as measured from graph


Transit lecture contents1
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 contents2
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 transit1
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
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 ratio1
Flux Ratio

  • Measurable: planet-to-star flux ratio

  • Outcome: planet-to-star area ratio

Drop in star brightness as measured from graph


Transit duration
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

Sackett 1998


Transit duration1
Transit Duration

  • Measurable: P, tT

  • Rewrite the transit formula with measurables on the right hand side


Transit duration2
Transit Duration

  • For a non-central transit is left for you to work out on your own

Sackett 1998


Kepler s third law
Kepler’s Third Law

  • Period is measurable, and we use the equation for Kepler’s Third Law


Stellar mass radius relation
Stellar Mass-Radius Relation

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
Putting the Equations Together

  • 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

1.

2.

3.

4.


Let s try it1
Let’s Try It!

  • P = 3.941534

  • x = 1, k = 1/0.928

  • tT = ?

  • F = ?

  • Then find Rp and a

Holman et al. 2006


Hint: use algebra before plugging in numbers

P = 3.941534 tT = ?

x = 1, k = 1/0.928 F = ?

Then find Rp and a


Path to the estimate
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


Answer from a full fit
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 contents3
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
Transit Light Curves

  • Hubble Space Telescope

  • HD209458b

Brown et al. ApJ 2001


Limb darkening
Limb Darkening

Knutson et al. 2006


Limb darkening1
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 darkening2
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




Why is limb darkening a problem
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

    • 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

Torres 2007

Drake and Cook 2004


Why is noise a problem
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
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
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


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