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

Planet Occurrence from Kepler Howard, 2013 Fraction of stars with planets (P < 50 days) Planet size (relative to Earth)

Planet Occurrence from Ground-Based RV Howard, 2013 Fraction of stars with planets (P < 50 days) Planet mass (relative to Earth)

Known Planets 2013 Based on data compiled by J. Schneider

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? ?

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.

Figure credit M. Brown Official definition precipitated by “new Plutos”, the so-called dwarf planets For an interesting discussion see caltech.edu/~m brown/eightpla nets/ caltech.edu/~m brown/dwarfpla nets/ and links therein.

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 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.

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 Pulsar timing Pulsation frequency (variable star timing) Transit timing variation method (TTV) Transit duration variation method (TDV) Eclipsing binary minima timing 1.7 Gravitational microlensing 1.8 Direct imaging Early discoveries Imaging instruments 1.9 Polarimetry 1.10 Astrometry Wow! Way too many concepts.

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 Pulsar timing Pulsation frequency (variable star timing) Transit timing variation method (TTV) Transit duration variation method (TDV) Eclipsing binary minima timing 1.7 Gravitational microlensing 1.8 Direct imaging Early discoveries Imaging instruments 1.9 Polarimetry 1.10 Astrometry

Known Planets 2013 Based on data compiled by J. Schneider

Wright and Gaudi 2012, arXiv: 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 See the Extrasolar Planets Encyclopedia ( and the Exoplanet Data Explorer ( 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.

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 Today we will estimate exoplanet mass from radial velocity data sets Mayor and Queloz 1995 K

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 – 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 edge- on orbit (i=90 and sin i = 1)

Animation ght/radialvelocitydemo.html 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 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 m 1 r 1 = m 2 r 2 binaries/astrometric.html

Planet Mass Derivation Star velocity K the variable arbitrarily assigned to the star velocity How many equations and how many unknown variables? Assume the period is known from the observations Definition Center of mass Kepler’s Third Law

Planet Mass Derivation From last page Sub above into Kepler’s Third Law Sub above into v = K = 2  a/P Algebra to get m p using m p << m *

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 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 Lopez-Morales 2005 Eclipsing binary star Each star is M * ~ 0.6 M sun P = days

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,

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 Butler et al Ups And A 3-planet system One we modeled for the first class

Example 7

P = 1.95 days M p = 12.6 M J R p = 2.1 R J But… turned out to be a spurious signal! Example 7

Example 8 Pepe et al. 2002

Example 8 Planet on an eccentric orbit e = P = 10.9 days a = M * = 1.22 M sun M p = 0.4 M J Pepe et al. 2002

Example 9 Naef et al. 200

Example 9 Planet on a very eccentric orbit! e = / P = 112 days a = M * = 1.1 M sun M p = 3.9 M J 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! Measure the minimum planet mass in the 51 Peg example K = 50 m/s; m * = 1.1 m sun, P = 4.23 days G = × m 3 kg -1 s -2 m sun = × kg, m J ~ Msun

Example 1 Mayor and Queloz 1995 K P = d a = M * = 1.1 M sun

Example 2 Orbital Phase Udry et al P = d a = M * = 0.31 M sun

Radial Velocity for Jupiter Find a scaling relationship from the previous Example 1. m * ~ 1 M sun K ~ 50 m/s m p sin i ~ 0.5 P ~4 d

Radial Velocity for Earth Find a scaling relationship from the previous Example 1. m * ~ 1 M sun K ~ 50 m/s m p sin i ~ 0.5 P ~4 d 320 M Earth ~ 1 M J

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, 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 = 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 Radial velocity (RV) definition Planet mass 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?

HD209458b. November Lynnette Cook. Venus. Trace Satellite. June Schneider and Pasachoff. Mercury. Trace Satellite. November Which Images are Real?

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 Q7Mhttp://astro.unl.edu/naap/esp/animation s/transitSimulator.html

Flux Ratio Measurable: planet-to-star flux ratio Outcome: planet-to-star area ratio 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 b: R planet =1.35 R Jup, R star =1.2 R sun Hubble Space Telescope Brown et al. 2001

HD b: R planet =0.8 R Jup, R star =1.15 R sun Hubble Space Telescope Pont et al. 2007starspots!

HD b: R planet =1.35 R Jup, R star =1.2 R sun Spitzer 24 microns Richardson et al. 2006

GJ 436b: R planet =4.3 R Earth, R star =0.42 R sun Spitzer 8 microns Deming et al. 2007

TrES-1: R planet =1.08 R Jup, R star =0.82 R sun Hubble Space Telescope (picture courtesy of oklo.org)

TrES-3: R planet =1.295 R Jup, R star =0.802 R sun Ground based telescopes O’Donovan et al. 2007

HD b: R planet =0.755 R Jup, R star =1.457 R sun Spitzer -- 8 microns Nutzman et al. 2008

Synthetic transits around sun: A = close-in Earth B = variable star C = Jupiter D = “Neptune” (5 R E ) E = "SuperEarth” (10 R E ) F=binary star All images: R star =1.0 R sun

HD b: R planet =1.35 R Jup, R star =1.2 R sun First-ever amateur observation of an exoplanet

(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 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 R p << R * << a Sackett 1998

Transit Duration Measurable: P, t T Rewrite the transit formula with measurables on the right hand side

Transit Duration For a non-central transit is left for you to work out on your own Sackett 1998

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

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 Four equations Four unknowns R p, a, R *, M *. Measured from the transit light curve: t T, F no transit, F transit, 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 = x = 1, k = 1/0.928 t T = ?  F = ? Then find R p and a Holman et al. 2006

P = t T = ? x = 1, k = 1/0.928  F = ? Then find R p 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 R p  F ~ 0.02, t T ~ 0.11

Answer From a Full Fit R p /R * = R * = M * = 1.0 R p = R J a = 0.05 AU (i = degrees) Holman et al 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

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? 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 *, R p, a for a central transit Real Transit Light Curves – Noise – Limb Darkening

Lecture I Summary Based on data compiled by J. Schneider 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