how are planets around other stars (apart from the sun) found? how do we determine the orbital...

How are planets around other stars (apart from the Sun) found? How do we determine the orbital parameters and masses of planets?

Binary Systems and Stellar Parameters

Learning Objectives Discovery of Extrasolar Planets

Radial-velocity techniquePrecision radial-velocity measurements

Other Techniques to Find Extrasolar PlanetsTransitsGravitational microlensing

Direct imaging

Discovery of the First Extrasolar Planet In October 1995, Michel Mayor and Didier Queloz of the Geneva Observatory

announced the discovery of the first planet around a “normal” star apart from our Sun. How was this planet discovered?

Didier Queloz & Michel Mayor

Artist’s conception of 51 Pegasi and its planet

51 Pegasi

Radial Velocity Technique This planet was discovered as a result of periodic variations in the radial velocity

of the host star, akin to single-line spectroscopic binaries.

The method of discovery is known today as the radial velocity technique.

Radial Velocity Technique

observer

Radial Velocity Technique In practice, the radial velocity of the host star is derived not just from one spectral

line, but typically thousands of spectral lines for optimal sensitivity. In the case of 51 Peg, the radial velocity curve shown was constructed from about 5000 spectral lines.

Radial Velocity TechniqueRadial Velocity Curve of 51 Peg

Discovery of the First Extrasolar Planet The star, 51 Pegasi, is a main-sequence G4-5 star (Sun is a G2 star) at a distance

of 15.6 pc.

Orbital/physical parameters of the planet around 51 Peg- semimajor axis 0.05 AU- eccentricity 0.013- orbital period 4.2 days- mass >0.5 MJ (>150 M)

For comparison, orbital/physical parameters of Mercury

- semimajor axis 0.39 AU- eccentricity 0.2- orbital period 88.0 days- mass 0.055 M

The discovery of such a massive planet so close to its host star was unexpected. Does this mean that our Solar System is unusual?

Discovery of the First Extrasolar Planet The star, 51 Pegasi, is a main-sequence G4-5 star (Sun is a G2 star) at a distance

of 15.6 pc.

Orbital/physical parameters of the planet around 51 Peg- semimajor axis 0.05 AU- eccentricity 0.013- orbital period 4.2 days- mass >0.5 MJ (>150 M)

For comparison, orbital/physical parameters of Jupiter

- semimajor axis 5.2 AU- eccentricity 0.048775- orbital period 4,332.59 days (11.86 years)- mass 1 MJ

The discovery of such a massive planet so close to its host star was unexpected. Is this an unusual system, or is our Solar System unusual?

Discovery of the Second/Third Extrasolar Planets In November 1995, Geoffery W. Marcy (University of California, Berkeley) and

R. Paul Butler (Carnegie Institution of Washington) announced the discovery of planets around two other Sun-like stars, 70 Vir (G4) and 47 UMa (G1).

Orbital/physical parameters of the planet around 70 Vir:- semimajor axis 0.48 AU- eccentricity 0.40- orbital period 116.7 days- mass >7.44 MJ

Geoff Marcy & Paul Butler

Discovery of the Second/Third Extrasolar Planets In November 1995, Geoffery W. Marcy (University of California, Berkeley) and

R. Paul Butler (Carnegie Institution of Washington) announced the discovery of planets around two other Sun-like stars, 70 Vir (G4) and 47 UMa (G1).

Orbital/physical parameters of the planet around 47 UMa:- semimajor axis 2.1 AU- eccentricity 0.03- orbital period 1078 days- mass >2.53 MJ

Yet again, the planets discovered are massive and orbit close to their host stars. Are all these systems unusual, or is our Solar System unusual?

Census of Extrasolar Planets Distribution of planet orbital semi-major axis (majority discovered by radial-

velocity technique). Is our solar system unusual?

Census of Extrasolar Planets Distribution of planet masses (majority discovered by radial-velocity technique),

mostly lower limits. Is our solar system unusual?

Radial Velocity Technique Not necessarily. The radial velocity technique is biased towards the detection of

massive planets close to their host stars; c.f. Eq. (7.7) for single-line spectroscopic binaries

Note that if the orbital inclination of the planet is not known, we can only set a lower limit to the planet mass.

mass of planet

mass of star + mass of planet mass of star≅

radial velocity of star

inclination of planet orbit to sky plane




Direct imaging

Precision Radial Velocity Measurements Recall that, in 1802, William Hyde Wollaston passed sunlight through a prism

(like Newton and many others had done before him) and noticed for the first time a number of dark spectral lines superimposed on the continuous spectrum of the Sun.

By the late 1880s, the radial velocities of several bright stars had been measured from Doppler shifts of their spectral lines.

By the early 20th century, measurements of stellar radial velocities had become routine.

When then were the first extrasolar planets not discovered until 1995?

Precision Radial Velocity Measurements The variation in the radial velocity of the host star imposed by its planetary

companion is very small, typically no more than ~100 m/s.

Radial Velocity Curve of 51 Peg

From Eq. (5.1),

At (say) λrest = 0.5 μm, for vr = 100 m/s, Δλ/λrest = 3.3 × 10-7.

For comparison, natural linewidths of hydrogen Balmer lines Δλ/λrest ≈ 2 × 10-6.

For comparison, Doppler (thermal) linewidths of hydrogen Balmer lines (at ~5000 K) Δλ/λrest ≈ 2 × 10-5.

Precision Radial Velocity Measurements Recall that the resolving power of a spectrograph

R = / = N m

where corresponds to the instrumental half-width of a spectral line (not including intrinsic linewidth) measured at zero intensity. Spectrographs used in planet searches typically have R ≈ 105.

Precision Radial Velocity Measurements It is impractical if not impossible to build a spectrograph that is sufficiently stable

to measure changes as small as ~10-8 in wavelength.

Instead, it is simpler to superimpose an artificially-produced reference spectrum on the observed stellar spectrum. Because we would like to measure spectral lines across a broad wavelength range, we require the reference spectrum to have multiple lines across a broad wavelength range.

Molecular iodine (I2) gas provides such a reference spectrum. The iodine gas absorption cell is placed in the light path between the telescope and the spectrograph, so that absorption lines corresponding to the excitation of different vibrational modes of the iodine molecule is superposed on the observed stellar spectrum.

Precision Radial Velocity Measurements Combined observed stellar spectrum and molecular iodine absorption spectrum.

The advantages of using iodine over other gases:- many absorption lines at optical wavelengths - extremely narrow linewidths

Census of Extrasolar Planets Mass (mostly lower limits) of

extrasolar planets as a function of their semimajor axis/orbital period discovered as of 2013.

Methods of discovery:

Radial velocity method favors relative massive planets in relatively close orbits.

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Direct imaging

Transit Method If the orbital plane of a planet is almost exactly or exactly perpendicular to the

plane of the sky so that the planet crosses the disk of its host star, the star dims periodically and for the duration that the planet transits the star.

Note that transit measurements alone only provide orbital periods; to derive the remaining orbital parameters as well as planet mass, follow-up radial-velocity measurements are still required.

Because the planet is much smaller in size than its host star, the change in the observed brightness of the star is very small and so such observations require precise photometry.

Bri

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Transit Method First observed extra-solar planet transit was that around the star HD 209458. This

extra-solar planet was originally discovered using the radial velocity method.

Why search for transits when the presence of the extra-solar planet already known?

Orbital/physical parameters of the planet around HD 209458: -semimajor axis 0.045 AU- eccentricity 0.014- orbital period 3.52 days- radius 1.27 RJ

- mass 0.63 MJ

Transit Method First observed extra-solar planet transit was that around the star HD 209458. This

extra-solar planet was originally discovered using the radial velocity method.

Why search for transits when the presence of the extra-solar planet already known? If detected, constrains orbital inclination to i ≈ 90°; also provides planetary radius.

Orbital/physical parameters of the planet around HD 209458: -semimajor axis 0.045 AU- eccentricity 0.014- orbital period 3.52 days- radius 1.27 RJ

- mass 0.63 MJ

Transit Method First discovery of an extra-solar planet using transit method was that of

OGLE-TR-56. The goal of OGLE – Optical Gravitational Lensing Experiment – is to detect dark matter through microlensing.

Orbital/physical parameters of the OGLE-TR-56 planet:- semimajor axis 0.0225 AU- eccentricity 0.0- orbital period 1.21 days- radius 1.30 RJ

- mass 1.45 MJ

Transit Method Photometry from above the Earth’s atmosphere provides higher precision. In

March 2009, NASA launched the Kepler mission to search for Earth-mass planets around solar-type stars using the transit method.

Transit Method Measured light curve of star hosting Kepler-4b: -

semimajor axis 0.045 AU -eccentricity 0 (adopted)- orbital period 3.21 days- radius 0.357 RJ

-mass 0.077 MJ

centered on occultation

centered on transit

Transit Method Orbital/physical parameters of Kepler-4b:

- semimajor axis 0.045 AU- eccentricity 0 (adopted)- orbital period 3.21 days- radius 0.357 RJ

-mass 0.077 MJ

Orbital eccentricity e = 0.22 formally provides a better fit, but more measurements are required for a definitive orbital determination.

e = 0

e = 0.22

Transit Method Measured light curve of star hosting Kepler-10b, the first rocky extrasolar planet

discovered:- semimajor axis 0.017 AU- eccentricity 0 (adopted)- orbital period 3.21 days- radius 1.416 RE

-mass 4.56 ME

Transit Method Orbital/physical parameters of Kepler-10b: -

semimajor axis 0.017 AU- eccentricity 0 (adopted)- orbital period 3.21 days- radius 1.416 R

-mass 4.56 M

individual measurements

averages over 0.1 orbital phase

Transit Method Transit method favors small orbital separations.

Transit Method Transit method are able to detect small planets.

Transit Method Transit method are able to detect small and therefore low-mass planets.


extrasolar planets as a function of their semimajor axis/orbital period discovered as of October 2010.


Transit method favors planets (above a minimum size) in very close orbits.

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Direct imaging

Microlensing Method General relativity predicts that light is deflected by gravity, as was confirmed

observationally during the solar eclipse of 1919. (In actual fact, gravity warps spacetime so that light follows the shortest path in curved space.)

Gravitational microlensing occurs when a (usually much dimmer) foreground star passes in front of a (usually much brighter) background star as viewed by an observer on Earth, causing the background star to brighten temporarily.

Microlensing Method Note that individual lens images cannot usually be discerned (angular separation

smaller than current angular resolutions of telescopes).

Microlensing Method A microlensing event detected in the MACHO (Massive Compact Halo Object)

experiment.

Microlensing Method Typical microlensing events as a dim foreground star passes in front of a bright

background star. Notice the symmetric pattern of the light curves.

Microlensing Method A microlensing event as a dim foreground star and its planet passes in front of a

bright background star. Notice the second peak in the light curve produced by the planet.

Microlensing Method Microlensing method favors relatively small orbital separations.

Microlensing Method Microlensing method favors relatively massive planets.




Microlensing method favors relatively small orbital separations and relatively massive planets.

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Direct imaging

Direct Imaging Planets shine by reflecting light from their host stars.

First image of an extrasolar planet (~5 MJ), and the first to be discovered through direct imaging (using adaptive optics), was made in 2005 around the Brown Dwarf 2M1207 using the 8.2-m Very Large Telescope (VLT) in Chile.

Direct Imaging

Image of a planet (mass ~10-40 MJ) discovered around the star GJ 758 (mass ~1.0 M) using a coronograph and adapative optics on the SUBARU 8.2-m telescope on Mauna Kea, Hawaii.

background star

Direct Imaging

Image of three planets (~7 MJ, 24-68 AU) around the young star HR 8799 (mass ~1.5 M) using adaptive optics on the Keck 10-m telescopes on Mauna Kea, Hawaii.

Direct Imaging

Image of three planets (~7 MJ, 24-68 AU) around the young star HR 8799 using adaptive optics and a vortex coronograph (which introduces a spiraling phase pattern to cancel light from the central star) on just a 1.5-m portion of the Hale 5-m telescope on Mount Palomar, California, USA.

Direct Imaging Parameters of planets around HR 8799.

Direct Imaging

Image of the planet (mass ~0.05-3 MJ) around the young A-type main-sequence star Formalhaut using a coronograph on the HST.

Direct Imaging Direct imaging method favors very large orbital separations.

Direct Imaging Direct imaging method favors relatively large planets.

Direct Imaging Direct imaging method favors relatively large and hence massive planets.




Direct imaging favors large, and therefore massive, planets at large orbital separations.

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how are planets around other stars (apart from the sun) found? how do we determine the orbital...

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