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Binary Systems and Stellar Parameters. How are planets around other stars (apart from the Sun) found? How do we determine the orbital parameters and masses of planets?. Learning Objectives.

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binary systems and stellar parameters

Binary Systems and Stellar Parameters

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

slide2

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar PlanetsTransits Gravitational microlensing Direct imaging
slide3

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar Planets Transits Gravitational microlensing Direct imaging
slide4

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?

Artist’s conception of 51 Pegasi and its planet

51 Pegasi

Didier Queloz & Michel Mayor

slide5

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

slide6

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 Technique

Radial Velocity Curve of 51 Peg

slide7

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?
slide8

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?
slide9

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

slide10

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?
slide11

Census of Extrasolar Planets

  • Distribution of planet orbital semi-major axis (majority discovered by radial-velocity technique). Is our solar system unusual?
slide12

Census of Extrasolar Planets

  • Distribution of planet masses (majority discovered by radial-velocity technique), mostly lower limits. Is our solar system unusual?
slide13

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

radial velocity of star

inclination of planet orbit to sky plane

mass of star + mass of planet ≅ mass of star

slide14

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar Planets Transits Gravitational microlensing Direct imaging
slide15

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?
slide16

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.
  • 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.

Radial Velocity Curve of 51 Peg

slide17

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.
slide18

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.
slide19

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
slide20

Census of Extrasolar Planets

log10P (yrs)

  • 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.

-3

-2

-1

0

1

2

3

4

2

4

1

3

0

log10m (MJ)

log10m (MJ)

2

log10m (ME)

-1

1

-2

0

-3

-1

-4

-2

-1

0

1

2

3

log10a (AU)

slide21

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar PlanetsTransits Gravitational microlensing Direct imaging
slide22

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar PlanetsTransits Gravitational microlensing Direct imaging
slide23

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.

Brightness

Time

slide24

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
slide25

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
slide26

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
slide27

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.
slide28

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

slide29

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

slide30

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
slide31

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

slide32

Transit Method

  • Transit method favors small orbital separations.
slide33

Transit Method

  • Transit method are able to detect small planets.
slide34

Transit Method

  • Transit method are able to detect small and therefore low-mass planets.
slide35

Census of Extrasolar Planets

log10P (yrs)

  • Mass (mostly lower limits) of extrasolar planets as a function of their semimajor axis/orbital period discovered as of October 2010.
  • Methods of discovery:
  • Transit method favors planets (above a minimum size) in very close orbits.

-3

-2

-1

0

1

2

3

4

2

4

1

3

0

log10m (MJ)

log10m (MJ)

2

log10m (ME)

-1

1

-2

0

-3

-1

-4

-2

-1

0

1

2

3

log10a (AU)

slide36

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar PlanetsTransits Gravitational microlensing Direct imaging
slide37

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.
slide38

Microlensing Method

  • Note that individual lens images cannot usually be discerned (angular separation smaller than current angular resolutions of telescopes).
slide39

Microlensing Method

  • A microlensing event detected in the MACHO (Massive Compact Halo Object) experiment.
slide40

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.
slide41

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.
slide42

Microlensing Method

  • Microlensing method favors relatively small orbital separations.
slide43

Microlensing Method

  • Microlensing method favors relatively massive planets.
slide44

Census of Extrasolar Planets

log10P (yrs)

  • Mass (mostly lower limits) of extrasolar planets as a function of their semimajor axis/orbital period discovered as of October 2010.
  • Methods of discovery:
  • Microlensing method favors relatively small orbital separations and relatively massive planets.

-3

-2

-1

0

1

2

3

4

2

4

1

3

0

log10m (MJ)

log10m (MJ)

2

log10m (ME)

-1

1

-2

0

-3

-1

-4

-2

-1

0

1

2

3

log10a (AU)

slide45

Learning Objectives

  • Discovery of Extrasolar Planets Radial-velocity technique Precision radial-velocity measurements
  • Other Techniques to Find Extrasolar PlanetsTransitsGravitational microlensingDirect imaging
slide46

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.
slide47

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

slide48

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.
slide49

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.
slide50

Direct Imaging

  • Parameters of planets around HR 8799.
slide51

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.
slide52

Direct Imaging

  • Direct imaging method favors very large orbital separations.
slide53

Direct Imaging

  • Direct imaging method favors relatively large planets.
slide54

Direct Imaging

  • Direct imaging method favors relatively large and hence massive planets.
slide55

Census of Extrasolar Planets

log10P (yrs)

  • Mass (mostly lower limits) of extrasolar planets as a function of their semimajor axis/orbital period discovered as of October 2010.
  • Methods of discovery:
  • Direct imaging favors large, and therefore massive, planets at large orbital separations.

-3

-2

-1

0

1

2

3

4

2

4

1

3

0

log10m (MJ)

log10m (MJ)

2

log10m (ME)

-1

1

-2

0

-3

-1

-4

-2

-1

0

1

2

3

log10a (AU)