Stars and Planets

< < Module 1 > >

—Exoplanets—

Chris Ormel

Roadmap module 1

 

Planets

what defines a planet; what type of planets are there in the solar system and in the exoplanet census

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Kepler laws of planetary motion

the laws governing the motions of planets

→

↓  

Exo-Planet detection techniques

What are the mechanisms observers use to detect planets; what are their respective advantages and disadvantages; How to use them in order to assess the exoplanet census

→

M2.Two-body problem

  • astrometry
  • imaging
  • microlensing
  • radial velocity
  • transits
Exoplanets by mass and orbital period over time

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
Moon-Earth-Sun system. Earth fulfills definition (1), the Moon does not. The Moon is Earth's satellite

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
Ida and its satellite Dactyl do orbit the Sun but are not in hydrostatic equilibrium. (c) ESA

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5
Pluto has not cleared its neighborhood and is not a planet (anymore). Picture taken with New Horizons spacecraft (c) NASA

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5
Kuiper belt is a belt full of "debris"

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5
(c) NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute/Roman Tkachenko
Ultima Thule Arrokoth — a Kuiper belt object (KBO)

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5

In the solar system, we distinguish:

  • Giant Planets — consist primarily of hydrogen and helium
  • Terrestrial Planets — consist primarily of "metals"
  • Ice Giants — consist mostly of "metals" (ice+rock), but with large amounts of hydrogen and helium
Jupiter/Cassini
The giant planet jupiter consist primarily out of H and He. Still it is enriched (compared to the Sun) in heavy elements

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5

In the solar system, we distinguish:

  • Giant Planets — consist primarily of hydrogen and helium
  • Terrestrial Planets — consist primarily of "metals"
  • Ice Giants — consist mostly of "metals" (ice+rock), but with large amounts of hydrogen and helium
Earth/Apollo
Earth is a terrestrial planet. Dominated by refractory metals. Virtually no H and He and very little H2O (~0.02%).

What is a planet?

 

Definition. According to the International Astronomical Union (IAU), a planet is a celestial body which:

  1. is in orbit around the Sun; and
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape); and
  3. has "cleared the neighborhood" around its orbit.
    See IAU resolution B5

In the solar system, we distinguish:

  • Giant Planets — consist primarily of hydrogen and helium
  • Terrestrial Planets — consist primarily of "metals"
  • Ice Giants — consist mostly of "metals" (ice+rock), but with large amounts of hydrogen and helium
Neptune/Voyager 2
Neptune is an ice planet. Its interior is dominated by rock/ice (the precise abundances is unclear). Its atmosphere does contain significant quantities of hydrogen and helium

Kepler's laws of planetary motion

read CO Ch 2.1

  1. motion follows an ellipse, with the Sun at one of its focii.

    Non-interial reference frame (!)

  2. a line sweeps out equal areas in equal time intervals:
  3. semi-major axis a and orbital period P are related as:

    Here the constant equals

Laws can be understood from Newton's law of universal gravitation:

Geometry of the orbit: The particle follows elliptical motion, in which the Sun is located at one of its focii (The other one is empty.) The orbit is given by:

(To be derived in M2.Two body problem)

Exoplanet dection techniques — Astrometry

 

"
(c) ESA — https://sci.esa.int/web/gaia/-/58788-detecting-exoplanets-with-astrometry

Astrometry is another indirect planet detection technique. It measures the angular motion of nearby stars across the sky. This motion consists of three components (which three?) :

  1. the proper motion of the star through the galaxy
  2. the motion of the Earth around the Sun (parallax)
  3. the deviation caused by the gravitational perturbation from companions (e.g., planets)


Presently, few planets have been detected with astrometry, but this is going to change with GAIA

Exoplanet dection techniques — Astrometry

 

GAIA. (c) ESO A. Ducros, 2013

Astrometry is another indirect planet detection technique. It measures the angular motion of nearby stars across the sky. This motion consists of three components :

  1. the proper motion of the star through the galaxy
  2. the motion of the Earth around the Sun (parallax)
  3. the deviation caused by the gravitational perturbation from companions (e.g., planets)


Presently, few planets have been detected with astrometry, but this is going to change with GAIA

Distance measurements — Parallax

In Astronomy, it is challenging to measure distances.

The parallax method is an astrometric method to obtain distances to relatively close stars. Over the course of a solar orbit, they will change their position on the sky. The definition of parallax is such that a shift of 1 arcsec ('') corresponds to a distance of 1 parsec (pc).

1'' = 1/3600 deg. It follows that

  • Proxima-Centauri, the closest star, has a parallax of 0.7685.
  • The GAIA spacecraft will measure parallax angles to an accuracy of 10 micro arcseconds (μas or μ''). The astrometric technique will also allow us to detect many planets around stars (why?)

→ Definition of parallax (c) Wikipedia

"
d

Radial velocity method (Doppler spectroscopy)

Credit: ESO/L. Calçada

Radial velocity method (Doppler spectroscopy)

 

(c) Johan Jarnestad/Royal Swedish Academy of Sciences

The method employs two concepts:

  1. Center of mass at 0:
  2. Kepler's 3rd law:  

    where: P is period, a semi-major axis, G Newton's constant

Assume that then:

the quantities on the RHS can be measured (P, or can be assumed
From the Doppler technique one actually gets only the radial velocity component of the star Hence, this detection method is known as the radial velocity (RV) method.

Radial velocity method (Doppler spectroscopy)

 

The method employs two concepts:

  1. Center of mass at 0:
  2. Kepler's 3rd law:  

    where: P is period, a semi-major axis, G Newton's constant

Assume that then:

the quantities on the RHS can be measured (P, or can be assumed
From the Doppler technique one actually gets only the radial velocity component of the star Hence, this detection method is known as the radial velocity (RV) method.

orbital phase
radial velocity
Mayor & Queloz (1995) From the period of P = 4.23 days and the amplitude of 60 m/s, the planet mass can be determined.
This discovery of the planet 51 Peg b — a hot Jupiter — was awarded the Nobel Prize in Physics in 2019.

Radial velocity method (Doppler spectroscopy)

 

orbital phase
radial velocity
Mayor & Queloz (1995) From the period of P = 4.23 days and the amplitude of 60 m/s, the planet mass can be determined.
This discovery of the planet 51 Peg b — a hot Jupiter — was awarded the Nobel Prize in Physics in 2019.
2019 Nobel prize awarded to Michel Mayor & Didier Queloz (together with Jim Peebles for Cosmology)

Radial velocity method (Doppler spectroscopy)

 

orbital phase
radial velocity
Mayor & Queloz (1995) From the period of P = 4.23 days and the amplitude of 60 m/s, the planet mass can be determined.
This discovery of the planet 51 Peg b — a hot Jupiter — was awarded the Nobel Prize in Physics in 2019.

Question — The RV method is best suited to detect massive planets on orbits close to the parent star

  • What is an issue with this technique to discover small planets like the Earth at 1 au?
  • What is an issue for observing Jupiter-mass planets at Jupiter's orbit (5.2 au) with this technique?

Transit method

 

  • The idea of finding planets through transits is straightforward: The planet reduces the brightness of the star by a small amount.
  • This amount ("transit depth") is proportional to the size of the planet
  • In 1999 the first "transiting planet" was detected.

Transit method

 

Charbonneau et al. (2000)   HD 209458 b was the first planet to be disovered by this technique.
From the observed depth of 1.5% in the brightness of the star, it follows that the radius of the planet is
  • The idea of finding planets through transits is straightforward: The planet reduces the brightness of the star by a small amount.
  • This amount ("transit depth") is proportional to the size of the planet
  • In 1999 the first "transiting planet" was detected.
Q: How do we get the planet radius from this curve?

Transit method

 

Kepler has been very successful,
detecting thousands of exoplanets
by looking at a small region of the sky.
TESS (Transiting Exoplanet Survey Satellite)
is finding many planets around bright star
across the entire sky.
PLATO (Planetary Transits and Oscillation of stars)
will be launched around 2026 by ESA.
Target: Earth-like planets in habitable zone.
Earth2.0 is a proposed Chinese transit
mission
 
  • The idea of finding planets through transits is straightforward: The planet reduces the brightness of the star by a small amount.
  • This amount ("transit depth") is proportional to the size of the planet
  • In 1999 the first "transiting planet" was detected.
  • Space missions as Kepler, TESS and in the future Plato, Earth2.0 will discover many exoplanets through transits

Microlensing

(micro)lensing amplifies the background star. (c) Adam Rogers

Microlensing

The presence of a planet "distorts" the lightcurve. (c) Adam Rogers

Microlensing

 

Gravitational lensing in the observer-lens-source (OLS) plane. Light from the source star S is gravitationally deflected by lens L at an angle of into the direction of the observer O. and are the distances to the source and the lens, respectively. In reality all angles are very small.

Microlensing

 

Distortion and magnification of the background star due to gravitational lensing as seen from the observer in a frame where the lens is fixed. The Einstein ring is indicated by the dotted circle. At each time the angles , , and lie on the same line.

Microlensing

 

Distortion and magnification of the background star due to gravitational lensing as seen from the observer in a frame where the lens is fixed. The Einstein ring is indicated by the dotted circle. At each time the angles , , and lie on the same line.
Gravitational lensing in the observer-lens-source (OLS) plane. Light from the source star S is gravitationally deflected by lens L at an angle of into the direction of the observer O. and are the distances to the source and the lens, respectively. In reality all angles are very small.

In (micro)lensing light from a background star is gravitationally deflected by foreground lens.

  • The amount of deflection is governed by the Lens equation:

    where is the between the source and the lens, and is the Einstein radius:

  • The lensing results in a magnification of the background star by a factor

    The magnification is therefore greatest near the Einstein ring. A planet in the lens plane may alter the lightcurve, however.

Microlensing

 

Yee et al. (2021) — magnification due to the microlensing. x-axis is time in Julian days; y-axis is I-band magnitude. If a planet is present in the lens plane, it may distort the curve.
P

In (micro)lensing light from a background star is gravitationally deflected by foreground lens.

  • The amount of deflection is governed by the Lens equation:
  • The lensing results in a magnification of the background star by a factor
  • A planet P in the lens plane affects the magnification profile.

Direct Imaging

 

NRC-HIA/Marois/Keck observatory
The HR8799 system a spectacular example: 4 (big) planets have been detected, showing clear Keplerian motion

Direct imaging techniques use a coronagraph (takes out the stellar light). It works best when:

  • planets are young and bright
  • planets are far from the star

Direct Imaging

 

(c) Jason Wang

Direct imaging techniques use a coronagraph (takes out the stellar light). It works best when:

  • planets are young and bright
  • planets are far from the star

end of module 1

—congrats—

questions?