Doppler spectroscopy (also known as the radial-velocity method, or colloquially, the wobble method) is an indirect method for finding extrasolar planets and brown dwarfs from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star. As of November 2022, about 19.5% of known extrasolar planets (1,018 of the total) have been discovered using Doppler spectroscopy. [2]
Otto Struve proposed in 1952 the use of powerful spectrographs to detect distant planets. He described how a very large planet, as large as Jupiter, for example, would cause its parent star to wobble slightly as the two objects orbit around their center of mass. [3] He predicted that the small Doppler shifts to the light emitted by the star, caused by its continuously varying radial velocity, would be detectable by the most sensitive spectrographs as tiny redshifts and blueshifts in the star's emission. However, the technology of the time produced radial-velocity measurements with errors of 1,000 m/s or more, making them useless for the detection of orbiting planets. [4] The expected changes in radial velocity are very small – Jupiter causes the Sun to change velocity by about 12.4 m/s over a period of 12 years, and the Earth's effect is only 0.1 m/s over a period of 1 year – so long-term observations by instruments with a very high resolution are required. [4] [5]
Advances in spectrometer technology and observational techniques in the 1980s and 1990s produced instruments capable of detecting the first of many new extrasolar planets. The ELODIE spectrograph, installed at the Haute-Provence Observatory in Southern France in 1993, could measure radial-velocity shifts as low as 7 m/s, low enough for an extraterrestrial observer to detect Jupiter's influence on the Sun. [6] Using this instrument, astronomers Michel Mayor and Didier Queloz identified 51 Pegasi b, a "Hot Jupiter" in the constellation Pegasus. [7] Although planets had previously been detected orbiting pulsars, 51 Pegasi b was the first planet ever confirmed to be orbiting a main-sequence star, and the first detected using Doppler spectroscopy. [8]
In November 1995, the scientists published their findings in the journal Nature; the paper has since been cited over 1,000 times. Since that date, over 1,000 exoplanet candidates have been identified, many of which have been detected by Doppler search programs based at the Keck, Lick, and Anglo-Australian Observatories (respectively, the California, Carnegie and Anglo-Australian planet searches), and teams based at the Geneva Extrasolar Planet Search. [9]
Beginning in the early 2000s, a second generation of planet-hunting spectrographs permitted far more precise measurements. The HARPS spectrograph, installed at the La Silla Observatory in Chile in 2003, can identify radial-velocity shifts as small as 0.3 m/s, enough to locate many possibly rocky, Earth-like planets. [10] A third generation of spectrographs is expected to come online in 2017.[ needs update ] With measurement errors estimated below 0.1 m/s, these new instruments would allow an extraterrestrial observer to detect even Earth. [11]
A series of observations is made of the spectrum of light emitted by a star. Periodic variations in the star's spectrum may be detected, with the wavelength of characteristic spectral lines in the spectrum increasing and decreasing regularly over a period of time. Statistical filters are then applied to the data set to cancel out spectrum effects from other sources. Using mathematical best-fit techniques, astronomers can isolate the tell-tale periodic sine wave that indicates a planet in orbit. [7]
If an extrasolar planet is detected, a minimum mass for the planet can be determined from the changes in the star's radial velocity. To find a more precise measure of the mass requires knowledge of the inclination of the planet's orbit. A graph of measured radial velocity versus time will give a characteristic curve (sine curve in the case of a circular orbit), and the amplitude of the curve will allow the minimum mass of the planet to be calculated using the binary mass function.
The Bayesian Kepler periodogram is a mathematical algorithm, used to detect single or multiple extrasolar planets from successive radial-velocity measurements of the star they are orbiting. It involves a Bayesian statistical analysis of the radial-velocity data, using a prior probability distribution over the space determined by one or more sets of Keplerian orbital parameters. This analysis may be implemented using the Markov chain Monte Carlo (MCMC) method.
The method has been applied to the HD 208487 system, resulting in an apparent detection of a second planet with a period of approximately 1000 days. However, this may be an artifact of stellar activity. [12] [13] The method is also applied to the HD 11964 system, where it found an apparent planet with a period of approximately 1 year. However, this planet was not found in re-reduced data, [14] [15] suggesting that this detection was an artifact of the Earth's orbital motion around the Sun.[ citation needed ]
Although radial-velocity of the star only gives a planet's minimum mass, if the planet's spectral lines can be distinguished from the star's spectral lines then the radial-velocity of the planet itself can be found and this gives the inclination of the planet's orbit and therefore the planet's actual mass can be determined. The first non-transiting planet to have its mass found this way was Tau Boötis b in 2012 when carbon monoxide was detected in the infrared part of the spectrum. [16]
The graph to the right illustrates the sine curve using Doppler spectroscopy to observe the radial velocity of an imaginary star which is being orbited by a planet in a circular orbit. Observations of a real star would produce a similar graph, although eccentricity in the orbit will distort the curve and complicate the calculations below.
This theoretical star's velocity shows a periodic variance of ±1 m/s, suggesting an orbiting mass that is creating a gravitational pull on this star. Using Kepler's third law of planetary motion, the observed period of the planet's orbit around the star (equal to the period of the observed variations in the star's spectrum) can be used to determine the planet's distance from the star () using the following equation:
where:
Having determined , the velocity of the planet around the star can be calculated using Newton's law of gravitation, and the orbit equation:
where is the velocity of planet.
The mass of the planet can then be found from the calculated velocity of the planet:
where is the velocity of parent star. The observed Doppler velocity, , where i is the inclination of the planet's orbit to the line perpendicular to the line-of-sight.
Thus, assuming a value for the inclination of the planet's orbit and for the mass of the star, the observed changes in the radial velocity of the star can be used to calculate the mass of the extrasolar planet.
| Planet Mass | Distance AU | Star's Radial Velocity Due to the Planet (vradial) | Notice |
|---|---|---|---|
| Jupiter | 5 | 12.7 m/s | |
| Neptune | 0.1 | 4.8 m/s | |
| Neptune | 1 | 1.5 m/s | |
| Super-Earth (5 M🜨) | 0.1 | 1.4 m/s | |
| L 98-59 b (0.4 M🜨) | 0.02 | 0.46 m/s | [17] |
| Super-Earth (5 M🜨) | 1 | 0.45 m/s | |
| Earth | 0.09 | 0.30 m/s | |
| Earth | 1 | 0.09 m/s |
Ref: [18]
| Planet | Planet Type | Semimajor Axis (AU) | Orbital Period | Star's Radial Velocity Due to the Planet (m/s) | Detectable by: |
|---|---|---|---|---|---|
| 51 Pegasi b | Hot Jupiter | 0.05 | 4.23 days | 55.9 [19] | First-generation spectrograph |
| 55 Cancri d | Gas giant | 5.77 | 14.29 years | 45.2 [20] | First-generation spectrograph |
| Jupiter | Gas giant | 5.20 | 11.86 years | 12.4 [21] | First-generation spectrograph |
| Gliese 581c | Super-Earth | 0.07 | 12.92 days | 3.18 [22] | Second-generation spectrograph |
| Saturn | Gas giant | 9.58 | 29.46 years | 2.75 | Second-generation spectrograph |
| L 98-59 b | Terrestrial planet | 0.02 | 2.25 days | 0.46 [17] | Third-generation spectrograph |
| Neptune | Ice giant | 30.10 | 164.79 years | 0.281 | Third-generation spectrograph |
| Earth | Habitable planet | 1.00 | 365.26 days | 0.089 | Third-generation spectrograph (likely) |
| Pluto | Dwarf planet | 39.26 | 246.04 years | 0.00003 | Not detectable |
The major limitation with Doppler spectroscopy is that it can only measure movement along the line-of-sight, and so depends on a measurement (or estimate) of the inclination of the planet's orbit to determine the planet's mass. If the orbital plane of the planet happens to line up with the line-of-sight of the observer, then the measured variation in the star's radial velocity is the true value. However, if the orbital plane is tilted away from the line-of-sight, then the true effect of the planet on the motion of the star will be greater than the measured variation in the star's radial velocity, which is only the component along the line-of-sight. As a result, the planet's true mass will be greater than measured.
To correct for this effect, and so determine the true mass of an extrasolar planet, radial-velocity measurements can be combined with astrometric observations, which track the movement of the star across the plane of the sky, perpendicular to the line-of-sight. Astrometric measurements allows researchers to check whether objects that appear to be high mass planets are more likely to be brown dwarfs. [4]
A further disadvantage is that the gas envelope around certain types of stars can expand and contract, and some stars are variable. This method is unsuitable for finding planets around these types of stars, as changes in the stellar emission spectrum caused by the intrinsic variability of the star can swamp the small effect caused by a planet.
The method is best at detecting very massive objects close to the parent star – so-called "hot Jupiters" – which have the greatest gravitational effect on the parent star, and so cause the largest changes in its radial velocity. Hot Jupiters have the greatest gravitational effect on their host stars because they have relatively small orbits and large masses. Observation of many separate spectral lines and many orbital periods allows the signal-to-noise ratio of observations to be increased, increasing the chance of observing smaller and more distant planets, but planets like the Earth remain undetectable with current instruments.
The radial velocity or line-of-sight velocity of a target with respect to an observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative velocity onto the relative direction or line-of-sight (LOS) connecting the two points.
Robert Paul Butler is an astronomer and staff scientist at the Carnegie Institution for Science in Washington, D.C., who searches for extrasolar planets.
HD 28185 b is an extrasolar planet 128 light-years away from Earth in the constellation of Eridanus. The planet was discovered orbiting the Sun-like star HD 28185 in April 2001 as a part of the CORALIE survey for southern extrasolar planets, and its existence was independently confirmed by the Magellan Planet Search Survey in 2008. HD 28185 b orbits its sun in a circular orbit that is at the inner edge of its star's habitable zone.
Upsilon Andromedae c, formally named Samh, is an extrasolar planet orbiting the Sun-like star Upsilon Andromedae A every 241.3 days at an average distance of 0.83 AU. Its discovery in April 1999 by Geoffrey Marcy and R. Paul Butler made this the first multiple-planet system to be discovered around a main-sequence star, and the first multiple-planet system known in a multiple star system. Upsilon Andromedae c is the second-known planet in order of distance from its star.
47 Ursae Majoris b, formally named Taphao Thong, is a gas planet and an extrasolar planet approximately 46 light-years from Earth in the constellation of Ursa Major. The planet was discovered located in a long-period orbit around the star 47 Ursae Majoris in January 1996 and as of 2011 it is the innermost of three known planets in its planetary system. It has a mass at least 2.53 times that of Jupiter.
Any planet is an extremely faint light source compared to its parent star. For example, a star like the Sun is about a billion times as bright as the reflected light from any of the planets orbiting it. In addition to the intrinsic difficulty of detecting such a faint light source, the light from the parent star causes a glare that washes it out. For those reasons, very few of the exoplanets reported as of January 2024 have been observed directly, with even fewer being resolved from their host star.
HD 164922 b is an exoplanet orbiting the star HD 164922 about 72 light-years from Earth in the constellation Hercules. Its inclination is not known, and its true mass may be significantly greater than the radial velocity lower limit of 0.36 Jupiter masses. The planet also has a low eccentricity, unlike most other long period extrasolar planets – 0.05 – about the same as Jupiter and Saturn in the Solar System. The exoplanet was found by using the radial velocity method, from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star.
This page describes exoplanet orbital and physical parameters.
HD 8574 b is an extrasolar planet discovered in 2001 by a team of European astronomers using Doppler spectroscopy as part of the ELODIE Planet Search Survey, and was published in a paper with five other planets. HD 8574 b is in the orbit of host star HD 8574. The planet is at most two times the mass of Jupiter, orbiting every 227 days at three quarters of the distance between the Earth and Sun. HD 8574 b has a very elliptical orbit, far more than that of Jupiter.
HD 154672 b is an extrasolar planet located approximately 210 light-years away in the constellation of Ara, orbiting the metal-rich and aged star HD 154672. This planet has a minimum mass five times that of Jupiter and orbits at about 60% the distance between the Earth to the Sun. Its orbit is very elliptical, which causes temperatures on the planet to vary significantly as it proceeds along its orbit. This planet was discovered in Las Campanas Observatory on September 5, 2008 using the radial velocity method. Along with HD 205739 b, the planets were the first to be discovered by the N2K Consortium using the Magellan Telescopes.
HD 205739 b is an extrasolar planet located approximately 350 light-years away.
Leonhard Euler Telescope, or the Swiss EULER Telescope, is a national, fully automatic 1.2-metre (47 in) reflecting telescope, built and operated by the Geneva Observatory. It is located at an altitude of 2,375 m (7,792 ft) at ESO's La Silla Observatory site in the Chilean Norte Chico region, about 460 kilometers north of Santiago de Chile. The telescope, which saw its first light on 12 April 1998, is named after Swiss mathematician Leonhard Paul Euler.
51 Pegasi b, officially named Dimidium, is an extrasolar planet approximately 50 light-years away in the constellation of Pegasus. It was the first exoplanet to be discovered orbiting a main-sequence star, the Sun-like 51 Pegasi, and marked a breakthrough in astronomical research. It is the prototype for a class of planets called hot Jupiters.
HD 28254 is a binary star system located 180 light-years away in the constellation Dorado. The primary component is an 8th magnitude G-type main-sequence star. This star is larger, cooler, brighter, and more massive than the Sun, and its metal content is 2.3 times as much as the Sun. In 2009, a gas giant exoplanet was found in orbit around the star.
GJ 3634 b is a super-Earth exoplanet in the orbit of the nearby red dwarf GJ 3634 at approximately 64.5 light-years in constellation Hydra. The planet is approximately eight times the mass of Earth, and orbits its star every two and a half days at a distance of 0.0287 AU. The planet was the first to be discovered by a group of astronomers searching for exoplanets in the orbit of very-low-mass stars after the team reorganized their strategy, choosing to search for targets that they could also confirm using the transit method. However, a transit event associated with GJ 3634 b was not detected. The planet's discovery was published in Astronomy and Astrophysics on February 8, 2011.
In astronomy, the binary mass function or simply mass function is a function that constrains the mass of the unseen component in a single-lined spectroscopic binary star or in a planetary system. It can be calculated from observable quantities only, namely the orbital period of the binary system, and the peak radial velocity of the observed star. The velocity of one binary component and the orbital period provide information on the separation and gravitational force between the two components, and hence on the masses of the components.
HD 240237 b is a super-Jupiter exoplanet orbiting the K-type giant star HD 240237 about 4,900 light-years (1,500 parsecs, or nearly 4.6×1016 km) away from Earth in the constellation Cassiopeia. It orbits outside of the habitable zone of its star at a distance of 1.9 AU. The exoplanet was found by using the radial velocity method, from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star. The planet has a mildly eccentric orbit.
HD 164922 c is an exoplanet orbiting the star HD 164922 about 72 light-years from Earth in the constellation Hercules. The exoplanet was found by using the radial velocity method, from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star.
38 Virginis b is a super-Jupiter exoplanet orbiting within the habitable zone of the star 38 Virginis about 108.5 light-years from Earth in the constellation Virgo. The exoplanet was found by using the radial velocity method, from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star.
HD 177565 b is an extrasolar planet orbiting the G-type main-sequence star HD 177565 55.3 light-years away from the Solar System.
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