The radial velocity of an object with respect to a given point is the rate of change of the distance between the object and the point. That is, the radial velocity is the component of the object's velocity that points in the direction of the radius connecting the object and the point. In astronomy, the point is usually taken to be the observer on Earth, so the radial velocity then denotes the speed with which the object moves away from or approaches the Earth.

In astronomy, radial velocity is often measured to the first order of approximation by Doppler spectroscopy. The quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity.[1] However, due to relativistic and cosmological effects over the great distances that light typically travels to reach the observer from an astronomical object, this measure cannot be accurately transformed to a geometric radial velocity without additional assumptions about the object and the space between it and the observer.[2] By contrast, astrometric radial velocity is determined by astrometric observations (for example, a secular change in the annual parallax).[2][3][4]

A plane flying past a radar station: the plane's velocity vector (red) is the sum of the radial velocity (green) and the tangential velocity (blue).

Light from an object with a substantial relative radial velocity at emission will be subject to the Doppler effect, so the frequency of the light decreases for objects that were receding (redshift) and increases for objects that were approaching (blueshift).

The radial velocity of a star or other luminous distant objects can be measured accurately by taking a high-resolution spectrum and comparing the measured wavelengths of known spectral lines to wavelengths from laboratory measurements. A positive radial velocity indicates the distance between the objects is or was increasing; a negative radial velocity indicates the distance between the source and observer is or was decreasing.

Diagram showing how an exoplanet's orbit changes the position and velocity of a star as they orbit a common center of mass.

In many binary stars, the orbital motion usually causes radial velocity variations of several kilometers per second (km/s). As the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries. Radial velocity can be used to estimate the ratio of the masses of the stars, and some orbital elements, such as eccentricity and semimajor axis. The same method has also been used to detect planets around stars, in the way that the movement's measurement determines the planet's orbital period, while the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function. Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a very high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight. It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit.[5][6]

## Detection of exoplanets

The radial velocity method to detect exoplanets

The radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By regularly looking at the spectrum of a star—and so, measuring its velocity—it can be determined if it moves periodically due to the influence of an exoplanet companion.

## Data reduction

From the instrumental perspective, velocities are measured relative to the telescope's motion. So an important first step of the data reduction is to remove the contributions of

• the Earth's elliptic motion around the sun at approximately ± 30 km/s,
• a monthly rotation of ± 13 m/s of the Earth around the center of gravity of the Earth-Moon system,[7]
• the daily rotation of the telescope with the Earth crust around the Earth axis, which is up to ±460 m/s at the equator and proportional to the cosine of the telescope's geographic latitude,
• small contributions from the Earth polar motion at the level of mm/s,
• contributions of 230 km/s from the motion around the Galactic center and associated proper motions.[8]
• in the case of spectroscopic measurements corrections of the order of ±20 cm/s with respect to aberration.[9]
• Sin i degeneracy is the impact caused by not being in the plane of the motion.

## References

1. ^ Resolution C1 on the Definition of a Spectroscopic "Barycentric Radial-Velocity Measure". Special Issue: Preliminary Program of the XXVth GA in Sydney, July 13–26, 2003 Information Bulletin n° 91. Page 50. IAU Secretariat. July 2002. https://www.iau.org/static/publications/IB91.pdf
2. ^ a b Lindegren, Lennart; Dravins, Dainis (April 2003). "The fundamental definition of "radial velocity"" (PDF). Astronomy and Astrophysics. 401 (3): 1185–1201. arXiv:astro-ph/0302522. Bibcode:2003A&A...401.1185L. doi:10.1051/0004-6361:20030181. Retrieved 4 February 2017.
3. ^ Dravins, Dainis; Lindegren, Lennart; Madsen, Søren (1999). "Astrometric radial velocities. I. Non-spectroscopic methods for measuring stellar radial velocity". Astron. Astrophys. 348: 1040–1051. arXiv:astro-ph/9907145. Bibcode:1999A&A...348.1040D.
4. ^ Resolution C 2 on the Definition of "Astrometric Radial Velocity". Special Issue: Preliminary Program of the XXVth GA in Sydney, July 13–26, 2003 Information Bulletin n° 91. Page 51. IAU Secretariat. July 2002. https://www.iau.org/static/publications/IB91.pdf
5. ^ Anglada-Escude, Guillem; Lopez-Morales, Mercedes; Chambers, John E. (2010). "How eccentric orbital solutions can hide planetary systems in 2:1 resonant orbits". The Astrophysical Journal Letters. 709 (1): 168–78. arXiv:0809.1275. Bibcode:2010ApJ...709..168A. doi:10.1088/0004-637X/709/1/168.
6. ^ Kürster, Martin; Trifonov, Trifon; Reffert, Sabine; Kostogryz, Nadiia M.; Roder, Florian (2015). "Disentangling 2:1 resonant radial velocity oribts from eccentric ones and a case study for HD 27894". Astron. Astrophys. 577: A103. arXiv:1503.07769. Bibcode:2015A&A...577A.103K. doi:10.1051/0004-6361/201525872.
7. ^ Ferraz-Mello, S.; Michtchenko, T. A. (2005). "Extrasolar Planetary Systems". Lect. Not. Phys. 683. pp. 219–271. Bibcode:2005LNP...683..219F. doi:10.1007/10978337_4.
8. ^ Reid, M. J.; Dame, T. M. (2016). "On the rotation speed of the Milky Way determined from HI emission". The Astrophysical Journal. 832 (2): 159. arXiv:1608.03886. Bibcode:2016ApJ...832..159R. doi:10.3847/0004-637X/832/2/159.
9. ^ Stumpff, P. (1985). "Regiorous treatment of the heliocentric motion of stars". Astron. Astrophys. 144: 232. Bibcode:1985A&A...144..232S.
Doppler spectroscopy

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.

669 extrasolar planets (about 29.6% of the total) were discovered using Doppler spectroscopy, as of April 2016.

Gliese 667 Cc

Gliese 667 Cc (also known as GJ 667Cc, HR 6426Cc, or HD 156384Cc) is an exoplanet orbiting within the habitable zone of the red dwarf star Gliese 667 C, which is a member of the Gliese 667 triple star system, approximately 23.62 light-years (6.8 parsecs, or about 217,000,000,000,000 km) away in the constellation of Scorpius. 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.

HARPS-N

HARPS-N, the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere is a high-precision radial-velocity spectrograph, installed at the Italian Telescopio Nazionale Galileo, a 3.58-metre telescope located at the Roque de los Muchachos Observatory on the island of La Palma, Canary Islands, Spain.

HARPS-N is the counterpart for the Northern Hemisphere of the similar HARPS instrument installed on the ESO 3.6 m Telescope at La Silla Observatory in Chile. It allows for planetary research in the northern sky which hosts the Cygnus and Lyra constellations. In particular it allows for detailed follow up research to Kepler mission planet candidates, which are located in the Cygnus constellation region.

The instrument's main scientific goals are the discovery and characterization of terrestrial super-Earths by combining the measurements using transit photometry and doppler spectroscopy which provide both, the size and mass of the exoplanet. Based on the resulting density, rocky (terrestrial) Super-Earths can be distinguished from gaseous exoplanets.The HARPS-N Project is a collaboration between the Geneva Observatory (lead), the Center for Astrophysics in Cambridge (Massachusetts), the Universities of St. Andrews and Edinburgh, the Queen's University Belfast, the UK Astronomy Technology Centre and the Italian Istituto Nazionale di Astrofisica.

HD 155233 b

HD 155233 b is a confirmed exoplanet orbiting around the K Giant star HD 155233 every 885 days some 244.94 light-years away. It has a mass of 636 Earth masses or 2 Jupiter masses and is likely a gas giant similar of that to Jupiter just double the mass. It was discovered by Wittenmyer et al. on October 22nd 2015.

HD 164595 b

HD 164595 b is a confirmed exoplanet orbiting around a Sun-like star HD 164595 every 40 days some 94.36 light-years away. It was detected with the radial velocity technique with the SOPHIE echelle spectrograph. The planet has a minimal mass equivalent of 16 Earths.It is believed to be a Neptune-like gassy planet incapable of supporting life. The planet has a minimal mass of 16 Earth masses.

HD 164922 c

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.

HD 219134 b

HD 219134 b (or HR 8832 b) is one of at least five exoplanets orbiting HR 8832, a main-sequence star in the constellation of Cassiopeia. As of July 2015, super-Earth HD 219134 b, with a size of about 1.6 R⊕, and a density of 6.4 g/cm3, was reported as the closest rocky exoplanet to the Earth, at 21.25 light-years away. The exoplanet was initially detected by the instrument HARPS-N of the Italian Telescopio Nazionale Galileo via the radial velocity method and subsequently observed by the Spitzer telescope as transiting in front of its star. The exoplanet has a mass of about 4.5 times that of Earth and orbits its host star every three days. In 2017, it was found that the planet likely hosts an atmosphere.

HD 219134 d

HD 219134 d, also known as HR 8832 d, is an exoplanet orbiting around the K-type star HR 8832 in the constellation of Cassiopeia. It has a minimum mass over 16 times that of Earth, indicating that it is likely a Hot Neptune. The exoplanet was initially detected by the instrument HARPS-N of the Italian Telescopio Nazionale Galileo via the radial velocity method. Unlike HD 219134 b and HD 219134 c it has not been observed by the Spitzer telescope and thus its radius and density are unknown. Only a minimum possible radius can be given.

HD 219134 e

HD 219134 e, also known as HR 8832 e, is an exoplanet orbiting around the K-type star HR 8832 in the constellation of Cassiopeia. It has a mass of 62 Earth Masses, which indicates that the planet is likely a gas giant. The exoplanet was initially detected by the instrument HARPS-N of the Italian Telescopio Nazionale Galileo via the radial velocity method. Unlike HD 219134 b it has not been observed by the Spitzer telescope and thus its radius and density are unknown. It is in the ammonia habitable zone, so if it has a large moon with an atmosphere, liquid ammonia could flow on the moon's surface.

HD 219134 h

HD 219134 h, also known as HR 8832 h, is an exoplanet orbiting around the K-type star HR 8832 in the constellation of Cassiopeia. It has a mass of 108 Earth Masses, which indicates that the planet is likely a gas giant. Unlike HD 219134 b it has not been observed by the Spitzer telescope and thus its radius and density are unknown. It is in the ammonia habitable zone, so if it has a large moon with an atmosphere, liquid ammonia could flow on the moon's surface.

HD 40307 g

HD 40307 g is an exoplanet orbiting in the habitable zone of HD 40307. It is located 42 light-years away in the direction of the southern constellation Pictor. The planet was discovered by the radial velocity method, using the European Southern Observatory's HARPS apparatus by a team of astronomers led by Mikko Tuomi at the University of Hertfordshire and Guillem Anglada-Escude of the University of Goettingen, Germany.

High Accuracy Radial Velocity Planet Searcher

The High Accuracy Radial Velocity Planet Searcher (HARPS) is a high-precision echelle planet-finding spectrograph installed in 2002 on the ESO's 3.6m telescope at La Silla Observatory in Chile. The first light was achieved in February 2003. HARPS has discovered over 130 exoplanets to date, with the first one in 2004, making it the most successful planet finder behind the Kepler space observatory. It is a second-generation radial-velocity spectrograph, based on experience with the ELODIE and CORALIE instruments.

Kepler-20g

Kepler-20g is a non-transiting exoplanet orbiting Kepler-20. Its radius is about twice that of Earth, with a minimum mass 19.96+3.08−3.61 Earth masses. Kepler-20g was announced on 24 August 2016.

List of exoplanets detected by radial velocity

The following is a list of 456 extrasolar planets that were only detected by radial velocity method –– 31 confirmed and 323 candidates, sorted by orbital periods. Since none of these planets are transiting or directly observed, they do not have measured radii and generally their masses are only minimum. The true masses can be determined when astrometry calculates the inclination of the orbit.

There are 160 members of the multi-planet systems –– 21 confirmed and 139 candidates.

Methods of detecting exoplanets

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 extrasolar planets reported as of April 2014 have been observed directly, with even fewer being resolved from their host star.

Instead, astronomers have generally had to resort to indirect methods to detect extrasolar planets. As of 2016, several different indirect methods have yielded success.

The MINiature Exoplanet Radial Velocity Array (MINERVA) is a ground-based robotic dedicated exoplanet observatory. The facility is an array of small-aperture robotic telescopes outfitted for both photometry and high-resolution Doppler spectroscopy located at the U.S. Fred Lawrence Whipple Observatory at Mt. Hopkins, Arizona. The project's principal investigator is the American astronomer John Johnson. The telescopes were manufactured by PlaneWave Instruments.

NGC 5090 and NGC 5091

NGC 5090 and NGC 5091 are a set of galaxies approximately 160 million light-years (50 million parsecs) away in the constellation Centaurus. They are in the process of colliding and merging with some evidence of tidal disruption of NGC 5091.NGC 5090 is an elliptical galaxy while NGC 5091 is a barred spiral galaxy. The radial velocity of the nucleus of NGC 5090 has been measured at 3,185 km/s (1,979 mi/s), while NGC 5091 has a radial velocity of 3,429 km/s (2,131 mi/s). NGC 5090 is associated with the strong, double radio source PKS 1318-43.

PRL Advanced Radial-velocity Abu-sky Search, abbreviated PARAS, is a ground-based extrasolar planet search device. Based at 1.2m telescope is located at Mt. Abu, India.The project is funded by Physical Research Laboratory, India. The spectrograph works at a resolution of 67000. With the help of simultaneous calibration technique, PARAS has achieved an RV accuracy of 1.3 m/s for the bright sun like quiet stars. Thorium-Argon lamp is used for calibration. New calibration techniques are also being explored by the project team. PARAS can detect planet in the habitable zone around M-type stars.

Sloan Digital Sky Survey

The Sloan Digital Sky Survey or SDSS is a major multi-spectral imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after the Alfred P. Sloan Foundation, which contributed significant funding.

Data collection began in 2000; the final imaging data release (DR9) covers over 35% of the sky, with photometric observations of around nearly 1 billion objects, while the survey continues to acquire spectra, having so far taken spectra of over 4 million objects. The main galaxy sample has a median redshift of z = 0.1; there are redshifts for luminous red galaxies as far as z = 0.7, and for quasars as far as z = 5; and the imaging survey has been involved in the detection of quasars beyond a redshift z = 6.

Data release 8 (DR8), released in January 2011, includes all photometric observations taken with the SDSS imaging camera, covering 14,555 square degrees on the sky (just over 35% of the full sky). Data release 9 (DR9), released to the public on 31 July 2012, includes the first results from the Baryon Oscillation Spectroscopic Survey (BOSS) spectrograph, including over 800,000 new spectra. Over 500,000 of the new spectra are of objects in the Universe 7 billion years ago (roughly half the age of the universe). Data release 10 (DR10), released to the public on 31 July 2013, includes all data from previous releases, plus the first results from the APO Galactic Evolution Experiment (APOGEE) spectrograph, including over 57,000 high-resolution infrared spectra of stars in the Milky Way. DR10 also includes over 670,000 new BOSS spectra of galaxies and quasars in the distant universe. The publicly available images from the survey were made between 1998 and 2009.

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