Radial velocity

Not to be confused with Radial motion.

Diagram showing how an exoplanet orbiting a star produces changes in position and velocity of the star as they orbit their common center of mass (which is here the reference point)

Radial velocity is the velocity of an object in the direction of the line of sight (i.e., its speed straight towards or away from an observer). In astronomy, radial velocity most commonly refers to the spectroscopic radial velocity. The spectroscopic radial velocity is the radial component of the velocity of the source at emission and the observer at observation, as determined by spectroscopy. Astrometric radial velocity is the radial velocity as determined by astrometric observations (for example, a secular change in the annual parallax).

Radial velocity

Spectroscopic radial velocity

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.

In many binary stars, the orbital motion usually causes radial velocity variations of several kilometers per second. 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. 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.

Radial velocity comparison tables

The radial velocity method to detect exoplanet 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 - one can see if it moves periodically due to the influence of a companion.

Planet Mass	Distance AU	Radial velocity (vradial)	Notice
Jupiter	1	28.4 m/s
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
Alpha Centauri Bb (1.13 ± 0.09 M⊕)	0.04	0.51 m/s	(1)
Super-Earth (5 M⊕)	1	0.45 m/s
Earth	1	0.09 m/s

Ref: Notice 1: Most precise v_radial measurements ever recorded. ESO's HARPS spectrograph was used.

For MK-type stars with planets in the habitable zone

Stellar Mass (M☉)	Planet Mass (M⊕)	Lum. (L0)	Type	RHAB (AU)	vradial (m/s)	Period (days)
0.10	1.0	8e-4	M8	0.028	1.68	6
0.21	1.0	7.9e-3	M5	0.089	0.65	21
0.47	1.0	6.3e-2	M0	0.25	0.26	67
0.65	1.0	1.6e-1	K5	0.40	0.18	115
0.78	2.0	4.0e-1	K0	0.63	0.25	209

Ref:

See also

• Extrasolar planet
• Proper motion
• Peculiar velocity
• Doppler spectroscopy - the radial velocity method for detecting extrasolar planets