Radial speed

In Astronomy, the radial speed Speed of a Celestial object measured in the direction of the line of sight. The light of an object having a significant radial speed is prone to the Doppler effect, consequently the Wavelength of the light emitted by this star increases if the object moves away (one speaks about Décalage towards the red) and decreases if it approaches (shift towards blue).

Radial velocity measurement

The radial speed of a star or another distant luminous object can be measured precisely by taking a spectrum with high-resolution and by comparing measured the wavelengths spectral lines known with the wavelengths of these same lines measured in laboratory. By convention, a positive radial speed indicates that the object moves away and a negative speed that the object approaches.

Formulate mathematical

In practice, which one measurement is the shift of a spectral line. If one notes $\backslash \; lambda\_0$ the wavelength of the spectral line which would be measured if the object were at rest and $\backslash \; lambda\_\; \{\backslash \; rm\; m\}$ the measured wavelength, radial speed v is written

$v\_\; \{\backslash \; rm\; R\}\; =\; \backslash \; frac\; \{1\}\; \{C\}\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; lambda\_\; \{\backslash \; rm\; m\}\}\; \{\backslash \; lambda\_0\}\; -\; 1\; \backslash \; right)$,

where C is the Speed of light. In practice this formula is worth only for low speeds, i.e. speed significantly lower than speed of light. In particular, the concept radial speed is not very relevant in Cosmologie where the Expansion of the universe should not be seen in term of displacement of objects in space, but in term of an expansion of space itself.

Nonradial component speed

Radial speed does not give the value of the Vecteur speed of the object, but only the component of this one on the line of sight. To know the other component, i.e. the orthogonal component with the line of sight, it is in general necessary to observe the own Mouvement of the object on the celestial sphere, and to know its distance. These two components are often difficult to determine, in particular the first, in general unknown for objects located out of our Galaxie. For the Pulsar S, it is also possible to determine their orthogonal speed by measuring very precisely to them radial Accélération. This method rests on a very simple physical phenomenon called the Effet Shklovski. However, in the case of the pulsars, it is the radial speed which is difficult to determine.

Applications

Binary stars

For much of binary stars, the orbital movement often involves variations radial speed of several Kilomètre S by second. As the spectrum of these stars varies because of the Doppler effect, they are called binary spectroscopic. The studies radial speed can be used to force the masses of stars thus some orbital elements, such as the eccentricity, even the Equatorial radius if the masses are in addition given. The same method is also used to detect Planet S around stars. In practice, knowing the radial speed and the orbital Period of the system, one deducts a quantity called function from mass, depend on the mass on the two objects and Inclinaison of the orbital Plan of the system. Whenever some of these quantities can be deduced (for example in a Binaire X, one of both masses is in general very close to the Masse of Chandrasekhar if the compact Objet of the system is a neutron star; the slope can be estimated if one observes the phenomenon of eclipse S - one speaks then about Binaire to eclipses).

Exoplanètes

The method known as of Méthode radial speeds is today most effective to detect Exoplanète S around a star. In this situation, the mass of planet is very low, causing a weak but measurable movement of star. This movement can be transcribed thereafter using the function of mass like a measurement of a certain combination of the mass of two stars and slope of its orbital plan. If the spectrum of star is sufficiently well measurement, one can starting from his spectral Type and of his distance (if it is known) to estimate his mass. Knowing the mass of star, one deducts then the quantity M   sin  I , where M is the mass of planet and sin  I the Sine of the slope of the system. That gives an estimate (actually a lower limit) to the mass of planet.

See too

• Movement of a clean star

• Movement
• Function of mass
• Effect Shklovski
• Expansion of the universe
• Method radial speeds

References

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