Many stars t hat appear as a single pinpoint of light in the sky, when examined by means of a spectroscope produce a spectrum which appears to be the combination of the spectra from two separate stars. If the relative positions of features on the two spectra remain unaltered, the stars are known as a SPECTRUM BINARY and they constitute a widely -separated binary system; generally no more, and usually less, can be learnt from such a system than can be learnt from the spectra of a pair of single stars. Very often, how¬ever, positions of lines in the two separate spectra are seen to move relative to one another in a regular and periodic manner and these stars are known as SPECTROSCOPIC BINARIES of course, a number of spectroscopic binaries are also visual binaries.

Let us consider each each spectrum separately – in some stars all one is a single spectrum oscillating to and fro, since its inferred companion is too faint to be soon. .At each moment in time the shift of the spectrum with respect to the laboratory frame of reference tells us the relative velocity of the Earth and the star along the line of sight i.e . the radial velocity. It is necessary to make a large number of observations well separated in time. We must allow for the motion of the Earth around the Sun, to deduce the radial velocity of the star with respect to the Sun. as a function of time. Once the binary period has been established, observations are plotted relative to this period, to obtain the radial velocity through the orbit. The period of a spectroscopic binary is usually measured in days From the velocity curves it is possible to deduce some of the orbital parameters.

The eccentricity e and longitude of periastron ? can be deduced from the shape of the velocity curve. Obviously the longitude of the node is indeterminate since the system could be rotated through an angle about our line of sight without affecting the radial velocities. However, since the orbital motion of the stars is always in the same plane, the actual velocities of the stars around the orbit can only be seen by the spectroscope as projected onto our line of sight. We only measure the radial, and not the actual, orbital velocities. Because of this, spectroscopic measurements alone do not allows to determine the value of. The magnitude of the velocity variation tells us. about the size of the system and hence, via Kepler’s Law, about the mass. When the spectra of both stars are visible we can determine the masses of both stars, each multiplied by the unknown quantity sin3i. We can, however, determine the mass ratio uniquely, being simply the inverse of the ratio of the magnitude of the velocity variations of each star. If only one spectrum is visible, the star is termed a single- rather than double-lined spectroscopic binary. In this case, we can only determine a relationship between the individual masses and the inclination angle known as the mass function.

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