Binary mass function

In astronomy, the binary mass function or simply mass function is a function that constrains the mass of the unseen component (typically a star or exoplanet) in a single-lined spectroscopic binary star or 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 (limited) information on the separation and gravitational attraction between the two components, and hence on the masses of the components.

The binary mass function follows from Kepler's third law when the radial velocity of one (observed) binary component is introduced. Kepler's third law describes the motion of two bodies orbiting a common center of mass. It relates the orbital period (the time it takes to complete one full orbit) with the distance between the two bodies (the orbital separation), and the sum of their masses. For a given orbital separation, a higher total system mass implies higher orbital velocities. On the other hand, for a given system mass, a longer orbital period implies a larger separation and lower orbital velocities.

Because the orbital period and orbital velocities in the binary system are related to the masses of the binary components, measuring these parameters provides some information about the masses of one or both components. But because the true orbital velocity cannot be determined generally, this information is limited.

Radial velocity is the velocity component of orbital velocity in the line of sight of the observer. Unlike true orbital velocity, radial velocity can be determined from Doppler spectroscopy of spectral lines in the light of a star, or from variations in the arrival times of pulses from a radio pulsar. A binary system is called a single-lined spectroscopic binary if the radial motion of only one of the two binary components can be measured. In this case, a lower limit on the mass of the other (unseen) component can be determined.

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