### mass function

**(binary mass function)**
(measure of binaries that constrains the masses)

For binary stars, the **mass function**
(or **binary mass function**) is a formula
of observable values that yields constraints
on the masses of the two stars, usable
if their radial velocities
can be determined through Doppler shifts.

P
——— V³
2πG

This value is equal to the following constraint on the masses:

m³
—————— sin³i
(M+m)²

**M** - mass of the same star as the velocity measurement.
**m** - mass of the other star.
**i** - inclination of the orbit with the line of sight.

The inclination is generally presumed negligible if it also transits,
and may be roughly approximated by an "average" inclination if not.
For star population studies,
useful statistics may be derived assuming the inclinations are random.

Note that the phrase, *mass function* is to indicate it
deals with physical masses.
The phrase, **mass function** is also used in probability,
for an incompatible concept: a probability mass function, which is
a function yielding the probability that some discrete
random variable takes on a given specific value.

(*binary stars,stellar mass,function*)
**Further reading:**

http://en.wikipedia.org/wiki/Binary_mass_function

**Referenced by pages:**

probability mass function (PMF)

Index