Binary Masses with Limited Information
In practical applications of mass determination we are often faced with
insufficient information to apply the preceding method. This is
typically because of some combination of two problems:
- We may not be able to
map the orbits exactly (obviously true if the binary is astrometric and we see only
one star).
-
Even if the orbits can be mapped, they correspond to the
2-dimensional projections on the celestial sphere of the true 3-dimensional orbit
and further information is required to construct the true orbit.
In these instances, we often can only determine only the sum of the masses rather
than the individual masses, or we may only be able to place limits on the
masses rather than actually determine them.
In the case of astrometric binaries, we can often find families of solutions for
masses or limits on the masses if certain assumptions are made about the system
such as the mass of the primary (which can often be estimated indirectly from
systematics of its luminosity and spectral type).