  Close detached binaries were theoretically predicted to evolve into contact
by three subtypes of case A binary evolution: case AD, AR, and AS, which
correspond to the formation of contact during dynamic-, thermal-, and
nuclear-timescale mass transfer phase, respectively. It is unclear, however,
what is the difference between contact binaries in these subtypes, and whether
all of these subtypes can account for the formation of observed W UMa binaries.
Using Eggleton's stellar evolution code with the nonconservative assumption, I
obtained the low-mass contact binaries produced by case AD, AR, and AS at the
moment of contact, and their parameter spaces. The results support that the
progenitors of low-mass contact binaries are detached binaries with orbital
periods shorter than $\sim2-5\,$d, and their borderlines depend strongly on the
primary mass. In addition, the period-colour relations for case AR and AS can
be in better agreement with that for observed W UMa candidates, but case AD
shows a significantly worse agreement. Moreover, case AR and AS can produce a
short-period limit (corresponding to a low-mass limit) at almost any age, e.g.
from young age ($\sim0.2\,$Gyr) to old age ($\sim13\,$Gyr), agreeing with
observed W UMa binaries in star clusters, but no such limit occurs for case AD
at any age. These results support that case AR and AS, as opposed to case AD,
can lead to W UMa binaries (including young W UMa binaries).

Solar and Stellar Astrophysics