  We investigate the quasi-equilibrium state of one-dimensional
self-gravitating systems. If the null virial condition is satisfied at initial
time, it is found that the number density around the center of the system at
the quasi-equilibrium state has the universality similar to two- and
three-dimensional self-gravitating systems reported in
\cite{Tashiro16,Tashiro10}. The reason why the null virial condition is
sufficient for the universality is unveiled by the envelope equation. We
present a phenomenological model to describe the universal structure by using a
special Langevin equation with a distinctive random noise to self-gravitating
systems. Additionally, we unveil a mechanism which decides the radius of the
system.
