into the marginally stable state, after which the increasing of velocity dispersion practically ceases in the absence of the heating mechanisms listed above (see e.g. Khoperskov et al. (2003)).

For a thin disk with parameters slowly varying with $R$ the local critical value of radial velocity dispersion of stars is defined by Toomre criterion: $c_r=c_T$, where $c_T =
{3.36 G \sigma}/{\kappa}$, $\sigma$ is the disk surface density at given $R$, $\kappa$ is epicyclic frequency determined by angular velocity $\Omega$ and its radial derivative: $$\kappa =2\Omega\cdot \sqrt{(1+(R/2\Omega)\cdot(d\Omega/dR))}.$$ A finite disk thickness makes disk more stable, while non-radial perturbations have the opposite effect (they decrease the stability threshold). The stability condition taking into account both of these effects can not be expressed in analytic form. If to express the critical radial velocity dispersion as $(c_r)_{cr}=Q\cdot c_T$, then, as numerical simulations of 2D and 3D disks show, the parameter $Q$ for a wide range of $R$ lies in the interval 1.2 — 2.5 (see e.g. Bottema (1993), Khoperskov et al. (2003)). Note, that the analytically obtained local stability condition of 2D disk taking into account non-radial perturbations gives for a flat rotation curve $Q_c\approx 3$ (Polyachenko et al. (1997)).

The assumption of marginally 