  The vertical density distribution of stars in a galactic disc is
traditionally obtained by assuming an isothermal vertical velocity dispersion
of stars. Recent observations from SDSS, LAMOST, RAVE, Gaia etc show that this
dispersion increases with height from the mid-plane. Here we study the
dynamical effect of such non-isothermal dispersion on the self-consistent
vertical density distribution for the thin disc stars in the Galaxy, obtained
by solving together the Poisson equation and the equation of hydrostatic
equilibrium. We find that in the non-isothermal case the mid-plane density is
lower, and the scale height is higher than the corresponding values for the
isothermal distribution, due to higher vertical pressure, hence the
distribution is vertically more extended. The change is ~35% at the solar
radius for a stars-alone disc for the typical observed linear gradient of +6.7
km $s^{-1}kpc^{-1}$ and becomes even higher with increasing radii and
increasing gradients explored. The distribution shows a wing at high z, in
agreement with observations, and is fitted well by a double $sech^{2}$ , which
could be mis-interpreted as the existence of a second, thicker disc, specially
in external galaxies. We also consider a more realistic disc consisting of
gravitationally coupled stars and gas in the field of dark matter halo. The
results show the same trend but the effect of non-isothermal dispersion is
reduced due to the opposite, constraining effect of the gas and halo gravity.
Further, the non-isothermal dispersion lowers the theoretical estimate of the
total mid-plane density i.e, Oort limit value, by 16%.
