  We estimate the density laws of the Galactic stellar populations as a
function of absolute magnitude in a near-polar Galactic field. The density laws
are determined by the direct fit to photometric parallaxes from Vega photometry
in the ELAIS (l=84.27, b=+44.90; 6.571 deg^2) field both independently for each
population and simultaneously for all stellar populations. Stars have been
separated into different populations based on their spatial location. The thick
disc and halo best fit by an exponential. However, the thin disc best fits by
using a sech^2 law for stars at faint absolute magnitudes, (10,11], (11,12] and
(12,13], whereas an exponential law for stars at relatively bright absolute
magnitudes, (5,6], (6,7], (7,8], (8,9] and (9,10]. The scaleheights for the
sech^2 density laws are the equivalent exponential scaleheights. Galactic model
parameters are absolute magnitude dependent: The scaleheight for thin disc
decreases monotonically from stars at bright absolute magnitudes to stars at
faint absolute magnitudes in the range 363-163 pc, except the minimum H=211 pc
at (9,10] where sech density law fits better. Its local density is flat at
bright absolute magnitudes but it increases at faint absolute magnitudes. For
thick disc, the scaleheight is flat within the uncertainties. The local space
density of thick disc relative to the local space density for the thin disc is
almost flat at absolute magnitude intervals (5,6] and (6,7], 7.59 and 7.41%
respectively, whereas it decreases down to 3.31% at absolute magnitude interval
(7,8]. The axial ratio for the halo is e=0.60, 0.73 and 0.78 for the absolute
magnitude intervals (4,5], (5,6] and (6,7] respectively, and its local space
density relative to the local space density for the thin disc is 0.06 and 0.04%
for the intervals (5,6], and (6,7] respectively.

Astrophysics