We present a study of the luminosity density distribution of the Galactic bar
using number counts of red clump giants (RCGs) from the OGLE-III survey. The
data were recently published by Nataf et al. (2013) for 9019 fields towards the
bulge and have $2.94\times 10^6$ RC stars over a viewing area of $90.25
\,\textrm{deg}^2$. The data include the number counts, mean distance modulus
($\mu$), dispersion in $\mu$ and full error matrix, from which we fit the data
with several tri-axial parametric models. We use the Markov Chain Monte Carlo
(MCMC) method to explore the parameter space and find that the best-fit model
is the $E_3$ model, with the distance to the GC is 8.13 kpc, the ratio of
semi-major and semi-minor bar axis scale lengths in the Galactic plane
$x_{0},y_{0}$, and vertical bar scale length $z_0$, is $x_0:y_0:z_0 \approx
1.00:0.43:0.40$ (close to being prolate). The scale length of the stellar
density profile along the bar's major axis is $\sim$ 0.67 kpc and has an angle
of $29.4^\circ$, slightly larger than the value obtained from a similar study
based on OGLE-II data. The number of estimated RC stars within the field of
view is $2.78 \times 10^6$, which is systematically lower than the observed
value. We subtract the smooth parametric model from the observed counts and
find that the residuals are consistent with the presence of an X-shaped
structure in the Galactic centre, the excess to the estimated mass content is
$\sim 5.8%$. We estimate the total mass of the bar is $\sim 1.8 \times 10^{10}
M_\odot$. Our results can be used as a key ingredient to construct new density
models of the Milky Way and will have implications on the predictions of the
optical depth to gravitational microlensing and the patterns of hydrodynamical
gas flow in the Milky Way.Comment: 15 pages, 6 figures, 4 tables. MNRAS accepte