  The atomic hydrogen gas (HI) disk in the outer region (beyond ~10 kpc from
the centre) of Milky Way can provide valuable information about the structure
of the dark matter halo. The recent 3-D thickness map of the outer HI disk from
the all sky 21-cm line LAB survey, gives us a unique opportunity to investigate
the structure of the dark matter halo of Milky Way in great detail. A striking
feature of this new survey is the North-South asymmetry in the thickness map of
the atomic hydrogen gas. Assuming vertical hydrostatic equilibrium under the
total potential of the Galaxy, we derive the model thickness map of the HI gas.
We show that simple axisymmetric halo models, such as softened isothermal halo
(producing a flat rotation curve with V_c ~ 220 km/s) or any halo with density
falling faster than the isothermal one, are not able to explain the observed
radial variation of the gas thickness. We also show that such axisymmetric
halos along with different HI velocity dispersion in the two halves, cannot
explain the observed asymmetry in the thickness map. Amongst the
non-axisymmetric models, it is shown that a purely lopsided (m=1, first
harmonic) dark matter halo with reasonable HI velocity dispersion fails to
explain the North-South asymmetry satisfactorily. However, we show that by
superposing a second harmonic (m=2) out of phase onto a purely lopsided halo
e.g. our best fit and more acceptable model A (with parameters
\epsilon_{h}^{1}=0.2, \epsilon_{h}^{2}=0.18 and \sigma_{HI}=8.5 km/s) can
provide an excellent fit to the observation and reproduce the North-South
asymmetry naturally. The emerging picture of the asymmetric dark matter halo is
supported by the \Lambda CDM halos formed in the cosmological N-body
simulation.
