  We measure the non-axisymmetry in the luminosity distribution in the inner
few kpc of the remnants of advanced mergers of galaxies with a view to
understand the relaxation in the central regions. For this, we analyze the
images from the 2MASS archival data for a selected sample of 12 merging
galaxies, which show signs of interaction but have a single nucleus. The
central regions are fitted by elliptical isophotes whose centres are allowed to
vary to get the best fit. The centres of isophotes show a striking sloshing
pattern with a spatial variation of up to 20-30 % within the central 1 kpc.
This indicates mass asymmetry and a dynamically unrelaxed behaviour. Next, we
Fourier-analyze the galaxy images while keeping the centre constant and measure
the deviation from axisymmetry in terms of the fractional Fourier amplitudes
(A_1, A_2 etc) as a function of radius. All mergers show a high value of
lopsidedness (upto A_1 ~ 0.2) in the central 5 kpc. The m=2 asymmetry is even
stronger, with values of A_2 upto ~ 0.3, and in three cases these are shown to
represent bars. The corresponding values denoting non-axisymmetry in inner
regions of a control sample of eight non-merger galaxies are found to be
several times smaller. Surprisingly, this central asymmetry is seen even in
mergers where the outer regions have relaxed into a smooth elliptical-like
r^{1/4} profile or a spiral-like exponential profile. Thus the central
asymmetry is long-lived, estimated to be ~ 1 Gyr, and hence lasts for over 100
local dynamical timescales. These central asymmetries are expected to play a
key role in the future dynamical evolution of the central region of a merger,
and can help in feeding a central AGN.
