  We investigate the effect of feeble interaction of dark matter (DM) with
hadronic matter on the equation of state (EoS) and structural properties of
neutron stars (NSs) in static conditions. For the purpose we adopt the
effective chiral model for the hadronic sector and for the first time in the
context of possible existence of DM inside NSs, we introduce DM-SM interaction
through light new physics mediator. Moreover, the mass of DM fermion, the
mediator and the coupling are adopted from the self-interaction constraint from
Bullet cluster and from present day relic abundance. Within the considered
framework, the work highlights the underlying stiffening of EoS in presence of
DM fermion of mass of the order of a few GeV compared to the no-DM scenario.
Consequently, the maximum gravitational mass of NS is obtained consistent with
the bounds from the most massive pulsars which were not satisfied with the
hadronic matter EoS alone. The estimates of radius and tidal deformability of
1.4 $M_{\odot}$ NS and the tidal deformabilities of the individual components
of the binary neutron stars (BNS) associated with GW170817 are all in good
agreement with the individual constraints obtained from GW170817 observation of
BNS merger.
