  Motivated by astrophysical observations of excess electronic production in
the galaxy, new theoretical models of the dark matter sector have been proposed
in which the Standard model couples to the dark matter sector through an
attractive interaction. The coupling of the Standard model to "dark strings",
which are solutions of the low energy dark sector has been investigated
recently. Here, we discuss the interaction between dark strings and standard
cosmic strings and show that they can form bound states. In the presence of the
interaction term, a Bogomolny-Prasad-Sommerfield (BPS) bound exists that
depends on the interaction parameter and we observe that the attractive
interaction between dark strings and cosmic strings is most efficient if the
two strings are identical. Moreover, our model allows for dark string solution
that can lower their energy by coupling to an electromagnetic field. We also
investigate the gravitational properties of these solutions and show that they
become supermassive with a singular space-time for values of the gravitational
coupling larger as compared to the non-interacting case. Moreover, the deficit
angle of the solutions decreases with increasing interaction.
