$\Delta$ isobars in hyperon stars in a modified quark meson coupling model

The possibility of the appearance of $\Delta$ isobars in neutron star matter and the so called {\it $\Delta$ puzzle} is studied in a modified quark meson coupling model where the confining interaction for quarks inside a baryon is represented by a phenomenological average potential in an equally mixed scalar-vector harmonic form. The hadron-hadron interaction in nuclear matter is then realized by introducing additional quark couplings to $\sigma$, $\omega$, and $\rho$ mesons through mean-field approximations. The couplings of the $\Delta$ to the meson fields are fixed from available constraints while the hyperon couplings are fixed from the optical potential values. It is observed that within the constraints of the mass of the precisely measured massive pulsars, PSR J0348+0432 and PSR J1614-2230, neutron stars with a composition of both $\Delta$ isobars and hyperons is possible. It is also observed that with an increase in the vector coupling strength of the $\Delta$ isobars there is a decrease in the radius of the neutron stars.