Gravitational radiation from corotating binary neutron stars of incompressible fluid in the first post-Newtonian approximation of general relativity

We analytically study gravitational radiation from corotating binary neutron stars composed of an incompressible, homogeneous fluid in circular orbits. The energy and the angular momentum loss rates are derived up to the first post-Newtonian (1PN) order beyond the quadrupole approximation including effects of the finite size of each of the binary stars. It is found that the leading term of finite size effects in the 1PN order is only ${O(GM}_{*}{/c}^{2}{a}_{*})$ smaller than that in Newtonian order, where ${\mathrm{GM}}_{*}{/c}^{2}{a}_{*}$ means the ratio of the gravitational radius to the mean radius of each binary star, and the 1PN term acts to decrease the Newtonian finite size effect in gravitational radiation.