Stochastic Background of Gravitational Waves Generated by Eccentric
  Neutron Star Binaries
  Binary systems emit gravitational waves in a well-known pattern; for binaries
in circular orbits, the emitted radiation has a frequency that is twice the
orbital frequency. Systems in eccentric orbits, however, emit gravitational
radiation in the higher harmonics too. In this paper, we are concerned with the
stochastic background of gravitational waves generated by double neutron star
systems of cosmological origin in eccentric orbits. We consider in particular
the long-lived systems, that is, those binaries for which the time to
coalescence is longer than the Hubble time ($\sim 10$Gyr). Thus, we consider
double neutron stars with orbital frequencies ranging from $10^{-8}$ to
$2\times 10^{-6}$Hz. Although in the literature some papers consider the
spectra generated by eccentric binaries, there is still space for alternative
approaches for the calculation of the backgrounds. In this paper, we use a
method that consists in summing the spectra that would be generated by each
harmonic separately in order to obtain the total background. This method allows
us to clearly obtain the influence of each harmonic on the spectra. In
addition, we consider different distribution functions for the eccentricities
in order to investigate their effects on the background of gravitational waves
generated. At last, we briefly discuss the detectability of this background by
space-based gravitational wave antennas and pulsar timing arrays.
