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Binary systems emit gravitational waves in a well-known pattern; for binariesin circular orbits, the emitted radiation has a frequency that is twice theorbital frequency. Systems in eccentric orbits, however, emit gravitationalradiation in the higher harmonics too. In this paper, we are concerned with thestochastic background of gravitational waves generated by double neutron starsystems of cosmological origin in eccentric orbits. We consider in particularthe long-lived systems, that is, those binaries for which the time tocoalescence is longer than the Hubble time ($\sim 10$Gyr). Thus, we considerdouble neutron stars with orbital frequencies ranging from $10^{-8}$ to$2\times 10^{-6}$Hz. Although in the literature some papers consider thespectra generated by eccentric binaries, there is still space for alternativeapproaches for the calculation of the backgrounds. In this paper, we use amethod that consists in summing the spectra that would be generated by eachharmonic separately in order to obtain the total background. This method allowsus to clearly obtain the influence of each harmonic on the spectra. Inaddition, we consider different distribution functions for the eccentricitiesin order to investigate their effects on the background of gravitational wavesgenerated. At last, we briefly discuss the detectability of this background byspace-based gravitational wave antennas and pulsar timing arrays.

Stochastic Background of Gravitational Waves Generated by Eccentric Neutron Star Binaries