  We present a detailed analysis of the expected signal-to-noise ratios of
supermassive black hole binaries on eccentric orbits observed by pulsar timing
arrays. We derive several analytical relations that extend the results of
Peters and Mathews [Phys. Rev. D 131, 435 (1963)] to quantify the impact of
eccentricity in the detection of single resolvable binaries in the pulsar
timing array band. We present ready-to-use expressions to compute the
increase/loss in signal-to-noise ratio of eccentric single resolvable sources
whose dominant harmonic is located in the low/high frequency sensitivity regime
of pulsar timing arrays. Building upon the work of Phinney
(arXiv:astro-ph/0108028) and Enoki and Nagashima [Prog. Theor. Phys. 117, 241
(2007)], we present an analytical framework that enables the construction of
rapid spectra for a stochastic gravitational-wave background generated by a
cosmological population of eccentric sources. We confirm previous findings
which indicate that, relative to a population of quasicircular binaries, the
strain of a stochastic, isotropic gravitational-wave background generated by a
cosmological population of eccentric binaries will be suppressed in the
frequency band of pulsar timing arrays. We quantify this effect in terms of
signal-to-noise ratios in a pulsar timing array.
