  Pulsar Timing Array (PTA) collaborations reported evidence of a nano-Hz
stochastic gravitational wave background (sGWB) compatible with an
adiabatically inspiraling population of massive black hole binaries (MBHBs).
Despite the large uncertainties, the relatively flat spectral slope of the
recovered signal suggests a possible prominent role of MBHB dynamical coupling
with the environment or/and the presence of an eccentric MBHB population. This
work aims at studying the capabilities of future PTA experiments to detect
single MBHBs under the realistic assumption that the sGWB is originated from an
eccentric binary population coupled with its environment. To this end, we
generalize the standard signal-to-noise ratio (SNR) and Fisher Information
Matrix calculations used in PTA for circular MBHBs to the case of eccentric
systems. We consider an ideal 10-year MeerKAT and 30-year SKA PTAs and apply
our method over a wide number of simulated eccentric MBHB populations. We find
that the number of resolvable MBHBs for the SKA (MeerKAT) PTA is ${\sim}\,30$
($4$) at $\rm SNR\,{>}\,5$ (${>}\,3$), featuring an increasing trend for larger
eccentricity values of the MBHB population. This is the result of eccentric
MBHBs at ${\lesssim}\,10^{-9}\, \rm Hz$ emitting part of their power at high
harmonics, thus reaching the PTA sensitivity band. Our results also indicate
that resolved MBHBs do not follow the eccentricity distribution of the
underlying MBHB population, but prefer low eccentricity values (${<}\,0.6$).
Finally, the recovery of binary intrinsic properties and sky-localization do
not depend on the system eccentricity, while orbital parameters such as
eccentricity and initial orbital phase show clear trends. Although simplified,
our results show that SKA will enable the detection of tens of MBHBs,
projecting us into the era of precision gravitational wave astronomy at nano-Hz
frequencies.
