  Recent results from pulsar timing arrays (PTAs) show evidence for a
gravitational wave background (GWB) consistent with a population of unresolved
supermassive black hole (SMBH) binaries (BHBs). While the data do not yet
constrain the slope of the spectrum, this appears to flatten at the lowest
frequencies, deviating from the power-law shape expected for circular binaries
evolving solely due to gravitational wave (GW) emission. Interestingly, such
flattening can be explained with a population of eccentric rather than circular
binaries. The eccentricity of BHBs is notoriously difficult to predict based
simply on the parameters of the host galaxies and the initial galactic orbit,
as it is subject to stochastic effects. We study the evolution of the
eccentricity of BHBs formed in galactic mergers with cosmological initial
conditions from pairing to coalescence, with a focus on potential PTA sources.
We select galactic mergers from the IllustrisTNG100-1 simulation and
re-simulate them at high resolution with the N-body code Griffin down to binary
separations of the order of a parsec. We then estimate coalescence timescales
with a semi-analytical model of the evolution under the effects of GW emission
and stellar hardening. We find that most mergers in IllustrisTNG100-1 occur on
highly eccentric orbits, and that the eccentricity of BHBs at binary formation
correlates with the initial eccentricity of the merger, if this is no larger
than approximately 0.9. For extremely eccentric mergers, the binaries tend to
form with modest eccentricities. We discuss the implications of these results
on the interpretation of the observed GWB.
