  Recent detections of a low-frequency gravitational wave background (GWB) from
various pulsar-timing-array (PTA) observations have renewed the interest in the
inspiraling supermassive black hole binaries (SMBHBs), whose population is
believed to be the most promising candidate of but disfavored by the observed
GWB spectrum naively fitted with purely GW-driven circular binaries. Including
either orbital eccentricity or dark matter (DM) spike can improve the fit to
the current data, but the inclusion of both can further display distinctive
features detectable in future PTA observations. With a typical initial
eccentricity $e_0\sim\mathcal{O}(0.1)$ for the inspiraling SMBHBs, even a
shallow DM spike can easily drive the orbital eccentricity close to unity,
leaving behind a large turnover eccentricity when GWs begin to dominate the
orbital circularization. In particular, the DM spike index $\gamma_\mathrm{sp}$
universally flattens the characteristic strain $h_c\sim
f^{7/6-\gamma_\mathrm{sp}/3}$ in the infrared and produces a novel structure
with an oscillating turnover followed by a flat dip and a bump-like peak at
low, intermediate, and high frequencies, respectively. Future PTA detection of
such characteristics would necessarily provide the smoking gun for the DM spike
and even reveal the nature of DM.
