  In the study of dynamic charge order correlations in the cuprates, most high
energy-resolution resonant inelastic x-ray scattering (RIXS) measurements have
focused on momenta along the high-symmetry directions of the copper oxide
plane. However, electron scattering along other in-plane directions should not
be neglected as they may contain information relevant, for example, to the
origin of charge order correlations or to our understanding of the isotropic
scattering responsible for strange metal behavior in cuprates. We report
high-resolution resonant inelastic x-ray scattering (RIXS) experiments that
reveal the presence of dynamic electron correlations over the $q_x$-$q_y$
scattering plane in underdoped
$\textrm{Bi}_2\textrm{Sr}_2\textrm{Ca}\textrm{Cu}_2\textrm{O}_{8+\delta}$ with
$T_c=54$ K. We use the softening of the RIXS-measured bond stretching phonon
line as a marker for the presence of charge-order-related dynamic electron
correlations. The experiments show that these dynamic correlations exist at
energies below approximately $70$ meV and are centered around a quasi-circular
manifold in the $q_x$-$q_y$ scattering plane with radius equal to the magnitude
of the charge order wave vector, $q_{CO}$. We also demonstrate how this
phonon-tracking procedure provides the necessary experimental precision to rule
out fluctuations of short-range directional charge order (i.e. centered around
$[q_x=\pm q_{CO}, q_y=0]$ and $[q_x=0, q_y=\pm q_{CO}]$) as the origin of the
observed correlations.
