  We find that, under certain conditions, protoplanetary disks may
spontaneously generate multiple, concentric gas rings without an embedded
planet through an eccentric cooling instability. Using both linear theory and
non-linear hydrodynamics simulations, we show that a variety of background
states may trap a slowly precessing, one-armed spiral mode that becomes
unstable when a gravitationally-stable disk rapidly cools. The angular momentum
required to excite this spiral comes at the expense of non-uniform mass
transport that generically results in multiple rings. For example, one
long-term hydrodynamics simulation exhibits four long-lived, axisymmetric gas
rings. We verify the instability evolution and ring formation mechanism from
first principles with our linear theory, which shows remarkable agreement with
the simulation results. Dust trapped in these rings may produce observable
features consistent with observed disks. Additionally, direct detection of the
eccentric gas motions may be possible when the instability saturates, and any
residual eccentricity leftover in the rings at later times may also provide
direct observational evidence of this mechanism.
