Soliton Oscillations and Revised Constraints from Eridanus II of Fuzzy
  Dark Matter
  Fuzzy dark matter (FDM) has been a promising alternative to standard cold
dark matter. The model consists of ultralight bosons with mass $m_b \sim
10^{-22}$ eV and features a quantum-pressure-supported solitonic core that
oscillates. In this work, we show that the soliton density oscillations persist
even after significant tidal stripping of the outer halo. We report two
intrinsic yet distinct timescales associated, respectively, with the
ground-state soliton wavefunction $\tau_{00}$ and the soliton density
oscillations $\tau_\text{soliton}$, obeying $\tau_\text{soliton} /\tau_{00}
\simeq 2.3$. The central star cluster (SC) in Eridanus II has a characteristic
timescale $\tau_\text{soliton} / \tau_\text{SC} \sim 2$ to $3$ that deviates
substantially from unity. As a result, we demonstrate, both analytically and
numerically with three-dimensional self-consistent FDM simulations, that the
gravitational heating of the SC owing to soliton density oscillations is
negligible irrespective of $m_b$. We also show that the subhalo mass function
to form Eridanus II does not place a strong constraint on $m_b$. These results
are contrary to the previous findings by Marsh & Niemeyer (2019).
