CRESST detectors to recoils within the absorber that have both thermal and athermal phonon components, it makes sense to calculate the expected sensitivities of the CRESST detector to the two limiting cases of a Dirac delta thermal energy deposition into the absorber and the TES. These estimates are shown in Table \[tab:PhononEres\].

  $\sigma_{E}$: Eq. \[eq:Eres\_lim\]          1.0 eV
  ------------------------------------------- ----------------------------------------
  $\sigma_{E_{a}}$: 2D Simulated              34 eV (no 1/f) / 44 eV (1/f)
  $\sigma_{E_{t}}$: 2D Simulated              0.5 eV (no 1/f) / 0.5 eV (1/f)
  $\sigma_{E_{\gamma}}$ Measured: “Julia”     420 eV [@CRESSTII_2009_SplitDetector])
  $\sigma_{E_{\gamma}}$ Measured: Composite   107 eV [@CRESSTII_2014_LowMass])

  : Simulated and measured CRESST phonon-detector energy resolutions. Note that the simulation does not include the effect of TES phase separation.[]{data-label="tab:PhononEres"}

What is immediately striking is the significantly degraded expected sensitivity for thermal energy deposition in the absorber ($\sigma_{Ea}$) compared to that for direct absorption in the TES ($\sigma_{Et}$). To understand the cause of this suppression factor, we can write $\sigma_{Ea}$ in terms of $\sigma_{Et}$ under the now well motivated assumption that the noise, when referenced to $\delta P_{t}$, should be flat below $\omega_{S/N \, \delta \! P_{t}}$ (since it is dominated by the naturally flat $G_{tb}$):

$$\begin{split}
\lim_{ \omega_{ta} \ll \omega_{S/N \, \delta \! P_{t}}} \sigma_{Ea}^2   