that thermal energy must be transported across the tiny $G_{ta}$ before it is seen by the TES. Likewise, the middle term of Eq. \[eq:dIdPa\] is a constant suppression factor because a portion of $\delta P_{a}$ is shunted through $G_{ab}$. This suppression should be small for the CRESST phonon detector. However, for the CRESST light detector, the Au wirebond pad on the substrate has an electron-phonon coupling that is larger than that of the W TES, and consequently this factor is significant [@Emilija_2008_thesis]. Another detector with significant shunting is found in CUORE where the vast majority of the absorber thermal signal flows through $G_{ab}$ [@CUORE_ThermalConductance_92].

Both the $\frac{\partial I}{\partial P_{t}}$ (Eq. \[eq:dIdPt\]) and $\frac{\partial I}{\partial P_{a}}$ (Eq. \[eq:dIdPa\]) transfer functions are important for understanding the signal response of massive calorimeters, because some of the high-energy athermal phonons produced by a particle recoil in the absorber may be collected and thermalized within the TES ($\delta P_{t}$) before they thermalize within the absorber ($\delta P_{a}$), since the electron-phonon coupling varies so significantly with phonon energy and temperature. Consequently, a true particle recoil within the absorber should be modeled within our 2 thermal DOF system as $$\begin{split}
\frac{\partial I_{t}}{\partial E_{\gamma}}  &= \frac{\partial I_{t}}{\partial P_{t}} 