Significant Molecular Gas Deficiencies in Star-forming Cluster Galaxies
  at $z\sim1.4$
  We present the average gas properties derived from ALMA Band 6 dust continuum
imaging of 126 massive (log $M_{\star} / M_{\odot} \gtrsim 10.5$), star-forming
cluster galaxies across 11 galaxy clusters at $z=1-1.75$. Using stacking
analysis on the ALMA images, combined with UV-far-infrared data, we quantify
the average infrared SEDs and gas properties (molecular gas masses, $M_{\rm
mol}$; gas depletion timescales, $\tau_{\rm depl}$; and gas fractions, f$_{\rm
gas}$) as a function of cluster-centric radius and properties including stellar
mass and distance from the Main Sequence. We find a significant dearth in the
ALMA fluxes relative to that expected in the field $-$ with correspondingly low
$M_{\rm mol}$ and f$_{\rm gas}$ and short $\tau_{\rm depl}$ $-$ with weak or no
dependence on cluster-centric radius out to twice the virial radius. The
Herschel+ALMA SEDs indicate warmer dust temperatures ($\sim36-38$ K) than
coeval field galaxies ($\sim30$ K). We perform a thorough comparison of the
cluster galaxy gas properties to field galaxies, finding deficits of 2-3x,
3-4x, and 2-4x in $M_{\rm mol}$, $\tau_{\rm depl}$, and f$_{\rm gas}$ compared
to coeval field stacks and larger deficits compared to field scaling relations
built primarily on detections. The cluster gas properties derived here are
comparable with stacking analyses in (proto-)clusters in the literature and at
odds with findings of field-like $\tau_{\rm depl}$ and enhanced f$_{\rm gas}$
reported using CO and dust continuum detections. Our analysis suggests that
environment has considerable impact on gas properties out to large radii, in
good agreement with cosmological simulations which project gas depletion begins
beyond the virial radius and largely completes by first passage of the cluster
core.
