  We present an investigation into a hitherto unexplored systematic that
affects the accuracy of galaxy cluster mass estimates with weak gravitational
lensing. Specifically, we study the covariance between the weak lensing signal,
$\Delta\Sigma$, and the "true" cluster galaxy number count, $N_{\rm gal}$, as
measured within a spherical volume that is void of projection effects. By
quantifying the impact of this covariance on mass calibration, this work
reveals a significant source of systematic uncertainty. Using the MDPL2
simulation with galaxies traced by the SAGE semi-analytic model, we measure the
intrinsic property covariance between these observables within the 3D vicinity
of the cluster, spanning a range of dynamical mass and redshift values relevant
for optical cluster surveys. Our results reveal a negative covariance at small
radial scales ($R \lesssim R_{\rm 200c}$) and a null covariance at large scales
($R \gtrsim R_{\rm 200c}$) across most mass and redshift bins. We also find
that this covariance results in a $2-3\%$ bias in the halo mass estimates in
most bins. Furthermore, by modeling $N_{\rm gal}$ and $\Delta\Sigma$ as
multi-(log)-linear equations of secondary halo properties, we provide a
quantitative explanation for the physical origin of the negative covariance at
small scales. Specifically, we demonstrate that the $N_{\rm
gal}$-$\Delta\Sigma$ covariance can be explained by the secondary properties of
halos that probe their formation history. We attribute the difference between
our results and the positive bias seen in other works with (mock)-cluster
finders to projection effects. These findings highlight the importance of
accounting for the covariance between observables in cluster mass estimation,
which is crucial for obtaining accurate constraints on cosmological parameters.

Cosmology and Nongalactic Astrophysics