Optimizing measurements of cluster velocities and temperatures for
  CCAT-prime and future surveys
  Galaxy cluster velocity correlations and mass distributions are sensitive
probes of cosmology and the growth of structure. Upcoming microwave surveys
will enable extraction of velocities and temperatures from many individual
clusters for the first time. We forecast constraints on peculiar velocities,
electron temperatures, and optical depths of galaxy clusters obtainable with
upcoming multi-frequency measurements of the kinematic, thermal, and
relativistic Sunyaev-Zeldovich effects. The forecasted constraints are compared
for different measurement configurations with frequency bands between 90 GHz
and 1 THz, and for different survey strategies for the 6-meter CCAT-prime
telescope. We study methods for improving cluster constraints by removing
emission from dusty star forming galaxies, and by using X-ray temperature
priors from eROSITA. Cluster constraints are forecast for several model cluster
masses. A sensitivity optimization for seven frequency bands is presented for a
CCAT-prime first light instrument and a next generation instrument that takes
advantage of the large optical throughput of CCAT-prime. We find that
CCAT-prime observations are expected to enable measurement and separation of
the SZ effects to characterize the velocity, temperature, and optical depth of
individual massive clusters ($\sim10^{15}\,M_\odot$). Submillimeter
measurements are shown to play an important role in separating these components
from dusty galaxy contamination. Using a modular instrument configuration with
similar optical throughput for each detector array, we develop a rule of thumb
for the number of detector arrays desired at each frequency to optimize
extraction of these signals. Our results are relevant for a future "Stage IV"
cosmic microwave background survey, which could enable galaxy cluster
measurements over a larger range of masses and redshifts than will be
accessible by other experiments.
