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Predictions for Observing Protostellar Outflows with ALMA

Protostellar outflows provide a means to probe the accretion process of forming stars and their ability to inject energy into their surroundings. However, conclusions based on outflow observations depend upon the degree of accuracy with which their properties can be estimated. We examine the quality of Atacama Large Millimeter/submillimeter Array (ALMA) observations of protostellar outflows by producing synthetic $^{12}$CO(1-0) and $^{13}$CO(1-0) observations of numerical simulations. We use various ALMA configurations, observational parameters, and outflow inclinations to assess how accurately different assumptions and setups can recover underlying properties. We find that more compact arrays and longer observing times can improve the mass and momentum recovery by a factor of two. During the first $\sim$0.3 Myr of evolution, $^{12}$CO(1-0) is optically thick, even for velocities $|v|\ge 1$ km s$^{-1}$, and outflow mass is severely underestimated without an optical depth correction. Likewise, $^{13}$CO(1-0) is optically thick during the first $\simeq 0.1$ Myr. However, underestimation due to shorter observing time, missing flux, and optical depth are partially offset by the assumption of local thermodynamic equilibrium and higher excitation temperatures. Overall, we expect that full ALMA $^{13}$CO(1-0) observations of protostellar sources within 500 pc with observing times $\gtrsim 1$ hrs and assumed excitation temperatures of $T<20$K will reliably measure mass and line-of-sight momentum to within 20\%.