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The factors that influence protostellar multiplicity II. Gas temperature and mass in Perseus with APEX

Protostellar multiplicity is a common outcome of the star formation process. To fully understand the formation and evolution of these systems, the physical parameters of the molecular gas together with the dust must be systematically characterized. Using observations of molecular gas tracers, we characterize the physical properties of cloud cores in the Perseus molecular cloud (average distance of 295 pc) at envelope scales (5000-8000 AU). We used Atacama Pathfinder EXperiment (APEX) and Nobeyama 45m Radio Observatory (NRO) observations of DCO$^+$, H$_2$CO and c-C$_3$H$_2$ in several transitions to derive the physical parameters of the gas toward 31 protostellar systems in Perseus. Gas kinetic temperature was obtained from DCO$^+$, H$_2$CO and c-C$_3$H$_2$ line ratios. Column densities and gas masses were then calculated for each species and transition. Gas kinetic temperature and gas masses were compared with bolometric luminosity, envelope dust mass, and multiplicity to search for statistically significant correlations. Gas kinetic temperature derived from DCO$^+$, H$_2$CO and c-C$_3$H$_2$ line ratios have average values of 14 K, 26 and 16 K, respectively, with a range of 10-26 K for DCO$^+$ and c-C$_3$H$_2$. The gas kinetic temperature obtained from H$_2$CO line ratios have a range of 13-82 K. Column densities of all three molecular species are on the order of 10$^{11}$ to 10$^{14}$ cm$^{-2}$, resulting in gas masses of 10$^{-11}$ to 10$^{-9}$ M$_{\odot}$. Statistical analysis of the physical parameters finds: i) similar envelope gas and dust masses for single and binary protostellar systems; ii) multiple (>2 components) protostellar systems tend to have slightly higher gas and dust masses than binaries and single protostars; iii) a continuous distribution of gas and dust masses is observed regardless of separation between components in protostellar systems.