Imaging the water snowline around protostars with water and HCO$^+$ isotopologues

Abstract: The water snowline location in protostellar envelopes provides crucial information about the thermal structure and the mass accretion process as it can inform about the occurrence of recent ($\lesssim$1,000 yr) accretion bursts. In addition, the ability to image water emission makes these sources excellent laboratories to test indirect snowline tracers such as H$^{13}$CO$^+$. We study the water snowline in five protostellar envelopes in Perseus using a suite of molecular line observations taken with the Atacama Large Millimeter/submillimeter Array (ALMA) at $\sim$0.2$^{\prime\prime}-$0.7$^{\prime\prime}$ (60--210 au) resolution. B1-c provides a textbook example of compact H$2^{18}$O ($3{1,3}-2_{2,0}$) and HDO ($3_{1,2}-2_{2,1}$) emission surrounded by a ring of H$^{13}$CO$^+$ ($J=2-1$) and HC$^{18}$O$^+$ ($J=3-2$). Compact HDO surrounded by H$^{13}$CO$^+$ is also detected toward B1-bS. The optically thick main isotopologue HCO$^+$ is not suited to trace the snowline and HC$^{18}$O$^+$ is a better tracer than H$^{13}$CO$^+$ due to a lower contribution from the outer envelope. However, since a detailed analysis is needed to derive a snowline location from H$^{13}$CO$^+$ or HC$^{18}$O$^+$ emission, their true value as snowline tracer will lie in the application in sources where water cannot be readily detected. For protostellar envelopes, the most straightforward way to locate the water snowline is through observations of H$_2^{18}$O or HDO. Including all sub-arcsecond resolution water observations from the literature, we derive an average burst interval of $\sim$10,000 yr, but high-resolution water observations of a larger number of protostars is required to better constrain the burst frequency.