Modeling Two First Hydrostatic Core Candidates Barnard 1b-N and 1b-S

A first hydrostatic core (FHC) is proposed to form after the initial collapse of a prestellar core, as a seed of a Class 0 protostar. FHCs are difficult to observe because they are small, compact, embedded, and short lived. In this work, we explored the physical properties of two well-known FHC candidates, B1-bN and B1-bS, by comparing interferometric data from Submillimeter Array (SMA) 1.1 and 1.3 mm and Atacama Large Millimeter/submillimeter Array (ALMA) 870 $\mu$m observations with simulated synthesis images of the two sources. The simulated images are based on a simple model containing a single, hot compact first-core-like component at the center surrounded by a large-scale, cold and dusty envelope described by a broken power-law density distribution with an index, $\alpha$. Our results show that the hot compact components of B1-bN and B1-bS can be described by temperatures of \sim 500 K with a size of \sim 4 au, which are in agreement with theoretical predictions of an FHC. If the $\alpha$ inside the broken radii is fixed to -1.5, we find $\alpha$ \sim -2.9 and \sim -3.3 outside the broken radii for B1-bN and B1-bS, respectively, consistent with theoretical calculations of a collapsing, bounded envelope and previous observations. Comparing the density and temperature profiles of the two sources with radiation-hydrodynamic simulations of an FHC, we find both sources lie close to, but before, the second collapse stage. We suggest that B1-bS may have started the collapsing process earlier compared to B1-bN, since a larger discontinuity point is found in its density profile.