Constraining Spatial Densities of Early Ice Formation in Small Dense Molecular Cores from Extinction Maps

Tracing dust in small dense molecular cores is a powerful tool to study the conditions required for ices to form during the pre-stellar phase. To study these environments, five molecular cores were observed: three with ongoing low-mass star formation (B59, B335, and L483) and two starless collapsing cores (L63 and L694-2). Deep images were taken in the infrared JHK bands with the United Kingdom Infrared Telescope (UKIRT) WFCAM (Wide Field Camera) instrument and IRAC channels 1 and 2 on the Spitzer Space Telescope. These five photometric bands were used to calculate extinction along the line of sight toward background stars. After smoothing the data, we produced high spatial resolution extinction maps ($\sim$13-29") . The maps were then projected into the third dimension using the AVIATOR algorithm implementing the inverse Abel transform. The volume densities of the total hydrogen were measured along lines of sight where ices (H$_2$O, CO, and CH$_3$OH) have previously been detected. We find that lines of sight with pure CH$_3$OH or a mixture of CH$_3$OH with CO have maximum volume densities above 1.0$\times$10$^5$ cm$^{-3}$. These densities are only reached within a small fraction of each of the cores ($\sim$0.3-2.1%). CH$_3$OH presence may indicate the onset of complex organic molecule formation within dense cores and thus we can constrain the region where this onset can begin. The maximum volume densities toward star-forming cores in our sample ($\sim$1.2-1.7$\times$10$^6$ cm$^{-3}$) are higher than those toward starless cores ($\sim$3.5-9.5$\times$10$^5$ cm$^{-3}$).