  Starless cores represent the initial stage of evolution toward (proto)star
formation, and a subset of them, known as prestellar cores, with high density
(~ 10^6 cm^-3 or higher) and being centrally concentrated are expected to be
embryos of (proto)stars. Determining the density profile of prestellar cores,
therefore provides an important opportunity to gauge the initial conditions of
star formation. In this work, we perform rigorous modeling to estimate the
density profiles of three nearly spherical prestellar cores among a sample of
five highly dense cores detected by our recent observations. We employed
multi-scale observational data of the (sub)millimeter dust continuum emission
including those obtained by SCUBA-2 on the JCMT with a resolution of ~5600 au
and by multiple ALMA observations with a resolution as high as ~480 au. We are
able to consistently reproduce the observed multi-scale dust continuum images
of the cores with a simple prescribed density profile, which bears an inner
region of flat density and a r^-2 profile toward the outer region. By utilizing
the peak density and the size of the inner flat region as a proxy for the
dynamical stage of the cores, we find that the three modeled cores are most
likely unstable and prone to collapse. The sizes of the inner flat regions, as
compact as ~500 au, signify them being the highly evolved prestellar cores
rarely found to date.
