Density profile evolution during prestellar core collapse: Collapse
  starts at the large scale
  We study the gravitationally-dominated, accretion-driven evolution of a
prestellar core. In our model, as the core's density increases, it remains
immersed in a constant-density environment and so it accretes from this
environment, increasing its mass and reducing its Jeans length. Assuming a
power-law density profile $\rho \propto r^{-p}$, we compute the rate of change
of the slope $p$, and show that the value $p=2$ is stationary, and furthermore,
an attractor. The radial profile of the Jeans length scales as $r^{p/2}$,
implying that, for $p<2$, there is a radius below which the region is smaller
than its Jeans length, thus appearing gravitationally stable and in need of
pressure confinement, while, in reality, it is part of a larger-scale collapse
and is undergoing compression by the infalling material. In this region, the
infall speed decreases towards the center, eventually becoming subsonic, thus
appearing "coherent", without the need for turbulence dissipation. We present a
compilation of observational determinations of density profiles in dense cores
and show that the distribution of their slopes peaks at $p \sim 1.7$--1.9,
supporting the notion that the profile steepens over time. Finally, we discuss
the case of magnetic support in a core in which the field scales as $B \propto
\rho^\beta$. For the expected value of $\beta = 2/3$, this implies that the
mass to magnetic flux ratio also decreases towards the central parts of the
cores, making them appear magnetically supported, while in reality they may be
part of larger collapsing supercritical region. We conclude that local
signatures of either thermal or magnetic support are not conclusive evidence of
stability, that the gravitational instability of a region must be established
at the large scales, and that the prestellar stage of collapse is dynamic
rather than quasistatic.
