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We study the gravitationally-dominated, accretion-driven evolution of aprestellar core. In our model, as the core's density increases, it remainsimmersed in a constant-density environment and so it accretes from thisenvironment, increasing its mass and reducing its Jeans length. Assuming apower-law density profile $\rho \propto r^{-p}$, we compute the rate of changeof 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 smallerthan its Jeans length, thus appearing gravitationally stable and in need ofpressure confinement, while, in reality, it is part of a larger-scale collapseand is undergoing compression by the infalling material. In this region, theinfall speed decreases towards the center, eventually becoming subsonic, thusappearing "coherent", without the need for turbulence dissipation. We present acompilation of observational determinations of density profiles in dense coresand 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 discussthe 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 themass to magnetic flux ratio also decreases towards the central parts of thecores, making them appear magnetically supported, while in reality they may bepart of larger collapsing supercritical region. We conclude that localsignatures of either thermal or magnetic support are not conclusive evidence ofstability, that the gravitational instability of a region must be establishedat the large scales, and that the prestellar stage of collapse is dynamicrather than quasistatic.

Density profile evolution during prestellar core collapse: Collapse starts at the large scale