We propose an evolutionary path for prestellar cores on the radius-mass diagram, which is analogous to stellar evolutionary paths on the Hertzsprung-Russell Diagram. Using James Clerk Maxwell Telescope (JCMT) observations of L1688 in the Ophiuchus star-forming complex, we analyse the HCO+ (J=4rightarrow3) spectral line profiles of prestellar cores. We find that of the 58 cores observed, 14 show signs of infall in the form of a blue-asymmetric double-peaked line profile. These 14 cores all lie beyond the Jeans mass line for the region on a radius-mass plot. Furthermore another 10 cores showing tentative signs of infall, in their spectral line profile shapes, appear on or just over the Jeans mass line. We therefore propose the manner in which a prestellar core evolves across this diagram. We hypothesise that a core is formed in the low-mass, low-radius region of the plot. It then accretes quasistatically, increasing in both mass and radius. When it crosses the limit of gravitational instability it begins to collapse, decreasing in radius, towards the region of the diagram where protostellar cores are seen.
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