We report the results of an HCO ^ { + } ( 3–2 ) and N _ { 2 } D ^ { + } ( 3–2 ) molecular line survey performed toward 91 dense cores in the Perseus molecular cloud using the James Clerk Maxwell Telescope , to identify the fraction of starless and protostellar cores with systematic radial motions .
We quantify the HCO ^ { + } asymmetry using a dimensionless asymmetry parameter { \delta } _ { v } , and identify 20 cores with significant blue or red line asymmetries in optically-thick emission indicative of collapsing or expanding motions , respectively .
We separately fit the HCO ^ { + } profiles with an analytic collapse model and determine contraction ( expansion ) speeds toward 22 cores .
Comparing the { \delta } _ { v } and collapse model results , we find that { \delta } _ { v } is a good tracer of core contraction if the optically-thin emission is aligned with the model-derived systemic velocity .
The contraction speeds range from subsonic ( 0.03 \mathrm { km s ^ { -1 } } ) to supersonic ( 0.4 \mathrm { km s ^ { -1 } } ) , where the supersonic contraction speeds may trace global rather than local core contraction .
Most cores have contraction speeds significantly less than their free-fall speeds .
Only 7 of 28 starless cores have spectra well-fit by the collapse model , which more than doubles ( 15 of 28 ) for protostellar cores .
Starless cores with masses greater than the Jeans mass ( M / M _ { \mathrm { J } } > 1 ) are somewhat more likely to show contraction motions .
We find no trend of optically-thin non-thermal line width with M / M _ { \mathrm { J } } , suggesting that any undetected contraction motions are small and subsonic .
Most starless cores in Perseus are either not in a state of collapse or expansion , or are in a very early stage of collapse .