This paper discusses the statistics of internal motions in starless dense cores and the relation of these motions to core density and evolution. Four spectral lines from three molecular species are analyzed from single-pointing and mapped observations of several tens of starless cores. Blue asymmetric profiles are dominant, indicating that inward motions are prevalent in sufficiently dense starless cores. These blue profiles are found to be more abundant, and their asymmetry is bluer, at core positions with stronger N2H+ line emission or higher column density. Thirty-three starless cores are classified into four different types according to the blueshift and redshift of the lines in their molecular line maps. Among these cores, contracting motions dominate: 19 are classified as contracting, 3 as oscillating, 3 as expanding, and 8 as static. Contracting cores have inward motions all over the core with those motions predominating near the region of peak density. Cores with the bluest asymmetry tend to have greater column density than other cores and all five cores with peak column density >6x1021/cm2 are found to be contracting. This suggests that starless cores are likely to have contracting motions if they are sufficiently condensed. Our classification of the starless cores may indicate a sequence of core evolution in the sense that column density increases from static to contracting cores: the static cores in the earliest stage, the expanding and/or the oscillating cores in the next, and the contracting cores in the latest stage.
ISM: clouds - ISM: kinematics and dynamics