N2H+ observations of molecular cloud cores in Taurus with the Nobeyama 45 m radio telescope are reported. We compare "cores with young stars" with "cores without young stars". The differences in core radius, linewidth, and core mass are small. Linewidth is dominated by thermal motions in both cases. N2H+ maps show that the intensity distribution does not differ much between cores without stars and those with stars. This is in contrast to the result previously obtained in H13CO+ toward Taurus

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... ecular cloud cores. Larger degree of depletion of H13CO+ in starless cores will be one possible explanation for this difference. We studied the physical state of molecular cloud cores in terms of "critical pressure" for the surface (external) pressure. There is no systematic difference between starless cores and cores with stars in this analysis. Both are not far from the critical state for pressure equilibrium. We suggest that molecular cloud cores in which thermal support is dominated evolve toward star formation by keeping close to the critical state. This result is in contrast with that obtained in the intermediate-mass star forming region OMC-2/3, where molecular cloud cores evolve by decreasing the critical pressure appreciably. We investigate the radial distribution of the integrated intensity. Cores with stars are found to have shallow (-1.8 to -1.6) power-law density profiles.