N2h+ observations of molecular cloud cores in Taurus

N2H+ observations of molecular cloud cores in Taurus with the Nobeyama 45 m radio telescope are reported. We compare cores with young stars to cores without young stars. The differences in core radius, line width, and core mass are small. Line width 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 (HCO+)-C-13 toward Taurus molecular cloud cores. A larger degree of depletion of (HCO+)-C-13 in starless cores is 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 equilibrium state. We suggest that molecular cloud cores in which thermal support dominates evolve toward star formation by keeping close to the critical equilibrium state. This result is in contrast to that obtained in the intermediate-mass star-forming region OMC-2/3, where molecular cloud cores evolve by decreasing the critical pressure ( dissipating turbulence). 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.