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We present a survey of the ortho-H2D+(1_{1,0}-1_{1,1}) line toward a sampleof 10 starless cores and 6 protostellar cores, carried out at the CaltechSubmillimeter Observatory. The high diagnostic power of this line is revealedfor the study of the chemistry, and the evolutionary and dynamical status oflow-mass dense cores. The line is detected in 7 starless cores and in 4protostellar cores. N(ortho-H2D+) ranges between 2 and 40x10^{12} cm^{-2} instarless cores and between 2 and 9x10^{12} cm^{-2} in protostellar cores. Thebrightest lines are detected toward the densest and most centrally concentratedstarless cores, where the CO depletion factor and the deuterium fractionationare also largest. The large scatter observed in plots of N(ortho-H2D+) vs. theobserved deuterium fractionation and vs. the CO depletion factor is likely tobe due to variations in the ortho-to-para (o/p) ratio of H2D+ from >0.5 forT_{kin} < 10 K gas in pre-stellar cores to ~0.03 (consistent with T_{kin} ~15 Kfor protostellar cores). The two Ophiuchus cores in our sample also require arelatively low o/p ratio (~0.3). Other parameters, including the cosmic-rayionization rate, the CO depletion factor (or, more in general, the depletionfactor of neutral species), the volume density, the fraction of dust grains andPAHs also largely affect the ortho-H2D+ abundance. The most deuterated andH2D+-rich objects (L429, L1544, L694-2 and L183) are reproduced by chemicalmodels of centrally concentrated (central densties ~10^{6} cm^{-3}) cores withchemical ages between 10^4 and 10^6 yr. Upper limits of the para-H3O+ (1_1--2_1+) and para-D2H+ (1_{1,0}-1_{0,1}) lines are also given. (Abridged)

Survey of ortho-H2D+(1_{1,0}-1_{1,1}) in dense cloud cores