Survey of ortho-H<SUB>2</SUB>D<SUP>+</SUP> (1<SUB>1,0</SUB>-1<SUB>1,1</SUB>) in dense cloud cores

International audienceAims. We present a survey of the ortho-H2D+ (1{1,0}-1{1,1}) line toward a sample of 10 starless cores and 6 protostellar cores, carried out at the Caltech Submillimeter Observatory. The high diagnostic power of this line is revealed for the study of the chemistry, and the evolutionary and dynamical status of low-mass dense cores. Methods: The derived ortho-H2D+ column densities (N(ortho-H2D+)) are compared with predictions from simple chemical models of centrally concentrated cloud cores. Results: The line is detected in 7 starless cores and in 4 protostellar cores. N(ortho-H2D+) ranges between 2 and 40 × 1012 cm-2 in starless cores and between 2 and 9 × 1012 cm-2 in protostellar cores. The brightest lines are detected toward the densest and most centrally concentrated starless cores, where the CO depletion factor and the deuterium fractionation are also largest. The large scatter observed in plots of N(ortho-H2D+) vs. the observed deuterium fractionation and vs. the CO depletion factor is likely to be due to variations in the ortho-to-para (o/p) ratio of H2D+ from >0.5 for T_kin < 10 K gas in pre-stellar cores to ≃0.03 (consistent with T_kin ≃ 15 K for protostellar cores). The two Ophiuchus cores in our sample also require a relatively low o/p ratio (≃0.3). Other parameters, including the cosmic-ray ionization rate, the CO depletion factor (or, more in general, the depletion factor of neutral species), the volume density, the fraction of dust grains and PAHs also largely affect the ortho-H2D+ abundance. In particular, gas temperatures above 15 K, low CO depletion factors and large abundance of negatively charged small dust grains or PAHs drastically reduce the deuterium fractionations to values inconsistent with those observed toward pre-stellar and protostellar cores. The most deuterated and H2D+-rich objects (L 429, L 1544, L 694-2 and L 183) are reproduced by chemical models of centrally concentrated (central densties ≃106 cm-3) cores with chemical ages between 104 and 106 yr. Upper limits of the para-H3O+(11^-21^+) and para-D2H+ (1{1,0}-1{0,1}) lines are also given. The upper limit to the para-H3O+ fractional abundance is ≃10-8 and we find an upper limit to the para-D2H+/ortho-H2D+ column density ratio equal to 1, consistent with chemical model predictions of high density (2 × 106 cm-3) and low temperature (T_kin < 10 K) clouds. Conclusions: Our results point out the need for better determinations of temperature and density profiles in dense cores as well as for observations of para-H2D+