2011ApJ...743..152O

We present millimeter-wave observations of several molecular ions in the disk around the pre-main-sequence star DM Tau and use these to investigate the ionization fraction in different regions of the disk. New Submillimeter Array (SMA) observations of H₂D⁺ J = 1_1, 0_–11, 1_, N₂H⁺ J = 4-3, and CO J = 3-2 are presented. H₂D⁺ and N₂H⁺ are not detected and using the CO 3-2 disk size the observations result in an upper limit of <0.47 K km/s for both lines, a factor of 2.5 below previous single-dish H₂D⁺ observations. Assuming LTE, a disk midplane temperature of 10-20 K and estimates of the H₂D⁺ o/p ratio, the observed limit corresponds to N_H2D+ < 4-21x10¹²/cm2. We adopt a parametric model for the disk structure from the literature and use new IRAM 30 m telescope observations of the H¹³CO⁺ J = 3-2 line and previously published SMA observations of the N₂H⁺ J = 3-2, HCO⁺ J = 3-2, and DCO⁺ J = 3-2 lines to constrain the ionization fraction, x_i, in three temperature regions in the disk where theoretical considerations suggest different ions should dominate: (1) a warm, upper layer with T >20 K where CO is in the gas phase and HCO⁺ is most abundant, where we estimate x_i≃ 4x10^–10; (2) a cooler molecular layer with T = 16-20 K where N₂H⁺ and DCO⁺ abundances are predicted to peak, with x_i≃ 3x10^–11; and (3) the cold, dense midplane with T <16 K where H⁺₃ and its deuterated isotopologues are the main carriers of positive charge, with x_i< 3x10^–10. While there are considerable uncertainties, these estimates are consistent with a decreasing ionization fraction into the deeper, colder, and denser disk layers. Stronger constraints on the ionization fraction in the disk midplane will require not only substantially more sensitive observations of the H₂D⁺ 1_1, 0_–11, 1_line, but also robust determinations of the o/p ratio, observations of D₂H⁺, and stronger constraints on where N₂ is present in the gas phase.