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 H _ { 2 } D ^ { + } J= 1 _ { 1 , 0 } -1 _ { 1 , 1 } , N _ { 2 } H ^ { + } J=4–3 and CO J=3–2 are presented .
H _ { 2 } D ^ { + } and N _ { 2 } H ^ { + } are not detected and using the CO 3–2 disk size the observations result in an upper limit of < 0.47 K km s ^ { -1 } for both lines , a factor of 2.5 below previous single-dish H _ { 2 } D ^ { + } observations .
Assuming LTE , a disk midplane temperature of 10–20 K and estimates of the H _ { 2 } D ^ { + } o / p ratio , the observed limit corresponds to N _ { H _ { 2 } D ^ { + } } < 4 - 21 \times 10 ^ { 12 } cm ^ { -2 } .
We adopt a parametric model for the disk structure from the literature and use new IRAM 30 meter telescope observations of the H ^ { 13 } CO ^ { + } J=3–2 line and previously published SMA observations of the N _ { 2 } H ^ { + } 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 } \simeq 4 \times 10 ^ { -10 } , ( 2 ) a cooler molecular layer with T = 16–20 K where N _ { 2 } H ^ { + } and DCO ^ { + } abundances are predicted to peak , with x _ { i } \simeq 3 \times 10 ^ { -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 } < 3 \times 10 ^ { -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 H _ { 2 } D ^ { + } 1 _ { 1 , 0 } -1 _ { 1 , 1 } line , but also robust determinations of the o / p ratio , observations of D _ { 2 } H ^ { + } and stronger constraints on where N _ { 2 } is present in the gas phase .