DCO$^+$ and DCN 1-0 survey toward a sample of Planck cold clumps

Deuterated molecules can be used to study the physical conditions and the astro-chemical evolution of molecular clouds. large-sample surveys for deuterated molecules are needed to understand the enhancement of deuterated molecules from diffuse molecular gas to cold cores. A single-pointing survey toward the 559 Planck cold clumps of the Early Cold Core Catalogue (ECC) has been conducted using the Arizona Radio Observatory 12-meter telescope, focusing on the $J$=1-0 transitions of DCO$^+$ and DCN. The survey included observations of 309 cores for DCO$^+$ and DCN 1-0 simultaneously, followed by 71 of these cores where DCO$^+$ 1-0 was detected for H$^{13}$CO$^+$ and H$^{13}$CN 1-0 simultaneously, aiming to determine the deuterated fraction ($D_{\rm frac}$). Additionally, 250 cores were observed for DCO$^+$, DCN, H$^{13}$CO$^+$ and H$^{13}$CN 1-0 simultaneously. Among the 309 sources, DCO$^+$ and DCN 1-0 were detected in 79 and 11 sources, with a detection rates of 25.6 % and 3.6 % respectively. In the 250 sources observed for all four species, DCO$^+$, DCN, H$^{13}$CO$^+$ and H$^{13}$CN 1-0 were detected in 58, 9, 57 and 13 sources, with a detection rate of 23.2 %, 3.6 %, 22.8 % and 5.2 % respectively. The $D_{\rm frac}$(HCO$^+$) values in 112 sources range from 0.89 % to 7.4 % with a median value of 3.1 %, while $D_{\rm frac}$(HCN) values in 11 sources range from 1.5 % to 5.5 % with a median value of 2.3 %. The line widths of DCO$^+$ and H$^{13}$CO$^+$ 1-0 detections are mostly within 1 km s$^{-1}$. The similarity in $D_{\rm frac}$ values between HCO$^+$ and HCN indicates that the higher detection rate of DCO$^+$ 1-0 compared with DCN 1-0 is due to the lower critical density of DCO$^+$ 1-0. We suggest that the enhancement of DCO$^+$ and DCN likely begins in the early diffuse stage of the molecular cloud, rather than during the cold core formation stage.