Physical parameters derived from APEX observations. Top row : gas kinetic temperature and corresponding errors obtained from molecular line ratios. Cyan circles show the temperature obtained from DCO⁺ J=5-4/J=3-2, orange squares show the average temperature obtained from the three H₂CO ratios, and black diamonds show the average temperature obtained from the two c-C₃H₂ ratios. Upper limits are indicated with a downward arrow. The horizontal dash-dotted red line indicates the average gas kinetic temperature (T_kin ~15 K) derived from the I(HCN)∕I(HNC) J =1-0 (Paper I). The gray crosses show the gas kinetic temperature from NH₃ observations (T_kin,NH3) obtained from the core catalog of Rosolowsky et al. (2008). The left and right panels plot gas kinetic temperature versus bolometric luminosity (L_bol) and envelope dust mass (M_env), respectively. Bottom row : column density for DCO⁺ (cyan circles), H₂CO (orange squares), and c-C₃H₂ (black diamonds) obtained from the respective lowest transition in the APEX data. Solid lines and shaded areas show the linear regression for the data with the corresponding color. The left and right panels plot column density versus L_bol and M_env. Error bars are smaller than the symbols.