Observations of up to ten carbon monoxide ( CO and isotopomers ) transitions are presented to study the interstellar C ^ { 18 } O/C ^ { 17 } O ratio towards 21 positions in the nearby ( d \sim 140 pc ) low-mass star forming cloud \rho Oph .
A map of the C ^ { 18 } O J =1–0 distribution of parts of the cloud is also shown .
An average ^ { 12 } C ^ { 18 } O/ ^ { 12 } C ^ { 17 } O isotopomeric ratio of 4.11 \pm 0.14 , reflecting the ^ { 18 } O/ ^ { 17 } O isotope ratio , is derived from Large Velocity Gradient ( LVG ) calculations .
From LTE column densities we derive a ratio of 4.17 \pm 0.26 .
These calculations also show that the kinetic temperature decreases from about 30 K in the cloud envelope to about 10 K in the cloud cores .
This decrease is accompanied by an increase of the average molecular hydrogen density from 10 ^ { 4 } cm ^ { -3 } to \ga 10 ^ { 5 } cm ^ { -3 } .
Towards some lines of sight C ^ { 18 } O optical depths reach values of order unity .