Assume that one wishes to detect with a S/N of 10 the CO(2-1) line from an extended envelope covering about the telescope main beam (). The expected line width and strengths are 6 MHz (7.8 km/s) and = 0.06 K (note that we assume in these crude calculations that we are still in the Rayleigh-Jeans regime). The line is assumed flat-topped.
we need then = 3 mK in a 6 MHz/2= 3 MHz band.
If we use the 230G1 alone with a 10 dB rejection (=0.1), K, zenith opacity , elevation = 42 applying the above formula lead to = 65 K and 410 K.
Assume we use 230G1 alone with the 1_1M filterbank. Then f=1, .
After 1h of ON+OFF integration, the r.m.s. noise in a 3 MHz band will be
We thus need theoretically to integrate during 1h 7h to reach the requested sensitivity. (If we wished to use the autocorrelator, this time would increase by a factor and would be 9 h.)
If we use the wobbling subreflector for these observations, the theoretical observing time will be 7h/R= 7/0.62= 11.3 h, to which we should add the receiver tuning (20min for 1 tuning, but one retuning after shifting the LO would be advised, so 30min) and the preparation steps (25min if this is the first observation).