Application of the formulae: one practical example

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.

• let us calculate the line strength in the scale:

we need then = 3 mK in a 6 MHz/2= 3 MHz band.

• now, :

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.

• the r.m.s. noise in a 3 MHz channel for = 1 h.

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
mK.

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).

Robert Lucas
Thu Mar 9 12:14:01 MET 1995