Time Estimator Recipe:

Changelog:
Original version by Volker Ossenkopf/Carsten Kramer: March, 2003
Comment on band 6 given by Frank Helmich: May 15, 2003
Changelog made: March 2, 2004
Added explanatory note by Volker Ossenkopf on Overheads and Observing Efficiencies : 4 March 2004
Added explanatory note by Juergen Stutzki on noise in observing modes.: March 5, 2004
Added explanatory note by Maryvonne Gerin on the radiometer equation : March 18, 2004
Substantial update for measured Flight Model (FM) receiver noise: 23 April 2006
Update for HRS efficiency treatment: 23 May 2006

Use SSB system temperatures T_sys everywhere and state the values used
The efficiency of the observations will be about half that of the corresponding "ideal mode".

Definition:

T_sys : system temperature (K)
δ_ν : frequency resolution (Hz)
T_tot : total observing time (s)
A : efficiency factor

Depending on observing modes, this efficiency factor (A) is :
Frequency Switching     A = 0.25
Chopping                        A = 0.125 (incl. Double Beam Switch and Position switch)
very long OTF scans     A = 0.5
short OTF scans             A = 0.3

Using these assumptions, the formula for computing the rms noise level (antenna temperature) is for a single mixer

T_rms = T_sys / sqrt( A * δ_ν * t_tot )

For band 1-5 we have two mixers available (per band, one for each polarization), which we expect to be combined.
This would lead to a factor sqrt( 2.0 ) better in rms noise.
Bands 3, 4 and 6 have diplexers, this results in about 50% more noise in the IF-band edges compared with the center IF frequency
The HRS efficiency is nominally 81%. To obtain a given signal-to-noise ratio one has to increase the integration time by a factor (0.81)^-2 in order to compensate for this efficiency.
---> System temperatures T_sys (SSB)

Band 1-5 200 K * ( ν / 500 GHz )
Band 6 1600 K

Band 1 160 K
Band 2 320 K
Band 3 480 K
Band 4 730 K
Band 5 2000 K
Band 6 2500 K

Be aware that all numbers are SSB. Continuum sources will be seen in the two mixer sidebands. The expected continuum level in K will therefore be twice the expected SSB continuum level.

Point source Continuum sensitivity:

450 Jy/K at 500 GHz and for bands 1-5
600 Jy/K at 1.9 GHz and for band 6