claw wrote:Regarding the frequency dependence, it sounds to me like the effective time on sky scales as the beam size. For a large survey with tight packing of scans, any point on sky will be surveyed by every part of the primary beam. If we assume a reference point at band center, all other parts of the band will have an effective time on sky that scales with the relative beam size. So:
t_int_eff ~ (nu/nu_center)**-2 and,
s_lim ~ (nu/nu_center)**-1.
Does that sound reasonable? If so, then any target sensitivity at a particular frequency can be scaled to the reference point. I suppose the ultimate s_lim would be set by the most stringent of any target sensitivity in the band. I could see this happening if some spectral lines were being targeted, but for most science cases, I imagine people can get by with a single s_lim at their frequency of choice.
That sounds reasonable. My guess is since this is averaged over the band just using the values at band center gets reasonably close (you could integrate over the band using source spectrum and the beam size effect I guess to be more accurate).