# 10.1.4 Imaging Sensitivities

Observations with HAWC+ for measurements of total (unpolarized) intensity can be performed using either on-the- fly scanning (where the telescope moves continuously at rates of ~10 - 200 arcsec/second without chopping of the secondary mirror) or using rapid modulation (chopping ~ 5 - 10 Hz) of the secondary accompanied by slow nodding of the telescope. The former mode is the far more efficient mode, but has not yet been tested by other imaging instruments on SOFIA. The chopping option consists only of a two-position chop, parallel to the nod direction where the chop amplitude matches the nod amplitude (C2N-NMC).

Figure 10-3 and Table 10-1 present HAWC+ imaging sensitivities for point sources, surface brightness, and mapping speed through each bandpass. Surface brightness is measured in units of MJy/sr and is the intensity required for a S/N=1 observation in a one-hour integration time averaged over a single HAWC+ beam. The Minimum Detectable Continuum Flux into a HAWC+ beam is that needed to obtain a S/N=4 in 900 seconds of on-source integration time. Figure 10-3 plots the MDCF for both observing modes OTFMAP and C2N (NMC) where the latter follows from the former based on overheads related to chopping and nodding the telescope.

Figure 10-3: HAWC+ Sensitivity estimates in units of the Minimum Detectable Continuum Flux (MDCF) into a single HAWC+ beam. (Recall that the beam area changes with bandpass). Values plotted here take into account all expected overheads. For example, Table 10-1 gives an MDCF of 57 mJy at 53 μm in OTFMAP, but is plotted here as 66 mJy to account for a 75% array detector yield. For polarization, the plotted data show the polarized intensity p x I, where p is the fractional polarization (not percent).

HAWC time estimates should be made using the on-line exposure time calculator, SITE. Here we note that integration times scale in the following manner from the values in Table 10-1:

or

where t is the integration time and σ is the desired sensitivity for S/N = 1, each in the appropriate units. For OTF mapping, a useful sensitivity value is the mapping speed

where γ is related to the filling factor, Ωarray is the solid angle of the HAWC detector array, and s is some measure of the instrument sensitivity (e.g., MDCF or NESB). The values in Table 10-1 are given for S/N = 1 in a one-hour integration time assuming γ = 1, while SITE and Figure 10-3 use a more realistic value γ = 0.75. The time to map an area Ω (≥ Ωarray) to a sensitivity level σ is given by

Note that this scaling only applies to map areas larger than the array field of view.

Atmospheric transmission will affect sensitivity, depending on water vapor overburden as will telescope zenith angle and telescope emissivity. For the estimates in Table 10-1 and Figure 10-3 we use a precipitable water vapor of 7.3 μm, a 50° zenith angle, and a telescope emissivity of 15%.