# 10.1.5 Polarization Imaging Sensitivities

HAWC contains four monochromatic HWPs. For Bands C, D, and E, the HWP thicknesses are matched to the bandpass filters. The thickness of the "Band A" HWP is matched to a wavelength between those of Bands A (53 μm) and B (63 μm), approximately 58 μm. However, this slight mismatch should not introduce significant systematics into the system. For the pre-flight HAWC+ sensitivity estimate here, the total system polarization efficiency (HWP + polarizing grid + all other optics) is assumed to be 90% for all five passbands.

The polarization sensitivity σ_{p} follows from the imaging sensitivity σ_{I} so that

where *I* is the source intensity, η_{p} is the system polarization efficiency, and σ_{p} is measured in units of percent (%). The Minimum Detectable Continuum Polarized Flux (MDCPF) reported in Table 10-1 is the value σ_{p} x *I* above, and follows from the unpolarized MDCF. SPT will add overhead values appropriate to C2N mode for polarimetry.

For polarization imaging another useful quantity is the Minimum unpolarized Intensity required in order to measure polarization (MIfP) to a given depth in a given time interval. Choosing σ_{p} = 0.3% allows a polarization S/N = 3 for a source polarization of 1%, a value not atypical of bright Galactic clouds and a likely lower limit for HAWC+ systematic uncertainties. Table 10-1 lists these values for a one-hour integration time in units of surface brightness for an extended source where, unlike other values in Table 10-1, all appropriate overhead values have been added.

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_{p} is the desired sensitivity for S/N = 1, each in the appropriate units.

A simple estimate for the polarization angle uncertainty is given by:

The above values assume only statistical uncertainties. Current best estimates for systematic uncertainties are no better than 0.3% in percent polarization and 2° in polarization position angle.