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The High-resolution Airborne Wideband Camera (HAWC+) is a multi-wavelength far-infrared imager and polarimeter with continuum bandpasses from 50 um to 240 um. HAWC+ Total Intensity Imaging uses a filter wheel and a polarizing grid to split incoming light into two orthogonal components of lineal polarization, the reflected (R) and transmitted (T) rays. For Imaging Polarimetry, a rotating half-wave plate (HWP) is introduced before the filter wheels. The current state of the instrument includes a 64x40 array measuring the R polarization state and a 32x40 array for the T polarization state. HAWC+ observations are diffraction-limited with a spatial resolution of 5 to 20 arcsec and a field of view (FOV) of ~2 to 10 arcmin.
HAWC+ will offer shared-risk observations using Band B (63 um) during Cycle 8. Historically, this band has suffered oversaturation effects, which make it unuseable. A cold aperature has been installed to minimize the saturation effects. This band will be under comissioning during Cycle 7. Proposals requesting Band B should specify the scientific purpose and alternative science output in case this band is not usable.
A schematic of the HAWC+ optical design is shown in Figure 7-1. Prior to entering the HAWC+ cryostat, light from the SOFIA telescope enters the set of warm fore-optics. The light is reflected from a folding mirror to a field mirror, capable of imaging the SOFIA pupil at the cold pupil inside the HAWC+ cryostat. After the fore-optics, light enters the cryostat through a 7.6 cm diameter high-density polyethylene (HDPE) window, then passing through a cold pupil on a rotatable carousel, a near-infrared blocking filters to define each bandpass and lenses designed to optimize the plate scale. The pupil carousel and the filter wheel are at a temperature of ~10 K. The carousel contains eight aperture positions, four of which contain half wave plates (HWPs) for HAWC+ bands, an open aperture whose diameter is matched to the SOFIA pupil, and three aperture options meant only for instrument alignment tests.
After the pupil carousel, the light passes through a wire grid that reflects one component of linear polarization and transmits the orthogonal component to the detector arrays (R and T arrays, respectively—see Figure 7-2). The polarizing grid is heat-sunk to the HAWC+ 1 Kelvin stage.
To perform polarimetry observations, a HWP matched to the band-pass is rotated (usually through four discrete angles) to modulate the incident light and allow computation of the Stokes parameters. The total intensity can be measured simply by removing the HWPs from the optical path and using the open pupil position, then summing the signal from the R & T arrays.
The 64x40 HAWC+ detector array is composed of two co-mounted 32x40 subarrays from NASA/GSFC and NIST. The detectors are superconducting transition-edge sensor (TES) thermometers on membranes with a wide-band absorber coating. The detector array is indium bump bonded to a matched array of superconducting quantum interference device (SQUID) amplifiers, all cooled to an operating temperature of ~0.2 K in flight.
The absorbing coatings on the HAWC+ detector arrays were optimized to produce about 50% efficiency across the wide (50–240 μm) range of bandpasses. The TESs were designed to optimize the sensor time constants and background power at which they saturate, with the goal being operation at both laboratory and stratospheric background levels. The final design includes a superconducting transition temperature of ~0.3 K and a detector yield of > 50%. Measurements of detector noise show that their contribution to total measurement uncertainties is negligible such that noise levels are dominated by background photons from the atmosphere.
Measurements of the HAWC+ optical system in the laboratory are consistent with optical models, and flight data have confirmed that the observations are diffraction limited at all wavelengths.
Table 7-1 shows the Full Width Half Maxiumum (FWHM) of each bandpass as measured using Gaussian profiles, the finite size of the HAWC+ detectors, and a convolution across the measured filter bandpasses. The Instrumental Polarization (IP) of HAWC+ at each band is shown in terms of the normalized Stokes parameters, q and u, which were estimated using the observations of planets during several observing runs on November 2016 and May 2017. The IP is mainly derived from the tertiary mirror of SOFIA with the position angle of polarization perpendicular to the tertiary mirror direction. The filter transmission curves (text tables) are available as a zip file or individually from Table 7-1.
For polarimetry observations, the current configuration of HAWC+ lacks a second T polarization state array; as such, the field of view is reduced to approximately half in the largest side of the array, providing a 32x40 pixel size rather than 64x40 pixels (the first element of the Field of View in Table 7-1). Total intensity observations are unaffected and can use the whole field of view via the R polarization state.
Parameter | Units | Band A | Band B | Band C | Band D | Band E |
---|---|---|---|---|---|---|
Mean Wavelength (λ_{0}) | μm | 53 | 63 | 89 | 154 | 214 |
Bandwidth (Δλ) | - | 8.70 | 8.90 | 17.00 | 34.00 | 44.00 |
Filter Width (Δλ/(λ) | - | 0.171 | 0.15 | 0.194 | 0.219 | 0.204 |
Beam Size (FWHM) | arcsec | 4.85 | 10.5 | 7.8 | 13.6 | 18.2 |
Pixel Size^{a} | arcsec | 2.55 | 4 | 4.02 | 6.90 | 9.37 |
Total Intensity FOV | arcmin | 2.8x1.7 | 4.2x2.7 | 4.2x2.7 | 7.4x4.6 | 8.4x6.2 |
Polarimetry FOV | arcmin | 1.4x1.7 | 2.1x2.7 | 2.1x2.7 | 3.7x4.6 | 4.2x6.2 |
NESB^{b} (photo) | MJy sr^{-1} h^{1/2} | 18.8 | 11.4 | 6.3 | 1.6 | 0.8 |
MDCF^{c} | mJy | 250 | 400 | 300 | 260 | 230 |
Mapping Speed^{d} | See footnote ^{d} | 0.0027 | 0.0290 | 0.029 | 1.10 | 7.0 |
MDCPF^{e} | Jy | 80 | 150.0 | 50 | 50 | 50 |
IP^{f} | q | -0.0154 | See footnote^{f} | -0.0151 | 0.0028 | -0.0129 |
u | -0.0030 | See footnote^{f} | 0.0090 | 0.0191 | 0.0111 | |
MIfP^{g} | MJy sr^{-1} h^{1/2} | 28,000 | 17,000 | 6,000 | 2,000 | 1,300 |
Response Curve |
Band B (63 μm) will be under commisioning during Cycle 7 and is offered as shared-risk observations during Cycle 8. (Instrumental Polarization (IP) for Band B will be estimated during Cycle 7.) Historically, this band has suffered of oversaturation effects that render it unsuable but a cold aperture has been installed to minimize the saturation effects. Proposals requesting Band B should specify the scientific purpose and alternative science output in case this band is not usable.
HAWC+ can produce images using continuum bandpasses in either Total Intensity Imaging or Imaging Polarimetry configurations. In Imaging Polarimetry, the dual-beam nature of HAWC+ allows for the simultaneous measurement of both orthogonal lineal polarization components and obtain the Stokes parameters I, Q, and U. In Total Intensity Imaging, the sum of the R and T arrays provides the total intensity, Stokes I. As the HWP are used in Imaging Polarimetry, there is a slight loss of sensitivity as the HWP transmission is < 100% and additional overhead is required to account for rotating the HWP.
Both observing modes can utilize any one of the five available filters (including Band B offered as shared-risk during Cycle 8). Figure 7-3 shows transmission profiles including all filters for all bandpasses. The effective wavelengths and bandwidths averaged over the total filter transmission are given in Table 7-1.
The equations provided below are included for informational purposes only, and should not be entered into USPOT. Integration times calculated using the equations below include overheads, and USPOT already adds the telescope overheads into the exposure times entered. For USPOT entries use SITE, which only takes into account on-source time.
Observations with HAWC+ for measurements of Total Intensity can be performed using either on-the-fly scanning (OTFMAP, 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 chopping option consists of a two-position chop, parallel to the nod direction where the chop amplitude matches the nod amplitude (NMC). However, we strongly encourage using OTFMAP mode for total intensity observations, which provides better sensitivity and lower overheads for an overall superior observing efficiency.
Table 7-1 presents 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.
(Eq. 7-1) $$t={\left(\frac{\mathrm{NESB}}{\sigma}\right)}^{2}$$
(Eq. 7-2) $$t=\left(\mathrm{900\; s}\right){\left(\frac{\mathrm{NESB}}{\sigma}\right)}^{2}$$
where t is the integration time and σ is the desired sensitivity for S/N = 1, each in the appropriate units. For OTFMAP, a useful sensitivity value is the mapping speed given in Equation 7-3:
(Eq. 7-3) $$M=\frac{d\Omega}{\mathrm{dt}}=\frac{{\mathrm{\gamma \Omega}}_{\mathrm{array}}}{{s}^{2}}$$
where γ is related to the filling factor, Ω_{array} 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 7-1 are given for S/N = 1 in a one-hour integration time assuming γ = 1, while SITE and Figure 7-3 use a more realistic value γ = 0.75. The time to map an area Ω (≥ Ω_{array}) to a sensitivity level σ is given by Equation 7-4:
(Eq. 7-4) $$t=\frac{{\Omega}_{}}{M{\sigma}^{2}}$$
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 7-1 and Figure 7-3 we use a precipitable water vapor of 7.3 μm, a 50° zenith angle, and a telescope emissivity of 15%.
The equations provided below are included for informational purposes only, and should not be entered into USPOT. Integration times calculated using the equations below include overheads, and USPOT already adds the telescope overheads into the exposure times entered. For USPOT entries use SITE, which only takes into account on-source time.
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 Equation 7-5 is true:
(Eq. 7-5) $${\sigma}_{P}=\frac{{\sigma}_{I}\sqrt{2}}{{\eta}_{p}I}$$
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 7-1 is the value σ_{p} x I above, and follows from the total intensity MDCF. USPOT will add overhead values appropriate to NMC mode for polarimetry.
For Imaging Polarimetry, another useful quantity is the Minimum total 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 7-1 lists these values for a one-hour integration time in units of surface brightness for an extended source where, unlike other values in Table 7-1, all appropriate overhead values have been added.
HAWC+ time estimates should be made using the online exposure time calculator, SITE. Note that integration times scale as shown in Equation 7-6 and Equation 7-7 from the values in Table 7-1:
(Eq. 7-6) $$t=\mathrm{(1\; h)}{\left(\frac{\mathrm{MIfP}}{I}\right)}^{2}{\left(\frac{\mathrm{0.3\%}}{{\sigma}_{p}}\right)}^{2}$$
(Eq. 7-7) $$t=\mathrm{(900\; s)}{\left(\frac{\mathrm{MDCPF}}{4{\sigma}_{p}I}\right)}^{2}$$
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 Equation 7-8:
(Eq. 7-8) $${\sigma}_{\phi}=\frac{180}{\pi}\frac{{\sigma}_{p}}{2p}\mathrm{[degrees]}$$
Current best estimates for systematic uncertainties are 0.8% in percent polarization and 10° in polarization position angle.