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Your options are as follows:
where ``alat" is the latitude of Kitt Peak (31.958); dec is the object's declination (in degrees); and ha is the object's hour angle in hours. A graph giving the parallactic angle as a function of hour angle and declination for Kitt Peak (modeled after Fig. 1 in Filippenko 1982) can be found in Fig. 12.
In practice, rotating the slit has to be performed near the zenith, and so there is some loss of time involved.
Figure 12: The parallactic angle as a function of hour angle WEST of the meridian for the latitude of Kitt Peak. For negative hour angles, use the complement of the angle indicated; i.e., an object at and and hour angle of -5 hrs has a parallactic angle of 180-110=70 degrees. This figure is a slightly modified version of Figure 1 in Filippenko 1982 PASP 94, 715.
The 4-m telescope is equipped with a pair of ``Risley prisms", which provide excellent atmospheric dispersion compensation (ADC). The Risleys can be inserted into the beam with some light loss (5-8% > 4000Å), but they will then protect you against the losses due to differential refraction.
In Fig. 13 we show how well the Risleys do their atmospheric compensation. The boxes denote the fluxes for a spectrophotometric standard. We then show two observations of this star, both obtained at airmass of 1.8, and both obtained in the worst possible scenario of the slit being 90 degrees to the parallactic angle. We see that the observation obtained with the Risley prisms follows that of the known flux distribution of the star, while that obtained without the Risleys was down by a factor of 3 in the blue. We do note that if you are doing spectrophotometry with the Risleys, you must observe your standards with the Risleys as well, to properly calibrate the small but wavelength-dependent light-losses of the Risleys.
One other logistical consideration to keep in mind when using the Risley prisms is that finding a guide star will be a little bit harder. Because the telescope focus is quite a bit different when the Risleys are in use (+1550 microns!) any guide star must be within the realm of the Risleys in order to be in focus. In practice it seems to work to find a guide star within 125mm (14 arcmin) of field center. Remember that the vignetting limit is 75mm within field center, so there is a good annulus left.
Figure 13: The boxes show the known standard star fluxes; the two spectra show the effects of observing at a high airmass with the slit oriented 90 degrees to the parallactic angle.