Astronomical Spectroscopy - Physics - University of Cincinnati

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on the same system, or there is significant risk of being quite disappointed in the final
throughput at the telescope.
3.2.4. Placing Two Stars on a Long Slit
If one is observing multiple objects whose separations are smaller than the slit length
(such as stars within a nearby galaxy or within a star cluster), and one does not need to be at
the parallactic angle (either because the instrument has an ADC or because one is observing
either near the zenith or over a small wavelength range) one may want to multiplex by
placing two stars on the slit by rotating the slit to the appropriate angle. To plan such an
observation, one must first precess the coordinates of both stars to the current equinox, as
precession itself introduces a rotation. Then, one must compute the “standard coordinates”,
i.e., de-project the spherical coordinates to the tangent plane.
Assume that one of the two stars is going to be centered in the slit, and that its precessed
coordinates are α 1 and δ 1 , converted to radians. Assume that the other star’s coordinates are
α 2 and δ 2 , where again these are expressed in radians after precession. Then the standard
coordinates ξ and η of star 2 will be
ξ = cosδ 2 sin(α 2 − α 1 )/F
η = (sin δ 2 cosδ 1 − cosδ 2 sin δ 1 cos(α 2 − α 1 ))/F,
where
F = sin δ 2 sin δ 1 + cosδ 2 cosδ 1 cos(α 2 − α 1 ).
The position angle from star 1 to star 2 will then simply be the arctangent of (ξ/η). If η
is 0, then the position angle should be 90 ◦ or 270 ◦ depending upon whether ξ is positive or
negative, respectively; if ξ is 0, then the position angle should be 0 ◦ or 180 ◦ , depending on
whether η is positive or negative, respectively. The distance between the two objects will be
√
ξ2 + η 2 .
3.2.5. Optimal Extraction
With CCDs coming into common use as detectors, Horne (1985) pointed out that simply
summing the data over the spatial profile of a point source did an injustice to the data, in