Astronomical Spectroscopy - Physics - University of Cincinnati

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can be answered given a complete catalog of sources. For a star centered in a slit with a
width of 2a, the relative contamination from a star a separation s away will depend upon the
seeing. We can characterize the latter by a Gaussian with a σ of 0.85f/2, where the seeing
full-width-at-half-maximum is f. Following equation (8) in Filippenko (1982), the relative
contribution of a nearby star is
10 (∆V/−2.5) F(a, s, σ)/F(a, 0, σ)
where the definition of F depends upon whether or not the second star is located partially
in the slit or not. Let a1=a-s and a2=a+s if the star is in the slit (s < a). Then F =
0.5(G(a1, σ) + G(a2, σ)). (Use this for the denominator as well, with a1=a2=a.) If the star
is located outside of the slit (s > a) then F = 0.5(G(a1, σ) − G(a2, σ)). G(z, σ) is the
standard Gaussian integral,
G(z, σ) = 1 √
2πσ
∫ z
−z
e −x2 /2σ 2 dx
The simplifying assumption in all of this is that the slit has been oriented perpendicular
to a line between the two stars. But, this provides a mechanism in general for deciding in
advance what stars in one’s program may be too crowded to observe.
3.2.3. Assigning Fibers and Designing Multi-slit Masks
In order to design either a fiber configuration or a multi-slit mask, one invariably runs
highly customized software which takes the celestial coordinates (right ascension and declination)
of the objects of interest and computes optimal centers, rotation, etc. that allow
the fibers to be assigned to the maximum number of objects, or the most slitlet masks to
be machined without the spectral overlapping. However, a key point to remind the reader is
that such instruments work only if there are alignment stars that are on the same coordinate
system as the program objects. In other words, if one has produced coordinates by using
catalog “X” to provide the reference frame, it would be good if the alignment stars were also
drawn from the same catalog. This was much harder ten years ago than today, thanks to
the large number of stars in uniform astrometric catalogs such as the 2MASS survey or the
various USNO publications. The most recent of the latter is the CCD Astrograph Catalogue
Part 3 (UCAC3). One advantage of the proper motion catalogs such as the UCAC3 is one
can then assure that the relative proper motion between the alignment stars and the program
objects are small.
This point bears repeating: there is a danger to mixing and matching coordinates
determined from one catalog with coordinates from another. The coordinates need to be