Homework #4: Spectroscopy
1. Spectroscopic setup (15 points)
Arriving at the
observatory for my spectroscopic observing run, I find that the only
grating I have available is a 300 line/mm grating blazed at 8000A in
the first order. But I want to observe in the blue from 3500 to
5000A.
 How could I best do this and what precautions should I
take?
 At what angle will 4000A light be found relative to the
grating normal?
 What is the blaze angle of the grating?
 What camera focal length should I use to fit the spectrum
on a CCD 20mm wide?
 If the 2 arcsecond wide slit projects to 66 microns on the
detector, what is the spectral resolution (give it in terms of both
deltalambda and R)?
 What is the velocity resolution (in km/s)?
For this problem, assume the grating surface is
normal to light from the collimator.
2. Slit positioning (10 points for 306, 20 points for 406)
Now, using the parameters from problem #1, think about the effect of moving a star from one edge of the slit to the other.
 If stars were truly point sources (unblurred by atmospheric
seeing or telescope optics), what would be the velocity change in the
star that you would observe if you moved the star from one edge of the slit to the other?
 Conceptually, how would you expect the velocity to change from one
side of the slit to the other if the seeing was extremely good, say 0.5
arcsec FWHM? What if it was awful, say 5.0 arcsec FWHM? How would it change as the seeing varied
in between those extremes? Explain your reasoning; a sketch might help your explanation.
ASTR 406: Make a plot
of the velocity difference as a function of FWHM for seeing
that ranges from FWHM=0.1 arcsec (unrealistically good!) to 5 arcsec
(utterly horrible). Make the simplifying assumption that in the spatial
direction we are only extracting the spectrum centered on the star, so
that you can treat the star's profile in the slit as a one dimensional
gaussian. Hint: you'll probably need to make use of the
scipy.special.erf() function at some point in making this plot!
3. Wavelength choices (5 points)
If you have a spectrograph (not the one in the previous problems) where you can observe at
either 4000A or 8000A with the same resoution (FWHM = 2
Angstroms), which of these two wavelength settings will give the
better velocity accuracy all other things being equal?
4. Spectrograph design (15 points)
You designing a spectrograph for a 5m telescope at f/10 Cass
focus. The collimator is a 6 inch collimator and the slit is 1 arcsec wide and projects to 30 microns
(3pixels) on the detector. An astronomer askes you what
resolution will she will have with a 1200 line/mm grating at
5000A. What do you tell her? Explain any assumptions you need to
make.
5. Lab Spectrograph (20 points)
 Grab
the spectra and choose a strong but unsaturated line to study. Measure
its FWHM in each of the spectra and make a plot of how its FWHM changes
as a function of slit width. Overplot your results for the two
different camera lenses. and explain why changing the lens makes a
difference. Discuss your results, explaining both how changing either
the slit width or the camera lens changes the measured FWHM of the line.
 Pick one of the f_{cam}=55 mm
images and measure the position of a set of lines that you've matched
to the helium lines. Make a plot of wavelength (yaxis) and pixel
position (xaxis) of the line and fit a straight line to calculate the
linear dispersion (in Angstroms/pixel). Then convert that to
Angstroms/mm using the pixel size on the CCD. Then do the same for one
of thef _{cam}=135 mm images. Compare the values you
measure to the linear dispersion you'd calculate from the expressions
we derived in class (adopt alpha=0 for this). For this part, when
choosing the image to work with when measuring the lines, use the
following constraints:
 Don't use the image with the narrowest lines (explain why).
 Don't use the image with the fattest lines (explain why).
Things you need:
Tips:
 In the f_{cam}=55mm spectra, the spectrum is
found around y=1042, and you should concentrate on lines in the region
x=9001150, which corresponds roughly to wavelengths of 4000A  5200A.
 In the f_{cam}=135mm spectra, the spectrum is found around y=1032, and the same lines span a range of x=7501300.
 Note that the line intensities won't match the spectrum to the right, but the line wavelengths will.

Spectrograph properties

f_{cam} 
55 mm (exposures 8993)
135 mm (exposures 9599)

f_{coll} 
40 inches 
grating 
600 lines/mm used in 1st order

CCD pixel size

13.5 microns

slit width

100, 200, 300, 400, 500 micron (exp 8993)
500, 400, 300, 200, 100 micron (exp 9599)



