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. 

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.

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 fcam=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 (y-axis) and pixel position (x-axis) 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:

Spectral line fitter: seespec.py


fcam=55 mm
fcam=135 mm
slit=100 micron
slit=200 micron
slit=300 micron
slit=400 micron
slit=500 micron

  • In the fcam=55mm spectra, the spectrum is found around y=1042, and you should concentrate on lines in the region x=900-1150, which corresponds roughly to wavelengths of 4000A - 5200A.
  • In the fcam=135mm spectra, the spectrum is found around y=1032, and the same lines span a range of x=750-1300.
  • Note that the line intensities won't match the spectrum to the right, but the line wavelengths will.
    Spectrograph properties
    fcam 55 mm (exposures 89-93)
    135 mm (exposures 95-99)
    fcoll 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 89-93)
    500, 400, 300, 200, 100 micron (exp 95-99)