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 delta-lambda 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 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

Spectra:
 fcam=55 mm fcam=135 mm slit=100 micron Image89.fits Image99.fits slit=200 micron Image90.fits Image98.fits slit=300 micron Image91.fits Image97.fits slit=400 micron Image92.fits Image96.fits slit=500 micron Image93.fits Image95.fits

Tips:
• 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)