ASTR 306 - HW#2



1. Plate Scale and CCDs (15 points)

I'm working on a project to get photometry for stars in the globular cluster M13 using the prime focus camera on the Paul Harding Telescope at Kitt Peak (where typical seeing is about 1 arcsec). When I turn up for my observing run, I am asked what CCD I wish to use. I don't want to let on that I have not read the observers manual, so a quick look at the telescope tells me the distance from the primary to the focal plane is 40 feet. I also want to make sure that the whole globular cluster fits in the field of view. The choice is between a CCD A, which has 3000x3000 pixels with each pixel 9x9 microns, and CCD B which has 2048x2048 pixels with each pixel 24x24 microns. Which CCD would you pick and why?

2. Filters (15 points for ASTR 306; 30 points for ASTR 406)

Here is the filter tracing (transmission as a function of wavelength) for one of the Kitt Peak R band filters. From this tracing, calculate the filter's central wavelength and the width of the "equivalent square filter." Plot the filter transmission function and overplot the transmission function for the equivalent square filter.

Helpful tip: the file has some transmission values < 0, which are obviously unphysical and you will want to set to zero. An easy way to zero out negative values in a numpy array is to say x[x<0]=0.

ASTR406: If an object has a spectrum given by I(lambda) = I0 * (lambda/5450A)^n, where I0 = 3.63x10-13 erg/s/cm2/A. For this filter, and for the equivalent square filter, calculate mR in the STMAG system for n=-2 (a blue spectrum) and n=+2 (a red spectrum). Comment on the differences between the numbers for the two filters with the different values of n -- that is, why do you get different values depending on whether you use the real filter tracing or the equivalent square filter, and why do the differences depend on the spectrum of the object?


3. Calculating a curve of growth for stellar photometry (20 points)


For this problem, use a gaussian profile as our model for the point spread function (PSF) of an image.
Helpful tip for this part: normalize radius by the gaussian sigma. In other words, make your radius measure r/sigma instead of r. In the integral, do the substitution x=r/sigma and calculate (and plot) enclosed light as a function of x. Then when overplotting your curve of growth from the data (the last step of this problem), do the same thing for your measured data, using the sigma you infer from your measurement of FWHM for stars on the image.

4. Charge Transfer Efficiency (10 points)
Charge Transfer Efficiency (CTE) describes the fraction of electrons successfully moved during a single pixel shift during CCD readout. That is, a CTE of 0.99 means that 1 out of every 100 electrons is left behind during a shift. If you have a 4096x4096 pixel CCD and want to make sure 99% (or more) of the electrons held in each pixel are moved successfully into the serial readout register (meaning they don't get left behind in a trailing pixel), what kind of CTE do you need for your CCD?

5.  Sky Background (15 points)

You are wanting to take spectra of stars using a fiber fed spectrograph. The typical seeing is not great, about 1.5" FWHM, and the night sky has a surface brightness of muR = 20.8 mag/arcsec2. Plot the fraction of total light in the aperture that comes from a star of magnitude mR=15 as a function of aperture diameter, with aperture diameters going from d=0-5 arcsec. Overplot similar curves for stars of magnitude mR=16, 17, and 18. Why would big fibers be good if you want to look at faint stars? Why would they be bad? (Don't worry about spectral resolution for this question.)

6. ASTR 406 only (25 points)