## 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.
• First, calculate the relationship between sigma and FWHM for a gaussian profile.
• Now download this SDSS image of the globular cluster M13. Characterize the data as follows: what is the FWHM of the stars in the image (in both pixels and arcseconds)? What is the background level and its dispersion (in counts)? You should check a few stars and a few sky areas to make sure you are getting consistent values. Make sure you ar
• Assuming a gaussian profile, calculate the total enclosed light as a function of radius (also known as a "curve of growth"). That is, given sigma (or FWHM), how what fraction of the total light from a star do you expect inside a circular aperture of size r? What is the radius which contains half the light? 80% of the light (a common "spec" by which optical designs are rated)? 90% of the light? 99% of the light? Make a plot of enclosed light as a function of radius, using the value of sigma you got from the image. It should go from 0% at r=0 to 100% at r=big.
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.
• Now use pyraf to measure a "curve of growth" for three good stars. That is, change the parameters in imexam for the apertures (in pyraf either do epar rimexam, or set them directly using the iraf.rimexam.<parameter>=<#> style commands), and see how the total flux of a star changes as a function of aperture size. Make sure you are choosing sensible values for the photometry parameters "radius", "buffer", and "width" -- describe what you set them to and why. And also describe which stars you picked to do this analysis, and why you picked them. Very important: before doing this task make sure you tell pyraf NOT to auto-adjust the aperture: say iraf.rimexam.iterations=1 before starting imexam.
• Finally, compare (ie overplot) your measured curve of growth to that of the gaussian model. How good is the model? Comment on what might be causing the differences you see.

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)
• In the AB system, in any filter the magnitude zeropoints are given by mAB=-2.5log(fnu)-48.6. Calculate the zeropoint in Janskys, which is workd out by calculating fnu in Janskys for an object with mAB=0.
• In the Vega system, magnitudes are referenced to the brightness of Vega is each filter, so each filter has a different zeropoint. For example, in Johnson B the zeropoint is 4260 Jy, and in Johnson V the zeropoint is 3640 Jy. If a solar-type star has a B-V color of 0.65 in the Vega system, what is its B-V color in the AB system?
• A galaxy has a B-band central surface brightness of 21.5 mags/arcsec2 in the Vega system. For this galaxy work out the following:
• what does that correspond to in units of MJy/steradian? (MJy = Mega-Janskys)
• what is the equivalent intrinsic luminosity density of the galaxy in solar luminosities per square parsec?