## ASTR 306 HW #3

For problems 1 and 2, imagine you are observing under the following conditions. You have a CCD with gain=2 e-/ADU, readnoise=12 e-. The sky intensity is about 1.3 ADU/sec/pixel, and we will be measuring stellar magnitudes using circular apertures of radius 5 pixels. Within this aperture, a 21st magnitude star has a flux of about one ADU/sec, and star that produces more than about 350,000 ADU total during the exposure will saturate the CCD and be a useless measurement.

1. Fixed exposure time calculation (10 points)

For a 5 minute exposure, make the following plots:
• log (total counts) vs star magnitude over the magnitude range m=10-25.
• log (signal-to-noise) vs star magnitude over the same magnitude range.
Note: "plot A vs B" means your plot should have A on the y-axis and B on the x-axis.

At what magnitude will stars begin to staturate? If your limiting magnitude is defined by a 3-sigma detection, what is your limiting magnitude?

2. Exposure time to reach a given S/N (10 points)

You want to study solar-type stars in M13, and need to get a S/N of 30 to achieve your goals. Plot log(signal-to-noise) vs log(exposure time) for these stars, for exposure time ranging from 1 second to 6 hrs. How long do you need to expose to get your desired S/N?

3. Surface brightness profile for M84 (25 points)

Here is a fits file containing imaging data for M84 taken from the Burrell Schmidt telescope. It has the following characteristics:
• pixel scale: 1.45 arcsec/pixel
• photometric zeropoint: mV = -2.5log(I) + 28.60 (in other words, a star with magnitude mV=28.6 would have one count on the image. Of course that star would be too faint to detect.....)
Write a code to construct a surface brightness profile for M84. First, bin the pixels by radius from the center of M84 (use, say, 75 bins of width 10 pixels each), and calculate the surface brightness in each radial bin. Your surface brightness profile plot should have surface brightness [mag/arcsec^2] on the y-axis (with brightness increasing upwards) and log(radius) [arcsec] on the x-axis. Overplot both the total surface brightness profile and the  median surface brightness profile, and comment on differences. Which one do you think is better? Calculate a total V-band magnitude for M84 and compare it to the value from the RC3 (listed in NED as VT under the photometry page for M84). How do you think it compares? What is your estimate for the galaxy's half-light radius? Comment on what you think are the biggest uncertainties in your derived total magnitude and half-light radius.

For this problem, please also turn in a copy of your code.

Helpful hint #1: Here is a python code snippet that will read in data from a fits file (using astropy) and calculate the distance of each pixel from some pixel defined (by the user) to be the galaxy center.

Helpful hint #2: Remember look at the lecture notes from Oct 3 for the discussion of how to do this kind of binning.

Helpful hint #3: In calculating profiles, the total surface brightness in a radial bin is simply the total flux in the bin (in counts), converted to magnitudes, and then converted to surface brightness using the total area of the radial bin. The median surface brightness is given by the median value of the flux per pixel, converted to magnitudes, and then converted to surface brightness using the area of a single pixel.

4. Colors and color gradients in spiral galaxies (20 points)

Research and write up a 2-3 page summary (word processed, single-spaced) of how colors in spiral galaxies can be used to study their evolutionary history. You should consider the following topics:
• What are the optical colors of spiral galaxies (particularly B-V)?
• What kind of color gradients do spiral galaxies show?
• What affects the colors of galaxies? (hint-- it's not just stars)
• What do the colors and color gradients tell us about the evolution and star-forming history of spiral galaxies?
Your write-up should cite sources, with an additional page listing those sources. You should have at least 8 professional-grade references, half of which (or more) should be articles in peer-reviewed research journals (ApJ, AJ, MNRAS, A&A, etc). The rest can come from research monographs or reviews (like the Annual Reviews of Astronomy and Astrophysics). Nothing from websites, Wikipedia, textbooks, etc.