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:
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:
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:
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.

Helpful links:

ASTR 406 Problem (20 points)

We often use "nepers" to talk about filter bandwidth. A neper is defined as (delta-lambda / lambda), which is equal to (delta-nu / nu) in terms of frequency. Show that the total photon flux through a filter in units of photons/s/cm^2/neper is given by fnu/h, where h is Planck's constant. Then from the definition of Jansky, show that a flux of 1 microJansky corresponds to 0.0015 photons/s/cm^2/neper. Then use that handy conversion to do the next part.

The WIYN telescope at Kitt Peak has a 3.5m (diameter) primary mirror that is obstructed by 17% by other optics in the system. The telescope system has 3 mirrors each with 89% reflectivity. The telescope feeds light into a camera with 8 optical surfaces, each of which has 1.5% photon losses per surface. The light then reaches the CCD which has a quantum efficiency of 70%, a read noise of 9 electrons, and a pixel scale of 0.11 arcsec/pixel.

When we observe with this system, we want to be "sky limited", meaning that the photon noise in the sky is greater than 3x the readnoise in the CCD. If we are observing in the I-band filter, which has a central wavelength of 7900 A, a bandwith of 1500 A, and a flux zeropoint of 2550 Jy, how long do we need to expose to become sky-limited? Note that the I-band surface brightness of the (dark) night sky is about 19.9 mag/arcsec^2.

How does your answer change if instead of a broadband filter, you were using a narrowband filter with the same central wavelength but with a bandwidth of only 80 A?