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Numerical Project

(credit goes to Saurabh Jha for this suggestion) The numerical project will be individually graded, but can be a group collaboration! This means you can tackle bigger projects together (if you choose to do so) but each person needs to have developed a single module and writeup. It needs to be clearly identified who did what.

I think a nice goal for all of these projects is doing something along the lines of http://arxiv.org/abs/1308.1908 (teaching tools that could be made citable if open sourced).

This need not be original research; in fact, a good idea would be to try an reproduce numerically something that was worked out analytically (or more likely, approximately analytically). Use the computer as a tool to do calculations that are too tedious to do by hand (e.g., make use of Monte Carlo, ray tracing, etc.).

Please identify what projects you want to do and in what group setting (outlining who does what) in 1 or 2 pages by November 9th. The projects will be due by December 2nd in the evening. The projects should consist of 1. the documented code (perhaps with a jupyter notebook); 2. a brief (few pages) write-up of what you did. We will try to schedule a brief in-class presentation of what you did.

Here are a few ideas to get you thinking; you could choose one of these, expand upon one of them, work off of a similar theme, or find something different altogether. It’s up to you. Other sources of ideas could include recent or ancient papers, talking to some of the other astronomy faculty, or looking at problems posed in textbooks.

  • Simple stellar radiative transfer. For one of the courses you made a very simple tool to calculate radiative transfer through for one specific frequency with a given Source function. Calculate a very simple part of a stellar spectra by using this and expanding it to include actual opacities (by solving for the level populations, including line broadening, etc.)

  • Polarization and Geometry in Supernova Ejecta Explore how spectropolarimetry of supernovae is used to infer the geometry of the ejecta. Try looking at an ellipsoidal electron scattering shell surrounding a point source. Calculate the polarization as a function of ellipticity and orientation. Compare to real observations.

  • Sunyaev-Zel’dovich effect Simulate the scattering of CMB photons off hot electrons in a galaxy cluster. Calculate the CMB spectrum distortion. Look at the thermal and kinetic effects, and polarization.

  • Cosmic Ray Acceleration; the First Order Fermi Process Model the energy distribution of particles as they get accelerated repeatedly in shock inter- actions to produce the most energetic particles known.

  • Modeling the Intensity and Polarization of the Solar Corona Simulate the Thomson scattering of solar photons off the low-density electrons in the Sun’s corona. Try different density distributions as a function of radius and look at the intensity and polarization properties to compare with observations.

  • Gamma-ray burst spectral energy distributions Model the extremely relativistic outflows in GRBs. Replicate (or refute) the piece-wise power- law SED and its temporal evolution, including cooling breaks, or jet breaks.