show that low-luminosity early-type galaxies are oblate

Here's an old one from the vault: Plot the surface brightness of early-type galaxies (red, dead) as a function of ellipticity and show that surface brightness rises with ellipticity. This is what is expected if early-type galaxies are transparent and oblate. I know from nearly completing this project many years ago that this will work well for lower-luminosity early types and badly for higher-luminosity early types. The cool thing is that, under the oblate assumption, the true three-dimensional axis-ratio and three-dimensional central stellar density distribution function can be inferred from the observed two-dimensional distributions under the (weak) assumption of isotropy of the observations. That assumption isn't perfectly true but it is close. You can use high signal-to-noise imaging and SDSS spectroscopy to do the object selection, so observational noise in selection and measurement won't provide big problems.

This is another Scott Tremaine (IAS) project. Mike Blanton (NYU) and I basically did this many years ago with SDSS data, but we never took it through the last mile to publication, so it is wide open. Actually, it seems likely that someone has done this previously, so start with a literature search! Bonus points: Figure out what's up with the high-luminosity early types. They are either triaxial or a mix of oblate and prolate.

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