mixture-of-Gaussian galaxies

I actually did real research today, writing and making figures for Lang and my paper on mixture-of-Gaussian approximations to standard two-dimensional galaxy intensity models (think exponential and de Vaucouleurs). I tweaked the figures so their notation matches the paper, I made figure captions, I adjusted the text, and I got the to-do items down to one day's hard work. I am so close! People: Don't use the de Vaucouleurs profile; use my approximation. It is so much better behaved. Details to hit arXiv very soon, I hope.


  1. Does that statement apply only to high signal-to-noise images, or also to faint smudges?

    Also, shouldn't the model you use be application dependent? Or are you also saying that a mixture of gaussians gives a better physical interpretation of the galaxy?

  2. Doug: Great questions! These models are better behaved than the traditional models in every situation; they are just more numerically tractable and stable. They are nearly identical to the traditional profiles, just a re-writing in terms of Gaussians rather than non-linear exponentials. They provide no new insights about galaxies; in fact my real position is that we shouldn't use such simplified models in many cases (for bulge-disk decomposition, for example, which is their main use!).

    It certainly is true that your best tools are application-dependent. But in *any* application where you are fitting exponentials and de Vaucouleurs to data using a computer, these m-o-G profiles will perform better (faster, more accurately computed, better for PSF-convolution, better for optimization) than the analytic functions. (At least I think so at this point.)