centering

Jeffrey Mei (NYUAD) came by to discuss his project to infer the dust extinction law from SDSS spectra of F stars. We talked about a "centering" issue: We are regressing out g-band brightness (flux; a brightness or distance proxy), H-delta equivalent width (a temperature proxy), and extinction amplitude from the Schlegel, Finkbeiner, & Davis map. The coefficient of the latter will be interpretable in terms of the extinction law (the dust law). Because we have regressed out the observed g-band brightness, we get that the mean effect of extinction is zero in the g-band; that is, our results about the dust extinction are distorted by what we choose, precisely, to regress out. Another way to put it: The brightness is a function of distance, temperature, and extinction. So if you regress that out, you distort your extinction results. The point is obvious, but it took us a while to figure that simple thing out! We have a fix, and Mei is implementing.