We looked at numerical derivatives of models of stellar spectroscopy, taken by Yuan-Sen Ting (Harvard). When you numerically differentiate someone else's computer code, you have to be careful! If you take a step size that is too large, the behavior won't be linear. If you take a step size that is too small, the differences won't be trustable (because the code has unknown convergence precision). So there should be a “sweet spot”. Ting's analysis doesn't clearly show such a sweet spot for his derivatives of the Kurucz stellar models. That's concerning.
Mid-afternoon I had an idea for a new project, related to the above, and also to The Cannon: If we have a pair of matched pairs (yes, four stars), all of which have similar Teff and logg, but two of which are from one open cluster and two of which are from another, we should be able to look at the precision of any possible abundance estimate, even without any model. That is, we can see at what signal-to-noise we can differentiate the pairs, or we can see how much more difference there is across clusters as compared to within clusters. This could be a baby step towards a fully data-driven, spectral-space chemical tagging method, something I have dreamed about before.