The Jeans Equations are remarkable: They relate moments and integrals of distribution functions to the underlying gravitational potential (or really force law), for phase-mixed populations. They are true for any distribution function! But they are equations, and they are not models. As my loyal reader knows, for me a model is a likelihood function!
When people do what is called Jeans modeling, they turn the equations into some procedure for estimating the gravitational potential (or force law or mass density). And although the Equations are independent of distribution function, the performance of this heuristic procedure—that goes from velocity moments to gravitational model parameters or densities—has statistical properties that do depend strongly on the distribution function. That is, you can't make a probabilistic statement (like a measurement and an uncertainty) of anything (like a density at the Milky Way disk midplane) without assuming things about the distribution function.
And because the Jeans Equations are independent of the distribution function, it is tempting to claim or believe that the results of the inference are also independent of the DF, which they aren't. There is no procedure you can write down that isn't. I spent time this weekend writing words about this, for reasons I can't currently understand.
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