# How to calculate Helium lensing

Jon Richfield
Forgive what might strike you as an excessively elementary question, as well as irrelevant, but...
Well, at least I guarantee that it is not any classroom project!

Imagine a mass of pretty clean helium (yeah, *I* know, but this is an academic exercise! It gets worse; read on!) Imagine that its near "surface" temperature is somewhere near 200k to 300K and that everything in the neighbourhood is pretty stable and benign, apart from being cool. The mass is spherical and not rotating significantly. It also is sufficient to retain most of the He gravitationally for a few hundred million years or so. (A couple of Earth masses or so?)

Now, how do I calculate the characteristics of such a hypothetical spherical cloud? Could it have a homogeneous temperature, and if not, what would the entropic implications of its temperature profiles be? How far could one see through it? (Well, before dust started messing it up anyway!)

Why helium? Well, I suppose N2 or Ar would do as well, maybe better, but He seemed to avoid some possible practical problems under conditions at which ideal gas laws might get a bit distorted.

Then, if anyone did kindly explicate, would s/he like to imagine what would happen if the mass were indeed to be rotated at a speed sufficient to rotate non-turbulently, fast enough to flatten the spheroid very markedly, say to an aspect ratio of 1 to 2 or so? Would the density profile have any useful characteristics for lensing?

If no one has the patience for this, I would not feel insulted. I am familiar with the observation that a fool can ask more questions than ten wise men would bother to try answering.

But thanks if anyone feels like trying!

Jon