The notation I think best describes it is
## F = \lVert\int^{space}_s|\vec{V}|ds\rVert ##
So you have a vector field V in a 3d space. For each point you integrate over all of space (similar to a gravitational or electromagnetic field) *but* vectors in opposite directions do not cancel, they...
OMG, thank you. I tried searching for "mass density of galaxy cluster gas" and variations but never intergalactic gas. The results I found focused on electron density and I struggled to understand the papers e.g. https://academic.oup.com/mnras/article/457/1/281/989241
Clearly I need google my...
This is outstanding and insanely helpful. This goes so far above and beyond the detail and thoughtfulness of response I could have hoped for. I can't thank you enough!
SPARC looks to be exactly what I wanted, however the richness in the breadth of other material is what I needed. Thanks again
Unsurprisingly the Milky Way seems to have been studied a lot. We have really good luminous mass profiles (e.g. McMillan 2011) and increasingly accurate circular velocity observations for stars at various radiuses (e.g. Eilers 2019) meaning we can confidently infer dark matter models.
So the...
Context
Boltzmann first defined his entropy as S = k log(W). This seems to be pretty consistently taught. However, the exact definitions of S & W seem to vary slightly.
Some say S is the entropy of a macrostate, while others describe it as the entropy for the system. Where the definition of...