Question: does the mass-weighted Sobolev/HSML surface density
per-particle along a column make any sense? I’m not so sure it does as
the idea of a single SPH particle having it’s own surface density is
kind of a stretch in it’s own right. To take a deeper look I ran
through the grid calculation again, but this time I returned the grid
indexes [x,y] for each particle. I then plotted the calculated
(smoothed) $$\Sigma$$ value for each cell vs. the raw per-particle
$$\Sigma_{\rm{sob}}$$ value. The result was a little different than
I was expecting:
At first I thought it was wrong. But then I took a deeper look at the
radial values for Sobolev/Sigma from a previous post (bottom left
panel):
and realized that they were indeed correct. This is basically telling
us that there is signifiant spread in the Sobolev surface density
values with a pretty substantial under-estimation as very few of those
blue dots lie on the 1-to-1 line. HSML looks very similar, but the
normalization is slightly higher. And apparently when one takes the
mass-weighted average along a column (with smoothing), the mass
contribution spills into neighboring cells pretty significant lowering
the sobolev $$\Sigma$$ substantially.
The saga continues…still no clear direction in how to resolve this issue.
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