Robert Thompson

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.

I then have a single \(\Sigma\) value per grid-cell and can make a direct comparison:

(plot made with gal_reduction/tools/sigmacompare.py via PIXELPLOT==1)

In an ideal situation, each line would lie on the one-to-one dotted black line. Unfortunately both Sobolev and HSML values under estimate the grid values. The good news is that there isn’t much difference due to the resolution. We might have to examine more galaxies within our sims in a similar fashion to see if this under prediction takes place at the same surface densities; if that is the case we can easily incorporate some sort of correction factor. But that leads to the question - how many galaxies do we have to look at?

legend(bbox_to_anchor=(0.1,1.05),loc=3,shadow=True,fancybox=True)

def histoit(values,COLOR,LABEL,HLS,BINSIZE=0.1):
indexes = where(values>0)[0] ##prevents -inf
vals = log10(values[indexes])
binner = arange(min(vals),max(vals),BINSIZE)
hist(vals,color=COLOR,log=True,
bins=binner,
label=LABEL,histtype='step',lw=1.5,ls=HLS)

[table] Before,After [/table] better right? hello?

And last but not least, I’ve plotted the gas particle positions for this galaxy at all three resolutions for visual inspection:

we go from slightly compressed cloud, to fluffy pancake, to regular pancake!

The new HI gradient stuff finished down to z=3.  Turns out it does make a small difference in the calculated Sobolev values of this particular galaxy.  At the same time however, we find now calculate the HI surface density via the grid calculation and drop that along with it, so the difference between grid & sobolev remains about ~1dex:(plot made via gal_reduction/tools/sigmacompare.py)

Sigma_HSML however remains a front-runner here as it’s separation is only about ~0.5dex or less depending on if we account for the spread.  2xSigma_HSML overshoots the grid calculation by a tiny bit.  In comparing these two galaxies I’ve also found that the Sigma_HI results in slightly less stellar and gas content:

It’s not entirely clear where to go from this point or which option is the best option to estimate the surface density within these SPH sims…