meeting 2024 08 27 n57 - JacobPilawa/TriaxSchwarzschild_wiki

Context

I've still been cleaning up some of the N57 results and looking into the NNLS vs. kinem chi2 differences like we've talked about the last few weeks.
- The first set of plots below contain the GPR + dynesty results coming from a few different tests we discussed last time. I've re-run all of our scales (and the best set of scales) with a complete set of nu's, Ks, and including/excluding the outer 4 kinematic bins (which seemed to have a preferentially high fraction of the total chi2).
  - Note that I'm including the scale = 0.97 and scale = 1.02 and 1.03 cases simply because it was free to run them as well, but their results are not to be taken seriously. I think we'll likely end up only using the scale = 1.0 cases (and maybe 0.5% scales if we add them, I just didn't have to the time to get around to that).
  - In total, it looks like we're converging on the reason for the NNLS and kinem differences -- it seems that the outermost bins have non-zero h1/h2, which then contribute to the difference in NNLS and kinem chi2. If we remove the outer 4 bins, we get rather normal looking posteriors which seem to be consistent with what the 1d panels suggest.
  - I think it might be worth running the 0.5% scales on either side of the scale = 1.0 grid, and then I think we can wrap up these results more or less. Unless we wanted to investigate h1/h2 parametrization a bit more.

First, here's a quick comparison of the 1D Panels with and without including the outer 4 Mitchell bins in the chi2, which seems to show the variance with rho0 is greatly diminished when masking the outermost data.

With Outer Bins	Without Outer Bins

One thing we wanted to see (and related to the LOSVD questioon below) is whether or not the outer 4 bins (which are low S/N in general) are driving the minimum location to anywhere in particular. This does seem to be the case, and removing the 4 outermost bins when computing the kinematic chi2 seems to improve the look of our posteriors. It does shift the parameters around a bit, but I think given how the outer bins seem to be driving our constraint, it might make sense to move forward with them being removed. Specifically, it seems the outer 4 bins drive us to the high Tmaj minimum which we have seen before, and removing those means our GPR + dynesty routine now prefers slightly closer to the low Tmaj minimum. Removing the outer 4 bins also seems to improve the shape of the rho0 landscape and the resulting posterior.
- Again, I would take the "best scales" here with a massive grain of salt since this includes the scaled models which we know are bad. We can adjust the "best scales" after running 0.5% scales after this meeting.

Bins	Scale = 1.0, nu = 0.5	Scale = 1.0, nu = 1.5	Scale = Best Scales, nu = 0.5	Scale = Best Scales, nu = 1.5
All Bins
No Outer 4

Cornerplots (all bins) with nu = 0.5

Cornerplots (all bins) with nu = 1.5

Cornerplots (excluding outer 4 bins) with nu = 0.5

Cornerplots (excluding outer 4 bins) with nu = 1.5

I've finished updating the LOSVD plotting script and have started to look at the LOSVDs in our model. The first few bullets here are simply plotting the LOSVD from all of our bins for a random model, but I think the more interesting bullet is just below.
- In the bullet at the bottom, I've taken the models we were looking at last time (in a thin slice of NNLS chi2 > 1315 & < 1320), and have plotted the first four and last four LOSVDs from the models.
- It seems to me that the quality of the LOSVDs at the outer edge of our data are significantly worse fit than our inner data. This makes sense. It's interesting because some of the outer bins do seem to have quite non-zero h1/h2, which I think is what we expected last time. This in turn is likely contributing the difference in NNLS chi2 and kinematic chi2. I still need to try to analytically derive this, but I think this is good evidence that it has to do with the moment parameterization.

Click to expand first 100 GMOS bins (takes awhile to load)

First 100 GMOS
images/240827/gmos_1-1.png

Click to expand the remaining GMOS bins (takes awhile to load)

First 100 GMOS
images/240827/gmos_2-1.png

Click to expand the Mitchell bins (takes awhile to load)

First 100 GMOS
images/240827/mitchell-1.png

A more useful way to look at these, I think, is to look at the LOSVDs for the models that we looked at last time, which feel in a thin slice of the NNLS chi2 between 1315 and 1320. This will allow us to see a great range of agreeing and disagreeing NNLS and kinem chi2s.
- So the plots below are the first 4 and last 4 bins for 13/39 models we were looking at last time in this thin slice.
- I've also included the plots we were loooking at last time to remind ourselves of the greater context.

Colored by	BH	ML	Rho0	T	Tmaj	Tmin
All Models
Base Models

As you'll see after we disucss the plots below, I've recreated these plots but have excluded the kinem chi2 contribution from the outer 4 and 8 bins to see if the relationships above improve, and that does seem to be the case:
- Note that the black lines here are 1:1 with a 30 and 50 offset along y for the 4, 8 excluded bin cases respectively.

Here's the cornerplot currently in the Overleaf for our reference. As a reminder, this uses the old, incorrect binning scheme AND the NNLS chi2 rather than the correct binning scheme and the kinematic chi2.


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