meeting 2025 06 16 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

Adding some plots here concerning the pairwise chi2 differences for the line of N315 models.
As a quick reminder, I had run essentially three lines of models:
- Line A: Delta Mbh = 0.1e9 between ~2 and ~4 billion
- Line B: filled in the gaps every 0.05e9 between ~2 and ~4 billion
- Line C: Line A + Line B points, but shifted up in BH Mass by 0.01e9
So cominbing Line A + B will give one set of Delta Mbh = 0.05 models, and Line C on its own will give another set with the same delta Mbh = 0.05.
Takeaways:
- It seems to be that the diagnositcs below are consistent with the claim that the model to model variation in our chi2 is something like ~6. In particular, the widths of the chi2 distributions for 0.01, 0.04, and 0.05 all have approximately the same width of ~6.
- Moreover, at the bottom of the page, I have two plots showing the median chi2 difference vs. BH Mass, and this seems to suggest that the chi2 differences are ~consistent with 0 up until ~0.2e9 or so, at which point they start to noticeably diverge from 0. It is a bit funny that this corresponds to approximately the size of our errorbar on the BH mass quoted in the paper, but I imagine that is somewhat of a coincidence.

To start, here are the two groups (Lines A + B) vs. (Line C) plotted as chi2 vs. Mbh:

Lines A + B	Line C Only	Line A + B + C
[images/250616/lines_a_and_b_fit.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250616/lines_c_fit.png)	images/250616/all_fit.png

	Line A + B Only	Line C Only	Line A + B + C
Full Range	[images/250616/line_a_b_full.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250616/line_c_full_range.png)	images/250616/all_full_range.png
Zoomed to Small Mbh Differences	[images/250616/line_a_b_zoom.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250616/line_c_zoom.png)	images/250616/all_zoomed.png

We can look at the distribution of chi2 differences for (Lines A + B) vs. Line C separately to get two sets of delta Mbh = 0.05e9 cases:

Case	Plots
raw difference	images/250616/raw_difference.png
absolute difference	images/250616/abs_difference.png

Putting together all three lines, we can look at the 0.01, 0.04, and 0.05 differences all together.

	Pairwise Chi2 Difference vs. Mbh Difference
Full Range	images/250616/all_lines_full_range.png
Zoomed	images/250616/all_lines_zoom.png

And breaking this into the distributions for the chi2 for the 0.01, 0.04, and 0.05 differences in Mbh:

Raw Difference	Absolute Difference
[images/250616/raw_difference_all_cases.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250616/abs_difference_all_cases.png)

I think this plot is somewhat useful too -- after computing pairwise differences for all models, I've overlaid the median pairwise difference for each delta MBH to get a sense of how the chi2 difference seems to depend on the black hole mass for all cases:

Raw Values	Absolute Values
[images/250616/grouped_medians.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250616/grouped_medians_abs.png)

Chung-Pei had the idea to try this with our actual model points, since this is similar in spirit to the 1d marginalized case, and more similar in spirit to how we do our constraints. To that end, I've taken the models within 3sigma of our minimum, computed the pairwise differences in both chi2 and parameters, and have the results here:
- It seems like the freedom of having the other 5 parameters allowed to vary reduces the model-to-model variation as we might expect. This brings down the variation as a function of parameters to something closer to ~3.2 rather than ~6 when we kept 5 out of 6 parameters fixed:

3 sigma pairwise points
images/250616/pairwise_3_sigma_points.png