meeting 2024 07 01 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I've re-run the libraries for a significant fraction of the models which went into building our cornerplot:

    • Specifically, the cornerplot was built from ~4400 models within K = 50 of the chi2 minimum model.
    • ~4400 models felt like a lot to check this question we have, so I trimmed this down to ~1100 models for which I recomputed the libraries.

  • I then minimized two sets of kinematics:

    • The first set is the same binning/kinematics we used in the original models.
    • The second set of kinematics uses the correct binning scheme and is symmetrized with this correct binning scheme. I have a comparison of the input kinematics below, as well as a comparison of the outputs/chi2 profiles/GPR and dynesty results.

  • Some notes:

    • In the old models, the best-fitting model has:
      • BH = 5.517e9, M/L = 1.9982, rho=2.2866e9, T = 0.357, Tmaj=0.3015, Tmin=0.0145, and chi2 = 1276.74
    • The new models with the incorrect binning scheme has:
      • BH = 6.16e9, M/L = 1.83, rho=2.399e9, T = 0.378, Tmaj=0.241, Tmin=0.0044, and chi2 = 1274.43
    • The new models with the CORRECT binning scheme has:
      • BH = 5.78e9, M/L = 1.90, rho=2.098e9, T = 0.253, Tmaj=0.80, Tmin=0.003, and chi2 = 1277.73

  • Summary:

    • Some good news -- it looks like the updated binning scheme has a very minor impact on the chi2 values and the resulting parameters.
    • Largely, I think the agreement is driven by (a) there not being much of a difference after point-symmetrizing the kinematics, and (b) the constraints being driven primarily by GMOS data/the innermost data.
    • One thing to note is that the updated binning scheme did seem to clarify the issue a bit we were having with Tmaj, and seems to prefer the higher value for Tmaj. This could be one thing to consider/modify (since we are currently solving this issue by imposing a prior on Tmaj to "flatten" the bimodality).
    • This also bodes well for N2693 since that was a faster rotator.
Cutoff K Num. Models < min(chi2) + K [Base] Num. Models < min(chi2) + K [Orig] Num. Models < min(chi2) + K [Rebin]
1 1 2
5 4 16
10 38 71
15 140 177
20 292 349
25 478 517
30 631 662
35 751 780
50 973 959

Inputs

Irina's Vmap Irina's Binmap
Incorrect Binning Correct Binning
Unsym
Sym

Results

  • First, here are the 1d panels of the chi2 vs. parameters for the ~1100 models we just ran:
Incorrect Binning Correct Binning Original Version
  • And here's a one-to-one comparison of these chi2 values:
Plot Histogram
Two more one-to-one plots, showing the latest correct/incorrect binning versus the older equivalents of the models
Bad Bin to Bad Bin Comparison Bad Bin to Good Bin Comparison
  • Here are comparable cornerplots from running GPR/dynesty:
K Incorrect Binning Correct Binning Original Reprocessed
40
50
60
80
100
Plot Incorrect Binning Correct Binning
Beta
Moments
I also am including two heatmaps for the best fitting model from each case, showing the chi2 for each bin and moment
Incorrect Binning Correct Binning

A bit more diagnostics:

Here are a few diagnostics for the worst performing bin in the rebinned and re-computed original case -- it seems like the outer Mitchell are driving much of the increase in chi2, but I need more time to look at these models/more than just the worst performing.
Heatmap Radial
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