meeting 2024 02 01 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I've run a second grid of dither 1 models, slightly zoomed in from our original set of points:

    • BH = [5e8, 4e9]
    • ML = [2.0, 3.2]
    • rho = [1.7e9 6.5e9]
    • T = [0.5,0.99]
    • Tmaj = [0.01,0.5]
    • Tmin = [0.4,0.99]

  • I've combined this new 1000 points with our previous grid of 2931 points (was supposed to be 2000 but ~70 models got caught in the queue at one point). The two cubes are consistent with one another as are the resulting posteriors.

  • This new grid looks nice! We definitely find a part of the space that has a lower chi2, and the minimum for the shape parameters is starting to look nicer/more rounded out.

    • Given some of the diagnositcs below, I think we're fine to submit a subset of these models. If we wanted to keep the cube sizes approximately the same, we can use the same cutoff of K = 1500 to select the best 881 models. This would add to our 866 models that we have with d3 already.
    • Alternatively I can add some scalings of these dither1 models to improve what we currently have. Though, given that the minimizations cost about as much as the models themselves, it might be a bit of a waste.

Diagnostics

  • First, here's the breakdown of the number of models vs. K for this new grid of 1000 points:
K counts
10 1
50 4
100 10
250 62
500 300
1000 729
1500 881
2000 948
5000 999
  • And for all 2931 dither1 models:
K counts
10 1
50 5
100 11
250 77
500 435
1000 1262
1500 1726
2000 2034
5000 2655
Updated 1d panels of chi2 vs. parameters for the combined grid and the new grid alone.
Old Grid(1931) New Grid(1000) Combined Grid(2931)
I've also run gpr+dynesty on the 2931 models with various cutoffs. The posteriors look quite nice and reasonable!
K nu=0.5 nu=1.5
250
500
1000
  • Just out of curiosity, I've made a version of our cornerplot using these d1 model results (K=1000, nu =1.5) to see what the (upq) space looks like:
Plot

Proposal For New Points

  • I think the best plan forward is to, again, cut these d1 models at some value and re-run these models with dither3 + scalings. Given that the breakdown looks like:
K Num
10 1
50 4
100 10
250 62
500 300
1000 729
1500 881
2000 948
5000 999
  • I think keeping a similar sized grid of models with a similar cutoff makes the most sense. If we cut this at K = 1500, here is what the new grid would look like:
1d panels containing only the 881 best fitting models from this newest grid. Running this with d3 should take ~12*866 + ~0.75*866 = 11,000 SU
Plot slightly zooomed, identical set of points

Other random tests and diagnostics

I was curious how the 866 base models compared to the "best-scaled" 866 models to see how beneficial scaling is at populating the minimum. Here's a quick plot showing the CDFs of the base models and the best-scaled 866 models, which seems to show that scaling greatly improves (roughly doubles) the number of models within a couple hundred of the minimum.
Plot
I also wanted to be a bit more quanitative on the cost of the N315 models at this stage, so here are histograms of the time to integrate orbits and the time ot run the minimizations for our modeling efforts so far. The typical integrations and minimizations are ~1.25 hours for d1 models and 0.75 hours respectively; for the d3 models, these numbers are 12 hours and 0.66 hours, respectively.
grid orb integrate minimization
d1
d3
I've briefly started to look at the d1 and d3 models compared to one another to figure out the source of the difference in their kinematic chi2s. Note that this is still early, but it looks like the largest discrepency is in fact in our h6 kinematics between the two. I've attached two plots here. The first is our normal heatmap style plot for the moments and bins, but instead of the chi2, I'm plotting the difference in chi2 (d3-d1). This should highlight where our d3 models are performing exceptionally worse than our d1 models. I've also summed all the bins and plotted the same number but for the moments themselves, which again shows that h6 is contributing ~2 to ~3 times the fractional chi2 of the other momemnts
Plot
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