meeting 2026 01 06 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

  • A few brief updates while trying to clean up the GW source catalog:

    • I first tried to track down some dynamical Mbhs that we can compare our W1 and W2 inferred masses to. This has been a bit of a pain to be confident in the matches, but at least currently, I have a set of results that I'm happy with.
    • I took the table of Mbh from van den Bosch (2016), and queried SIMBAD for the WISE designations for each source here.
    • I then matched these WISE designations with those in my catalog, and I found 35 galaxies which are common between our catalog and Remco's list of Mbh, which felt on the low end, so I instead opted to do coordinate-based matching until I figure out why the designation based matching might be not working.
      • Note that I tried to do a similar exercise with the growing list of Mbh I'm collecting, but found the matching to be a little less robust (and found only ~5 sources), so I'm sticking for now to the VDB set of sources.
    • COORDINATE MATCHING NOTES:
      • I've included a plot below of the ~160 sources for which I have a match. Note that the largest separation is ~1.5 arcsec for sources that I am conisdering 'matched,' though the typical separation is much much smaller.
      • If we are confident in the coordinate matching results (which I think I am so far), the result is that the dynamical Mbh appear to be ~0.1 dex larger than those from the W1 and W2 measurements, which is a really excellent level of agreement given how different the methods of mass determination are.

  • I've also done a bit of work trying to track down what the "straggler" low mass sources are, and wanted to repost the "simpler" prescription for the masses using W1 alone. I've got some plots near the bottom that I will elaborate on, but for now have mostly been working on the Mbh comparisons with different methods.

Diagnostics

  • One interesting note -- I have been trying to play around with AI agents recently, and fed it both the MM13 and vdb16 papers. I then asked it to compare and constrast the samples/generate samples/figure out overlapping sources, etc:

  • I was also curious how it would do at compiling some BH mass literature. Need to verify this, but I tested two different models, and then asked a third model to compare the two compilations to create a master "summary" document:

(VDB+16) Comparing Dynamical Mbh to W1/W2 Inferred Mbh

  • First, here's a (large) plot showing the matching procedure for the galaxies that I can confidently match. To get these matches, I basically cross-matched the coordinates between VDB+16's table and our catalog. I'm plotting all sources within ~0.1 degree of the target source, and I'm only keeping "matches" which have the nearest separation at 2 arcsec or less.
Arcsec sep. for the ~160 matches
images/260106/sep_arcsec_vdb_matches.png
  • And here's a larger plot showing the target source with all sources within 0.1 degree around it. You can see here how nice these ~160 sources are matched:
Matching Radii
images/260106/all_matches_combined.png
  • And here's the 1-to-1 plot (withthe vdb errors), as well as the residual with a fitted histogram:
1-to-1 Residuals
[images/260106/comparison_plot_upperlimits.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260106/resid.png)

(MM13) Comparing Dynamical Mbh to W1/W2 Inferred Mbh

  • Following Chung-Pei's email, I also tracked down as many of the matching sources in MM13 that I could find, and have the results plotted here. Again, this was a quick-and-dirty test, but I maanged to find ~40/72 sources in MM13 that I also have in WISE. Here's the arcsec separations to start:
Arcsec sep. for the ~40 matches
images/260106/sep_arcsec_mm_matches.png
  • And here's a larger plot showing the target source with all sources within 0.1 degree around it.
Matching Radii
images/260106/all_matches_combined_mm.png
  • And here's a 1-to-1 plot comparing the black hole masses recovered:
1-to-1 Residuals
[images/260106/comparison_plot_upperlimits_MM13.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260106/resid_mm13.png)

A quick comparison of the MM13 and

Simpler J23 Stellar Mass Prescription (from last time, to discuss)

  • First, here's a quick comparison of the M* obtained from the "simple" J23 prescription which uses W1 luminosity alone, compared with the prescription which takes the W1-W2 color into account.

  • For clarifying, here are the two most relevant expressions for calculating the masses:

  • Getting the luminosity:

L(band)/L_\odot = 10^{-0.4(M(band) - M_\odot(band))}
  • Getting M/L from the J23 prescription:
\log(M/L) = -0.030 - 1.960\,(W1 - W2)
  • Getting stellar mass with L and M/L
M^{*} = L_{W1} \times \frac{M}{L_{W1}}
  • Getting stellar mass from L alone:
\log_{10} M_\star = -12.62185 + 5.00155\,\log_{10}(L_{W1})
- 0.43857\,\left[\log_{10}(L_{W1})\right]^2
+ 0.01593\,\left[\log_{10}(L_{W1})\right]^3
  • And if I apply these prescriptions to our data, I get the following:
    • I included a version where the y-axis is logged so you can better see the wings of the residual distribution.
One-to-One Residuals Residuals (log y scale)
[images/251218/one_to_one.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251218/residuals.png) images/251218/residuals_log_scale.png

Tracking down the Low M* Tail of Sources (a bit from last time, to discuss)

  • We also have been curious about the low-lying tail of sources in this plot:
images/251218/stragglers.png

  • I've tried a few different ways of visualizing the data so we can narrow down what these sources are. It seems like they're in large part some of the FAINTEST sources in the data (with M_{W1}>=-16 or so), and they are all preferentially W1-W2<0 (restframe) colors.

    • This is noteworthy because WSCOS cuts out W1-W2<0 from their data (though it seems they do these cuts in the observed frame and not the rest frame).

  • The two most relevant plots showing this are here:

    • I think the Mass differences vs. Color plot is the most telling -- seems pretty clear that the majority of the low mass sources (and, in turn, the most discrepant from the K-band measurements), are located at or below W1-W2=0
    • The other plot confirms that we're looking at the faintest (absolute) sources. Going to look to see if the redshifts for these sources are particular.
Mass differences vs. Color Mass differences vs. Absolute W1 Magnitude
[images/251218/plot1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251218/plot2.png)
  • Maybe a path forward is to first apply the same W1-W2<0 cut to the 2MPZ data and see how things are cleaned up. Alternatively, we can also do the cut in the rest-frame, but that probably requires us to look a bit into the general population of W1-W2 colors for the galaxies we expect in our sample.

(some follow up on stragglers, 1/7/2026)

  • It's a bit complicated to disentangle why exactly we have the low lying tail of straggler points (since in the plot with the stragglers, we only have the K-band measurements for the 2MPZ galaxies, rather than also for the full WSCOS ~18 million galaxies).

  • With that said, I've plotted the rest frame color vs. inferred stellar mass (with the J23 prescription), colored by either 2MPZ or WSCOS catalog (the source catalog for each point). Note that I've also included one with contour lines, but note I had to drastically downsample the points to get the kernel density estimate to run in a reasonable time.

    • It seems like there's less of a bias between catalogs, and that both catalogs have a number of sources that are pretty low in stellar mass. It doens't appear like it's being driven by 2MPZ or WSCOS, but likely just some contaminating sources that are not flagged as stars, etc.

  • At this level, it seems like we might just have to impose some lower stellar mass cutoff (1e7 Msun?) to clear out the low-lying points. I'm not sure there will be a nice method to disentangle the stragglers from the main population.

    • Currently I'm looking into more than just the W1-W2 colors (we also have R and B band measurements), and I'll see if I can make any sense of those results!
Scatter plot 25x downsampled contours
[images/260106/color_mass_distributions.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260106/color_mass_distributions_contours.png)
  • I've also added a plot of the histograms for each catalog, and a plot of the M* vs. W1 absolute magnitude. These are just trying to see what the data looks like; they're not necessarily the most informative.
Histogram Mass vs. W1 abs mag
[images/260106/hist_distributions.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260106/mass_versus_W1.png)