meeting 2026 01 17 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

  • Exploring the highest mass galaxies in a bit more detail now that the k-corrections are understood.

  • In particular, I'm posting a variety of diagnostics comparing choices made when using the J23 and C14 stellar mass calculations.

  • Takeaways:

    • The C14 prescription does a much better job of reproducing Emily's GSMF, in particular at high masses. This is primarily because the M/L relation from C14 produces generally higher M/L ratios in the part of the color space where we have the most data.
    • The result is that, whereas we had only ~10 galaxies about 10^{12} Msun using the J23 prescription, this number gets boosted to ~several thousand using the C14 relation, without appreciably changing the lower mass tail of sources. This boosts the resulting high mass part of the GSMF, and we're in much better agreement with Emily's predictions.
    • The color-clipping has a very minor effect on the stellar masses, as tested below. This is in part due to the clipping suggested by J23 is approximately the same range of colors that C14 has data for. There's not an appreciable change in the results whether or not we do this clipping.

  • BHMF Discussion:

    • I've also recomputed the BHMF in two ways. One way assumes that the Mbh's are from the mean MM13 relation, whereas the other includes the intrinsic scatter term. From these plots, you can see that the shape of the BHMF (in particular at the high mass end) is being driven by the intrinsic scatter; without the intrinsic scatter, our BH densities are far too low at the high M end.

Diagnostics

  • There are a few key differences I'll mention here about the C14 vs. J23 prescriptions:

    • The formulae for going between M/L and W1-W2 are slightly different:
      • C14: log(M/L) = -1.96*(W1-W2) - 0.03
      • J23: log(M/L) = -1.053*(W1-W2) - 0.376
    • K-Corrections:
      • C14 seems to only k-correct the observed colors to rest-frame colors, and they do this with more complicated SED fitting to the optical and near-IR photometry. Doing these SED fits, they get the k-correction for each object. They do not seem to do any k-correction to the W1 magnitudes. They also do
      • J23 explictly k-corrects both the W1 flux and the W1-W2 colors.
    • Color Clipping
      • C14 does not do any "clipping" of the colors, but their data span roughly W1-W2 = (-0.2,0.4), so it probably makes most sense (in terms of sticking with the data) to clip colors here.
      • J23, on the other hand, "clips" the colors to be between (-0.2, 0.4), arguing that colors beyond this range are not realistic.

  • As a quick case study -- note that WISE2MBH, for example, chooses to use the C14 formula for M/L, but uses the J23 k-corrections. They also clip the colors to be between (-0.2, 0.6), meaning that WISE2MBH is a blend of both C14 and J23.

  • So what's the plan:

    • Given that the k-corrections are better understood now, my plan is to try both the C14 and J23 M/L relation, as well as trying the clipping both on and off for the C14 data. So for clarity, here are the cases that seem most relevant to me:
      • C14 without clipping
      • C14 with color clipping
      • J23
    • Note that I'm using the k-corrections from J23 in all of this.

Plots

  • As a quick reminder, here's a comparison of the J23 vs. C14 M/L relation:
M/L Relation
images/260119/ml_relations_251215.png
  • First, here's a comparison of the msases for the 3 cases above. In line with the J23 paper, the masses we are finding with the J23 prescription are generally smaller than the masses found with C14 , so swapping to the C14 prescription seems to improve our number of galaxies above say 10^{12} Msun.
    • I've also included a plot of the residuals. Note that C14 vs. C14 clipped panel is quite "squished" in these plots, and the vast majority of points lie directly on the 1-to-1 (since we only have a small number of sources which have their colors clipped to the extreme values).
Case Plot
One-to-one images/260119/one_to_one.png
Residuals images/260119/residuals.png
Distributions and CDF images/260119/dists.png
  • And here's a table showing the number of sources in various mass bins:
    • Note that the C14 prescriptions give us a healthy number of sources above log(M*) = 12 or so, which was a concern of ours when using the J23 prescription alone. This is also roughly independent of the color clipping.
Mass bin (log M*) C14 N C14 % C14_clipped N C14_clipped % J23 N J23 %
<6.0 1,062 0.01 971 0 1,134 0.01
6.00–6.25 444 0 399 0 452 0
6.25–6.50 609 0 548 0 642 0
6.50–6.75 877 0 749 0 898 0
6.75–7.00 1,382 0.01 1,142 0.01 1,421 0.01
7.00–7.25 2,337 0.01 1,908 0.01 2,290 0.01
7.25–7.50 3,811 0.02 3,073 0.02 3,802 0.02
7.50–7.75 6,362 0.03 5,141 0.03 6,402 0.03
7.75–8.00 10,970 0.06 8,762 0.04 11,534 0.06
8.00–8.25 19,466 0.1 16,007 0.08 21,548 0.11
8.25–8.50 34,872 0.18 29,507 0.15 40,678 0.21
8.50–8.75 63,173 0.32 55,153 0.28 78,358 0.4
8.75–9.00 113,767 0.58 101,864 0.52 150,100 0.77
9.00–9.25 209,126 1.07 191,120 0.98 290,177 1.48
9.25–9.50 380,396 1.94 357,099 1.82 571,380 2.92
9.50–9.75 695,577 3.55 669,677 3.42 1,141,256 5.82
9.75–10.00 1,293,095 6.6 1,265,068 6.45 2,115,568 10.79
10.00–10.25 2,326,234 11.87 2,335,314 11.92 3,427,969 17.49
10.25–10.50 3,542,494 18.07 3,627,710 18.51 4,524,916 23.09
10.50–10.75 3,839,010 19.59 3,869,457 19.74 3,809,689 19.44
10.75–11.00 3,228,355 16.47 3,231,651 16.49 2,217,169 11.31
11.00–11.25 2,205,490 11.25 2,206,225 11.26 904,654 4.62
11.25–11.50 1,120,911 5.72 1,121,174 5.72 256,968 1.31
11.50–11.75 412,935 2.11 413,018 2.11 20,317 0.1
11.75–12.00 84,817 0.43 84,829 0.43 38 0
12.00–12.25 1,792 0.01 1,797 0.01 7 0
12.25–12.50 6 0 9 0 4 0
>=12.5 4 0 2 0 3 0

Resulting GSMF and BHMF

  • I can then compute the GSMF from these as we have done before, and we're actually approaching a very nice agreement, in particular with the C14 mass prescription:
    • I've also included two versions of the black hole mass function. The first assumes that the black holes are the mean relation from MM13, whereas the second version does a single draw from a log-normal distribution centered on the mean relation from MM13, but with the intrinsic scatter term:
    • The BHMF are also in much better agreement with the Liepold+24 curve, with what seems to be an approximately fixed offset from the predicted curve.
J23 C14 C14 Clipped Colors
GSMF [images/260119/GSMF_J23.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260119/GSMF_C14.png) images/260119/GSMF_C14_clipped.png
BHMF no scatter [images/260119/BHMF_J23.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260119/BHMF_C14.png) images/260119/BHMF_C14_clipped.png
BHMF with scatter [images/260119/BHMF_J23_scatter.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260119/BHMF_C14_scatter.png) images/260119/BHMF_C14_clipped_scatter.png
  • Note that this still does the simple 1/Vmax method, and that we'll want to use the Leja+20 poisson process method, but I needed something here for reference.

Comparison with K-Band

  • I've also replotted the K-band stellar masses vs. the stellar masses presented above (J23, C14, and C14 no clipped):
    • It's certainly true that the naive line-of-best fit agrees more with the C14 and C14 clipped data vs. the J23 prescription, but it's probably not best we read too much into the actual fits.
  • Note that the top panels are the one-to-one plots; bottom are the same but plotted as residuals.
K-Band Comparison
images/260119/3panel_Mstar_comparison.png
images/260119/3panel_Mstar_diff_hist.png