meeting 2025 11 10 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki
Context
Black Hole Mass Function Calculation
- We were feeling more comfortable with our stellar mass calculation from the AllWISE/unWISE W1 and W2 that we saw on the previous page. The AllWISE w1mpro and w2mpro are given in the WISExSUPERCOSMOS galaxy catalog, so I can apply our stellar mass estimation method to this data to obtain stellar mass estimates for the ~18 million galaxies.
- To seed the galaxies with SMBH's, I assume that their stellar mass is given by the Cluver+14 relation:
L(band)/L_\odot = 10^{-0.4(M(band) - M_\odot(band))}
\log(M/L) = -0.030 - 1.960\,(W1 - W2)
M^{*}_{AllWISE} = L_{AllWISE} \times \Upsilon_{ALLWise}
- With these stellar masses, I place an SMBH in each galaxy. The mass of the SMBH is drawn from a normal distribution centered at log(Mbh) = 8.46 + 1.05(log10(Mstar) - 11) with standard deviation of 0.34 (dex). That is to say, the black holes mapped to galaxies have masses given by:
\log_{10} M_{\rm BH} \sim \mathcal{N}\Big(\mu = 1.05\left( \log_{10} (M_\star) - 11\right) + 8.46, \;\sigma = 0.34\Big)
Planned Refinements:
-
There are a few things about the stellar mass calculation that I am planning to refine:
- This assumes that every galaxy has the same Mstar-->Mbh relationship (e.g., I am assuming bulge fraction = 1 for all galaxies). We can likely refine this with the B/R/W1/W2 photometry to get better bulge fractions.
- I have not done any k-corretions on the magnitudes nor the colors. These are likely small but not negligible for the W1 and W2 bands.
-
For the BHMF calculation, there are also a few things I am asserting/assuming:
- The fraction of sky area I'm assuming is 0.68*41,253 = 28,052 square degrees. This comes from Bilicki's final sky map, which says that 68% of the sky remains after their masking. I'm assuming that the volume is out to the maximum redshift object (which I've been cutting at z=0.45 based on their text just before Sect 4).
Simplest BHMF Calculation Result
- The most straightforward way to calculate the BHMF is to count up all the SMBHs in a given mass bin, and divide the counts in that bin by the survey volume:
- The bin width is 0.2 dex.
- The full survey volume is obtained from a sphere with radius ~1722 Mpc (comoving distance to z=0.45). The total volume is thus 2.1e10 Mpc^3, but only ~68% of the sky is accessible, so this is actually 1.45e10 Mpc^3.
- The mass function is thus:
\Phi = \frac{\text{counts}}{\text{(bin width)}\text{(survey volume)}}
- The result from this calculation (along with Eq. 3 from Emily's paper [though I think the parameters quoted are not correct]):
- Given how crude of a method this is, I'm quite happy with the overall shape here. The low end is likely undercounted due to the lack of weighting by 1/Vmax (and therefore we're missing lots of faint sources)
- Note that the WISExSUPERCOSMOS data throw out the brightest sources, so I'm not surprised to see disagreement at the massive end too (though I'm a bit surprised that it's overpredicted, but again we're doing a strange normalization here), so maybe not the worst result.
| Simplest BHMF Calculation (z between 0.001 and 0.45) |
Simplest BHMF Calculation (only sources with z between 0.001 and 0.1) |
| [images/251110/simplest_updated_emily_curve.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251110/simplest_updated_emily_curve_z0p1.png) |
|
1/Vmax Result
-
We can be a bit better in our construction of the BHMF by using the 1/Vmax approach, as I had done with the GSMF a month or so ago. The idea there was, instead of each galaxy contributing 1 to its mass bin, we can weight each galaxy by 1/Vmax, where Vmax is the maximum volume within which we could detect this galaxy in our survey. There are a few parameters we need for this:
- limiting W1 magnitude = 17.0 (taken from Bilicki, but I think this is sligtly fuzzy since I'm not sure exactly what type of limit this is).
- Still using 68% of the full (41,253 deg^2) sky for the sky fraction
-
Here's the full calculation broken into steps:
1. Redshift Selection
- Taking the redshifts > 0 and less than the cutoff. These redshifts are the photo-z's esimated by Bilicki from their neural network.
2. BH Mass Binning
- I then bin the SMBHs into log mass bins of width ΔlogM = 0.2 dex:
\Phi(\log M) \equiv \frac{N(\log M)}{V_\text{eff}\,\Delta \log M}
where
- N(log M) = number of black holes in that bin
- V_eff = effective comoving survey volume available to galaxies of with that black hole mass.
3. Vmax/Veff calculation
- For each galaxy, I calculate the maximum redshift at which it would still be detected given the W1-band depth of WISE. I calculate this via:
D_{L,\max} = 10^{\frac{m_\text{lim} - M + 5}{5}}~\text{pc}
where mlim is the limiting W1-band magnitude of the survey and M is the absolute W1-band magnitude (calculated from the apparent W1 and the distance modulus [derived from the redshift])
- I then invert D_L(z) to find the maximum redshift at which the galaxy is still detectable, assuming H0=70 and Om0=0.3, and compute the accessible comoving volume for this galaxy:
V_\text{max} = \left[ V_c(z_\text{max}) - V_c(z_\text{min}) \right] \times f_\text{sky}
4. Number Density Estimate
- I can then estimate the number density via:
\Phi(\log M) = \frac{1}{\Delta \log M} \sum_{i \in \text{bin}} \frac{1}{V_{\max,i}}
5. Error Estimates
- Uncertainties on each mass bin are computed as:
\sigma_\Phi = \frac{1}{\Delta \log M}
\sqrt{ \sum_{i \in \text{bin}} \frac{1}{V_{\max,i}^2} }
Results
| 1/Vmax Result (z between 0.001 and 0.45) |
1/Vmax Result (only sources with z between 0.001 and 0.1) |
| [images/251110/1_over_vmax_updated_emily_curve.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251110/1_over_vmax_updated_emily_curve_z0p1.png) |
|
1/Vmax Result with Upper and Lower Magntiude Limits
- One of the interesting things about the WISExSUPERCOSMOS data is that Bilicki throws out the brightest sources as well (brighter than W1 = 13.8). I think that the fiducial 1/Vmax method wouldn't account for this, so I modified the 1/Vmax calculation to account for both the upper and lower magnitude limits (when computing Vmax for each galaxy). So instead of 1/Vmax, each galaxy would contribute 1/Vmax - 1/Vmin (defined by the magntiude upper and lower limits). This seems to be more correctly capturing the spirit of the WISExSUPERCOSMOS dataset.
| 1/Vmax with upper and lower limits Result (z between 0.001 and 0.45) |
1/Vmax with upper and lower limits Result (only sources with z between 0.001 and 0.1) |
| [images/251110/1_over_vmax_with_upper_and_lower_with_updated_emily_curve.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251110/1_over_vmax_with_upper_and_lower_with_updated_emily_curve_z0p1.png) |
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GSMF for the WISExSCOS Data
- Chung-Pei had suggested I try to construct the GSMF from the Cluver+14-derived masses on the WISExSCOS data, so here's some related diagnostics. With the stellar masses from the Cluver+14 prescription, I computed the GSMF for all sources and for only those sources between z=0 and z=0.1. The results are here:
| All Sources |
z<0.1 |
| [images/251110/GSMF.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/251110/GSMF_z0p1.png) |
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testing a stellar mass offset
- We had found before that the masses I had been deriving were anywhere from ~0.65 to ~0.75 dex lower than Emily's estimates from the K-band absolute magnitude. One silly test I checked really quickly is the impact if we assume a ~0.70 dex offset in the masses. Adding this fix amount of mass to every galaxy, I get the following:
- Note that I'm including a case where I include a lower limit on the redshift too (rather than just >0). I suspect some objects have very small (and incorrect) redshifts, contaminating especailly the lower end of the relation.
Refined BHMF Calculation
- As mentioned above, my first pass at the BHMF hadn't accounted for any of the k-corrections from Jarrett+23. The k-corrections I'm talking about are in Figure 9 of Jarrett+23. It's roughly a ~10% correction for the W1 fluxes, and roughly ~0.1 mag correction for the W1-W2 colors. So not huge, but definitely not negligible.
- I've repeated the 1/Vmax calculation with and without the k-corrections, and have a comparison here:
- Note that I'm taking sources within 0.001 to 0.1 for this plot.
- Seems like the general effect is that the low mass end is not too appreciably affected; the high mass end gets bumped up a little bit, but not by multiple orders of magntiude.
Some other follow ups from last week
A NOTE ON THE SECTION BELOW
- This section is a copy of the work on from the bottom of this page. I wanted to include it here since we never got a chance to discuss the results here.
Crossmatching with WISE2MBH and Siudek+24
- With the MASSIVE galaxy W1 and W2 obtained from AllWISE/unWISE, I cross matched the WISE2MBH and Siudek catalog with our MASSIVE galaxies. Note that I'm including all of the galaxies here (even the 3 noted above with very strange W1 and stellar masses).
Matching with Siudek
- Only 3/115 MASSIVE galaxies are included in the Siudek value-added catalog. Their data are in this table:
|
Name |
WISE2MBH_Z |
SIUDEK_z |
emily_estimate |
allwise_Mstar_Cluver14 |
unwise_Mstar_Cluver14 |
WISE2MBH_LOGSM |
SIUDEK_logM |
| 35 |
NGC 1600 |
0.015824 |
0.0157116 |
11.9151 |
11.1381 |
10.8686 |
11.1384 |
11.1911 |
| 80 |
NGC 4816 |
0.023083 |
0.0230616 |
11.5917 |
11.1403 |
10.9293 |
11.1233 |
11.3017 |
| 81 |
NGC 4839 |
0.02448 |
0.0245265 |
11.8465 |
11.1864 |
10.9563 |
11.2071 |
11.3294 |
Matching with WISE2MBH
-
110/115 of the MASSIVE Galaxies are in WISE2MBH, but the final sample I'm comparing here is 107/115 of the galaxies. I've removed three additional galaxies which had weird looking W1 measurements from above along with the 5 non-matches. The galaxies which are removed are:
- NGC 0910 (strange W1)
- NGC 4472 (strange W1)
- NGC 4649 (strange W1)
- UGC 01389 (non-match)
- NGC 0890 (non-match)
- NGC 1497 (non-match)
- NGC 2256 (non-match)
- NGC 7426 (non-match)
-
From the 107/115 sample, two galaxies stood out as having very discrepant stellar masses compared with the WISE2MBH values. I've also removed these two from the comparison below, since there's likely something going on with them that I don't fully understand yet. These galaxies are listed below along with their data:
|
Name |
WISE2MBH_Z |
SIUDEK_z |
emily_estimate |
allwise_Mstar_Cluver14 |
unwise_Mstar_Cluver14 |
WISE2MBH_LOGSM |
SIUDEK_logM |
| 88 |
NGC 5252 |
0.02294 |
nan |
11.5868 |
9.99235 |
9.76594 |
10.4481 |
nan |
| 77 |
NGC 4486 |
0.0042 |
nan |
11.5819 |
10.2638 |
9.86291 |
11.53 |
nan |
- We can look at the remaining set of 107/115 MASSIVE galaxies, and compare the various stellar mass estimates.
- NOTE: THIS IS STILL A WORK IN PROGRESS FRIDAY AFTERNOON!
