meeting 2025 09 24 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

Following up on some of the questions from email exchanges with Chung-Pei about the Zou+22 catalogs vs. the Siudek+24 catalogs.
First, just some information on the catalogs:
- Zou+22's data are combinations of the 9th data release of the DESI Legacy Imaging survey (~320 million objects), DES (~292 million objects), and HSC-SSP (~133 million objects).
- Siudek+24's data are from the DESI early data release, which obtains spectroscopic information on ~1.3 million objects of the ~320 million in the full DESI 9th data release. So the Siudek data are spectroscopic redshifts and information from the spectra, rather than from 5-band imaging data. More Siduek data is likely to be released when they process DESI's DR1.

First, here's a plot showing the sources from each catalog along with the sources in Siudek+24. Note that for DESI/DES/HSC I'm downsampling by a factor of 1000, otherwise there's an overwhelming number of points on the plot and I run into some memory issues. However I'm including ALL 1.3 million Siudek sources.
- You can see that the Siudek+24 sources are roughly randomly sampled from the larger DESI footprint:
- Also note that my figure seems to match the DESI EDR page here: https://data.desi.lbl.gov/doc/releases/edr/

Sky Coverage
images/250924/reproducing_zou_figure1.png

I've tried to turn the three catalogs into their own GSMFs using this procedure.
- Basing this off of the procedure outlined here: https://academic.oup.com/mnras/article/459/2/2150/2595150

Every galaxy has a photoz measurement; some of them have a specz measurement as well. Where available, I take the specz measurement to be the "truth." If there's no specz measurement, I take the photoz.
I then select only galaxies falling between z=0 and z=0.1.

\Phi(\log M) \equiv \frac{N(\log M)}{V_\text{eff}\,\Delta \log M}

where

N(log M) = number of galaxies in that bin
V_eff = effective comoving survey volume available to galaxies of that stellar mass.

For each galaxy, I calculate the maximum redshift at which it would still be detected given the r-band 5sigma depth of each survey. I calculate this via:

D_{L,\max} = 10^{\frac{m_\text{lim} - M + 5}{5}}~\text{pc}

where mlim is the limiting r-band magnitude of the survey and M is the absolute r-band magnitude reported in the catalogs I've downloaded.

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}

\Phi(\log M) = \frac{1}{\Delta \log M} \sum_{i \in \text{bin}} \frac{1}{V_{\max,i}}

\sigma_\Phi = \frac{1}{\Delta \log M} 
\sqrt{ \sum_{i \in \text{bin}} \frac{1}{V_{\max,i}^2} }

Some relevant information for each of the surveys (taken from Zou+22):
- HSC-SSP: Survey Area = 1128 deg^2; 5sigma depths: g=26.5, r=26.5, i=26.2, z=25.2, y=24.4
- DES: Survey Area = 5194 deg^2; 5sigma depths: g=25.4, r=25.1, i=24.5, z=23.8, Y=22.4
- DESI: Survey Area = 19876 deg^2; 5sigma depths = g = 24.7, r = 23.9, z = 23.0, W1 = 20.7, W2 = 20.0
For those parameters, here are the z=[0,0.1] GSMFs that I've computed:
- GSMF with all galaxies
- GSMF for galaxies with specz measurements only

All Galaxies	Specz Measurements Only
[images/250924/vmax_method_combined.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/250924/vmax_method_combined_specz_only.png)

One of the important things I haven't been considering up until now is the completeness (in stellar mass) of these catalogs, so I've been trying to quantify this a bit.
It seems like most folks use the approach outlined in Pozzetti (2010). Here's a brief description of this method:
- Note some of the subsequent follow-ups have made additional cuts based on color which I haven't incoprorated here, but that could be something to add in the future. Ok, now for a summary of the method:
To compute a minimum mass M_{min}, above which the GSMF is essentially complete because all types of galaxies are potentially observable above this mass, we:

Calculate the limiting stellar mass (M_{lim}) of each galaxy, i.e., the mass it would have, at its redshift (specz or photoz if not available), if its apparent magnitude were equal to the limiting magnitude of the survey (Ilim = 22.5) given by log(Mlim) = log(Mbest) + 0.4(Rapp − Rlim).
- In this expression, log(Mbest) and Rapp are taken from the survey catalogs. I assume the magnitude limit of the R band for the 3 surveys given in Zou+22.
- The result is a distribution of limiting stellar masses, Mlim, that reflects the distribution of stellar M/L ratios at each redshift in our sample.
To derive a representative limit for the sample, find the 20% faintest galaxies (by apparent R band mag) and find the corresponding M_{lim} for those galaxies computed in (1).
- This choice takes into account the colourluminosity relation and therefore includes only galaxies with a typical M/L close to the magnitude limit. By doing this, we avoid the artificial use of a too stringent limit related to the brightest and reddest (with the highest M/L) galaxies, which do not significantly contribute close to the magnitude limit of the survey
We then define Mmin(z) as the upper envelope of the Mlim distribution below which lie 95% of the Mlim values at each redshift. This Mmin corresponds to a 95% completeness limit to the M/L ratio at each redshift observable by the survey, and is taken to be the completeness limit of the GSMF.

HSCSSPDR3	DESDR2	DESIDR9
[images/250924/MLIM_RESULTS_hscpdr3_wide_galaxy_cspcat.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/250924/MLIM_RESULTS_desdr2_galaxy_cspcat.png)	images/250924/MLIM_RESULTS_desidr9_galaxy_cspcat.png

And here's a second version of these plots I made with the "fiducial" 20% faint fraction and 95% completeness:

HSCSSPDR3	DESDR2	DESIDR9
[images/250924/hscssp_z_vs_stellar_mass.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/250924/desdr2_z_vs_stellar_mass.png)	images/250924/desidr9_z_vs_stellar_mass.png

I'd probably get the most value by further trimming away the full catalog to some higher quality sources? Not exactly sure how I might make this more in line with some of the curves presented here for example.