AGN galaxy-galaxy lensing basics

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Mesure galaxy-galaxy lensing using UNIONS shapes as sources and SDSS AGNs as lenses.

Goals:

• Measure dark-matter halo masses of AGNs
• Get constraints on M*-sigma relation (relation between mass of super-massive black hole (SMBH) and bulge velocity dispersion of stars, which is a tracer of the bulge total mass).

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19759 of 48346 AGNs are potentially in UNIONS footprint.

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[erussier]

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Next step: Split sample into mass bins. Use cdf(mass).

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Two mass bins:

Problem: Mass-selected samples also have different redshift distributions, cannot easily compare GGL.

Solution (suggested by Qinxun): Reweigh samples with n(z).

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Resulting GGL for the two mass samples:

[WentaoLuo]

Next step is to model the signal and measure the halo mass and check the SMBH-halo relation.

[WentaoLuo]

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Compare results to Illustris TNG simulations.

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Plot of M_BH - sigma (bulge velocity dispersion) from https://ui.adsabs.harvard.edu/abs/2009arXiv0912.3898G/abstract:

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The relationship between $\sigma$ and mass $M$ is a bit more complicated than I had assumed. I found this relationship:
$\sigma = \sqrt{ G M / (C R)}$ where $C$ is a constant, around 6.7 for dispersion-dominated systems (https://ui.adsabs.harvard.edu/abs/2009ApJ...706.1364F/abstract).

That results in
$M \approx 1.5 \times 10^{11} \left( \frac{\sigma}{100 \mbox{km s}^{-1} } \right)^2 \left( \frac{R}{10 \mbox{kpc}} \right) M_\odot $

Assuming a bulge radius of $10$ kpc, this is much closer compared to Qinxun/Wentao's plot from Illustris, where a BH mass of $10^7 M_\odot$ corresponds to a halo mass of some $10^{11} M_\odot$.

I am unsure whether the above reasoning is sound, since I don't know whether we compare so simply bulge and halo mass,
and whether the application of the $M$ - $\sigma$ formula is appropriate.

[martinkilbinger]

Fit of linear bias to AGN foreground lenses.

Scales used for fit: [2; 20] arcmin.

Re-weighted redshift distribution.

Entire mass sample.

Split into two mass bins, 0=low, 1=high-mass.

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Fit to both ShapePipe (SP) and LensFit (LF) catalogues.

Fit with all three blinded versions of dndz (A, B, C):

One mass sample
SP A 1/1 b = 0.907±0.069
SP B 1/1 b = 0.925±0.071
SP C 1/1 b = 0.890±0.067

LF A 1/1 b = 0.973±0.085
LF B 1/1 b = 0.992±0.088
LF C 1/1 b = 0.955±0.082

Two mass samples

Low-mass
SP A 1/2 b = 0.901±0.058
SP B 1/2 b = 0.920±0.059
SP C 1/2 b = 0.885±0.058

LF A 1/2 b = 0.89±0.14
LF B 1/2 b = 0.90±0.14
LF C 1/2 b = 0.87±0.13

High-mass
SP A 2/2 b = 1.0344±0.0067
SP B 2/2 b = 1.0559±0.0058
SP C 2/2 b = 1.0152±0.0075

LF A 2/2 b = 1.14±0.23
LF B 2/2 b = 1.16±0.23
LF C 2/2 b = 1.11±0.22

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LensFit case:

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Re-weighted redshift distribution (update):

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Next steps/ideas:

• compute n_AGN in UNION footprint
• auto-correlation clustering
• Qinxun's code, works in physical coordinates
• Use updated SDSS catalogue
• z-cut to remove high-z AGNs
• mass cut to remove low-M AGNs (<7)
• use SP on LF footprint
• spectroscopic UNIONS matched galaxies only?

[martinkilbinger]

The linear bias is a function of halo mass, e.g. using Tinker et al. (2010), this is how this relations looks like:

The reason that with b~1 we get much higher masses than the earlier estimates of ~ 10^11 M_sol is that this relation assumes that all galaxies are central galaxies in their host halos. This is certainly not true for our AGN sample.

So the next step to estimate the halo mass is to use the halo model and HOD (Halo Occupation Distribution).

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HOD model from pyccl:

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Example n_g(M):

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Fitting M_min to gamma_t:

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Ideas for next steps:

• clustering, combined likelihood?
• compare to Wentao's HOD code
• AGN clustering, use SDSS masks. within UNIONS footprint
• improve SNR by: match high-M_BH bin to low-mass z distribution. Can also then use Liu cataogue.

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With explicit pyccl options for integration over ell, reduction of wigges.

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References:

• https://arxiv.org/abs/2209.03987
  Shen et al: updated AGN catalogue
• https://ui.adsabs.harvard.edu/abs/2002ApJ...578...90F/abstract
  Ferrarese: M - sigma relation
• https://ui.adsabs.harvard.edu/abs/2002ApJ...578...90F/abstract
  Marasco et al: M_BH - M_DM relation
• https://ui.adsabs.harvard.edu/abs/2021ApJ...912..160R/abstract
  Robinson et al: distances and masses of AGN hosts
• https://ui.adsabs.harvard.edu/abs/2020NatAs...4..282S/abstract
  Shankar et al: BH scaling relations from galaxy clustering
• doi:10.1093/mnras/stw2735
  Bower et al., The dark nemesis of galaxy formation: why hot haloes trigger black hole growth and bring star formation to an end
• https://arxiv.org/pdf/2303.11368.pdf
  Complex models of co-evolution of BH, stellar, halo mass, and other properties, as fct of z

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Reminder to self, next steps:

• Understand difference between SP and LF:
  • Make sure to use same AGNs
  • Redshift cuts to AGN sample.
  • Look at low z<0.4, is SP and LF diff smaller?
  • Use matched LF and SP cat.
• Compute Sigma(R) from gamma_t(theta), stack AGNs in
  physical coordinates.
• Improve HOD fit.

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To check:

• Reweighting working well? How about just cut sample to match n(z)? Also working for z subsamples?
• 1h, 2h influence of fit?
• plot lensing efficiency?