[Paper Review] KiDS+VIKING+GAMA: Halo occupation distributions and correlations of satellite numbers with a new halo model of the galaxy-matter bispectrum for galaxy-galaxy-galaxy lensing

Laila Linke, P. Šimon+4 more|arXiv (Cornell University)|Apr 5, 2022

Galaxies: Formation, Evolution, Phenomena92 references11 citations

TL;DR

This paper presents a novel halo model for galaxy-galaxy-galaxy lensing (G3L) that constrains halo occupation distributions (HODs) and correlations between satellite galaxy numbers in different populations. Using G3L signals from KiDS+VIKING+GAMA data, it finds strong, mass-dependent correlations (>3σ) between red and blue satellite counts in halos above 10^13 M⊙, challenging the default assumption of uncorrelated satellite numbers and enabling more accurate HOD inference for cosmological and mock catalog applications.

ABSTRACT

Halo models and halo occupation distributions (HODs) are important tools to model the galaxy and matter distribution. We present and assess a new method for constraining the parameters of HODs using the gravitational lensing shear around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo numbers of galaxies from different populations. We use G3L to probe these correlations and test the default hypothesis that they are negligible. We derive a halo model for G3L and validate it with realistic mock data from the Millennium Simulation and a semi-analytic galaxy model. Then, we analyse public data from the Kilo-Degree Survey (KiDS), the VISTA Infrared Kilo-Degree Galaxy Survey (VIKING) and data from the Galaxy And Mass Assembly Survey (GAMA) to infer the HODs of galaxies at $z<0.5$ in five different stellar mass bins between $10^{8.5}h^{-2} M_\odot$ and $10^{11.5}h^{-2} M_\odot$ and two colours (red and blue), as well as correlations between satellite numbers. The analysis recovers the true HODs in the simulated data within the $68\%$ credibility range. The inferred HODs vary significantly with colour and stellar mass. There is also strong evidence ($>3\sigma$) for correlations, increasing with halo mass, between the numbers of red and blue satellites and galaxies with stellar masses below $10^{10} \Msun. Possible causes of these correlations are the selection of similar galaxies in different samples, the survey flux limit, or physical mechanisms like a fixed ratio between the satellite numbers of distinct populations. The decorrelation for halos with smaller masses is probably an effect of shot noise by low-occupancy halos. The inferred HODs can be used to complement galaxy-galaxy-lensing or galaxy clustering HOD studies or as input to cosmological analyses and improved mock galaxy catalogues.

Motivation & Objective

• To develop a halo model for galaxy-galaxy-galaxy lensing (G3L) that extends beyond standard two-point statistics to probe higher-order correlations in galaxy distributions.
• To test the default assumption in halo models that satellite numbers from different galaxy populations (e.g., red vs. blue) are uncorrelated.
• To infer HODs and cross-correlations of satellite numbers for galaxies in five stellar mass bins and two colours using real data from KiDS, VIKING, and GAMA.
• To validate the model using mock data from the Millennium Simulation with semi-analytic galaxies, ensuring robustness against systematics.
• To provide a framework for future lensing surveys to include non-Poissonian satellite number variances and correlated galaxy populations.

Proposed method

• Develop a halo model for the galaxy-matter bispectrum and G3L signal, incorporating cross-correlations between satellite numbers in different galaxy samples.
• Use the Limber approximation to project the 3D bispectrum into 2D angular statistics, enabling efficient computation of the G3L signal.
• Implement a Bayesian inference framework to constrain HOD parameters and satellite number correlations using G3L measurements from real data.
• Validate the model on mock data from the Millennium Simulation populated with semi-analytic galaxies (Henriques et al. 2015), confirming accurate recovery of true HODs within 68% credibility intervals.
• Apply the model to public data from KiDS, VIKING, and GAMA, using GAMA-selected lenses and KiDS+VIKING sources to measure G3L in five stellar mass bins and two colours.
• Assess the impact of non-Poissonian satellite number variance by comparing predictions with and without the actual variance from the SAM, finding negligible effects within statistical errors.

Experimental results

Research questions

• RQ1 Does the default assumption of uncorrelated satellite numbers between different galaxy populations hold in real data?
• RQ2 Can G3L be used to constrain HODs and cross-correlations of satellite numbers in a way that improves upon standard galaxy-galaxy lensing?
• RQ3 How do HODs and satellite number correlations vary with stellar mass and galaxy colour in halos below z=0.5?
• RQ4 To what extent do non-Poissonian satellite number variances affect G3L-based HOD inference?
• RQ5 Can this G3L halo model be used to improve the realism of mock galaxy catalogs for cosmological surveys?

Key findings

• The G3L halo model accurately recovers the true HODs in simulated data for all galaxy samples within the 68% credibility interval, confirming model robustness.
• The model's best-fit predictions agree with the observed G3L signal at the 95% confidence level, validating its predictive power on real data.
• Red galaxies are found preferentially in more massive halos (≳10^12 M⊙), while blue galaxies reside in halos of mass ≳10^11 M⊙, indicating strong colour-dependent halo occupation.
• There is strong evidence (>3σ) for a positive correlation between red and blue satellite numbers, increasing with halo mass, particularly in halos ≳10^13 M⊙.
• The decorrelation of satellite numbers in low-mass halos is likely due to shot noise from low-occupancy systems, not physical anti-correlation.
• The inferred HODs and correlations can be used to enhance mock galaxy catalogs and improve cosmological inference by extending the scale range accessible to galaxy bias modeling.