Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gravitational Lensing Effects by Galaxy Clusters on Ionised Bubble Size Distribution during the Epoch of Reionisation

Di Wu, Nan Li, Huanyuan Shan, Zhenghao Zhu

Abstract

The statistical properties of ionisation structures during the Epoch of Reionisation (EoR) provide valuable insights into the formation of the first stars and galaxies. However, statistics such as size distributions of ionisation structures can be affected by gravitational lensing caused by foreground massive structures like galaxy clusters. Hence, to quantify the impacts of lensing by galaxy clusters on ionised Bubble Size Distribution (BSD), we conducted a series of multiple-lens-plane lensing simulations involving the light cones of clusters alongside source light cones based on various ionisation models. The deflector population is generated using the Monte Carlo method, guided by halo mass function and empirical scaling relations, while deflectors' mass profile is modelled using the Truncated Navarro-Frenk-White (TNFW) model. Source light cones are produced via a semi-numerical approach or directly sourced from the Evolution of 21 cm Structure (EOS) project. By employing the Mean Free Path method, we measure unlensed and lensed BSD to reveal the lensing impacts. Our results indicate that lensing effects increase the number of large bubbles while leaving the number of small bubbles unchanged across all source models we adopted. Specifically, for the EOS faint galaxies model, the number of R > 15 cMpc bubbles increases by 219% at z = 14; for the EOS bright galaxies model, the above number increases by 832% under the same circumstances. Above all, lensing introduces unavoidable systematics for BSD, which must be carefully taken into account for relevant studies in the Square Kilometre Array (SKA) era.

Gravitational Lensing Effects by Galaxy Clusters on Ionised Bubble Size Distribution during the Epoch of Reionisation

Abstract

The statistical properties of ionisation structures during the Epoch of Reionisation (EoR) provide valuable insights into the formation of the first stars and galaxies. However, statistics such as size distributions of ionisation structures can be affected by gravitational lensing caused by foreground massive structures like galaxy clusters. Hence, to quantify the impacts of lensing by galaxy clusters on ionised Bubble Size Distribution (BSD), we conducted a series of multiple-lens-plane lensing simulations involving the light cones of clusters alongside source light cones based on various ionisation models. The deflector population is generated using the Monte Carlo method, guided by halo mass function and empirical scaling relations, while deflectors' mass profile is modelled using the Truncated Navarro-Frenk-White (TNFW) model. Source light cones are produced via a semi-numerical approach or directly sourced from the Evolution of 21 cm Structure (EOS) project. By employing the Mean Free Path method, we measure unlensed and lensed BSD to reveal the lensing impacts. Our results indicate that lensing effects increase the number of large bubbles while leaving the number of small bubbles unchanged across all source models we adopted. Specifically, for the EOS faint galaxies model, the number of R > 15 cMpc bubbles increases by 219% at z = 14; for the EOS bright galaxies model, the above number increases by 832% under the same circumstances. Above all, lensing introduces unavoidable systematics for BSD, which must be carefully taken into account for relevant studies in the Square Kilometre Array (SKA) era.
Paper Structure (15 sections, 20 equations, 11 figures, 1 table)

This paper contains 15 sections, 20 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theory
  3. Basics of EoR simulation
  4. Basics of Gravitational Lensing
  5. Simulations
  6. EoR simulations
  7. Models of foreground deflectors
  8. Lensing Simulation
  9. Estimation of BSD
  10. Results
  11. Lensing Effects on BSD
  12. Influence of Source Models on the Estimation of BSD
  13. Influence of the Setups of Lensing Simulations on the Estimation of BSD
  14. Influence of the Setups of MFP on the Estimation of BSD
  15. Conclusions

Figures (11)

  • Figure 1: Demonstration of a slice in the redshift direction of one HIGH-RES simulation. The upper panel shows the evolution of the $x_{\mathrm{HI}}$ (neutral hydrogen fraction). The middle panel displays the 21 cm differential brightness temperature. The lower panel presents the global 21 cm differential brightness temperature evolution.
  • Figure 2: Number counts of ionised bubbles as a function of projected area of bubble for simulation slices at redshifts $z$$= 9$ (left), $z$$= 12$ (middle), and $z$$= 14$ (right), respectively. Bubbles were identified via a Friends‑of‑Friends (FoF) algorithm 2006MNRAS.369.1625I using an ionisation fraction threshold of 0.5. The HIGH-RES resolves the highest abundance of small‑scale ionised regions across all three epochs, highlighting the impact of spatial resolution on the recovered small-scale ionisation topology.
  • Figure 3: Global volume-averaged HII (ionised hydrogen) fraction evolutions for the five ionisation models (listed in Table \ref{['table: simulation information']}) used in this work. Left: Ionised fraction evolution for three ionisation models with different ionisation parameter settings: EOS Faint Galaxies model, EOS Bright Galaxies model, and HIGH-RES. Right: Ionised fraction evolution for three models with the same ionisation parameter settings but different resolution settings: HIGH-RES, MID-RES, and LOW-RES. The different colours represent different models. Left panel shows that simulations with different parameter settings exhibit distinct ionisation processes, such as variations in the reionisation redshift range and the speed of ionisation. Conversely, the right panel shows that simulations with the same ionisation parameter settings ($\zeta$ and $M_{\rm min}$) have similar reionisation processes, despite differences in ionisation simulation resolution.
  • Figure 4: Comparison between the mass functions of the deflectors in our light cones (red points) and the theoretical outcomes given by 2008ApJ...688..709T (blue lines) at redshifts $z$= $0.5$, $1.5$, and $2.5$, from left to right, respectively.
  • Figure 5: Comparison between the PDFs of projected mass ellipticity $e$ of the deflectors in our light cone (orange bars) and theoretical outcomes of the mean $e$ evolution given by 2005ApJ...618....1H with Gaussian dispersion $\sigma_e=0.16$ (blue lines) at redshifts $z$= $0.5$, $1.5$, and $2.5$, from left to right, respectively.
  • ...and 6 more figures