Towards a non-Gaussian Generative Model of large-scale Reionization Maps Yu-Heng Lin

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Towards a non-Gaussian Generative Model of

large-scale Reionization Maps

Yu-Heng Lin

Department of Physics

University of Minnesota

Minneapolis, MN 55455

lin00025@umn.edu

Sultan Hassan

Center for Computational Astrophysics

Flatiron Institute

New York, NY 10010

Department of Astrophysical Sciences

Princeton University, Peyton Hall

Princeton, NJ, 08544

Department of Physics & Astronomy

University of the Western Cape

Cape Town 7535

shassan@flatironinstitute.org

NHFP Hubble Fellow

Bruno Régaldo-Saint Blancard

Center for Computational Mathematics

Flatiron Institute

New York, NY 10010

bregaldosaintblancard@flatironinstitute.org

Michael Eickenberg

Center for Computational Mathematics

Flatiron Institute

New York, NY 10010

meickenberg@flatironinstitute.org

Chirag Modi

Center for Computational Astrophysics

Flatiron Institute

New York, NY 10010

cmodi@flatironinstitute.org

Abstract

High-dimensional data sets are expected from the next generation of large-scale

surveys. These data sets will carry a wealth of information about the early stages

of galaxy formation and cosmic reionization. Extracting the maximum amount of

information from the these data sets remains a key challenge. Current simulations

of cosmic reionization are computationally too expensive to provide enough real-

izations to enable testing different statistical methods, such as parameter inference.

We present a non-Gaussian generative model of reionization maps that is based

solely on their summary statistics. We reconstruct large-scale ionization ﬁelds

(bubble spatial distributions) directly from their power spectra (PS) and Wavelet

Phase Harmonics (WPH) coefﬁcients. Using WPH, we show that our model is

efﬁcient in generating diverse new examples of large-scale ionization maps from a

single realization of a summary statistic. We compare our model with the target

ionization maps using the bubble size statistics, and largely ﬁnd a good agreement.

As compared to PS, our results show that WPH provide optimal summary statistics

that capture most of information out of a highly non-linear ionization ﬁelds.

Preprint. Under review.

arXiv:2210.14273v1 [astro-ph.CO] 25 Oct 2022

1 Introduction

In the early universe, neutral gas accreted to the over-density region inside dark matter halos, and

formed the ﬁrst generations of galaxies. The intergalactic medium was later ionized by the ultraviolet

photons emitted from these galaxies. Studying this epoch, known as the cosmic reionization, is

crucial to understand the earliest stages of galaxy formation and evolution. Various properties of

high-redshift galaxies are poorly constrained and cannot be measured directly. Instead, studying the

integrated emission from these galaxies over large-scales, a technique known as intensity mapping, is

emerging as a powerful cosmological probe. Several intensity mapping experiments, such as SKA

[

], HERA [

], LOFAR [

], Euclid [

], SPHEREx [

], and Roman [

], are expected to provide

large-scale maps in different bands, including hydrogen ionization maps in the early universe.

Translating these growing observational efforts into astrophysical and cosmological constraints on

our theoretical models of reionization and galaxy formation remains a key challenge. One limitation

is the computational cost of reionization simulations, which is an obstacle to generate enough samples

of detailed large-scale maps, fully explore the parameter space controlling different astrophysical

ingredients, and perform parameter inference. However, many of these experiments focus on statistical

measurements (e.g. the power spectrum). Efﬁcient sampling from summary statistics is therefore

required in order to extract most of information from the upcoming reionization surveys.

In this work, we introduce a non-Gaussian generative model of large-scale ionization maps that is

based on wavelet phase harmonic (WPH) statistics [

]. We compare it to a Gaussian model

constrained by power spectrum statistics. We then use the bubble-size statistics as an independent

metric to compare the input map with our reconstructed maps.

2 Methods

Simulations of cosmic reionization generate ionization ﬁelds using the following steps: (i) generation

and evolution of the initial density ﬁeld. (ii) identiﬁcation of the sources (galaxies/halos) with group

ﬁnder methods. (iii) computation of the radiative transfer to generate the ionization ﬁeld using the

density and source ﬁelds at different epochs. Steps (ii) and (iii) are computationally very expensive,

thus we aim to accelerate them with our fast generative model.

Figure 1: The pipeline of the generative model. This forward generative model (green arrows)

transfers the density summary statistics to the ionization summary statistics and then reconstructs the

ionization ﬁeld. We test the reconstructed maps using the bubble size statistics against the target map.

This pipeline consists of two parts and the red box indicates the focus of this paper.

Our paper focuses on the sampling procedure of the following proposed pipeline:

•

Create conditional mapping between the summary statistics of the density ﬁeld and the

summary statistics of the ionization ﬁeld, using either Multilayer perceptron or Symbolic

regression (This is beyond the scope of this paper).

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Towardsanon-GaussianGenerativeModeloflarge-scaleReionizationMapsYu-HengLinDepartmentofPhysicsUniversityofMinnesotaMinneapolis,MN55455lin00025@umn.eduSultanHassanCenterforComputationalAstrophysicsFlatironInstituteNewYork,NY10010DepartmentofAstrophysicalSciencesPrincetonUniversity,PeytonHallPrinceton,...

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Towards a non-Gaussian Generative Model of large-scale Reionization Maps Yu-Heng Lin

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