Inference of gravitational lensing and patchy reionization with future CMB data Federico Bianchini1 2 3 and Marius Millea4 5 1Kavli Institute for Particle Astrophysics and Cosmology

2025-05-05 0 0 786.58KB 11 页 10玖币

侵权投诉

Inference of gravitational lensing and patchy reionization with future CMB data

Federico Bianchini1, 2, 3, ∗and Marius Millea4, 5, †

1Kavli Institute for Particle Astrophysics and Cosmology,

Stanford University, 452 Lomita Mall, Stanford, CA, 94305, USA

2SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025

3Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305

4Department of Physics, University of California, Berkeley, CA 94720

5Department of Physics, University of California, Davis, CA 95616

(Dated: November 26, 2024)

We develop an optimal Bayesian solution for jointly inferring secondary signals in the Cosmic

Microwave Background (CMB) originating from gravitational lensing and from patchy screening

during the epoch of reionization. This method is able to extract full information content from the

data, improving upon previously considered quadratic estimators for lensing and screening. We

forecast constraints using the Marginal Unbiased Score Expansion (MUSE) method, and show that

they are largely dominated by CMB polarization, and depend on the exact details of reionization.

For models consistent with current data which produce the largest screening signals, a detection

(3 σ) of the cross-correlation between lensing and screening is possible with SPT-3G, and a detection

of the auto-correlation is possible with CMB-S4. Models with the lowest screening signals evade the

sensitivity of SPT-3G, but are still possible to detect with CMB-S4 via their lensing cross-correlation.

I. INTRODUCTION

The large-scale structure (LSS) of the universe is back-

lit by cosmic microwave background (CMB) photons as

they travel from the last scattering surface towards us.

Maps of the CMB anisotropies can therefore be used to

image gravitational potentials – through weak gravita-

tional lensing, integrated Sachs-Wolfe and Rees-Sciama

eﬀects – and the gas distribution – through Thomson and

inverse Compton scattering processes like the Sunyaev-

Zel’dovich eﬀects [e.g., 3,9,33,61,62]. The current gen-

eration of CMB surveys such as Planck [49], SPT [52] and

ACT [4] has started to tap into the promising potential of

these CMB secondary anisotropies. Next-generation ex-

periments – including the Simons Observatory (SO) [58],

FYST/CCAT-prime [5], and CMB-S4 [13] – will provide

a transformative high ﬁdelity view of the secondary CMB

anisotropies in intensity and polarization over large ar-

eas of the sky, revealing fundamental insights into both

cosmology and astrophysics [11].

Mapping out the spatial distribution of diﬀuse ion-

ized gas throughout the universe can, for example, help

us understand the physics of reionization, at high red-

shifts (z≳6), and of the intergalactic medium (IGM),

at lower redshifts (z≲6) [e.g., 25,42]. One approach

to achieve this is by searching for the characteristic

spatially-dependent suppression of the CMB temperature

and polarization anisotropies produced by diﬀerent scat-

tering histories along diﬀerent line of sights, an eﬀect

known as “patchy screening”. The magnitude of the ef-

fect is proportional to e−τ(ˆ

n), where τ(ˆ

n) is the direction-

dependent optical depth.

∗federico.bianxini@gmail.com

†mariusmillea@gmail.com

The so-called “quadratic estimator” (QE) has be-

come the workhorse for extracting sources of statistical

anisotropies, such as patchy screening and lensing, from

CMB maps [e.g., 30,31,67]. The QE in the context of

inhomogeneous optical depth reconstruction has been in-

troduced by Dvorkin & Smith [19] and applied to WMAP

and Planck data in [23,44,46] but the spatial ﬂuctua-

tions of τhave not been detected yet. While the QE

has been successfully used on current datasets, it has

some shortcomings. First, the presence of other distort-

ing ﬁelds, like lensing, point-sources, and inhomogeneous

noise, will introduce additional non-Gaussianities in the

data which in turn, lead to biases in the reconstructed

ﬁeld [60]. “Bias-hardened” estimators oﬀer a solution to

this problem at the cost of a signal-to-noise (S/N) degra-

dation, which can be as large as ≈40% [e.g., 46,60].

Second, the QE will become signiﬁcantly sub-optimal

at the instrumental noise levels soon-to-be reached by

the most sensitive experiments [2,41]. At these depths,

secondary anisotropies, rather than instrumental noise,

limit the variance of the estimated ﬁeld. To improve

upon the QE, a variety of methods based on the full

CMB Bayesian posterior have been proposed to extract

the higher-order information and restore near-optimality

[e.g., 10,27,28,38–40]. Machine-learning approaches are

also being currently investigated but while promising, ad-

ditional work towards the characterization of these meth-

ods and their biases is needed before they can be reliably

applied to real data [8,26].

In this paper, we develop a complete Bayesian solution

that uniﬁes the optimal inference of the optical depth τ

and CMB lensing potential ϕtogether with delensing and

cosmological parameter inference. Our method presents

a number of appealing features. First of all, by making

use of the full Bayesian posterior, the method is capable

of optimally extracting the information content in CMB

data at all noise levels. Furthermore, by simultaneously

arXiv:2210.10893v2 [astro-ph.CO] 25 Nov 2024

forward modeling the eﬀects of lensing and screening on

CMB observables, we are able to naturally account for

any contamination (of lensing to screening and vicev-

ersa) in the reconstruction and to enhance the sensitivity

to screening through the cosmic variance reduction due

to delensing. Our method can also internally measure

the correlation ⟨ϕτ⟩between the CMB lensing potential

and optical depth ﬂuctuations, which is larger than ⟨ττ⟩,

contains additional information on relation between the

ionized gas and dark matter distribution, and is expected

to be detected with upcoming CMB surveys [20]. Finally,

the CMB data are eﬀectively “descreened” by our pro-

cedure, which can in turn mitigate any residual B-mode

bias from screening to tensor-to-scalar ratio rsearches

(although the contamination is expected to be at the level

of r∼10−4for standard reionization histories, see, e.g.,

[43,53], therefore not a signiﬁcant concern for experi-

ments targeting O(10−3)).

We begin the paper with a review of the theoretical

background and the eﬀect of patchy screening on CMB

observables in Sec. II. We present our method and il-

lustrate its performance in Sec. III, before concluding in

Sec. IV.

II. MODELING

A. Optical depth

The electron scattering optical depth measures the in-

tegrated electron density along the line-of-sight and is

given by

τ(ˆ

n) = σTZdχ a ne(ˆ

n, χ),(1)

where ne(ˆ

n, χ) is the free electron number density at co-

moving distance χalong the direction ˆ

n,σTis the Thom-

son scattering cross-section, and ais the scale factor. The

mean number density of free electrons can be expressed

as ¯ne= (1 −3/4YP)¯ρb0/mpa−3¯xe= ¯np0¯xe/a3, where YP

is the primordial helium abundance, ρb0is the present-

day baryon density, the proton mass is mp, ¯xeis the mean

ionization fraction, and we assumed that helium is singly

ionized. We model the evolution of the volume-averaged

ionization fraction ¯xeusing a simple tanh ﬁtting function

parametrized by the redshift of reionization zre, deﬁned

as the redshift at which ¯xeis half of its maximum, and

the duration of reionization ∆z, i.e. the diﬀerence be-

tween the redshifts at which the universe is 5% and 95%

reionized [32]

¯xe(z) = 1

21 + tanh yre −y

∆yre ,(2)

where y(z) = (1 + z)3/2,yre =y(zre), and ∆yre =

√1 + zre∆z.

Perturbations in the free electron number density δne

can be sourced both by ionization ﬂuctuations δx=

δxe/¯xeand by inhomogeneities in the gas density δ[42].

The former are only generated during the epoch of reion-

ization while the latter are produced both when reioniza-

tion occurs as well as in the post-reionization universe.

Fluctuations in the free electron density will then induce

spatial ﬂuctuations in the optical depth [e.g., 29]:

τ(ˆ

n) = σTnp0Zdχ

a2¯xe(χ) (1 + δx(ˆ

n, χ)) (1 + δ(ˆ

n, χ))

(3)

= ¯τ+δτ(ˆ

n),(4)

The contribution to the τanisotropies from the spatial

distribution of free electrons in galaxies and clusters is

then given by the redshifts below which ¯xe= 1.

Under the Limber approximation [34], valid for angular

scales ℓ≫20 relevant for this work, the angular power

spectrum of the optical depth ﬂuctuations can be evalu-

ated as

Cττ

ℓ=σ2

Tn2

p0Zdχ

a4χ2Pδeδe(kℓ, χ),(5)

where Pδeδeis the power spectrum of the density-

weighted ionization fraction ﬂuctuations, and kℓ= (ℓ+

2)/χ.

The quantity Pδeδeencodes all the relevant astrophys-

ical aspects of the EoR, including its morphology and

timing. Modeling reionization and the spatial distribu-

tion of free electrons is a challenging task due to the com-

plexity of the physical processes involved and the limited

observational access we currently have to those cosmic

epochs. Therefore, instead of specifying a given physical

mechanism of reionization [e.g., 22], we choose to adopt

the “bubble model” introduced in [19,42,64] that allows

us to phenomenologically parametrize the Hii spectrum,

Pδeδe. In this framework, the Hii regions around the

ionizing sources, such as galaxies or quasars, are biased

tracers of the underlying dark matter halos. The ionized

bubbles are assumed to be spherical with an average ra-

dius ¯

R(in Mpc) while their radii distribution is modeled

as a log-normal distribution of width σlnR, i.e. skewed

towards smaller bubble sizes. The size and evolution of

these Hii bubbles are sensitive to the mass and bright-

ness of the ionizing sources. As time advances, the Hii

bubbles grow in size and percolate, eventually leading to

a complete reionization of the intergalactic medium. In

App. Awe provide a more detailed discussion of the halo

model.

To summarize, our inhomogenous reionization model-

ing is described by a set of four parameters: the redshift

and duration of reionization {zre,∆z}, which specify the

mean ionization history ¯xe(z), and the characteristic size

and standard deviation of the log-normal bubble radius

distribution, {¯

R, σlnR}.

B. Cross-correlation with CMB lensing

In this work we are also interested in evaluating the

correlation between the optical depth ﬂuctuations and

the integrated matter distribution along the line-of-sight

as traced by the CMB lensing potential ϕ(ˆ

n) deﬁned as

[e.g., 33]

ϕ(ˆ

n) = −2Zdχχ−χ∗

χχ∗

Ψ(ˆ

n, χ).(6)

Here, Ψ(ˆ

n, χ) is the Weyl (gravitational) potential, that

in standard cosmologies can be directly related to the

comoving matter perturbations δ(ˆ

n, χ) through the Pois-

son equation, and χ∗is the comoving distance to the last

scattering surface at z∗≃1090.

A cross-correlation between optical depth ﬂuctuations

and CMB lensing is naturally expected since the same

dark matter halos signposted by the Hii bubbles at high

redshift (z≳6) and by galaxies and galaxy clusters at

low redshift (z≲6) act as lenses for the CMB photons.

In fact, the CMB lensing kernel has non-zero support

out to high redshift and it is about half of its maximum

around z≈10.

Using Eqn. (6), the cross-power spectrum between the

ﬂuctuating part of τand CMB lensing potential takes

the following form:

Cϕτ

ℓ=3H2

0ΩmσTnp0

cℓ2Zdχ

χ−χ∗

χχ∗

Pδδe(kℓ, χ),(7)

where H0is the Hubble constant and Pδδe(kℓ, χ) denotes

the three-dimensional cross-spectrum between the matter

density contrast δand the free electron ﬂuctuations δe.

C. Fiducial scenarios

While we do not specify a given physical model for

reionization, here we consider two limiting reionization

scenarios to study the performance of our approach and

to get a sense for the expected S/N with current and

upcoming surveys.

In the ﬁrst case (optimistic model), reionization starts

early on, proceeds for an extended period of time, and

is driven by larger bubbles with a broad radii distribu-

tion spread. For this scenario we ﬁx {zre,∆z,¯

R, σlnR}=

{10,4,5,ln(2)}. Aside from giving a signal which is large

but not currently detectable, a value of σlnR= ln(2), is

on the upper end of allowed values given existing cross-

correlations between QE reconstructions of τand Comp-

ton y-maps using Planck data [46]. In the second case

(pessimistic model), reionization occurs at lower redshift

and its duration is shorter, while the bubbles that reion-

ize the universe are smaller in size and their radii dis-

tribution is narrower. When analyzing this scenario we

set {zre,∆z,¯

R, σlnR}={7,1,1,0.1}. As we will see, the

nomenclature of optimistic or pessimistic refers to the

prospects of detecting the patchy screening eﬀect in the

two cases.

In the left hand panel of Fig. 1, we show the two reion-

ization histories. The higher redshift of reionization in

the optimistic model results in a larger integrated mean

optical depth ¯τthan in the pessimistic model. Both val-

ues are consistent within 2σwith the constraint from

Planck on ¯τ= 0.058 ±0.012 [49]. The middle and right

panels of Fig. 1show the optical depth ﬂuctuation an-

gular auto spectrum and its cross-correlation with CMB

lensing, respectively. Qualitatively, a longer duration of

reionization translates to more pronounced ﬂuctuations

in τ, corresponding to a larger overall amplitude of Cττ

ℓ

and Cϕτ

ℓ. The peak of these spectra is mostly determined

by the eﬀective radius of the Hii bubbles, with larger bub-

bles enhancing the power spectra at lower multipoles.

D. Hierarchical model for CMB data

The patchy nature of the reionization process at z≳

6 and the clumpiness of the spatial distribution of free

electrons at lower redshifts (z≲6) lead to an anisotropic

optical depth, τ=τ(ˆ

n). In turn, spatial variations of the

optical depth will introduce new observational signatures

in the CMB sky.

Three main eﬀects can be identiﬁed. First, Thomson

scattering of the remote CMB temperature quadrupole

by ionized bubbles generates new polarization [e.g.,

7,17,18,25,42,48].1Second, the radial peculiar veloc-

ity of ionized bubbles relative to the observer sources a

temperature ﬂuctuation through the kinematic Sunyaev-

Zel’dovich (kSZ) eﬀect [e.g., 7,12,24,48,56,66]. Third,

anisotropies in the optical depth will induce a spatially-

dependent screening of the primary CMB anisotropies

caused by the CMB photons being scattered into and

out of our line-of-sight [e.g., 18,47]. In this paper, we

focus exclusively on the latter eﬀect.

Considering an unperturbed CMB ﬁeld f∈ {T, Q, U},

the map-level eﬀect of anisotropic screening is to spatially

modulate the amplitude of the CMB temperature and

polarization anisotropies by a factor e−τ(ˆ

n)as

(S(τ)f)(ˆ

n) = e−τ(ˆ

n)f(ˆ

n),(8)

where we have introduced the screening operator S(τ).

On the other hand, the gravitational potentials asso-

ciated to the intervening matter distribution between us

and the last scattering surface induce a remapping of the

primary CMB anisotropies, which we model (in the ab-

sence of screening) as

(L(ϕ)f)(ˆ

n) = f(ˆ

n+∇ϕ(ˆ

n)),(9)

1While new E-mode polarization is generated even in the case

of homogeneous reionization, additional B-modes can only be

sourced if the distribution of free electrons is inhomogeneous.

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

InferenceofgravitationallensingandpatchyreionizationwithfutureCMBdataFedericoBianchini1,2,3,∗andMariusMillea4,5,†1KavliInstituteforParticleAstrophysicsandCosmology,StanfordUniversity,452LomitaMall,Stanford,CA,94305,USA2SLACNationalAcceleratorLaboratory,2575SandHillRoad,MenloPark,CA940253Departmentof...

展开>> 收起<<

Inference of gravitational lensing and patchy reionization with future CMB data Federico Bianchini1 2 3 and Marius Millea4 5 1Kavli Institute for Particle Astrophysics and Cosmology.pdf

共11页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Inference of gravitational lensing and patchy reionization with future CMB data Federico Bianchini1 2 3 and Marius Millea4 5 1Kavli Institute for Particle Astrophysics and Cosmology

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: