Exploring Early Universe with Neutral Hydrogen Signals

Exploring early universe with neutral hydrogen
@CCNU（2021/4/26）
©Aman Chokshi
Hayato Shimabukuro (Yunnan university, SWIFAR)

•Born in 冲绳
•Ph.D from
Nagoya university(2016)
•Postdoc at
Paris observatory(2016-2018)
About me
•Postdoc at
Tsinghua University(2018-)

•Born in 冲绳
•Ph.D from
Nagoya university(2016)
•Postdoc at
Paris observatory(2016-2018)
About me
•Postdoc at
Tsinghua University(2018-)
•云南⼤学（2019ー）

Outline
• Introduction

• Basics of 21cm line

• Current 21cm cosmology status and future

• 21cm signal analysis with machine learning

• Challenges

• Summary

Current universe
©Hubble space telescope

Current universe
Stars, galaxies, bright universe
©Hubble space telescope

Past universe
No stars, galaxies, dark universe

Past universe
No stars, galaxies, dark universe
How did the universe evolve from dark ages to present universe?

The history of the universe
Present
Past
https://universe-review.ca/
Epoch of
Reionization
Dark ages
Dark Ages・・・No luminous object exists.
Epoch of Reionization(EoR)・・・UV photons by luminous objects ionize
neutral hydrogen in the IGM (z~6-15).
Cosmic Dawn・・・First stars and galaxies form (z~20-30).

（C)Kenji Hasegawa（Nagoya University）
Credit: M. Alvarez, R. Kaehler and T.Abel

Current observations for EoR
•Lyman alpha emitter galaxies（LAE） •Lyman alpha forest
Konno et al (2014)
(http://pages.astronomy.ua.edu/keel/agn/forest.html)
QSO
HI cloud
>The number of ionizing photons
Sensitive to neutral hydrogen fraction

Current observations tell us
(Greig et al 2017)
Constraints on average neutral(ionized) hydrogen fraction (Global history).

Current observations tell us
(Greig et al 2017)
Constraints on average neutral(ionized) hydrogen fraction (Global history).
Current observations tell us only global
history (at late stage of EoR).

We want to find out more about the EoR (and cosmic
dawn, dark ages) beyond global history .
(Ex)
•Whole stage of the EoR
•Spatial distribution of ionized bubbles
•Ionizing sources
•Time evolution of ionized bubbles
•Relation to galaxy formation and evolution
etc…

21cm line
•21cm line radiation : Neutral hydrogen atom in IGM emits the
radiation due to the hyperfine structure.
z=6 → 1.5m or 202 MHz
z=20 → 4.4m or 68MHz
Radio wavelength.
Proton
Electron
21cm line emission(1.4GHz)

21cm line
•21cm line radiation : Neutral hydrogen atom in IGM emits the
radiation due to the hyperfine structure.
z=6 → 1.5m or 202 MHz
z=20 → 4.4m or 68MHz
Radio wavelength.
Proton
Electron
21cm line emission(1.4GHz)
We have not observed 21cm line at
high redshift yet !

Spin temperature
n""
n"#
= 3 exp
✓
h⌫21cm
kTS
◆
Key quantity in 21cm line physics
T 1
S =
T 1
CMB + xcT 1
K + x↵T 1
c
1 + xc + x↵
Spin temperature is determined by
•interaction with CMB photons
•collision with hydrogen atoms
•interaction with Ly-alpha photons
(TCMB)
(TK, xc)
(Tc ⇠ TK, x↵)
Properties of X-ray sources (e.g.
spectral energy distribution (SED))
Relevant astrophysics
Properties of first stars (e.g.
Initial mass function)

Mesinger et al 2010
heating
WF eﬀect
Wouthuysen-Field(WF) effect
Spin temperature couples to
IGM kinetic temperature via
Ly-alpha photons from first
stars.
Thermal history
X-ray heating
X-ray photons drastically heat
kinetic temperature of the IGM
Spin temperature
Kinetic temperature
CMB temperature

21cm line signal
Red : cosmology Blue : astrophysics
Global signal has characteristic peaks
and troughs according to key epochs
Tb =
TS T
1 + z
(1 exp(⌧⌫))
⇠ 27xH(1 + m)
✓
H
dvr/dr + H
◆ ✓
1
T
TS
◆ ✓
1 + z
10
0.15
⌦mh2
◆1/2 ✓
⌦bh2
0.023
◆
[mK]
Brightness temperature
Global signal (sky averaged brightness temperature)
*We actually observe brightness temperature

Images by 21cm line
Mellema et al (2013)
We can see how ionised regions are distributed by 21cm image.
xi = 0.8
xi = 0.5
Ionised regions
However, it is difficult to observe 21cm image by current observations due to specification…

21cm power spectrum (PS) :
Scale dependence
Pober et al (2014)
EoR
X-ray
heating
WF
effect
z
Redshift dependence
21cm power spectrum
h Tb(k) Tb(k
0
)i = (2⇡)3
(k + k
0
)P21
We first try to detect the 21cm line signal statistically with ongoing telescopes.

Current 21cm cosmology
status and future project

Current 21cm experiments
MWA LOFAR HERA
GMRT
Radio interferometer
•Array of radio telescope
antennas
•Measure time delay
between antennas
•Work together as a single
telescope

Current upper limits on 21cm PS
HERA collaboration 2019
Current 21cm experiments put upper limit of the 21cm line power spectrum 2-3 order
of magnitude higher than theoretical expectation.
Challenges: systematics, calibration, etc

EDGES (Bouman et al 2018)
Too deep trough
Too flat
We detected the 21cm line signal?
Very strange result ! Need exotic physics? mis-calibration? unknown systematics?

Did we detect the 21cm global signal ?
EDGES (Bouman et al 2018)
Too deep trough
Too flat
We detected the 21cm line signal?
Very strange result ! Need exotic physics? mis-calibration? unknown systematics?

SKA-Low
High resolution
&
High sensitivity

SKA-Low
•Start observation ~2027(Construction in
2021)
•Frequency 50-350MHz(z=3~27)
•Resolution : ~3.3-23 arcsec
•FoV :~ tens -a few hundreds of square
degree
•Effective collecting area : ~300’000 m2
•China is a member ship of SKA
High resolution
&
High sensitivity

Images by 21cm line
⃝~ a few arc-minutes resolution ⃝~ a few degree FoV
(Minimum) required specification for imaging
xi = 0.8
xi = 0.5

Images by 21cm line
⃝~ a few arc-minutes resolution ⃝~ a few degree FoV
(Minimum) required specification for imaging
xi = 0.8
xi = 0.5
SKA can do !

21cm signal analysis with
machine learning

What I have done so far
•Cosmology at small scales with 21cm forest (Warm dark
matter, axion dark matter and so on)
[Shimabukuro et al.(2014), Shimabukuro, Ichiki & Kadota
(2020a,2020c)]
•21cm statistics (bispectrum, one point statistics)
[Shimabukuro et al.(2015), (2016), (2017a)]
•21cm signal analysis with artificial neural network (ANN)
[Shimabukuro & Semelin (2017b), Shimabukuro, Mao & Tan
(2020b)]

1.EoR parameter estimation
with ANN

Statistical challenge in 21cm cosmology
(Mesinger 2018)
Cosmology
CMB map (angular) power spectrum cosmological parameter
21cm
21cm 3D map 21cm power spectrum astrophysical parameter
Based on Bayesian inference

Statistical challenge in 21cm cosmology
(Mesinger 2018)
Cosmology
CMB map (angular) power spectrum cosmological parameter
21cm
21cm 3D map 21cm power spectrum astrophysical parameter
Based on Bayesian inference
We proposed alternative method.

Artificial Neural Network (ANN)
An ANN is a mathematical
model of human brain network.
ex.) Rumelhart et. al (1986)
LeCun et. al (1989)
Recently, it has been applied to
field of astronomy.

Artificial Neural Network (ANN)
•Training network with training
dataset, ANN can approximate any
function which associates input and
output values.
y = f(x)
• Applying trained network to unknown
data for prediction.
yANN = f(xtest)
• ANN consists of input layer, hidden
layer and output layer. Each layer has
neurons.
Regression Problem

Dataset
⇣ : the ionizing efficiency.
: the minimum viral temperature of halos producing ionizing
photons
: the mean free path of ionizing photons through the IGM
(Maximum HII bubble size)
Tvir
Rmfp
~
d = [P(k), ~
✓]
21cm power spectrum (input)
EoR parameter (output)
EoR Parameter
✓EoR = f(P21)

z=11, PS without any noise
Reconstructed by 21cmPS at z=11
10
20
30
40
50
60
10 20 30 40 50 60
R
mfp,ANN
[Mpc]
Rmfp,true[Mpc]
z=12
10
20
30
40
50
60
10 20 30 40 50 60
ANN
true
z=12
1
10
100
1 10 100
T
vir,ANN
[K/10
3
]
Tvir,true[K/103
]
z=12
14 neurons, 100’000 iterations
• True value .vs. Reconstructed value
•The scatter of is large.
Rmfp ⇣
Tvir
•Other reconstructed parameters match
true one relatively well.
Shimabukuro &
Semelin (2017)
Rmfp

z=9, 10, 11. PS with thermal noise and cosmic variance
Reconstructed by 21cm PS at z=9,10,11
Rmfp ⇣
Tvir
10
20
30
40
50
60
10 20 30 40 50 60
R
mfp,ANN
[Mpc]
Rmfp,true[Mpc]
10
20
30
40
50
60
10 20 30 40 50 60
ANN
true
1
10
100
1 10 100
T
vir,ANN
[K/10
3
]
Tvir,true[K/10
3
]
Red : z=9,10,11
Blue : z=9
The parameters obtained by the ANN
match true values. ANN work well !

2.Recovering HII bubble size
distribution with ANN

Bubble size distribution (BSD)
''How large bubbles are distributed ?’'
Giri 2019
What can we learn from BSD?
Giri et al 2017
•EoR source (galaxy or AGN?)
•ionizing efficiency, recombination, radiative feedback.
(ex.)

BSD from 21cm observation
Kakiichi et al 2017
IFT
21cm Image BSD
Incomplete IFT due to limited number of antenna in interferometer.
visibility
We do not observe 21cm image directly by radio interferometer!
We first observe visibility and perform Inverse Fourier
Transformation (IFT) to obtain 21cm image. Then, compute BSD.

BSD from 21cm PS
Kakiichi et al 2017
21cm power spectrum BSD
visibility
We can directly compute 21cm power spectrum from visibility
without Inverse Fourier Transformation.
Avoid information loss by incomplete IFT.

BSD from 21cm PS
Kakiichi et al 2017
21cm power spectrum BSD
visibility
We can directly compute 21cm power spectrum from visibility
without Inverse Fourier Transformation.
Can we recover BSD from 21cm PS ?
Avoid information loss by incomplete IFT.

21cm power
spectrum
Input Output
ionised bubble size
distribution
Our datasets consist of 21cm power spectrum as input data and bubble
size distribution as output data.
Our strategy
We try to recover ionised bubble size distribution from 21cm PS

Recovered BSD
Black: Distribution obtained
by 21cm 3D image directly.
Red: Distribution obtained
by ANN.
xHI = 0.39
R2
= 0.957

Different stage of reionization

Effect of thermal noise
21cm PS with thermal
noises (SKA level)
Errors are estimated
by 10 realizations
thermal noises
xHI = 0.39

Foreground problem
Jelic et al 2008
The 21cm signal is buried under strong foreground !
Remove foreground ?
or
Avoid (strong)foreground?
Santos 2005
~8 order
Dillon et al 2013

Take home messages of my talk are…

•The epoch from the Dark Ages to cosmic reionization is the
frontier in the history of the universe.

•21cm signal is a promising tool to study this epoch.

•SKA will bring us fruitful information on the epoch
through Dark Ages to EoR

•SKA will bring us fruitful information on the epoch
through Dark Ages to EoR
•We proposed a method based on machine learning to
analyze the 21cm line signal.

•"21cm cosmology" (Prithcard & Loeb, astro-ph/1109.6012)
Textbook
Review paper
•"Cosmology at low frequencies" (Furlanetto et al, astro-ph/0608032)
•''In the beginning : the first sources of light and the deionization of the
universe” R,Bakana & A,Loeb (astro-ph/0010468)
References

Accuracy for all test data
Relative error between two size
distributions at fixed bubble
radius for all test data.
Good recovery for all test data.

n""
n"#
= 3 exp
✓
h⌫21cm
kTS
◆
The spin temperature is determined by following equilibrium
T 1
S =
T 1
CMB + xcT 1
K + x↵T 1
c
1 + xc + x↵
de-excitation rate by collision
de-excitation rate by UV
photons
excitation rate by UV
photons
excitation rate by collision
Stimulated by CMB photons
Spontaneous de-
excitation with Einstein
coefficient

Wouthuysen Field (WF)effect
•The mechanism that couples the spin
temperature of neutral hydrogen atom to
Lyman-alpha photons(Wouthuysen
1952,Field 1959)
•The hyperfine state is changed via 2P state
Solid lines : allowed path
Dashed lines : not allowed path

21cm PS with SKA
SKA covers wide epoch and range of the 21cm PS !!
Redshift evolution Scale dependence
z=8.95
z=15.98
Koopmans et al. (2014)
Pritchard et al. (2014)

• 1000 EoR models
• 48000 training datasets (20% of which is used for validation)
• 2000 test datasets
• 21cm PS is ranged from k=0.11/Mpc to 1.1/Mpc with 14 bins
• 5 hidden layers
• 212 neurons at each hidden layer
• 2000 iterations
Setup

Evaluate accuracy: noise
We evaluate accuracy of obtained parameters by chi-square. Smaller
chi-square means better accuracy.
single z
As expected, accuracy becomes worse if we add noise to 21cm
power spectrum.
without noise with noise

Evaluate accuracy: redshift
We evaluate accuracy of obtained parameters by chi-square. Smaller
chi-square means better accuracy.
multiple z
The accuracy of parameter estimation is improved when we
consider redshift evolution of 21cm power spectrum.
Single z
Both include noise

(Ex.) Emulator
EoR parameters 21cmPS
ANN MCMC
Before : 2.5days on 6 cores
After: 4minutes
speed up by 3 orders of magnitude
(Schmit et al 2018)
(input) (output)

Exploring Early Universe with Neutral Hydrogen Signals

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