# Searching for the hydrogen 21 cm line in cosmos

Mahta Moazzenzadeh  Department of Physics, K. N. Toosi University of
Technology, P.O. Box 15875-4416, Tehran, Iran<EMAIL_ADDRESS>Javad T.
Firouzjaee<EMAIL_ADDRESS>Department of Physics, K. N. Toosi
University of Technology, P.O. Box 15875-4416, Tehran, Iran  School of
Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box
19395-5531, Tehran, Iran

###### Abstract

Abstract: It is widely agreed that studying the 21 cm emission line from
neutral hydrogen may be our best hope for understanding the creation of the
first structures during the dark ages and the Epoch of Reionization (EoR).
This hyperfine transition occurs as a result of the spin-spin interaction
between the electron and the proton in hydrogen: The energy of the parallel
spins (triplet) state is greater than that of the anti-parallel spins
(singlet). This transition is strongly banned, with a transition probability
of $2.6\times 10^{-15}\mathrm{s}^{-1}$ being exceedingly low. Despite its low
chance, the 21 cm hyperfine transition is one of the most important tools in
observational astronomy due to the abundance of hydrogen in the Universe. The
relative occupation number of the ground state and the occupation number of
the excited state determine the strength of the 21 cm emission or absorption.
Collisions or the so-called Wouthuysen-Field effect can both excite the 21 cm
line. In this article, we give a brief review of the basic physics of 21 cm
emission and highlight the current main worldwide 21 cm signal experiments. We
also discuss several related concepts in astronomy and cosmology with these
observations.

###### Contents

  1. I Introduction
    1. I.1 A brief introduction on 21 cm emission
    2. I.2 Prediction of 21 cm line radiation
  2. II Physics of the 21 cm emission
    1. II.1 Basic physics
    2. II.2 Collisional coupling
    3. II.3 Wouthuysen-Field effect
  3. III Current Global 21 cm Signal Experiments
    1. III.1 Experiment to Detect the Global Epoch of Reionization Signature (EDGES)
    2. III.2 The Large-Aperture Experiment to Detect the Dark Ages (LEDA)
    3. III.3 The Hydrogen Epoch of Reionization Array (HERA)
    4. III.4 The Precision Array to Probe the Epoch of Reionization(PAPER)
    5. III.5 Probing Radio Intensity at high-Z from Marion(PRIZM)
    6. III.6 Measurement of Background Radio Spectrum (SARAS)
    7. III.7 Broadband Instrument for Global Hydrogen Reionisation Signal (BIGHORNS)
    8. III.8 Sonda Cosmol ogica de las Islas para la Detecci on de Hidr ogeno Neutro (SCI-HI)
    9. III.9  Square Kilometre Array (SKA)
      1. III.9.1 Cosmology with other hyperfine structure lines and SKA
    10. III.10 Murchison Widefield Array (MWA)
    11. III.11 Low-Frequency Array (LOFAR)
  4. IV Using 21 cm line radiation to Map the Galaxy
    1. IV.1 Three dimensional ‘Intensity Mapping’ of the Universe
    2. IV.2 Measuring Baryon Acoustic Oscillations with the 21 cm line of hydrogen
    3. IV.3 Foreground Emission
  5. V 21-cm Emission Around The Sun
    1. V.1 Brightness Temperature Of The Sun
    2. V.2 The Radio Brightness Distribution On The Sun At 21 Cm From Combined Eclipse And Pencil-Beam Observations
  6. VI Probing for dark matter and dark energy with 21 cm signal
    1. VI.1 Milky Way Galaxy Rotation Curve And Dark Matter
    2. VI.2 A brief review on dark matter
    3. VI.3 21 cm signal and Dark Matter
    4. VI.4 Dark Cooling
    5. VI.5 21 cm signal and interacting dark energy model
  7. VII Conclusion

##  I Introduction

###  I.1 A brief introduction on 21 cm emission

As hydrogen is the main component of interstellar gas, we often classify
regions of space according to the amount of neutral or ionized hydrogen in
them. Ionized hydrogen clouds are known as H II regions. (Scientists who work
with spectra use the Roman numeral I to indicate that an atom is neutral;
successively higher Roman numerals are used for each higher stage of
ionization. H II signifies hydrogen which has lost one electron.)

During each downward transition between the multiple energies of hydrogen
atoms, electrons give up a portion of their energy in the form of light. A
process by which ultraviolet light is converted into visible light is called
fluorescence. Interstellar gas contains many other elements besides hydrogen.
Sometimes, they are also ionized near hot stars; they capture electrons and
emit light just like hydrogen, making them observable. But generally, the red
hydrogen lines are the strongest, which is why H II regions appear red
pressbooks .

Fluorescent lights on Earth use the same mechanism as fluorescent H II
regions. When you turn on the current, electrons collide with atoms of mercury
vapor in the tube. The mercury becomes excited to a high-energy state as a
result of these collisions. The mercury atoms emit some of their energy as
ultraviolet photons when they return to lower-energy levels, which strikes a
screen coated with phosphor on the inside wall of the tube. (These atoms emit
a wider range of light colors than those in H II, giving fluorescent lights
their characteristic white glow. Hydrogen atoms in an H II region have a more
limited range of colors.) Only very few of the stars in the interstellar
medium are hot enough to produce H II regions; most of the interstellar medium
is filled with neutral (non-ionized) hydrogen. In what way should we search
for it?

There is no visible light emitted or absorbed by neutral hydrogen atoms at the
temperatures of interstellar space. The same holds true for most other trace
elements in the interstellar hydrogen mixture. Despite the interstellar
temperatures, some of these other elements have the ability to absorb visible
light. As a consequence, we may sometimes see additional lines in the spectrum
of a bright source such as a hot star or a galaxy when interstellar gas
absorbs light at specific frequencies. Insufficient sensitivity, we can also
detect many other stellar absorption lines, besides calcium and sodium
lumenlearning .

Including the redshift, this line will be observed at frequencies from 200 MHz
to about 9 MHz on Earth. Hydrogen lines are a highly valuable tool in Big Bang
theory because it allows us to figure out what happened during the ”dark
ages.” The analysis of the incoming redshifted 21 cm radiation could serve two
purposes, as well. First, it could provide a very precise account of the
matter spectrum in the period following recombination by mapping the intensity
of the incoming redshifted 21 cm radiation. Second, it provides evidence of
radiation produced by stars or quasars that ionized neutral hydrogen, since
these stars and quasars will appear as holes in the 21 cm background.

###  I.2 Prediction of 21 cm line radiation

As a result of Grote Reber’s radio astronomical discoveries, the great Dutch
astronomer Jan Oort recognized that a radio spectral line could be used to
discover the structure of our galaxy. During the course of his studies, Oort
used optical means to study the rotation and structure of the galaxy. He
noticed the immense amount of dust accumulating in the galactic plane, which
blocked visible light. Due to the absorption of light by distant stars, we can
see only a few thousand light years towards the galactic center. However,
radio waves can penetrate the dust and show us the galactic center and
actually the other side of our galaxy. By the Doppler effect, the frequency of
the line shifts, which enables the measurement of the velocity of the gas.
Using differential rotation, one can estimate the distance to gas clouds in
the galaxy and map the distribution of matter within.

Van de Hulst was given a task by Oort to find out if there were any radio
spectral lines and at what frequency they would exist. Since hydrogen is the
most abundant element, this was the element he studied first. According to his
calculations, a ”hyper-fine” transition in the ground state of hydrogen
produces radiation at 1420 MHz, generally occurring at a wavelength of about
21 cm. Electrons can either have their magnetic moment parallel to or anti-
parallel to those of their proton counterparts in hydrogen’s ground state.
Because of this, when the electron transitions to the anti-parallel state, it
produces 21 cm wavelength radiation nrao .

In 1951, Ewen and Purcell discovered the 21 cm line (1420.4 MHz), whose
findings then were confirmed by Dutch astronomers Muller and Oort, and by
Christiansen and Hindman in Australia. It wasn’t until 1952 that the first
maps of neutral hydrogen in the Galaxy were made, and the spiral structure of
the Milky Way was uncovered.

The goal of this review is to introduce the main projects to detect the 21 cm
signal in cosmology and astrophysics. Search on 21 cm physics continues to be
a very active field due to the upcoming telescopes data. This review is
organized as follows: in Section II, we explain the basic physics of the
hydrogen 21 cm emission line. In Section III, the main experiments to detect
the 21 cm emission line are reviewed. The role of 21 cm emission line in
galaxy physics is explained in Section IV. In Section V, we study the 21 cm
emitted from the sun. Section VI is devoted to probing the dark matter and
dark energy physics in 21 cm emission line. Finally, we conclude and summarize
the main results in Section VII.

##  II Physics of the 21 cm emission

###  II.1 Basic physics

Since hydrogen radiation penetrates the dust clouds at 1420 MHz, we get a more
complete picture of hydrogen than the stars themselves, whose visible light
cannot penetrate the dust clouds.

A radiation of 1420 MHz is generated from the interaction between the electron
spin and the nuclear spin in hydrogen 1S orbital. It represents the transition
between the two levels of this ground state. This splitting is known as hyper-
fine structure. Hydrogen in its lower state, as a result of its quantum
properties, will absorb 1420 MHz, and its emission indicates that a prior
excitation occurred in the upper state.

Because of the mass in the exponent, the proton also has a magnetic dipole
moment, though that moment is much smaller than that of the electron which can
be written Hyperfine splitting in the ground state of hydrogen

$\boldsymbol{\mu}_{p}=\frac{g_{p}e}{2m_{p}}\mathbf{S}_{p},\quad\boldsymbol{\mu}_{e}=-\frac{e}{m_{e}}\mathbf{S}_{e},$
(1)

where ${\mu}_{p}$ is the proton magnetic dipole moment and ${\mu}_{e}$ is the
electron magnetic dipole moment. Also, ${g}_{p}$ indicates the proton’s
$g$-factor, ${g}_{e}$ represents the electron’s $g$-factor, $\mathbf{S}_{p}$
is the spin of the proton, $\mathbf{S}_{e}$ indicates the electron’s spin.
${m_{e}}$ is the mass of the electron and ${m_{p}}$ is the mass of the proton.

(The proton is a composite structure composed of three quarks, and it has a
different gyromagnetic ratio than the electron-that is why its $g$-factor,
$\left(g_{p}\right)$, is $5.59$, not the electron’s $2.00$). As a matter of
electrodynamics, a dipole $\mu$ generates a magnetic field:

$\mathbf{B}=\frac{\mu_{0}}{4\pi
r^{3}}[3(\boldsymbol{\mu}\cdot\hat{r})\hat{r}-\boldsymbol{\mu}]+\frac{2\mu_{0}}{3}\boldsymbol{\mu}\delta^{3}(\mathbf{r}),$
(2)

where ${\mu_{0}}$ is vacuum permeability and ${\mu}$ is Magnetic permeability.
Thus, in the magnetic field created by a proton’s dipole moment, the electron
would have the following Hamiltonian:

$H_{\mathrm{hf}}^{\prime}=\frac{\mu_{0}g_{p}e^{2}}{8\pi
m_{p}m_{e}}\frac{\left[3\left(\mathbf{S}_{p}\cdot\hat{r}\right)\left(\mathbf{S}_{e}\cdot\hat{r}\right)-\mathbf{S}_{p}\cdot\mathbf{S}_{e}\right]}{r^{3}}+\frac{\mu_{0}g_{p}e^{2}}{3m_{p}m_{e}}\mathbf{S}_{p}\cdot\mathbf{S}_{e}\delta^{3}(\mathbf{r}).$
(3)

First-order corrections to energy are defined according to perturbation theory
as the expectation value of the perturbing Hamiltonian:

$\displaystyle E_{\mathrm{hf}}^{1}=$
$\displaystyle\frac{\mu_{0}g_{p}e^{2}}{8\pi
m_{p}m_{e}}\left\langle\frac{3\left(\mathbf{S}_{p}\cdot\hat{r}\right)\left(\mathbf{S}_{e}\cdot\hat{r}\right)-\mathbf{S}_{p}\cdot\mathbf{S}_{e}}{r^{3}}\right)$
(4)
$\displaystyle+\frac{\mu_{0}g_{p}e^{2}}{3m_{p}m_{e}}\left\langle\mathbf{S}_{p}\cdot\mathbf{S}_{e}\right\rangle|\psi(0)|^{2}.$

As the wave function is spherically symmetric in the ground state (or in any
other state that $l=0$ ) the first expectation value disappears. In the
meantime, from Equation

$\psi_{100}(r,\theta,\phi)=\frac{1}{\sqrt{\pi a^{3}}}e^{-r/a},$ (5)

we find that $\left|\psi_{100}(0)\right|^{2}=1/\left(\pi a^{3}\right)$, hence

$E_{\mathrm{hr}}^{1}=\frac{\mu_{0}g_{p}e^{2}}{3\pi
m_{p}m_{e}a^{3}}\left\langle\mathbf{S}_{p}\cdot\mathbf{S}_{e}\right\rangle,$
(6)

in the ground state. The spin-spin coupling involves the dot product of two
spins (contrasted with the spin-orbit coupling that involves
$\mathbf{S}\cdot\mathbf{L}$ ).

Spin-spin coupling results in no more conservation of individual spin angular
momenta; the ”good” states are the eigenvectors of the total spin,

$\mathbf{S}\equiv\mathbf{S}_{e}+\mathbf{S}_{p}.$ (7)

As before, we square this out to get

$\mathbf{S}_{p}\cdot\mathbf{S}_{e}=\frac{1}{2}\left(S^{2}-S_{e}^{2}-S_{p}^{2}\right).$
(8)

Both the electron and proton have a spin of $1/2$, so
$S_{e}^{2}=S_{p}^{2}=(3/4)\hbar^{2}$. In the triplet state (spins ”parallel”)
the total spin is $1$. As a result, $S^{2}=2\hbar^{2}$; in the singlet state
the total spin is 0, and $S^{2}=0$. Therefore, from Eq. (6) we get

$E_{\mathrm{hf}}^{1}=\frac{4g_{p}\hbar^{4}}{3m_{p}m_{e}^{2}c^{2}a^{4}}\left\\{\begin{array}[]{ll}+1/4,&(\text{
triplet })\\\ -3/4,&\text{ (singlet) }\end{array}\right.$ (9)

Spin-spin coupling eliminates spin degeneracy of the ground state, thereby
promoting the triplet and depressing the singlet. Evidently, the energy gap is

$\Delta E=\frac{4g_{p}\hbar^{4}}{3m_{p}m_{e}^{2}c^{2}a^{4}}=5.88\times
10^{-6}\mathrm{eV}.$ (10)

In the transition from a triplet state to a singlet state, a microwave photon
is emitted of a frequency

$v=\frac{\Delta E}{h}=1420\mathrm{MHz}.$ (11)

Among all the radiation occurring throughout the universe, this 21 cm line is
one of the most ubiquitous.

The line center frequency is:

$\nu_{10}={8\over 3}g_{\rm I}\biggl{(}{m_{\rm e}\over m_{\rm
p}}\biggr{)}\alpha^{2}(R_{\rm M}c)\approx 1420.405751{\rm~{}MHz},$ (12)

where $g_{\rm I}\approx 5.58569$ is the nuclear $g$-factor for a proton,
$\alpha\equiv e^{2}/(\hbar c)\approx 1/137.036$ is the dimensionless fine-
structure constant, and $R_{\rm M}c$ is the hydrogen Rydberg frequency. After
simplifying we get,

$\nu_{10}\approx 1420.4{\rm~{}MHz}.$ (13)

The 21 cm line spin temperature $T_{S}$ corresponds to its excitation
temperature. It is defined by the ratio between the number densities of
hydrogen atoms $n_{i}$ in the two hyper-fine levels (which we label with a
subscript 0 and 1 for the $1S$ singlet and $1S$ triplet levels, respectively)

$n_{1}/n_{0}=\left(g_{1}/g_{0}\right)\exp\left(-T_{\star}/T_{S}\right)$ (14)

where $\left(g_{1}/g_{0}\right)=3$ is the ratio of the statistical degeneracy
factors of the two levels, and $T_{\star}\equiv
hc/k\lambda_{21\mathrm{cm}}=0.068\mathrm{K}$ With this definition, a cloud of
hydrogen has an optical depth of

$\tau_{\nu}=\int\mathrm{d}s\left[1-\exp\left(-E_{10}/k_{B}T_{S}\right)\right]\sigma_{0}\phi(\nu)n_{0},$
(15)

where $n_{0}=n_{H}/4$ with $n_{H}$ being the hydrogen density, and we have
denoted the $21\mathrm{cm}$ cross-section as
$\sigma(\nu)=\sigma_{0}\phi(\nu),$ with $\sigma_{0}\equiv
3c^{2}A_{10}/8\pi\nu^{2},$ where $A_{10}=2.85\times 10^{-15}\mathrm{s}^{-1}$
indicates the rate at which the spin-flip transition spontaneously decays, so
that $\int\phi(\nu)\mathrm{d}\nu=1.$

The spin temperature can be calculated by the following formula:

$T_{S}^{-1}=\frac{T_{\gamma}^{-1}+x_{\alpha}T_{\alpha}^{-1}+x_{c}T_{K}^{-1}}{1+x_{\alpha}+x_{c}}$
(16)

where $T_{\gamma}$ is the temperature of the surrounding bath of radio
photons, typically determined by the CMB so that
$T_{\gamma}=T_{\mathrm{CMB}};T_{\alpha}$ is the color temperature of the
Lyman-alpha line (typically denoted by Ly-$\alpha$) radiation field at the
Ly-$\alpha$ frequency and is closely coupled to the gas kinetic temperature
$T_{K}$ by recoil during repeated scattering, and $x_{c},x_{\alpha}$ are the
coupling coefficients due to atomic collisions and scattering of Ly $\alpha$
photons, respectively. Spin temperature is tightly coupled with gas
temperature when $x_{\mathrm{tot}}\equiv x_{c}+x_{\alpha}\gtrsim 1$ and
relaxes to $T_{\gamma}$ when $x_{\text{tot }}\ll 1$.

The spin temperature can be determined as follows:

$T_{\mathrm{spin}}^{-1}\simeq\frac{T_{\mathrm{CMB}}^{-1}+\sum_{i}x_{i}T_{\mathrm{b}}^{-1}}{1+\sum_{i}x_{i}}.$
(17)

Brightness temperature (radiative transfer) could also be find by the
following formula:

$T_{\text{bright }}=T_{\text{spin
}}\left(1-e^{-\tau}\right)+T_{\mathrm{CMB}}e^{-\tau}.$ (18)

Brightness temperature contrast is therefore determined as follows:

$T_{21}\equiv\delta T_{\text{bright
}}=\frac{T_{\mathrm{spin}}-T_{\mathrm{CMB}}}{1+z}\left(1-e^{-\tau}\right)\approx\frac{T_{\mathrm{spin}}-T_{\mathrm{CMB}}}{1+z}\tau.$
(19)

In figure LABEL:The_Cosmological_21cm_Signal the Cosmological 21 cm Signal is
shown where one of the observable is

$T_{21}(z)\approx\frac{T_{\mathrm{Spin}}-T_{\mathrm{CMB}}}{1+z}\sim
23\mathrm{mK}\times
x_{\mathrm{HI}}(z)\left[\left(\frac{0.15}{\Omega_{m}}\right)\left(\frac{1+z}{10}\right)\right]^{1/2}\left(\frac{\Omega_{b}h}{0.02}\right)\left(1-\frac{T_{\mathrm{CMB}}(z)}{T_{\mathrm{Spin}}(z)}\right).$
(20)

In the 21 cm line, two types of background radio sources play a critical role
in probing astrophysics. CMB can be used as a radio background source, first
and foremost. In this case, $T_{R}=T_{\mathrm{CMB}}$ and the
$21\mathrm{~{}cm}$ features can be viewed as spectral distortions of the CMB
blackbody at appropriate radio frequencies (since the temperature fluctuations
of the CMB are low $\delta T_{\mathrm{CMB}}\sim 10^{-5}$, the CMB appears
uniformly bright). As with the CMB anisotropies, the distortion forms a
diffuse background that can be studied across the whole sky. In order to build
a $3\mathrm{D}$ map of the observable Universe, observations at different
frequencies probe different shells of the observable Universe.

Radio loud point sources such as quasars are used as the background in the
second situation. Sources in this situation will always emit more light than
weak emission from diffuse hydrogen gas, $T_{R}\gg T_{S},$ so that gas is
observed in absorption when compared to the source. Various distances away
from the source produce lines that form a ”forest” known as the ”21 cm
forest,” like the Ly $\alpha$ forest. The high brightness of the background
source allows the $21\mathrm{~{}cm}$ forest to be studied with high frequency
resolution so probing small scale structures $(\sim kpc)$ in the IGM. For
useful statistics, a number of lines of sight are needed to reach different
radio sources, prioritizing the discovery of high redshift radio sources.

We have a number of quantities that contain units of temperature, and many of
them are not true thermodynamic temperatures. $T_{R}$ and $\delta T_{b}$ are
radio intensity measurements. $T_{S}$ measures the relative occupation numbers
of the two hyperfine levels. $T_{\alpha}$ is a color temperature describing
the photon distribution in the vicinity of the Ly-$\alpha$ transition. There
is no true thermodynamic temperature other than the CMB blackbody temperature
$T_{\mathrm{CMB}}$ and $T_{K}$.

###  II.2 Collisional coupling

As the gas density is high in the early Universe, collisions between particles
can cause spin-flips in atoms of hydrogen and dominate the coupling there.
Collisions between two hydrogen atoms, collisions between a hydrogen atom and
an electron, and collisions between a hydrogen atom and a proton, are the
three principal channels. Assuming ’$i$’ is a species, the collisional
coupling is as follows:

$x_{c}^{i}\equiv\frac{C_{10}}{A_{10}}\frac{T_{\star}}{T_{\gamma}}=\frac{n_{i}\kappa_{10}^{i}}{A_{10}}\frac{T_{\star}}{T_{\gamma}}.$
(21)

Collisional excitation rate is $C_{10}$ , $\kappa_{10}^{i}$ is the specific
rate coefficient for spin deexcitation by collisions with species $i$ (in
units of $\left.\mathrm{cm}^{3}\mathrm{~{}s}^{-1}\right)$. The total
coefficient of collision can be expressed as:

$\displaystyle x_{c}$ $\displaystyle=x_{c}^{HH}+x_{c}^{eH}+x_{c}^{pH}$ (22)
$\displaystyle=\frac{T_{\star}}{A_{10}T_{\gamma}}\left[\kappa_{1-0}^{HH}\left(T_{k}\right)n_{H}+\kappa_{1-0}^{eH}\left(T_{k}\right)n_{e}+\kappa_{1-0}^{pH}\left(T_{k}\right)n_{p}\right],$

where $\kappa_{1-0}^{HH}$ is the scattering rate between hydrogen atoms,
$\kappa_{1-0}^{eH}$ is the scattering rate between electrons, hydrogen atoms,
and protons and hydrogen atoms scatter at a rate of $\kappa_{1-0}^{pH}$ .

Quantum mechanical calculations are needed to calculate collisional rates. On
the basis of $T_{k}$ we have tabulated $\kappa_{1-0}^{HH}$ values, the
scattering rate between electrons and hydrogen atoms $\kappa_{1-0}^{eH}$ was
considered and the scattering rate between protons and hydrogen atoms
$\kappa_{1-0}^{pH}$ was considered in Furlanetto . This scattering rate can be
fitted by the following fitting functions: A well-fitting HH scattering rate
can be seen in the range $10\mathrm{~{}K}<T_{K}<10^{3}\mathrm{~{}K}$ by

$\displaystyle\kappa_{1-0}^{HH}\left(T_{K}\right)\approx 3.1\times
10^{-11}T_{K}^{0.357}\exp\left(-32/T_{K}\right)\mathrm{cm}^{3}\mathrm{~{}s}^{-1},$
(23)

and the scattering rate of e-H is well described by

$\displaystyle\log\left(\kappa_{1-0}^{eH}/\mathrm{cm}^{3}\mathrm{~{}s}^{-1}\right)=-9.607+0.5\log
T_{K}\times\exp\left[-\left(\log T_{K}\right)^{4.5}/1800\right],$ (24)

for $T\leq 10^{4}\mathrm{~{}K}$ and
$\kappa_{1-0}^{eH}\left(T_{K}>10^{4}\mathrm{~{}K}\right)=\kappa_{1-0}^{eH}\left(10^{4}\mathrm{~{}K}\right)$.
The details of the coupling process become important during the cosmic dark
ages, where collisional coupling dominates. The above calculations assume
collisional cross-sections are independent of velocity; in fact, velocity
dependence results in a non-thermal distribution for the hyperfine occupation.
This effect can lead to a suppression of the 21 cm signal at the level of
$5\%$, although small, the signal measures 21 cm, which can be used for
precision cosmology utilizing the 21 cm signal from the dark ages.

###  II.3 Wouthuysen-Field effect

As a result of the resonant scattering of Ly-$\alpha$ photons, the photon
spectrum around Ly-$\alpha$ frequency $\nu_{0}$ will have a local Boltzmann
distribution with a color temperature equal to the kinetic temperature of
hydrogen gas. This implies that the spin temperature $T_{s}$ of neutral
hydrogen will directly be coupled to the kinetic temperature of hydrogen gas.
Here is what’s known as the Wouthuysen-Field (W-F) coupling. It is essential
to estimate the redshifted 21 cm signal from the halos of the first generation
of stars due to the substantial spin temperature deviation from the cosmic
microwave background (CMB) temperatures ($T_{cmb}$). It is not as simple as a
simple description would suggest the physics behind the Wouthuysen-Field
equation. The coupling could be written as Wouthuysen-Field Coupling :

$x_{\alpha}=\frac{4P_{\alpha}}{27A_{10}}\frac{T_{\star}}{T_{\gamma}},$ (25)

where $P_{\alpha}$ is the scattering rate of Ly-$\alpha$ photons. Here we have
related the scattering rate between the two hyperfine levels to $P_{\alpha}$
using the relation $P_{01}=4P_{\alpha}/27,$ which results from the atomic
physics of the hyperfine lines and assumes that the radiation field is
constant across them. An atom of hydrogen scatters Ly-$\alpha$ photons
according to the following equation:

$P_{\alpha}=4\pi\chi_{\alpha}\int\mathrm{d}\nu
J_{\nu}(\nu)\phi_{\alpha}(\nu).$ (26)

The local absorption cross section can be calculated by using
$\sigma_{\nu}\equiv\chi_{\alpha}\phi_{\alpha}(\nu)$,
$\chi_{\alpha}\equiv\left(\pi e^{2}/m_{e}c\right)f_{\alpha}$ is the
oscillation strength of the Ly $\alpha$ transition, $\phi_{\alpha}(\nu)$ is
the Ly-$\alpha$ absorption profile, and in the background radiation field,
$J_{\nu}(\nu)$ is the angle-averaged specific intensity, (by number$)$.

Wouthuysen-Field coupling, or the Wouthuysen-Field effect, occurs when the
excitation temperature of neutral hydrogen is coupled to the Lyman-$\alpha$
(Ly-$\alpha$) radiation. When the Dark Ages ended and the epoch of
reionization began, this coupling led to there being a difference in
temperature between neutral hydrogen and the cosmic microwave background.

There are times when neutral hydrogen’s thermodynamic equilibrium with the
cosmic microwave background (CMB) prevails, but the hydrogen line cannot be
observed because the CMB and neutral hydrogen are ”coupled”. The hydrogen line
is only visible when the two temperatures differ, i.e. when they are
decoupled.

Wouthuysen-Field coupling is a mechanism by which neutral hydrogen’s spin
temperature is coupled to Ly-$\alpha$ radiation, which decouples it from the
CMB. In astrophysical sources such as stars and quasars, the Ly-$\alpha$
transition produces energy of approximately 10.2 eV, which is approximately 2
million times greater than the hydrogen line. As Ly-$\alpha$ photons are
absorbed, Ly-$\alpha$ photons are re-emitted, and hydrogen can go into either
one of two possible spin states. Electrons are redistributed between the
hyperfine states in this process, allowing neutral hydrogen to be decoupled
from CMB photons.

The coupling between the Ly-$\alpha$ photons and the hyperfine states depends
not on the intensity of the radiation, but on the shape of the spectrum
located in the vicinity of Ly-$\alpha$ transitions. It was first suggested by
S. A. Wouthuysen in 1952 that this mechanism might affect the population of
hyperfine states in neutral hydrogen, and later developed by B. George Field
in 1959.

Hyperfine levels are affected by the Ly-$\alpha$ photons depending on the
intensity of the red and blue wings of the line, which reflects a very small
difference in energy between the hyperfine states and the transition. A
cosmological redshift of 6 will cause Wouthuysen-Field coupling to raise the
spin temperature of neutral hydrogen above its CMB counterpart, which will
produce hydrogen-line emission.

##  III Current Global 21 cm Signal Experiments

Despite the newness of this method, there are only a few telescopes in use
today. Another major project, the Square Kilometer Array, is in the planning
stages. In April 2013, a research team using data collected by the Green Bank
Telescope reported a detection that placed upper and lower limits on the 21 cm
background global experiments .

###  III.1 Experiment to Detect the Global Epoch of Reionization Signature
(EDGES)

The Experiment to Detect the Global EoR Signature (EDGES) is a ground-based
experiment that seeks to detect the 21 cm radiation from neutral hydrogen in
the intergalactic medium (IGM) at redshifts $27>z>6$. The redshifts are caused
by the formation of the first stars, galaxies, and black holes, as well as the
reionization process of the IGM. The redshifts of the 21 cm radiation can be
measured with radio frequency bands between 50 and 200 MHz. This mission
serves as a pathfinder for the Moon-orbiting DARE mission and the NESS-funded
Moon-based low-frequency cosmology telescope.

In 2007, EDGES began conducting measurements and has been placed at the
Murchison Radioastronomy Observatory in Australia’s desert to take full
advantage of the low levels of artificial interference (RFI). The largest
challenge in this measurement is to distinguish between the very weak 21 cm
signal ($<500mK$) and the strongly diffuse foregrounds between hundreds and
thousands of Kelvin. Because of this, it is necessary to calibrate an
instrument to a level of about 1 part in 10,000 in order to achieve sufficient
sensitivity for detection. EDGES has enabled the tightest constraints to date
on the global 21 cm signal due to its sensitivity being comparable to this
requirement colorado .

###  III.2 The Large-Aperture Experiment to Detect the Dark Ages (LEDA)

Large-Aperture Experiment to Detect the Dark Age (LEDA) will detect the
predicted O(100) mK sky-averaged absorption of the cosmic microwave background
by hydrogen in the neutral pre- and intergalactic medium just after the
cosmological Dark Age. When ’Cosmic Dawn’ occurs, the spectral signature will
be associated with emergence of a diffuse Ly-$\alpha$ background from
starlight. Recently, Bowman et al  reported detecting an amplitude of 530 mK,
centered at 78 MHz, of the predicted absorption in this signal. It is
imperative that LEDA independently validates this finding. The LEDA system is
part of the Owens Valley Radio Observatory Long Wavelength Array, which
consists of a station correlator, five redundant dual polarization radiometers
well positioned apart, and back-end electronics. In an attempt to calibrate,
the radiometers operate in a 30-85 MHz frequency band $(16<z<34)$ as part of a
larger interferometric array ui.adsabs.harvard.edu ; tauceti .

###  III.3 The Hydrogen Epoch of Reionization Array (HERA)

Hydrogen Epoch of Reionization Array (HERA) attempts to measure the emissions
of the primordial intergalactic medium (IGM) throughout cosmic reionization (z
= 6 - 12). In addition, it is also possible to study earlier eras of our
Cosmic Dawn ($z\sim 30$). As stars and black holes heated and ionized the IGM
during these periods, 21 cm emission fluctuated. It will use the properties of
the first galaxies, the evolution of large-scale structure, and the early
sources of heat to constrain the timing and morphology of reionization. The
HERA instrument will consist of 350 elements in South Africa and will be a
14-m parabolic dish interferometer that observes with a frequency range of 50
to 250 MHz ,astro.phy.cam.ac.uk ; reionization .

###  III.4 The Precision Array to Probe the Epoch of Reionization(PAPER)

The Precision Array for Probing the Epoch of Reionization (PAPER) is a low-
frequency radio interferometer used to measure the occurrences of the first
stars and galaxies around 500 million years after the Big Bang. Researchers
measured the power spectrum of intergalactic medium fluctuations introduced by
the first luminous sources at high redshifts (z = 7 - 12) by mapping the
intensity of hydrogen emission at 21 cm.

With foregrounds five orders of magnitude brighter than the background
standards for detecting reionization, the PAPER project takes an incremental
engineering approach, optimizing each component in the array in a staged
process to minimize potential problems with subsequent calibration and
analysis. With the help of this staged approach, we can systematically address
observations challenges resulting from very wide field, high dynamic range
imaging within large bandwidths under the influence of transient terrestrial
interference berkeley .

###  III.5 Probing Radio Intensity at high-Z from Marion(PRIZM)

Using globally averaged redshifted 21 cm emission, a new experiment examines
the cosmic dawn absorption feature. PRIZM is among a number of previous and
current global signal experiments. This experiment uses two dual-polarization
radiometers with centers frequencies of 70 and 100 MHz; their combined
frequency range is 30 - 200 MHz. An overview of the PRIZM signal chain for a
single polarization can be seen in Figure 15. As with the original SCI-HI
experiments, PRIZM radiometer cells use an antenna design developed for the
HIBiscus experiment Probing Radio Intensity .

###  III.6 Measurement of Background Radio Spectrum (SARAS)

All-sky 21 cm signals are distorted by 10’s to about 100 mK, and this is
present in the cosmic radio background at 30-200 MHz as a trace additive
component. The galactic and foreground brightnesses of these long wavelengths
of contaminating radio sky are between 100 and 10,000 K. Furthermore,
systematics from within radio-frequency spectrometers and outside interference
(RFI) is a major challenge in the task of designing the detection system and
developing the algorithms required. Towards this key science goal we are
working on the experiment SARAS (Shaped Antenna measurement of the background
RAdio Spectrum), as part of this program, there is a continuous development,
deployment, testing, and improving of a spectral radiometer that is based on
an independent frequency antenna, self-calibrating receivers, and a broadband
precision digital spectrometer.

As a correlation spectrometer, SARAS was designed to make measurements of the
cosmic radio background and faint features in the sky spectrum at long
wavelengths caused by gas redshifted to 21 cm at the time of reionization.
System parameters are calibrated by measuring the difference in antenna
temperature and an internal reference and a complex switching scheme to cancel
systematics. In ref. Patra et al 2013 , details of the architecture and data
analysis procedure used in SARAS are given.

In the observed spectrum, the foregrounds and systematics are dominant, and
the antenna and receiver characteristics link the foregrounds and systematics
to the detector with complex transfer functions that are also different for
different components of the response. The reionization signal will be confused
by all of this. To minimize instrument signatures, it is important to pay
attention to the system design, characterization, and calibration. Therefore,
we are concentrating on developing algorithms and methods for properly
calibrating the system, minimizing systematics, and modeling the factors
contributing to the system response with mK accuracy to discover the
cosmologically redshifted 21 cm signal.

In addition to continuous improvements in antenna design, analog and digital
receiver design, we test potential observing sites to choose ones with
relatively little radio frequency interference (RFI) rri ; SARAS .

###  III.7 Broadband Instrument for Global Hydrogen Reionisation Signal
(BIGHORNS)

The Broadband Instrument for Global Hydrogen ReioNisation Signal (BIGHORNS) is
a total power radiometer designed to detect reionisation signatures in low-
frequency radio waves (70 - 300 MHz).

An Epoch of Reionization (EoR) represents a period of time when the previously
neutral intergalactic medium became ionized by the first luminous sources.
This transition line is extremely difficult to observe for this period, but
its detection has been considered a vital objective for radio astronomy. As a
result, a variety of detection systems are being investigated, from single
antennas such as BIGHORNS to large interferometer arrays such as the MWA.

A conical log spiral antenna, known as BIGHORNS, was deployed at the Murchison
Radio-astronomy Observatory (MRO) in October 2014, and has been collecting
data ever since. In ref. BIGHORNS , present details of the original biconical
antenna system and its upgrades has been published.

BIGHORNS was also instrumental in assessing the level of radio frequency
interference (RFI) at the future site for the low-frequency component of the
Square Kilometre Array BIGHORNS .

###  III.8 Sonda Cosmol ogica de las Islas para la Detecci on de Hidr ogeno
Neutro (SCI-HI)

The ’Sonda Cosmologica de las Islas para la Deteccion de Hidrogeno Neutro’
(SCI-HI) experiment is a 21 cm brightness temperature spectrum experiment that
studies the cosmic dawn ($z\sim 15-35$). It is a collaboration between
Carnegie Mellon University (CMU) and Instituto Nacional de Astrofísica, Óptica
Electrónica (INAOE) in Mexico. This experiment was launched in June 2013 on
the small island of Guadalupe, which is about 250 km off the coast of Baja
California in Mexico. The first observations from this deployment have placed
the first constraint on the 21 cm all sky spectrum around 70 MHz ($z\sim 20$),
Voytek et al (2014) . There are a great deal of neutral hydrogen (HI)
molecules found in the intergalactic medium (IGM). In this case, the HI can be
seen through the 21 cm (1.4 GHz) spectral line as a result of hyperfine
structure. A wavelength of this spectral line extends at a rate defined by the
redshift $z$ with the expansion of the universe, producing a signal traceable
through time.

It turns out that the strength of the 21 cm signal in the IGM is only affected
by a few variables: the temperature and density of the IGM, the amount of HI
in the IGM, the UV energy density in the IGM, and the redshift. 21 cm
measurements, therefore, provide us with insights into the history and
structure of the IGM. During the cosmic dawn before reionization, the SCI-HI
experiment analyzes the spatially averaged 21 cm spectrum to observe the
evolution of the IGM over time. The SCI-HI experiment aimed to constrain the
initial data. However, the preliminary data centered around a narrow band
between 60 and 85 MHz. Radio frequency interference (RFI) and instrumental
difficulties limited radio transmission in the FM radio band ($\sim 88-108$
MHz). A new deployment of SCI-HI is currently in progress and we plan to have
another soon. This deployment will take place at Socorro and Clarion, two
islands farther from mainland Mexico than Guadalupe ui.adsabs.harvard.edu2 .

###  III.9  Square Kilometre Array (SKA)

With a square kilometre of collecting area, the Square Kilometre Array (SKA)
will be the world’s most sensitive radio telescope. A multi-nation project,
the SKA design and construction involves 15 countries. It was decided in 2012
to select two sites in Australia and one in South Africa, as well as to have
headquarters in the United Kingdom.

A technique known as aperture synthesis will be used to combine the signals
received from thousands of small antennas spread over thousands of kilometres
to simulate an extremely sensitive and angular-resolution radio telescope.
There will also be sub-arrays of the SKA that will have very large field-of-
view (FOV), allowing for surveying very large areas of the sky simultaneously.
Using the SKA, researchers will be able to analyze a wide range of questions
in astrophysics, fundamental physics, cosmology, and particle astrophysics, in
addition to expanding the observable universe. A key purpose of the SKA is to
provide observations from the so-called Dark Ages (between 300,000 and 600,000
years after the Big Bang when the universe first became sufficiently cool for
hydrogen to become neutral and decoupled from radiation)
https://www.skatelescope.org/layout/ .

Jodrell Bank Observatory in Cheshire, England, hosted the SKA’s headquarters,
while the telescopes will be installed in Australia and South Africa
111https://www.industry.gov.au/policies-and-initiatives/co-hosting-the-square-
kilometre-array. It is important that SKA telescope sites are unpopulated
areas with very low levels of radio interference caused by humans. South
Africa, Australia, Argentina, and China were among the first four proposed
sites. 222http://www.ncra.tifr.res.in:8081/SKA-India/.

####  III.9.1 Cosmology with other hyperfine structure lines and SKA

Hyperfine structure lines can also be found in other atomic species that may
be useful for cosmological studies with the SKA. $\lambda=91.6\mathrm{~{}cm}$
represents the hyper-fine line of neutral deuterium. This line is more
challenging to detect than hydrogen’s $21\mathrm{~{}cm}$ line due to its
longer wavelength and also to higher abundance $[\mathrm{D}/\mathrm{H}]$
relative to hydrogen; however, it provides the most accurate measurement of
primordial abundance since it is free of contamination by processes of
structure formation at lower $z$. Using this method, we can indirectly
determine the baryon-to-photon ratio $\eta=n_{\mathrm{b}}/s.$ Big bang
nucleosynthesis $(\mathrm{BBN})$ provides the only known source of deuterium,
which in turn lets us determine the cosmic baryon abundance,
$\Omega_{\mathrm{b}}h^{2}$ skatelescope .

###  III.10 Murchison Widefield Array (MWA)

Among the few experiments designed to detect the statistical signal from the
Epoch of Reionisation, the MWA EoR is one of the more prominent ones. In each
of these experiments, the challenges, such as removing from the foreground,
have become more understood. Through the MWA Collaboration’s expertise and
understanding of the telescope array, the end-to-end pipelines, the
ionospheric conditions, and the foreground emissions, the collaboration has
developed expertise and understanding. It has been possible to detect the
theoretically predicted EoR signal based upon the collected data. There are
periodic limit updates, but the detection is still several orders of magnitude
away. Throughout this paper, recent progress is summarized, along with future
directions.

The next decade will hold unprecedented opportunities for understanding the
Cosmic Dawn, the period when the first galaxies and stars were formed. A radio
interferometer that has been using the MWA to detect redshifted 21 cm line
emission from neutral hydrogen gas in the intergalactic medium (IGM) during
this period may be one of the first to detect these emissions. In order to
optimize the array’s capability to detect brightness temperature variations in
the 21 cm emission during the EoR, it was designed to have the redshift range
$6<z<10$ optimized. It is during the EoR that the first luminous sources begin
to ionize the primordial neutral hydrogen. Through measurements of the power
spectrum and other statistical properties of the fluctuations, the MWA is
capable of detecting the presence of large ionized bubbles that form during
reionization to a significance level of 14 sigma Beardsley et al . It will be
used as a test bed to demonstrate and develop techniques to subtract the
bright radio foregrounds that obscure the 21 cm background in order to
implement this objective MWA ; mwatelescope .

###  III.11 Low-Frequency Array (LOFAR)

LOFAR, the Low-Frequency Array, is a new-generation interferometer being built
in the Netherlands and throughout Europe. Through the use of a phased-array,
LOFAR provides access to the low-frequency range from 10–240 MHz, which has
been largely unexplored. LOFAR stations are being constructed throughout the
Netherlands, spread out from the village of Exloo in the northeast. There are
also five other stations deployed in Germany, and three stations have been
built in France, Sweden, and the United Kingdom. By using digital beam-forming
techniques, LOFAR can be made more agile and able to carry out many
simultaneous observations at once. LOFAR achieves amazing angular resolution
and sensitivity in the low-frequency radio regime thanks to its dense core
array and long interferometric baselines. As an observatory operated by the
International LOFAR Telescope (ILT) foundation, LOFAR facilities are available
to astronomers throughout the world. It is, in fact, one of the first radio
observatories to provide its users with fully calibrated science products via
automated processing pipelines.

Due to LOFAR’s new capabilities, techniques, and operational modes it is an
important stepping stone to the SKA. In the very distant Universe $(6<z<10)$,
LOFAR can identify the results of hydrogen reionization. As the first stars
and galaxies form at the epoch of the so-called ”dark ages”, this phase change
will occur at the same time. When reionization begins, the 21 cm line of
neutral hydrogen at $1420.40575\mathrm{MHz}$ will enter the LOFAR observing
window. There is a factor of $1/(z+1)$ difference in frequency observed today
LOFAR: The LOw-Frequency ARray .

##  IV Using 21 cm line radiation to Map the Galaxy

The 21 cm emission line intensity varies with the density of atomic hydrogen
centered along a line of sight. Radio emission Doppler-shifted can be
converted into distances to hydrogen clouds by using the rotation curve.

Rotation curves are plots of the orbital velocity of clouds around the
galactic center against their distance from the galaxy center. When used in
this context, ’rotation’ refers to a galactic disk’s motion as a whole. It
appears as though a disk of stars and gas clouds is spinning. The gas clouds
are presumed to revolve on nearly circular orbits in the disk’s plane. In
1927, Jan Oort discovered that stars closer to the galactic center complete
more of their orbits in a given time than those farther out. Differential
rotation describes the difference between the angular speeds of different
parts of the galactic disk.

By observing the Doppler velocities of hydrogen gas along different lines of
sight, the rotation curve can be determined. Hydrogen at varying distances
from the galactic center will contribute to the 21 cm emission, which will
have a different Doppler shift with respect to us. Gas clouds inside the orbit
of the sun will emit some of the radiation because they move at slightly
faster angular speeds than the sun. Small redshifts are expected. Gas moving
at the greatest angular speed will contribute the most to the total emission
coming from the closest region to the galactic center,
http://www.astronomynotes.com/ismnotes/s3.htm ,21 cm Intensity Mapping .

###  IV.1 Three dimensional ‘Intensity Mapping’ of the Universe

Up until now, the primary method for determining the large scale structure of
the universe was through galaxy redshift surveys, that is by isolating
millions of individual galaxies, recording their spectra, and measuring their
redshifts. The primary technique used for this is optical spectroscopy. In
total, optical surveys have mapped just under 1% of the observable universe.

###  IV.2 Measuring Baryon Acoustic Oscillations with the 21 cm line of
hydrogen

In order to analyze the expansion history, the Baryon Acoustic Oscillations
method (BAO) is proposed. The first 380,000 years of expansion were
characterized by extremely ionized cosmic matter and, as a consequence,
acoustic waves could propagate across the universe. Wave crests from the
ionized era left behind density enhancements, but acoustic waves no longer
propagated at its end BAO .

According to simulations, the 21 cm intensity map technique allows very
precise constraints to be applied to the equation of state for dark energy.
The survey was sensitive due to its large volume.

###  IV.3 Foreground Emission

Both galactic and extragalactic foregrounds are strongly dominated by
synchrotron emission at these wavelengths. A nearly power law distribution of
electron cosmic ray energies is what is expected to produce a nearly power law
distribution of synchrotron radiation foreground. According to recent
estimates, the foreground spectrum of a synchrotron must always be smooth,
regardless of how the electron energies are distributed. Under the extreme
assumption that electrons are monoenergetic, it is still more smooth by more
than ten orders of magnitude than is required for successful subtraction.
Because the synchrotron emission process does not require spectral features,
the 3-D 21 cm intensity signal stands out due to its lack of spectral features
intensity mapping .

##  V 21-cm Emission Around The Sun

###  V.1 Brightness Temperature Of The Sun

Using the interstellar hydrogen emission, one can measure the sun’s brightness
temperature at 21 cm. The substate of high energy hydrogen is found in two-
thirds of hydrogen atoms at 100 K, the temperature of the interstellar medium.
Despite the fact that only one hydrogen atom emits 1420.4 MHz radiation every
$10^{7}$ years, enough hydrogen atoms transition for measurable quantities of
this radiation to occur. It results from the vast numbers of hydrogen atoms
that are found within any galactic line of sight.

When the antenna temperature is calculated from the solar temperature, it is
the solar temperature plus the area surrounding the sun. The sun radiates from
a surface $\pi\left(L\psi_{\operatorname{sm}}^{\mu}\right)^{2}$ and the view
area is $x\left(L\psi_{\text{view}}\right)^{2}$. The actual brightness
temperature of the sun is

$T_{b}\left(\nu_{0}\right)=\frac{T_{ant}}{\eta}\left(\frac{\psi_{view}}{\psi_{sun}}\right)^{2},$
(27)

where $\psi_{sun}=32^{\prime}=0.533^{\circ}\pm 0.018^{\circ}$ is the angular
diameter of the sun seen from the earth and $\psi_{\text{view}}=$
$6.41^{\circ}\pm 0.03^{\circ}$ is the viewing angle of the telescope. With
these equations, the brightness temperature of the sun can be determined
$T_{b}=(4.5\pm 0.3)10^{4}K$, http://joans.io/papers/21cm.pdf .

###  V.2 The Radio Brightness Distribution On The Sun At 21 Cm From Combined
Eclipse And Pencil-Beam Observations

Observations of the emission of radiation from the sun at decimetre
wavelengths at that time showed that it fluctuated with a period comparable to
the rotation period of the Sun, but was normally steady over short periods.
These observations were made with aerials whose beamwidths to half-power
points were much greater than the angular size of the Sun. The low resolution
devices that we use to observe the Sun will henceforth be referred to as
”radiometers”.

At a wavelength of $10.7\mathrm{cm}$ wavelengths, Covington in 1947 observed a
partial eclipse of the Sun. A sharp decrease in flux density was found
simultaneous with the occultation of a large visible sunspot group, suggesting
the presence of a localized radio source. According to a statistical analysis
of the day-to-day variation in radio emission from the sun at various
wavelengths, this is true, (Pawsey and Yabsley 1949  and Denisse 1949 ). In
the research Krishnan Labrum , it was found that the radio flux at a specific
wavelength was always strongly correlated with the projected sunspot area,
which is the main component of solar radiation. By fitting a regression line
to the data, we could distinguish between the two components. In addition to
the extrapolated flux value for an unspotted disk, the variable solar
radiation component was called the ”slowly varying component” since its ratio
was proportional to sunspot area.

The quiet-Sun component could be explained by thermal radiation from the
entire Sun. There were however fewer evidences that the slowly varying
component and sunspot area were associated. Due to the fact that radio
emission at decimetre wavelengths originates at levels thousands of kilometres
above the photosphere, the associations between the slowly varying component
and sunspot area were less clear. As in ref. Pawsey and Yabsley 1949
confirmed this with eclipse observations showing in some cases radio sources
were present where old sunspot groups were no longer visible. There seemed to
be a need to search for long-lasting solar features that could emit radio
waves due to their association with sunspot groups. According to Waldmeier and
Muller 1950 , coronal condensations may be responsible for the slowly varying
component.

As in ref. Christiansen Warburton Davies  been discovered that radio sources
and astrophysical plages were always associated, and when the radio sources
were resolved, the astrophysical plages matched their sizes. The plage areas
and sizes of radio sources show a strong correlation, as confirmed by
Christiansen and Mathewson (1958) .

Similarly, for 21 cm wavelengths, radio bright regions or ”radio plages” have
a shape and size that are comparable to those of related chromospheric plages.
They have given an illustration that shows the correspondence in shape very
well.

The quiet-Sun component has been studied at sunspot minimum and maximum in
high resolution. According to references Christiansen and Warburton (1955)
and Christiansen and Warburton (1955)2 , the distribution of brightness on the
quiet Sun at a wavelength of 21cm displayed quadrant rather than circular
symmetry; the limb of the Sun was bright at the equator but not the poles. The
limbs on the equator reached a temperature of $6\cdot 8\times
10^{5}\mathrm{K}$ , while the temperature at the centre of the Sun’s disk was
$4\cdot 6\times 10^{5}$ $\mathrm{K}$
http://adsabs.harvard.edu/full/1961AuJPh..14..403K .

sunplot.pdf

##  VI Probing for dark matter and dark energy with 21 cm signal

To know the 21 cm observation application in cosmology, first we should know
how dark side of universe appear in cosmological observation.

###  VI.1 Milky Way Galaxy Rotation Curve And Dark Matter

If all of the mass in the galaxy is visible, and if the galaxy is radially
symmetric, the Keplerian curve can be calculated. Considering the currently
accepted model of galaxy formation is a dense bulge surrounded by spiral arms,
the latter is true at large radii. A large radius brings out the effect of a
uniform disk. To calculate the rotation curve, Newton’s law and universal
gravitation can be applied as follows:

$\frac{mv^{2}}{r}=\frac{GmM}{r^{2}}\Longrightarrow v(r)=\sqrt{\frac{GM}{r}}.$
(28)

The universal gravitational constant G is equal to $10^{42}$kg, and the
visible mass M equals the visible mass of the galaxy. Based on the plot of the
rotation curve, it is evident that the experimental data are contrary to
Keplerian prediction. Accordingly, since the Keplerian curve is predicated
upon a visible mass of the galaxy, this implies that there is less visible
mass in the galaxy. According to the current hypothesis, dark matter explains
the difference between the two curves by being invisible
,http://joans.io/papers/21cm.pdf .

RotationCurveoftheMilkyWayGalaxy.pdf

###  VI.2 A brief review on dark matter

Approximately 85% of the universe’s matter consists of dark matter and it
accounts for about a quarter of its total mass-energy density, or $2.241\times
10^{-27}\mathrm{~{}kg}/\mathrm{~{}m}^{3}$. Many astrophysical observations
indicate the existence of dark matter, including gravitational effects that
cannot be explained by other theories of gravity if there is more matter
present than can be seen. Most scientists believe that dark matter has a
strong influence on the structure and evolution of the universe since it is
abundant in it. Due to the fact that dark matter is invisible, it cannot be
detected by electromagnetic fields, meaning that it cannot absorb, reflect, or
emit electromagnetic radiation.

According to calculations, if galaxies did not contain dark matter, they would
fly apart, wouldn’t have emerged or wouldn’t move as they do. As well as
gravitational lensing and the CMB, astronomers have detected observable
galaxies and observed galaxy formation and evolution, as well as the motion of
galaxies within galaxy clusters. In $\Lambda$CDM cosmology dictates that the
total mass and energy of the universe consists of 5% ordinary matter and 27%
dark matter, and 68% of a mysterious form of energy called dark energy.

Unless dark matter interacts with ordinary baryonic matter, gravity must be
its major interaction with the matter. Dark matter hasn’t been observed
directly, but if it does exist, it has a minimal effect on baryonic matter.
Unlike baryonic matter, dark matter could consist of particles that are yet to
be discovered. It’s likely dark matter is made up of a new type of elementary
particle that has yet to be discovered, for instance weakly interacting
massive particles (WIMPs). Although many experimental efforts have been made
to detect and study dark matter particles directly, none have been successful.
According to its velocity (more specifically, its free streaming length), dark
matter can be classified as ”cold”, ”warm”, or ”hot”. A cold dark matter
scenario is currently preferred, in which structures occur as particles
accumulate gradually.

Scientists generally accept the existence of dark matter, but certain
observations that do not fit the standard theories, such as those that refute
modified Newtonian dynamics and tensor-vector-scalar gravity, have led some to
contemplate modifying the standard laws of general relativity modifiedgravity
. Using these models, it is attempted to explain all observations without
adding non-baryonic matter.

###  VI.3 21 cm signal and Dark Matter

All observations can be explained with the aid of these models, without
including any non-baryonic matter. The corresponding energy input resulting
from the decay or annihilation of dark matter (DM) affects the hydrogen
kinetic temperature and ionized fraction and impacts the Ly-$\alpha$
background. The 21 cm signal can then be used to constrain the proposed DM
candidates, and we choose three of the top three:

(i) 25-keV decaying sterile neutrinos, (ii) 10-MeV decaying light dark matter
(LDM) and (iii) 10-MeV annihilating LDM. Even though the DM effects are much
smaller than previously documented (because we model the energy transfer from
the DM to the gas more physically), we conclude that the combination of
observations of the 21 cm background and its gradient should allow constraints
at least on LDM candidates constraining dark matter ; indico .

It is believed that primordial density perturbations smaller than the free-
streaming length-scale get dampened in the early Universe. At these scales,
dark matter particles stream out of overdense regions into underdense regions,
while fluctuations on scales larger than this one remain unchanged. An
individual dark matter particle can be defined as having traversed a free
streaming scale before the density perturbations become significant. Based on
the calculation by kolb :

$\lambda_{\mathrm{fs}}=\int_{0}^{t_{\mathrm{mre}}}\frac{v(t)\mathrm{d}t}{a(t)}\approx\int_{0}^{t_{\mathrm{nr}}}\frac{c\mathrm{~{}d}t}{a(t)}+\int_{t_{\mathrm{nr}}}^{l_{\mathrm{mre}}}\frac{v(t)\mathrm{d}t}{a(t)},$
(29)

where $t_{\text{mre }}$ indicates the epoch of matter-radiation equality, and
$t_{\mathrm{nr}}$ is the onset of non-relativistic behaviour of dark matter
particles. As well, we have benefited from the fact that in relativistic
domain, $v(t)\sim c.$ In the non-relativistic regime as $v(t)\sim a(t)^{-1}$
and during the radiation-dominated era, $a(t)\propto t^{1/2}$. In other words,
the first equation ends up being:

$\lambda_{\mathrm{Is}}\sim\frac{2ct_{\mathrm{nr}}}{a_{\mathrm{nr}}}\left[1+\log\left(\frac{a_{\mathrm{mre}}}{a_{\mathrm{nr}}}\right)\right].$
(30)

Thus, increasing the time at which the nature of dark matter particles was
relativistic, i.e. $t_{\mathrm{nr}},$. The free streaming scale
$\lambda_{\mathrm{fs}}$ can be increased. Due to free streaming, we can
calculate that a halo whose formation is suppressed has a mass of:

$M_{\mathrm{fs}}=\frac{4}{3}\pi\left(\frac{\lambda_{\mathrm{Is}}}{2}\right)^{3}\bar{\rho}.$
(31)

As a result of CDM, dark matter particles become non-relativistic as they
decouple $t_{\mathrm{nr}}\sim t_{\mathrm{dec}},$ meaning the free streaming
length becomes negligible. In other words, it does not delete the initial
perturbations on small scales. In CDM cosmology, therefore, galaxies form
first, and galaxy clusters occur later. It has been confirmed in several
simulations, Diemand Moore 2011  and Frenk White 2012 . A model like this is,
however, inconsistent with small scale observations.

The WDM model’s particles become non-relativistic later than the CDM model,
and the $t_{\mathrm{nr}}$ is somewhere in between the two scenarios
$t_{\mathrm{dec}}<t_{\mathrm{nr}}<t_{\mathrm{mre}}.$ The WDM model is
therefore able to suppress density perturbations at small scales because the
free streaming scales for dark matter particles are larger than for CDM
particles. A bottom-up structure is created at scales above
$\lambda_{\mathrm{fs}}$ and structure formation occurs at scales much less
than $\lambda_{\mathrm{fs}}$ via a top-down approach Signs of Dark Matter at
21-cm . The result is also supported by various WDM simulations Bode et al
2001 , Schneider et al 2012  and Viel et al 2013 .

According to EDGES’s recent measurements of the global 21 cm spectrum, the
strong absorption signal starts about $z=17$. The excess over the expectation
is estimated to be $3.8\sigma$.

The idea behind this new measurement is intriguing. As the first stars are
born around $z\simeq 20$, the cosmic gas in the universe is at its coolest
before it is heated by X-ray radiation. The cosmic dawn occurs in this epoch
(roughly $15\leqslant z\lesssim$ 35 ). As it is usually interpreted, the
hydrogen 21 cm transition measurement provides a unique indication of hydrogen
temperature. The gas’s temperature drops below that of the radiation as it
decouples from the CMB at around $z\simeq 200$. There may be measurable
effects of modifications to the cosmic history during that period on the 21 cm
absorption spectrum corresponding to that period.

Dark matter is at its coldest phase at the same time, having not yet been
sparked up by non-linear gravitational collapse. Baryon elastic scatterings at
approximately or prior to that time could cool the gas, which might affect the
21 cm absorption spectrum. This concept was further considered in and analysed
in showing that light (sub-GeV) dark matter can leave the desired imprint once
Ly-$\alpha$ radiation turns on, providing an exciting explanation of the
phenomenon. These interactions must, however, compete with Compton
scatterings, which serve as a coupling device between the gas and the CMB
radiation, and as a consequence must be quite strong. The strongest possible
evasion of present-day, astrophysical and cosmological constraints. In
particular, the BBN and CMB bounds on the number of relativistic degrees of
freedom, the CMB anisotropy 5-th force experiments, and the stellar cooling
bound on DM interactions and millicharge. In order for these interactions to
occur, a light degree of freedom will be required, allowing Rutherford-like
scattering with baryons. In the two-particle interaction,
$\sigma=\hat{\sigma}v_{\mathrm{rel}}^{-4}$, where $v_{\text{rel }}$ is the
relative velocity.

As in Tashiro ,Mu_oz_2015 ,Barkana , approach used for DM-hydrogen
interaction, as well as CMB studies, is a model-independent one, where the
velocity dependence in the cross section is assumed without stating its
origin. Recent advancements are compelling enough to ask whether there exists
a particle physics model which can account for both the EDGES observations and
be consistent with current limits. To address this issue, we argue that the
dominant component in DM cannot explain the cooling of hydrogen by the
dominant component in DM.

The de Broglie wavelength of a DM particle with
$m_{\mathrm{DM}}\lesssim\mathrm{GeV}$ may help us to understand this, and
always greater than the atomic Bohr radius, $a_{0}=\left(\alpha
m_{e}\right)^{-1}.\quad$ Therefore $\mathrm{DM}$ interacts with the hydrogen
atom as a whole. In order to have a $v_{\text{rel }}^{-4}$ enhanced scattering
cross-section, its overall charge must not vanish. However, that very same
property implies that this mediator induces a long range force. Indeed, the
mediator mass, $m_{\phi},$ must be smaller than the typical momentum transfer
in order to induce a $1/v_{\mathrm{rel}}^{4}$ enhancement. Since the relative
velocity at the cosmic dawn is $v_{\text{rel }}\lesssim 10^{-6}$ one finds
$m_{\phi}\lesssim\mathrm{keV}$ for $m_{\mathrm{DM}}<\mathrm{GeV}$.

In the case of a light mediator of this type, the constraints from 5th-force
experiments are extremely strong (except for the upper allowed region, where
stellar cooling constraints are stronger), eliminating the possibility of
cooling via neutral hydrogen interaction. There are similar constraints for
any mediator where heavier atoms are charged.

Due to the small residual fraction of free electrons and protons, there can
still be Rutherford-like interactions between the DM and the gas. In
comparison with DM-hydrogen, the interaction rate required is about three
orders of magnitude larger. Early in the universe, proton interactions
dominate the interaction rate, which implies a larger DM electron cross
section. The DM-gas scattering cross sections will be probed with upcoming
direct detection experiments With this discussion, two options remain for the
mediation of the scattering: A $U(1)_{D}$ gauge boson (hidden photon) that is
kinematically mixed with the Standard Model (SM) photon, or with the SM photon
itself with a DM millicharge. Massless limits imply millicharged DM under
electromagnetism, however the two theories are not equivalent: hidden photons
can cause DM self-interactions, whereas DM in millicharge is strongly
constrained by the galactic disk.

###  VI.4 Dark Cooling

It is possible for dark matter to cool the spin temperature in two ways:
first, the hotter baryonic gas can be cooled by the darker matter fluid by
scattering off gas particles. After the spin temperature couples with the gas
temperature, the gas temperature decreases. Second, DM can drain spin
temperatures directly by, for example, directly spin-flip interactions (for
sufficiently light DM) or through induced bosonically enhanced emissions.

It was in Tashiro  that dark matter cooling was first realized, and further
studied in Mu_oz_2015  and Barkana .

The physics behind the phenomenon is summarized below. The interaction between
DM and the gas should cool it down since DM is much colder. Under certain
conditions, the predicted relative bulk velocity between the two gases
dissipates and causes the gas to heat up. The Boltzmann equations can be used
to illustrate the competing effect of temperature and velocity evolution:

$\frac{dT_{\chi}}{d\log a}=-2T_{\chi}+\frac{2}{3}\frac{\dot{Q}_{\chi}}{H},$
(32)

$\frac{dT_{\mathrm{gas}}}{d\log
a}=-2T_{\mathrm{gas}}+\frac{\Gamma_{C}}{H}\left(T_{\mathrm{CMB}}-T_{\mathrm{gas}}\right)+\frac{2}{3}\frac{\dot{Q}_{\mathrm{gas}}}{H},$
(33)

$\frac{dv_{\mathrm{rel}}}{d\log
a}=-v_{\mathrm{rel}}-\frac{D\left(v_{\mathrm{rel}}\right)}{H}.$ (34)

Here $a$ indicates the scale factor,
$H(z)\simeq\sqrt{\Omega_{m}}H_{0}(1+z)^{3/2}$ is the Hubble parameter during
matter domination, $v_{\text{rel }}$ represents the relative velocity between
DM and the gas, $\Gamma_{C}$ is the Compton scattering rate, and
$D\left(v_{\text{rel }}\right)$ is the drag term that accounts for the
relative velocity change due to DM gas interactions. From the scattering of
the DM with the gas, $\dot{Q}_{\chi,\text{ gas }}$ is the heat transfer per
unit time.

The original calculations only took into account interactions with hydrogen.
Free electrons and protons, however, are incredibly important, as we discussed
in the introduction and will discuss below, due to the severe constraints on
mediators which can cause velocity-enhanced DM hydrogen interactions. The
terms describing interactions with hydrogen, helium, electrons and protons are
carefully analyzed. The different contributions to heat transfer are thus
described as follows

$\dot{Q}_{\text{gas
}}=\sum_{I=\\{\mathrm{H},\mathrm{He},\mathrm{e},\mathrm{p}\\}}\dot{Q}_{\mathrm{gas}}^{I}.$
(35)

An approximate description of each contribution can be given as follows:
$\dot{Q}_{\text{gas }}^{I}\sim x_{I}\Gamma^{I}\Delta E_{I}$ with
$\Gamma^{I}\sim n_{\chi}\sigma^{I}v_{\mathrm{rel}}$ and $\Delta
E^{I}\sim\mu_{I}v_{rel}^{2},$ ( $\mu_{I}$ represents the reduced mass of the
corresponding DM-gas component, $x^{I}\equiv n_{I}/n_{\mathrm{H}}$ and the DM
number density is $n_{\chi}$). That leaves us with just one rationale for the
need for large cross sections: To efficiently cool down the gas, the rate of
DM-gas interactions must be comparable to the heating caused by Compton
scattering. $\Gamma_{C}.$ As such, by requiring $\dot{Q}_{\text{gas
}}\sim\Gamma_{C}T_{\text{CMB }}$ it is possible to estimate the required cross
section $\hat{\sigma}^{I}$ that is needed to explain the 21 cm global
spectrum.

For example requiring $\dot{Q}_{\text{gas }}\sim\Gamma_{C}T_{\mathrm{CMB}}$ at
$z=20$ with a $\mathrm{GeV}$ DM particle, one finds that $\sigma^{H}\simeq
10^{-19}\mathrm{~{}cm}^{2}$. In the case of DM-hydrogen interactions only. It
is possible for DM to grow at small relative velocities at most as
$v_{\text{rel }}^{-4}$, which is equivalent to a Coulomb-like force, if it is
a new fundamental particle obeying the basic rules of relativistic quantum
field theory. The following measures are taken to enhance the cross section at
low velocities as much as possible. Based on calculations in Tashiro  and
Mu_oz_2015 :

$\sigma^{I}=\hat{\sigma}^{I}v_{\mathrm{rel}}^{-4}.$ (36)

Enhance dark cooling and provide the highest possible cross-sectional area to
influence the 21 cm spectrum without violating CMB or direct detection
objectives. As $v_{\mathrm{rel}}=29\mathrm{~{}km}/\mathrm{sec}\sim 10^{-4}$
the root mean square relative velocity between the DM and the gas, at
decoupling and a later time, it redshifts correspondingly. It can be dismissed
if it has a mass well below the mass of a GeV (when sufficiently cooled) and
so it doesn’t affect gas temperature evolution. The approximate expression can
then be determined by assuming a cross section,

$\dot{Q}_{\text{gas
}}^{I}\simeq\sqrt{\frac{2}{\pi}}\frac{\mu_{I}}{m_{I}+m_{p}}\frac{x^{I}}{u_{\text{th
}}^{3}}\left(T_{\chi}-T_{\text{gas }}\right)n_{\chi}\hat{\sigma}^{I},$ (37)

$\left(u_{\mathrm{th}}^{I}\right)^{2}=T_{\mathrm{gas}}/m_{I}+T_{\chi}/m_{\chi}$
is defined in this section. Exchanging $\chi\leftrightarrow$ gas yields
$\dot{Q}_{\chi}$. Using the above formula, it seems to be possible to obtain a
reasonably accurate description of the cooling rate behavior for light dark
matter, since the cross section is not dependent of mass.

###  VI.5 21 cm signal and interacting dark energy model

In cosmology, it is well established that $3D$ power spectrum $P_{k}$ contains
many more modes than the CMB angular power spectrum $C_{l}$. Thus, one can use
this to discriminate among Dark Energy models. One can also use HI combined
signal which is much larger than that of individual sources to have the
mapping of large volumes in short periods of time. This technique has already
been tested in small surveys Chang-nature ; Santos:2015gra  (references
therein), and is a basic method for probing the dark energy models in 21 cm
observation.

Using the $\Lambda$CDM model to describe the universe, EDGES returns cannot be
explained even though $\Lambda$CDM is quite good compared to other
observations. As well, this tension is present in the interaction
model,Evidence for interacting dark energy from BOSS  and Constraints on
interacting dark energy models from Planck 2015 and redshift-space distortion
data , we can’t find $T_{21}$ as small as the one found in Edges despite using
the constraint derived from CMB. For EDGES to meet its data requirements, the
interaction should be unreasonably large, which conflicts with previous
constraints. However, the interaction reduces the 21 cm value, resulting in a
better model than the $\Lambda$CDM model ed .

We can use this tension to assert that EDGES may have underestimated the
brightness temperature. In fact, the $T_{21}$ should be reduced according to
the Wouthuysen-Field effect. Taking the concerns raised in Concerns about
Modelling of the EDGES Data  into account, the EDGES results do need further
evaluation. Observations such as these can also constrain dark energy models
that have interactions. Hopefully, future experiments will confirm this
measurement. This kind of measurement can break the degeneracy between the
interaction parameter and the equation of state because, in the standard
scenario, brightness temperature is not dependent on the equation of state ed
.

##  VII Conclusion

By interacting with the magnetic moments of the proton and electron, the 21 cm
line indicates the hyperfine transition from triplet to singlet of the atomic
hydrogen ground state. This splitting leads to two distinct energy levels
separated by $\Delta E=5.9\cdot 10^{-6}\mathrm{eV}$ which corresponds to a
photon wavelength $\lambda=2\pi/\Delta E\simeq 21.1\mathrm{~{}cm}$. We
reviewed briefly the physics of 21 cm emission in this article.

New experiments such as EDGES, LEDA, and PAPER have enabled probing of the
Universe with the 21 cm wavelength. The details of these experiments are
described in this review.

Next, the 21 cm emission around the sun was discussed. Radio astronomy
observations at wavelengths of 1.42 GHz (equivalent to 21 cm) provide crucial
information about the structure and dynamics of the solar atmosphere. It is
possible to measure the brightness temperature of the sun, the solar radio
flux, and the physical processes that exist in quiet and active regions of the
solar atmosphere at this frequency.

A further discussion focused on the role and importance of 21 cm signals on
mapping the galaxy and its rotation, and how its measurements and data have
led to the discovery of dark matter. Also, a brief description of constraints
of 21 cm signal on dark energy was given.

Overall, we can conclude that we are very close to detection of the 21cm
signal, close enough to make the move closer to directly observing radio
signals absorption or emission from hydrogen atoms to fill gaps in the cosmic
timeline. Astrophysics and cosmology are entwined in the 21 cm cosmology. The
21 cm cosmology offers a window into fundamental physics and represents a push
on time, sensitivity, and scale frontiers.

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