21 cm Physics and Cosmology

[Eli]

The 21cm line, a hyperfine transition in neutral hydrogen (HI), provides a powerful probe of the early universe. It arises from the interaction between the spin of the proton and the spin of the electron in a hydrogen atom. These spins can be parallel (higher energy state) or anti-parallel (lower energy state). The transition between these two states results in the emission or absorption of a photon with a wavelength of approximately 21cm (corresponding to a frequency of 1420 MHz).

21cm Physics

The energy difference between the parallel and anti-parallel spin states is extremely small, leading to a low transition probability. The spontaneous emission rate is incredibly slow, with a typical lifetime of around 10$^7$ years. However, this transition is crucial for cosmology because it allows us to trace the distribution of neutral hydrogen across vast cosmic distances and epochs.

The transition's energy, $\Delta E$, is given by:

\[ \Delta E = \frac{3}{4} \frac{g_p^2 g_e^2 \mu_0^2}{h^3} \]

where:

$g_p$ and $g_e$ are the gyromagnetic ratios of the proton and electron, respectively, $\mu_0$ is the Bohr magneton, $h$ is Planck's constant.

This energy difference directly relates to the frequency ($f$) and wavelength ($\lambda$) of the emitted photon via the equation:

\[ \Delta E = hf = h \frac{c}{\lambda} \]

where $c$ is the speed of light.

21cm Cosmology

The 21cm signal provides unique information about the early universe, especially during the Epoch of Reionization (EoR). Before reionization, the universe was largely neutral, filled with a vast expanse of HI gas. The 21cm signal from this epoch carries information about:

Density fluctuations: Variations in the density of neutral hydrogen lead to corresponding variations in the 21cm brightness temperature.

Spin temperature ($T_s$): The 21cm brightness temperature is related to the spin temperature ($T_s$) of the hydrogen gas. The spin temperature is coupled to the kinetic temperature ($T_k$) through collisions and to the Cosmic Microwave Background (CMB) temperature ($T_{CMB}$) through radiative processes. The difference between these temperatures affects the observed 21cm signal.

Reionization history: The detection of the 21cm signal during reionization provides crucial information about the process of reionization itself, including its timing, duration, and sources (e.g., first stars and galaxies).

Observing the 21cm signal from the EoR is challenging due to its faintness and the foreground contamination from radio sources such as our own galaxy. Nevertheless, significant progress has been made with dedicated radio telescopes, which are designed to minimize the foreground contamination and extract the faint 21cm signal from the early universe.

Conclusion

The 21cm line serves as a remarkable probe of the early universe. By studying its properties and mapping its distribution, cosmologists can gain invaluable insights into the formation of the first stars and galaxies, the process of reionization, and the overall evolution of cosmic structures. Continued observations and advancements in instrumentation promise to reveal even more secrets of the early universe through this unique cosmological window.