Lyman Alpha Forest

Computer simulation of Lyman-alpha Forest at z = 3

Lyman-alpha forest (Ly _α -forest) - multiple repetition of the Lyman-alpha absorption line in the spectra of distant astronomical objects. For very distant objects, this phenomenon can be so strong that it causes a significant decrease in intensity in a certain frequency range; this is called the Gunn-Peterson effect .

Ly _α forest is due to clouds of neutral hydrogen through which light from the observed object passes. These clouds are at different redshifts z . The wavelengths of the lines that each such cloud adds to the spectrum of an object depend on its redshift. As a result, the density and intensity of these lines carries information about the state of the intergalactic gas located along the path of the received light.

The Lyman-alpha hydrogen line lies (under laboratory conditions) at a wavelength of 1215.668 angstroms (1.216⋅10 ⁻⁷ m), which corresponds to a frequency of 2.47⋅10 ¹⁵ Hz. Thus, it lies in the ultraviolet part of the electromagnetic spectrum, however, due to its large distance (strong redshift), it shifts to the visible range, which makes it possible to detect it even by ground-based observation means.

Content

Effect Physics

The Lyman series consists of the energy values needed to excite an electron in a hydrogen atom from the first lowest level to higher states, or vice versa - released when the electron moves to the first level from the overlying one. In particular, according to Rydberg's formula , the energy difference between the first (n = 1) and second (n = 2) excited states corresponds to a photon with a wavelength of 1216 Å . So if light with a wavelength of 1216 Å passes through a cluster of neutral hydrogen atoms, they will absorb the photons of this light, using them to excite their electrons from the first level to the second. And the more such hydrogen atoms are in the path of light, the greater the number of photons with a wavelength of 1216 Å will be absorbed. Quantitatively, this is expressed in a dip as a function of the intensity of the light detected by an observer on Earth, depending on the wavelength.

However, one can obtain in this way information not only on the number of neutral hydrogen atoms along the path of light from a certain source, but also on the distance to them due to the expansion of the Universe. If the source of the photons is far enough, then as they follow us they experience a strong redshift , their wavelength increases. Meanwhile, hydrogen atoms also absorb photons, which initially had a higher energy, but during the time elapsed since their emission, reddened to 1216 Å. Further, if the quasar is the radiation source, then its spectrum contains almost all possible wavelengths, in particular, and the strongly pronounced Lyman-alpha emission line also at 1216 Å. Since photons with $\lambda$ ${\ displaystyle \ lambda}$ = 1216 Å are absorbed by neutral hydrogen, it can be concluded that at the time of its absorption a certain photon had precisely this wavelength. Obviously, it was smaller at the moment of quasar emission, and during the time required for passage from an absorbing hydrogen atom to an observer on Earth, it would increase even more. So we observe a dip in that part of the emission spectrum where the wavelength of the photon that had a wavelength of 1216 Å at the moment of absorption by the hydrogen atom along the path from the quasar to the observer is located. It can be written as $\lambda _{obs}=\lambda _{rest}(1+z)$ ${\ displaystyle \ lambda _ {obs} = \ lambda _ {rest} (1 + z)}$ where $\lambda _{obs}$ ${\ displaystyle \ lambda _ {obs}}$ - failure in the observed spectrum, $\lambda _{rest}$ ${\ displaystyle \ lambda _ {rest}}$ = 1216 Å, z is the redshift of the absorbing hydrogen atom; that is, knowing the rate of expansion of the Universe, it is possible to calculate at which redshift (that is, at what distance from us) this hydrogen atom is located. Thus, based on the detected set of absorption lines, we can draw conclusions about the location of clouds of neutral hydrogen on the line of light from the quasar.

The intergalactic medium contains quite a lot of neutral hydrogen, therefore, in the observed spectrum of quasars there are many such absorption lines, called the Lyman-alpha forest. The density of such systems is $10^{14}-10^{16}$ ${\ displaystyle 10 ^ {14} -10 ^ {16}}$ atoms per square centimeter ^[1] . If in a certain area the density increases to $10^{17}$ ${\ displaystyle 10 ^ {17}}$ cm ⁻² , then the radiation of the quasar is unable to penetrate into the inner region of such a system where neutral hydrogen remains shielded by the outer layer. Historically, such objects are called systems of the Lyman limit , since they correspond to a sharp break in the spectrum at $\lambda _{rest}$ ${\ displaystyle \ lambda _ {rest}}$ = 912 Å is the energy needed to ionize a hydrogen atom. Finally, if the density increases to $10^{20}$ ${\ displaystyle 10 ^ {20}}$ cm ⁻² and higher, a wide dip is observed in the spectrum — Lyman suppression , since all radiation in this region is absorbed. The main contribution to the corresponding part of the spectrum is made by the “wings” of the Lorentzian intensity distribution, which describes the natural broadening of the absorption spectral line.

Gan - Peterson Effect

Clouds of neutral hydrogen efficiently absorb light at wavelengths from Lα (1216 Å) to the Lyman limit, forming the so-called. "Lα-forest." Radiation, which is initially shorter than on the way to us, is absorbed due to the expansion of the Universe where its wavelength is equal. The interaction cross section is very large and the calculation shows that a small fraction of neutral hydrogen is enough to create a large depression in the continuous spectrum. Given the scale of the intergalactic medium, it is easy to conclude that the dip in the spectrum will be on a fairly wide interval. The long-wavelength boundary of this interval is due to Lα, and the short-wavelength depends on the nearest redshift, closer to which the medium is ionized.

The Gan - Peterson effect is observed in the spectra of quasars with redshift z> 6. From this it is concluded that the era of intergalactic gas ionization began at z≈6.

The evolution of the spectra of quasars

Application in cosmology

The large-scale structure of the universe . The intergalactic regions corresponding to the Lyman-alpha forest have a rather small mass in comparison with galaxies, therefore their evolution is easier to simulate numerically, taking into account only the effect of gravity. Such a simulation of the collapse of the initial density fluctuations under the action of gravity gives results that are consistent with the observed quasar spectrum.
Dark matter . Since Lyman-alpha regions are gas falling into potential wells formed not only by visible but also dark matter, such observations also make it possible to track the distribution of dark matter in the Universe. In addition, they help to introduce restrictions on the properties of dark matter: the observed structure at small scales (of the order of dwarf galaxies ) is against hot dark matter, which, if present in large quantities, would erase such a structure, would make it homogeneous ^[2] .
Primary nucleosynthesis . Lyman-alpha systems can contain not only ordinary hydrogen, but also deuterium, formed in the first 3 minutes of the existence of the Universe during primary nucleosynthesis. It can also absorb quasar radiation, so that by the same principle, conclusions can be drawn about the prevalence of deuterium and, as a consequence ^[3] , such a fundamental quantity as the density of baryonic matter ^[4] .
Cosmological constant . The distance to the object with a certain redshift is determined by the rate of expansion of the Universe. The angular extent of the object also depends on it, but according to a different law. So you can compare the angular and radial distances to the object . And knowing their correlation for a given object from other considerations, one can obtain information about the law of expansion of the Universe at different periods of its history, in particular, about the cosmological constant responsible for accelerated expansion.

Notes

↑ The artificial value obtained by the product of the number of atoms per cm ⁻³ and the length of the hydrogen cloud in cm and thus equal in meaning to the number of atoms in the volume of the column with the height of a cloud and the cross section of 1 cm ⁻²
↑ Joel R. Primack. Dark matter, galaxies, and large scale structure in the Universe (neopr.) . Lectures presented at the International School of Physics “Enrico Fermi” Varenna, Italy (1984).
↑ Edward L. Wright (trans.V.G. Misovets). Nucleosynthesis of the Big Bang (neopr.) . Cosmology textbook Ned Wright .
↑ Balashev S.A. Interstellar clouds of molecular hydrogen in the early stages of the evolution of the universe (neopr.) (2011). - Abstract of the dissertation for the degree of candidate of physical and mathematical sciences.

Literature

[1] The artificial value obtained by the product of the number of atoms per cm ⁻³ and the length of the hydrogen cloud in cm and thus equal in meaning to the number of atoms in the volume of the column with the height of a cloud and the cross section of 1 cm ⁻²

[2] Joel R. Primack. Dark matter, galaxies, and large scale structure in the Universe (neopr.) . Lectures presented at the International School of Physics “Enrico Fermi” Varenna, Italy (1984).

[3] Edward L. Wright (trans.V.G. Misovets). Nucleosynthesis of the Big Bang (neopr.) . Cosmology textbook Ned Wright .

[4] Balashev S.A. Interstellar clouds of molecular hydrogen in the early stages of the evolution of the universe (neopr.) (2011). - Abstract of the dissertation for the degree of candidate of physical and mathematical sciences.