Lyman alpha systems are becoming a very useful source of information in physical cosmology.

The Lyman series is the series of energies required to excite an electron in hydrogen from its lowest energy state to a higher energy state. The case of particular interest for cosmology is where a a hydrogen atom with its electron in the lowest energy configuration gets hit by a photon (light wave) and is boosted to the next lowest energy level. The energy levels are given by E_n = -13.6 eV/n² and the energy difference between the lowest (n=1) and second lowest(n=2) levels corresponds to a photon with wavelength 1216 angstroms. The reverse process can and does occur as well, where an electron goes from the higher n=2 energy state to the ground state, releasing a photon of the same energy.

The absorption or emission of photons with the correct wavelength can tell us something about the presence of hydrogen and free electrons in space. That is, if you shine a light with wavelength 1216 at a bunch of neutral hydrogen atoms in their ground state, the atoms will absorb the light, using it to boost the electron to a higher energy state. If there are a lot of neutral hydrogen atoms in their ground state, they will absorb more and more of the light. So if you look at the light you receive, intensity as a function of wavelength, you will see a dip in the intensity at 1216 angstroms, depending on the amount of neutral hydrogen present in its ground state. The amount of light absorbed ('optical depth') is proportional to the probability that the hydrogen will absorb the photon (cross section) times the number of hydrogen atoms along its path.

Because the universe has many high energy photons and hydrogen atoms, both the absorption and emission of photons occurs frequently. In Lyman alpha systems, the hydrogen is found in regions in space, and the source for the photons are quasars (also called qsos), very high energy light sources, shining at us from behind these regions.

Because the universe is expanding, one can learn more than just the number of neutral hydrogen atoms between us and the quasar. As these photons travel to us, the universe expands, stretching out all the light waves. This increases the wavelengths lambda and lowers the energies of the photons (`redshifting').

Neutral hydrogen atoms in their lowest state will interact with whatever light has been redshifted to a wavelength of 1216 angstroms when it reaches them. The rest of the light will keep travelling to us.

The quasar shines with a certain spectrum or distribution of energies, with a certain amount of power in each wavelength. At right, the top picture shows a cartoon of how a quasar spectrum (the flux of light as a function of wavelength) might look if there were no intervening neutral hydrogen between the qso and us. In reality, gas around the quasar both emits and absorbs photons. With the presence of neutral hydrogen, including that near the quasar, the emitted flux is depleted for certain wavelengths, indicating the absorption by this intervening neutral hydrogen. As the 1216 wavelength is preferably absorbed, we know that at the location the photon is absorbed, its wavelength is probably 1216 angstroms. Its wavelength was stretched by the expansion of the universe from what it was initially at the quasar, and, if it had continued to travel to us, it would have been stretched some more from the 1216 angstroms wavelength it had at the absorber. Thus we see the dip in flux at the wavelength corresponding to that which the 1216 angstrom (when it was absorbed) photon would have had if it had reached us. As we can calculate how the universe is expanding, we can tell where the photons were absorbed in relation to us. Thus one can use the absorption map to plot the positions of region of intervening hydrogen between us and the quasar. The middle picture at right shows the flux for one nearby region while the bottom picture shows the case for several intervening regions.

It is common to see a series of absorption lines, called the Lyman alpha forest. Systems which are slightly more dense, Lyman limit systems, are thick enough that radiation doesn't get into their interior. Inside these regions there is some neutral hydrogen remaining, screened by the outer region layers. If the regions are very thick, there is instead a wide trough in the absorption, and one has a damped Lyman alpha system. Absorption lines generally aren't just at one fixed wavelength, but over a range of wavelengths, with a width and intensity (line shape) determined in part by the lifetime of the excited n=2 hydrogen atom state. These damped Lyman alpha systems have enough absorption to show details of the line shape such as that determined by the lifetime of the excited state. These dense clumps are thought to have something to do with galaxies that are forming.

One can use the ionization of neutral hydrogen to find galaxies as well, for example the Lyman break systems described in these technical conference proceedings.

There is a very cool visualization of how different systems absorb Lyman-alpha here by Andrew Pontzen.

Some numbers:

• How dense are the Lyman alpha forest systems (column densities)?
  10¹⁴ atoms per square centimeter. Lyman limit systems are 10³ times denser and damped Lyman alpha systems another factor of 10³ times more.
• How far away are the quasar sources?
  To be observed from the ground, the Lyman alpha wavelength needs to be stretched by factors of 3 to 5. The amount of "stretching" is related to redshift z by stretch = (z +1). So ground observed sources have redshifts z of 2-4. A qso with redshift of z=2 emitted its light when the universe was less than about 1/4 of its current age (that is, about 1/4 of 13 billion years or so), while at redshift z=4 we are seeing objects from when the universe was less than 1/10 of its current age.
• How many systems are expected in upcoming surveys?
  Large statistical samples which have been publicly relased include the 2dF-SDSS quasar survey (2SLAQ) SDSS and the SDSS Quasar catalogue (latest releast spring 2010 abstract is here with 105783 quasars). Currently, BOSS is underway to produce Lyman-alpha forest spectra of 160,000 quasars at redshifts 2.2

  Uses: We learn several things from these systems, including the following.

  • Neutral hydrogen: because we see any light at all, we can limit how much neutral hydrogen is out there between us and the quasar and what its distribution is. It used to be thought that there was a smooth intergalactic medium (IGM) with regions embedded in it, and the smooth background would provide an absorption at all positions between us and the quasar (Gunn-Peterson effect). But observers only see evidence of lumpy regions. There isn't evidence for a spatially smooth component of neutral hydrogen between us and the quasar sources. It is a question of active research what is making the amount of neutral hydrogen so small (that is, what is ionizing the rest of the hydrogen).

    

  • Structure formation: the regions in the Lyman alpha systems are not very massive compared to objects like galaxies. As a result, reliable computer simulations (numerical experiments) of their gravitational collapse (formation) from primoridal fluctuations are possible. Until the 90's, it was thought that gravity alone could not form all the structure, in particular the filaments, walls, and voids which we observe. However, the Lyman alpha simulations did produce this structure by starting with small fluctuations in matter density and then letting gravity and other known forces act. It was not necessary to add other mechanisms to get the observed structure in these systems. The detailed properties of the structure and distribution of matter are frontiers of current research. At right is a picture of the distribution of neutral hydrogen found in simulations.

  • Hot dark matter: The numerical simulations have also shown, via their successful reproduction of properties of the regions, that one cannot have too much hot dark matter if one wants to agree with observations. (Too much hot dark matter erases structure on small scales.)

  • Distribution of matter: The Lyman alpha regions are formed by gas falling into gravitational potential wells of all the matter, not just the luminous matter. So they provide another tracer of dark matter.

  • Nucleosynthesis: deuterium is produced in 'the first three minutes' in the early universe, and afterwards is believed to only be destroyed. The Lyman alpha systems have deuterium in them too, and as these systems also have low amounts of metals (heavier elements), one might hope that they are measuring unprocessed or primordial deuterium. The deuterium also absorbs light from quasars, and thus its abundance can be measured in a similar way. Searches in many of these systems have provided the current strongest constraint on the amount of primoridal deuterium and thus the baryon density in the universe. See this link or this poster on big bang nucleosynthesis.

  • Cosmological constant: the path back to a given redshift depends on how the universe has expanded since that time. The angular extent of an object at any redshift also depends on the expansion of the universe since the light was emitted, but in a different way. Thus one can compare angular and radial (more precisely redshift) lengths for objects. If one knows the expected ratio of these lengths for an object for other reasons, one can constrain the expansion history of the universe, in particular the cosmological constant. A variant of this Alcock Pacynzski test involves tracing lines of sight through the Lyman alpha regions for neighboring quasars.

  Further reading:

  • Lya notes by M. White (~2005) for reading group at UC Berkeley
  • "The Lyman-alpha Forest as a Cosmological Tool", David H. Weinberg, Romeel Dav'e, Neal Katz, Juna A. Kollmeier, AIP Conf.Proc. 666 (2003) 157-169
  • "Shadows of Creation: Quasar Absorption Lines and the Genesis of Galaxies," Jill Bechtold, Sky and Telescope, Sept. 1997
  • Perspectives in Astrophysical Cosmology, by Martin Rees, Cambridge University Press, pp. 88-94.
  • Lecture notes by D. Weinberg on QSO absorption lines and the IGM
  • Lecture notes by D. Weinberg on Cosmology with the Ly-alpha forest

  Back to theoretical cosmology

  Please send suggestions to jcohn@berkeley.edu,
  thanks to M. White and L. Hernquist for suggestions and figures.