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A Stroll Through the Lyman-Alpha Forest

by John G. Cramer

Alternate View Column AV-116
Keywords: Lyman-alpha, forest, hydrogen, clumps, absorption, lines, Doppler, shift, quasars, cosmological, red, shift
Published in the March-2003 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 08/06/2002 and is copyrighted 2002 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

As the author of these columns describing cutting edge physics and astronomy, I get quite a few letters and E-mail from readers who are more interested in “over-the-edge physics and astronomy”.  One recurring theme is various alternatives to the standard model of Big Bang cosmology.  Perhaps the universe is not expanding; it’s just that light “gets tired” on its path from far away and loses some of its energy.  Perhaps quasars are closer than we think, particularly since some of them appear to be linked to closer galaxies.  Perhaps relativity is wrong, and it’s the speed of light that is different in different parts of the universe or changing with time.  Perhaps quasars are the tailpipes of nearby alien spaceships, and they have such large red shifts because we only see them when they are moving away from us.  And so on…

In this column, I want to discuss the Lyman-alpha forest, a characteristic of distant quasars that has become a standard tool of astrophysics and that provides convincing evidence that the cosmological red shift is real and the quasars are as far away as their red shifts would imply.  We’ll start by considering a bit of atomic physics.

Hydrogen is the simplest atom provided by nature.  It has a single electron in orbit around a single proton, which forms the nucleus of the hydrogen atom and contains most of the mass.  Because of the laws of quantum physics, the electron cannot have just any old orbit around the proton.  Instead, it must have an orbit such that a certain number of wavelengths of the electron’s wave function fit precisely into the circumference of the orbit.  The number of such wavelengths is called the “principal quantum number” n of the electron’s orbit.  The size or the orbit is dictated by the value of N, with n=1 for the smallest allowed orbit, and n=2, 3, 4, … for higher orbits of increasing radii.

The negatively charged electron is strongly attracted to the positively charged proton, so that the closer they are together, the stronger the force between them and the more tightly the electron is “bound” in the atom.  An electron in the innermost n=1 orbit is bound with an energy of 13.6 electron volts (or eV).  Here, an electron volt is the energy required to move an object with an electron charge through a potential of one volt.   The higher orbits are bound with energy En=(13.6 eV)/n2, so the n=2 orbit has a binding energy of E2=(13.6 eV)/4 = 3.4 eV.

When an electron jumps from one atomic orbit to a more tightly bound orbit, it emits a photon of light that contains the energy difference of the orbits.  Therefore, when an electron jumps from the n=2 orbit to the n=1 orbit, the transition makes a photon with an energy of 10.2 eV and a wavelength of 1216 angstrom units (1 = 10-10 meters).  The reader should remember that the shorter the wavelength, the more energetic the photons, and that visible light falls in the wavelength region between 7,000 (red) and 4,000 (violet).  Ultraviolet is any light with a wavelength smaller than 4,000 .

The ultraviolet light accompanying an electron jump from the n=2 to the n=1 orbit is called “Lyman Alpha” radiation, because it is the longest wavelength member of a series of photons (or spectroscopic “lines”) corresponding to jumps ending in the n=1 orbit.  The Lyman series was first discovered in 1906 by Harvard physicist Theodore Lyman (1874-1954), who was studying the ultraviolet spectrum of electrically excited hydrogen gas.  Lyman had to do his work using a vacuum chamber, because all of the light in the Lyman series is in the far-ultraviolet region and is strongly absorbed by air.

In atomic physics, the interaction of photons with atoms is a two-way street.  When an electron jumps to a smaller, more tightly bound orbit, a photon is generated.  Conversely, if a photon of the right energy arrives at the atom, it can be absorbed by causing the electron to jump to a larger orbit.  In particular, if a broad spectrum of ultraviolet light  passes through a cloud of interstellar hydrogen, the wavelengths corresponding to the Lyman series will be selectively absorbed, making holes or “absorption lines” in the ultraviolet spectrum.

Now let’s consider the situation for light from a quasar that is observed in an Earth-based telescope.  Quasars are somewhat mysterious objects that populate the early universe.  They are very bright and very far away.  Because a quasar is very distant, because of the expansion of the universe it will be receding from the Earth at a sizable fraction of the speed of light.  For this reason, the light it produces is Doppler-shifted (i.e., red-shifted) to longer wavelengths.  For example, the wavelength of light from quasar Q1422+2309, one of the most distant quasars so far discovered, is lengthened by a factor of 4.62 because it is receding from the Earth at 97.63% of the velocity of light.   Therefore, its Lyman-alpha photons were emitted as far ultraviolet light with a wavelength of 1216 , but the same photons are detected in an Earth-based telescope as green light with a wavelength of 5618 .  The observed spectrum from such a quasar will contain a peak from the Lyman-alpha emission at this wavelength, and that peak will be superimposed on a broad spectrum of ultraviolet light from the quasar that is produced by other processes.

The light reaching the Earth from the quasar to must pass through many million light-years of intergalactic space, which will inevitably contain some concentration of neutral hydrogen.  Astronomers have learned that this hydrogen is not distributed uniformly along the path.  Rather, it is tightly clumped into threads and filaments, alternating between high and low concentrations of hydrogen along the line-of-sight path.  And because the universe is expanding, each clump of hydrogen on this path is moving away from the Earth at a different velocity, somewhere between the quasar velocity (0.9763 c) and zero, depending on the distance.

The broad spectrum of ultraviolet radiation of the quasar, which is at smaller wavelengths than the Lyman-alpha line, will be absorbed by the concentrations of hydrogen.  There is succession of Lyman-Alpha absorption lines (or holes in the spectrum) at many wavelengths that are shorter than the quasar’s Lyman-Alpha peak.  In distant quasars there are hundreds of such absorption lines, which is the basis for calling this region of the quasar spectrum the “Lyman-Alpha Forest”.  The long wavelength side of the Lyman-Alpha peak is smooth and relatively structureless, while the short wavelength side, the location of the Forest, is highly structured by the irregular comb of absorption lines.

The remarkable structure of the Lyman-Alpha Forest has a number is implications and uses.  First, it provides a clear demonstration that the light from quasar has been Doppler-actually shifted to the long wavelength at which it is detected on Earth, since in the Lyman-Alpha Forest we can observe all of the intermediate wavelengths that it had during the course of its passage.  This lays to rest the hypothesis that the large quasar red shift might have been due to a gravitational or some other mechanism.

Further, the strengths of the individual absorption lines of the Forest provide a map of the density of neutral hydrogen all along the path from quasar to Earth.  This map tells an interesting story.  Before the Lyman-Alpha Forest was discovered, astronomers believed that the intergalactic hydrogen was distributed relatively uniformly through the universe.  It was suggested that a careful measurement of the suppression of light on the short-wavelength side of the Lyman-Alpha peak would provide a measure of the density of this diffuse hydrogen cloud.  As it turns out, there is no evidence for a diffuse hydrogen cloud.  Instead, the hydrogen in the universe is organized into a complex filamentary structure, with the hydrogen density changing by factors of 1,000 to 1,000,000 between a filament and its surroundings.

The structure of these filaments is related to the gravitational clumping of matter and dark matter in the universe.  Measurements can be compared with computer simulations of the evolution of the early universe after the Big Bang.  Effectively, such models tell us about the dynamic evolution of matter and energy in the universe as it expand and as the matter “curdles” into filaments, clusters, galaxies, and stars under the influence of gravity.

There is good observational evidence that most of the matter in our universe is in the form of some mysterious particles of dark matter that cannot be atoms or molecules or stars or planets.  There are several “dark matter candidate” particles, theoretical guesses for what dark matter might be, and these can be divided into two categories, fast-moving “hot” dark matter (e.g., massive neutrinos and most light exotic particles) and slow-moving “cold” dark matter (e.g., heavy exotic particles, mini-black holes, wimps, and axions).

Model calculations of the filament structure of hydrogen revealed by the Lyman Alpha Forest are very sensitive to the presence of hot dark matter.  Because its fast particles tend to connect distant parts of the universe, hot dark matter has the effect of fuzzing out structures like the hydrogen filaments.  The result is that only a small amount of hot dark matter is permitted, and this is much less that the amount needed to explain the observations.  Therefore, the presence of the Lyman Alpha Forest provides evidence that the dark matter present in our universe must be mainly of the cold variety.

The Lyman Alpha Forest can also be used to probe another characteristic of the early universe, the density of normal matter that it contained.  One can think of the universe in the first three minutes after the Big Bang as a pressure cooker in which light nuclei, particularly primordial deuterium, helium, and lithium, were synthesized.  The problem is that these elements are also produced in stars, so it is difficult to obtain a “clean” sample of primordial elements that is uncontaminated by subsequent element-cooking in stars.

Atomic deuterium is a hydrogen atom with a heavy nucleus made of a neutron and proton bound together by the nuclear force.  An effect of doubling the mass of the nucleus is to slightly shift the electron orbits of the atom to higher energies.  Therefore, the absorption line for deuterium is slightly shifted from that of hydrogen in the Lyman Alpha Forest.  As a consequence, each absorption dip has a small “notch where deuterium absorbs the light at a slightly different wavelength than does hydrogen.  This makes it possible to obtain information on the deuterium-to-hydrogen ratio using each of the hundreds of absorption lines that make up the Forest.   This technique has been used to give very accurate estimates of the density of normal matter in the early universe.

OK, this is a science fiction magazine.  Does the Lyman Alpha Forest have any implications for SF stories?  Perhaps.

I have written about axion ramjets (see my AV column in the February-1985 issue of Analog) and a number of works of SF, including those of Larry Niven and Poul Anderson, have been based on interstellar and even intergalactic travel using the Brussard ramjet, a spaceship engine that scoops up interstellar hydrogen and uses it as fusion fuel.  The filament of the Lyman Alpha Forest represent rich veins of hydrogen (and axions, if they exist) that form large scale “highways” between one galaxy and another.  A ship that was fueled with such interstellar material would be well advised to follow the track of such a filament, even if it did not represent the shortest path to the destination.

Starship Pilots be advised: Stay in the darkest part of the Lyman Alpha Forest!


The Lyman Alpha Forest:
"Lyman alpha systems and cosmology”, J. Cohn, U. California at Berkeley, on the web at .
“Quasars as lighthouses: The Lyman-Alpha Forest at high and low redshift”, Bill Keel, U. Alabama, on the web at: .

SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : .

AV Columns Online: Electronic reprints of about 177 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at:

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