21 cm cosmology

I haven't blogged in a very long time! I've been spending most of my intellectual energy and free time trying to learn spanish and graduate college instead of nerding out. However, for the next two months I plan on: 1.) Being really broke and 2.) Having lots of free time. This means many more blogs are on the way! Suggestions are welcome. In the meantime, I'd like to share a paper I wrote for my cosmology class this quarter.  It used to be full of lots of equations to describe the quantum behavior of hydrogen but I can't figure out how to insert equations in this thing. Does anyone know how to do that?

 It's a little different than the way I usually write in this blog but maybe you'll dig it anyway!

21 Centimeter Astronomy

The Dark Age

Applications of quantum mechanics have proven to be of great utility in the expanding field of radio cosmology. As astronomers begin to piece together answers to the question, “what did the early universe look like?”, the quantum model of hydrogen plays a large role. Understanding the nature of hydrogen’s hyperfine structure and it’s interaction with radiation becomes crucial to this investigation.

Hydrogen has a forking energy structure: each branch separates into a different set of branches. This branching begins with electrons, which exist in quantized energy levels, known as orbitals, around hydrogen nuclei. Within these orbitals the electrons are subject to two types of angular momentum: orbital (associated with motion of the center of mass) and spin (associated with motion about the center of mass).  While it should be noted that electrons are fundamental particles without interior structure, (and therefore cannot literally spin) this analogy is useful in analyzing the splitting behavior of orbiting electrons. Suffice it to say that electrons carry an intrinsic angular momentum which can alter the total energy.  It is spin that creates the hyperfine structure of hydrogen.

According to classical electrodynamics, a rotating electric charge creates a magnetic dipole. This sets up the electron as a magnetic dipole. The proton, like the electron, has an intrinsic spin, which sets up its own dipole moment in the same direction as the proton’s spin. The dipole of the proton is more complex because it is a composite structure, made up of three quarks, which gives a different gyromagnetic ratio. The proton’s dipole moment creates a magnetic field.

            The difference between levels in hydrogen’s hyperfine structure is an artifact of the interaction between the electron’s dipole moment and the proton’s magnetic field. If the dipole moments of the electron and proton point in the same direction (parallel) the energy of this configuration is slightly higher than if the dipoles point in the opposite direction (antiparallel). It is found that the frequency of a photon emitted during the transition from parallel to antiparallel is 1420MHz, which corresponds to a wavelength of c/v=21 cm. This falls within the microwave region of the electromagnetic spectrum.

The probability of this transition taking place is so small that it is classified as forbidden. To be precise, the probability of such an event taking place is 2.9*10^-15 1/s, or once every 10 million years. As a result, it can never be manufactured in a laboratory. However, evidence of this transmission is detected pervasively in all directions as astronomers look into space. Carl Sagan and Frank Drake considered the 21cm line to be so ubiquitous and universal that they utilized it on the Pioneer Plaque of the Voyager Mission as a single unit measurement in defining length and time. The omnipresence of this extremely improbable detection indicates that the universe contains a tremendous amount of neutral hydrogen.

The dumbbell looking thing the the upper left hand corner represents hydrogen undergoing a spin-flip transition. For those of you that don't know about this plaque, it's floating out in space with the hopes that someday aliens will find it. This plaque and the rest of the bizarro messages on board the Voyager definitely deserves it's own blog. Hopefully I'll get to that soon!

Of special importance to big bang cosmologists are the 21cm transmissions detected at redshifts between z=25 and z=10^3. Radiation detected in this range comes from a period between two important epochs of gas phase change in the early universe: recombination and reionization. To give a brief history of the state of hydrogen throughout time, shortly after the big bang, the universe was radiation dominated. During this period, protons and electrons could not combine to form neutral atoms without being quickly ionized by energetic photons. However, the universe cooled as it expanded, eventually allowing for this reaction to take place. This is known as the epoch of recombination and took place around redshift z=1100.  For several hundred million years following recombination there were no radiating sources, only cold, dark hydrogen. For this reason, the period is referred to as the Dark Age. In this epoch the universe was transparent, meaning photons could travel unimpeded through space. This is important to cosmologists as it means there is much information retained in the photons. The second epoch of the universe, known as reionization, occurred after the gravitational interaction between neutral hydrogen atoms allowed for the formation of the first structures large enough to radiate and ionize surrounding atoms. Astronomers interested in probing the structure of the universe between these two phase changes, when the universe was dominated by cold, dark hydrogen, must examine the fingerprints of such an era:  21cm photons.

Photon emission due to the spin-flip transition of hydrogen is temperature dependent. This means as 21 cm photons are released they will catalyze other reactions from neutral hydrogen nearby. By mapping the intensity of this radiation, cosmologists can develop a precise picture of the topography of the universe during the Dark Age. This is predicted to provide crucial constraints on current models for dark matter and dark energy. Furthermore, neutral hydrogen that has been ionized by those first radiating structures will appear as dark spots in the 21cm background. By examining these anisotropies, cosmologists can gain a firmer understanding of how the process of universal reionization occurred.

Research involving the 21cm line places cosmology on the verge of a new era. However, this field has a long way to go as observation of this transmission is extremely difficult. After redshift, this line is observed on Earth deep into the radio spectrum. This presents many challenges in collecting data as photons in the 21cm spectrum are drowned out by background noise from television transmission and the ionosphere. In the last few years, progression has been made both theoretically and observationally: theoretically, computer simulations of reionization have achieved larger dynamic range and can make more reliable predictions; observationally, plans have been made for four machines to start sensitive 21cm detection in the near future. Precise observations of the 21cm line from distant redshifts promise to revolutionize our understanding of the early universe.   

Sources

Griffiths, David. Quantum Mechanics. 2nd. Upper Saddle River: Pearson Education, 2005. Print.

Pritchard, Jonathan, and Loeb Abraham. "Evolution of the 21 cm Signal Throughout Cosmic History."

Miguel, Morales, and Wyithe Stuart. "Reionization and Cosmology with 21-cm Fluctuations." Annual Rev. Astron. Astrophys.. (2010)