As the expanding universe cooled, the first neutral1 hydrogen atoms formed about 380,000 years after the Big Bang (ABB), and most of the hydrogen in the universe remained neutral until the first stars began forming at least 65 million years ABB.

The period of time from 380,000 to 65 million years or so ABB is referred to as the “dark ages” since at the beginning of this period the cosmic background radiation from the Big Bang had redshifted from visible light to infrared so the universe was truly dark (in visible light) until the first stars began to form at the end of this period.

All the while, neutral hydrogen atoms occasionally undergo a “spin-flip” transition where the electron transitions from the higher-energy hyperfine level of the ground state to the lower-energy hyperfine level, and a microwave photon of wavelength 21.1061140542 cm and frequency 1420.4057517667 MHz is emitted.

Throughout the dark ages, the 21 cm emission line was being emitted by the abundant neutral hydrogen throughout the universe, but as the universe continued to expand the amount of cosmological redshift between the time of emission and the present day has been constantly changing. The longer ago the 21 cm emission occurred, the greater the redshift to longer wavelengths. We thus have a great way to map the universe during this entire epoch by looking at the “spectrum” of redshifts of this particular spectral line.

380,000 and 65 million years ABB correspond to a cosmological redshift (z) of 1,081 and 40, respectively. We can calculate what the observed wavelength and frequency of the 21 cm line would be for the beginning and end of the dark ages.

$\lambda _{obs} = (z+1)\cdot \lambda_{emit}$

The observed wavelength (λobs) for the 21 cm line (λemit) at redshift (z) of 1,081 using the above equation gives us 22,836.8 cm or 228.4 meters.

$\nu = \frac{c}{\lambda }$

That gives us a frequency (ν) of 1.3 MHz (using the equation above), where the speed of light c = 299,792,458 meters per second.

So a 21 cm line emitted 380,000 years ABB will be observed to have a wavelength of 228.4 m and a frequency of 1.3 MHz.

Using the same equations, we find that a 21 cm line emitted 65 Myr ABB will be observed to have a wavelength of 8.7 m and a frequency of 34.7 MHz.

We thus will be quite interested in taking a detailed look at radio waves in the entire frequency range 1.3 – 34.7 MHz, with corresponding wavelengths from 228.4 m down to 8.7 m.2

The interference from the Earth’s ionosphere and the ever-increasing cacophony of humanity’s radio transmissions makes observing these faint radio signals all but impossible from anywhere on or near the Earth. Radio astronomers and observational cosmologists are planning to locate radio telescopes on the far side of the Moon—both on the surface and in orbit above it—where the entire mass of the Moon will effectively block all terrestrial radio interference. There we will finally hear the radio whispers of matter before the first stars formed.

1 By “neutral” we mean hydrogen atoms where the electron has not been ionized and resides in the ground state—not an excited state.

2 Incidentally, the 2.7 K cosmic microwave background radiation which is the “afterglow” of the Big Bang itself at the beginning of the dark ages (380,000 years ABB), peaks at a frequency between 160 and 280 GHz and a wavelength around 1 – 2 mm. So this is a much higher frequency and shorter wavelength than the redshifted 21 cm emissions we are proposing to observe here.

References

Ananthaswamy, Anil, “The View from the Far Side of the Moon”, Scientific American, April 2021, pp. 60-63

Burns, Jack O., et al., “Global 21-cm Cosmology from the Farside of the Moon”, https://arxiv.org/ftp/arxiv/papers/2103/2103.05085.pdf

Koopmans, Léon, et al., “Peering into the Dark (Ages) with Low-Frequency Space Interferometers”, https://arxiv.org/ftp/arxiv/papers/1908/1908.04296.pdf

Ned Wright’s Javascript Cosmology Calculator, https://astro.ucla.edu/~wright/CosmoCalc.html

## Metallicity

No, it’s not the name of a rock band. Astronomers (unlike everybody else) consider all elements besides hydrogen and helium to be metals. For example, our Sun has a metallicity of at least 2% by mass (Vagnozzi 2016). That means as much as 98% of the mass of the Sun is hydrogen (~73%) and helium (~25%), with 2% being everything else.

Traditionally, elemental abundances in the Sun have been measured using spectroscopy of the Sun’s photosphere.  In principle, stronger spectral lines (usually absorption) of an element indicate a greater abundance of that element, but deriving the correct proportions from the cacophony of spectral lines is challenging.

A more direct approach to measuring the Sun’s elemental abundances is analyzing the composition of the solar wind, though the material blown away from the surface of the Sun that we measure near Earth’s orbit may be somewhat different from the actual photospheric composition.  The solar wind appears to best reflect the composition of the Sun’s photosphere in the solar polar regions near solar minimum.  The Ulysses spacecraft made solar wind measurements above both the Sun’s north and south polar regions during the 1994-1995 solar minimum.  Analysis of these Ulysses data indicate the most abundant elements are (after hydrogen and helium, in order of abundance): oxygen, carbon, nitrogen, magnesium, silicon, neon, iron, and sulfur—though one analysis of the data shows that neon is the third most abundant element (after carbon).

The elephant in the room is, of course, are the photospheric abundances we measure using spectroscopy or the collection of solar wind particles indicative of the Sun’s composition as a whole?  As it turns out, we do have ways to probe the interior of the Sun.  Both helioseismology and the flux of neutrinos emanating from the Sun are sensitive to metal abundances within the Sun.  Helioseismology is the study of the propagation of acoustic pressure waves (p-waves) within the Sun.  Neutrino flux is devilishly hard to measure since neutrinos so seldom interact with the matter in our instruments.  Our studies of the interior of the Sun (except for sophisticated computer models) are still in their infancy.

You might imagine that if measuring the metallicity of the Sun in our own front yard is this difficult, then measuring it for other stars presents an even more formidable challenge.

In practice, metallicity is usually expressed as the abundance of iron relative to hydrogen.  Even though iron is only the seventh most abundant metal (in the Sun, at least), it has 26 electrons, leading to the formation of many spectral lines corresponding to the various ionization states within a wide range of temperature and pressure regimes.  Of the metals having a higher abundance than iron, silicon has the largest number of electrons, only 14, and it does not form nearly as many spectral lines in the visible part of the spectrum as does iron.  Thus defined, the metallicity of the Sun [Fe/H] = 0.00 by definition.  It is a logarithmic scale: [Fe/H] = -1.0 indicates an abundance of iron relative to hydrogen just 1/10 that of the Sun.  [Fe/H] = +1.0 indicates an abundance of iron relative to hydrogen 10 times that of the Sun.

The relationship between stellar metallicity and the existence and nature of exoplanets is an active topic of research.  It is complicated by the fact that we can never say for certain that a star does not have planets, since our observational techniques are strongly biased towards detecting planets with an orbital plane near our line of sight to the star.

References
Vagnozzi, S. 2016, 51st Recontres de Moriond, Cosmology, At La Thuile