Astronomy & Celestial Mechanics
the sky, computed
Concept

Reionisation — where it appears

The epoch at which radiation from the first galaxies ionised the intergalactic medium again, after recombination had made it neutral. It is dated at a midpoint near redshift eight by the microwave background's scattering optical depth and near six by the appearance of quasar troughs.

Named by 9 essays across one field — each of them below, with the objects they name alongside it.

One ionising photon per atom, and where that happens. The number of photons energetic enough to ionise hydrogen, per baryon, against temperature — with temperature falling to the right, so the universe ages to the right. The quantity is the fraction of a Planck distribution above 13.6 eV, integrated numerically, divided by the 6.13·10⁻¹⁰ baryons there are per photon. It crosses one at 5,844 K, which is z = 2143, and it falls by 19 orders of magnitude across the plot because it is the tail of an exponential. That crossing is the answer to why recombination waits until three thousand kelvin. At hydrogen's own ionisation temperature of 157,803 K there are two billion ionising photons per atom and the gas has no chance; the temperature has to fall by a factor of forty before the supply runs out, and it runs out suddenly because an exponential tail does. The number that sets the factor of forty is not an energy at all — it is the photon-to-baryon ratio, which is to say the entropy per baryon, which is to say a number fixed long before any of this and measured today from the second acoustic peak and from deuterium alike.

The surface the background actually is

Hydrogen ionises at 157,800 kelvin and the universe became transparent at 3,000. The factor of fifty between them is not an error, and it is not about energy — it is about there being two billion photons for every atom, so the far tail of the distribution can keep the gas ionised long after the typical photon has become useless.

cosmology · Microwave background A neutral fraction of 2.4·10⁻⁶ is already opaque. The Gunn–Peterson optical depth against the neutral fraction of the intergalactic medium, at z = 3, 5, 6.3, for Ω_b = 0.0493 and h = 0.674. Note the range of the vertical axis. A fully neutral medium at z = 6.3 gives τ = 4.1·10⁵, which is not absorption but extinction of everything; the medium reaches τ = 1 — the point at which it stops transmitting most of the light — at neutral fractions of 6.1·10⁻⁶ at z = 3, 3.3·10⁻⁶ at z = 5, 2.4·10⁻⁶ at z = 6.3. That is why the argument runs from the flux that survives rather than from the flux that does not. A spectrum showing any transmission at all between Lyman α and Lyman β is a measurement that the medium is ionised to better than one part in 164,727, and no fit to any absorption line is needed to establish it.

A trough that proves the forest survived

A uniform neutral medium at redshift six would absorb Lyman alpha with an optical depth of four hundred thousand. So the existence of any transmitted light in a quasar's spectrum is a measurement — of a neutral fraction below one part in ten thousand — made from a detection rather than from an absorption.

cosmology · Reionisation Bubbles that meet at z = 5.3, and a scattering depth of 0.047. The fraction of the volume of the universe filled by ionised bubbles, integrated from redshift 20 down to 4.5. The equation has two terms and no others: photons escaping from young galaxies open new volume, at a rate taken from the measured cosmic star formation history with an escape fraction of 0.2; recombinations inside the bubbles close it again, on a timescale that is one over the density times the recombination coefficient times a clumping factor of 3. Early on the density is high and recombination wins almost everything; the curve is nearly flat. As the universe expands the recombination time lengthens as the cube of one plus the redshift while the star formation rate is still rising, the balance tips, and the filling factor runs to one in under half a billion years. It reaches unity at redshift 5.31, which is overlap — the moment the bubbles meet and the last neutral walls between them disappear. The same integration gives an electron-scattering optical depth of 0.0465 for the microwave background, against the 0.054 that is measured, and that agreement is the check: the two observations constrain the same history from opposite ends, one fixing when it finished and the other how long it took.

It ends when the walls meet

Reionisation is usually described as the universe becoming transparent, which makes it sound like a change of state. It is not. Each young galaxy opens a bubble of ionised gas around itself and recombination closes it again, and what ends the epoch is geometric — the bubbles meet, and the last neutral walls between them disappear.

cosmology · Reionisation The sky-averaged 21-centimetre signal, and the trough that was claimed. The brightness temperature of neutral hydrogen's 21-centimetre line relative to the microwave background, averaged over the sky, in millikelvin, against observed frequency (the redshift is 1420.4 MHz over the frequency, minus one). In this model the first stars' ultraviolet couples the hydrogen's spin to the gas near redshift 17, X-rays heat the gas near 11, and reionisation is half complete at 7.7. Because the gas has cooled faster than the background since it decoupled, coupling makes it absorb: the trough reaches −171 mK at 71 MHz (redshift 19.1). Heating turns the signal into a weak emission, and reionisation removes it above about 197 MHz. The dashed curve is the deepest absorption standard physics allows at each frequency — gas that has only cooled, fully coupled — and the point is the one claimed detection, −500 mK at 78 MHz: about 1.9 times deeper than that floor.

A shadow cast on the microwave background

Before the first stars lit it up, the neutral hydrogen between the galaxies was colder than the microwave background behind it, and once starlight tied its 21-centimetre line to that cold, it absorbed. The absorption, redshifted to radio frequencies near 70 megahertz, is a thermometer for gas nobody has seen — and the one claimed detection was twice as deep as cooling alone allows, which is either a discovery about dark matter or a lesson about antennas.

cosmology · Reionisation Haloes at the centre of a void, and in an average place. The number of dark matter haloes per unit volume and per factor e in mass, against halo mass in solar masses per h, in the universe on average (dashed) and inside a sphere of 5 Mpc/h radius at the centre of a void whose density there is 20 per cent of the mean (solid), from the excursion-set theory at redshift zero. The void's sphere holds 9.2e+12 solar masses per h of matter altogether, and no halo can be heavier than that. At the dwarf end the void holds 38 per cent of the average abundance per unit volume — more than its 20 per cent share of the matter. At the mass of the Milky Way's halo, 10¹² M☉/h, it holds 1.62 per cent. An emptiness of galaxies like the Milky Way is guaranteed by the theory; an emptiness of dwarfs is not.

A void is not short of dwarf haloes

The centre of a large void holds a fifth of the average density of matter and almost no galaxies, and it is natural to read the two facts as one. They are not. The theory of how haloes form says a void turns its matter into dwarf-sized haloes at least as readily as anywhere else — it is short of big haloes, not small ones — so a void empty of dwarf galaxies is a statement about which haloes were allowed to light up.

cosmology · Large-scale structure The polarisation peaks sit in the temperature troughs. A tight-coupling sketch of the two acoustic sources against multipole, each scaled to its own maximum: the temperature, from the compression of the photon–baryon fluid at last scattering plus its Doppler term, and the E-mode polarisation, which is driven by the fluid's velocity gradient. The sound horizon and the distance to last scattering put the acoustic scale at ℓ = 302, the measured phase of the peaks is 0.267 and the damping scale is ℓ = 1400; the baryons' weight, which changes the heights of the temperature peaks and not their places, is left out. The temperature peaks fall at ℓ ≈ 218, 515, 813, 1110, 1408; the polarisation peaks at ℓ ≈ 130, 391, 681, 975, 1272, between them, because a compression is at its extreme when the fluid is momentarily still, and the velocity is largest a quarter of a cycle later. The model has no projection, no decaying potentials and no thickness, so it places the peaks and says nothing about their shapes.

Polarised only where the glow was lopsided

An electron bathed in light from every side scatters it unpolarised, and so does one bathed in light brighter on one side. Only a glow brighter along one axis than across it leaves a polarisation behind, and in the microwave background that glow existed for a short time, in a thin part of a thin shell, because the plasma was moving.

cosmology · Microwave background 40 galaxies detected, and a map of all of them: the summed light traces the structure the catalogue misses. A 160 by 160 Mpc/h slice of a simulated universe at redshift 6, its galaxies clustered on a density field and given luminosities from a Schechter function with a faint-end slope of -1.5. Left: the 40 galaxies bright enough to detect individually, above 1.5 times the characteristic luminosity. Right: the same slice as a map of summed line intensity in 32 by 32 cells, shaded linearly between the 5th and 97th percentiles of the cells, with no galaxy detected at all. The catalogue is a sparse scatter in which the structure is barely visible; the map shows it, and its cells correlate with the underlying density at 0.65. The map's light comes overwhelmingly from galaxies below the detection limit.

A map of galaxies none of which was seen

A survey that lists galaxies one by one stops at the faintest it can detect, and at high redshift most of the light comes from galaxies fainter than that. Map one spectral line in summed intensity instead, pixel by pixel and frequency by frequency, and every galaxy contributes whether it is detected or not. The fluctuations of that map have two parts — clustering, which weighs the total light, and graininess, which weighs how unevenly it is shared — so one power spectrum measures two moments of a luminosity function nobody has counted.

cosmology · Olbers's paradox [C II] power is round in the plane of k; CO(4–3) mapped at the wrong distance is elongated 5.1 times along k∥. Contours of the clustering power spectrum in the plane of wavenumber across the sky, k⊥, and along the line of sight, k∥, in h/Mpc, at 10², 10²·⁵, 10³, 10³·⁵ (Mpc/h)³ in arbitrary units, for the target line, [C II] from redshift 6.60 (black), and for the CO(4–3) interloper from redshift 0.84 placed at the target's distance (colour). The target's contours are quarter-circles, because its structure has no preferred direction. The interloper's are ellipses, drawn in towards the k∥ axis and elongated along it by the ratio of the two rescalings, α∥/α⊥ = 5.1: a structure that is round where it really is looks magnified across the sky and flattened along the line of sight where the map puts it. That difference of shape, not of amplitude, is what separates the two in a map where both have been summed.

A line from the wrong redshift lands at the wrong distance

A map of ionised carbon from redshift six is built by assuming every photon at a given frequency came from that line. Carbon monoxide from galaxies at redshift one sends photons to the same frequency, and the map places them five billion light-years too far away. Their structure arrives magnified across the sky and squashed along the line of sight — round where it really is, flattened in the map — and that distortion of shape, which no amount of brightness can hide, is how the impostor is found.

cosmology · Olbers's paradox The number of lit dwarfs at a void's centre, against the date it was reionised. The number of haloes heavier than 3.2·10⁹ M☉/h that had collapsed from the matter of a 5 Mpc/h sphere by the redshift at which that sphere was reionised, on a logarithmic axis, against that redshift — for a sphere at the centre of a void with 20 per cent of the mean density today (solid) and an average sphere of the same size (dashed). If only those haloes could make stars, they are the sphere's dwarf galaxies. Reionised at 5.3: 4.3 in the void sphere, 195 in the average one; reionised at 6: 2.0 in the void sphere, 121 in the average one; reionised at 7.7: 0.22 in the void sphere, 29 in the average one. Each unit of delay in the date multiplies the void's count by 3.2 and the average sphere's by 2.1: the void's dwarfs sit further out in the tail of the distribution, and a tail is steep. A count of a few galaxies at a void centre is a statement about when that void's gas was heated, to within a fraction of a unit of redshift — provided the threshold is known.

A void dated by the dwarfs that lit in time

Reionisation did not heat the universe all at once, and the centres of the large voids were among the last places it reached. A dwarf halo there could make stars only if it had grown heavy enough before its own gas was heated — so the number that did is a clock for one void, and a clock that runs faster the emptier the void.

cosmology · Large-scale structure

Named alongside it

The objects these essays reach for when they reach for this one.

Optical depthThomson scatteringRecombinationCosmic voidDark matter haloDwarf galaxyGalaxy biasThe Gunn–Peterson troughHalo mass functionIntergalactic mediumLast scattering surfaceLine-intensity mapping

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