Astronomy & Celestial Mechanics
the sky, computed
Concept

Interstellar medium — where it appears

The gas and dust between the stars, which is not one substance but several distinct states in rough pressure equilibrium. Its densities span five decades and its temperatures five more, and the one filling most of the volume holds almost none of the mass.

Named by 11 essays across 2 fields — each of them below, with the objects they name alongside it.

The extinction law, for three kinds of dust. How much of a star's light dust removes, against inverse wavelength, normalised to one at the V band. Blue light is extinguished more than red, which is why reddening and extinction are the same measurement — and the hump at 4.6 inverse microns is a feature of the grains themselves, present on almost every sight line and still without an agreed carrier. Larger grains give a flatter law and a larger R_V.

Dust makes everything look further away

A star behind dust is fainter, so a distance taken from its brightness comes out too large. The same dust also makes it redder, and the reddening is measurable where the dimming is not — which is the only reason the correction can be applied at all.

starlight · Extinction Two densities in thermal balance at one pressure, 121 times apart. Thermal equilibrium for interstellar gas, drawn as pressure against density with both axes logarithmic. Every point on the curve is a temperature between 40 and 9000 K at which cooling exactly balances the 2·10⁻²⁶ erg per second per hydrogen nucleus that grain photoelectrons deliver. The curve is not monotonic: it rises to 5007 K cm⁻³, falls to 1597, and rises again, so a horizontal line anywhere between those two crosses it three times. At the 3000 K cm⁻³ of the local medium the three crossings are a warm phase at 0.47 cm⁻³ and 6354 K, a cold phase at 57 cm⁻³ and 52 K, and one in between drawn dashed because it cannot survive — a parcel there that is squeezed cools and keeps contracting, and one that expands heats and keeps expanding. The two survivors differ by a factor of 121 in density and by exactly the same factor in temperature — necessarily the same, because their product is the pressure both are held at — and yet they press on one another equally, which is why they can share the same volume of the disc indefinitely rather than mixing.

Two temperatures, and nothing in between

The gas between the stars is not one gas at one temperature. Thermal balance has three solutions at any ordinary interstellar pressure, the middle one cannot survive being nudged, and the two that can differ by a factor of over a hundred in both density and temperature — which is why a map of the interstellar medium looks like clouds rather than like fog.

galaxies · Interstellar medium Gas kept inside 3.6 to 6.8 kiloparsecs, depending only on the speed of the fall. The pressure holding a disc galaxy's gas down, against radius, with the ram pressure of the cluster gas it is falling through drawn as three levels. The restoring pressure is two pi times the gravitational constant times the product of the stellar and gaseous surface densities, both exponential with scale lengths of 3 and 5 kiloparsecs, so it falls steeply outward; the ram pressure is the intracluster density times the square of the infall speed and does not depend on radius at all. Where the level crosses the curve, the gas goes. A galaxy entering at 700 kilometres a second keeps everything inside 6.8 kiloparsecs; at 1600 it keeps only 3.6. Nothing in this touches the stars, which are not a fluid and feel no pressure at all, so the galaxy emerges with its stellar disc and its rotation curve intact and its star formation stopped from the outside in. That is the mechanism behind the most conspicuous fact about clusters: their spirals are red, gas-poor and still spiral-shaped, which no process acting on the stars could produce.

Red, gas-poor, and still spiral-shaped

A galaxy falling into a cluster meets a headwind of hot gas at two thousand kilometres a second. Where that ram pressure exceeds the disc's own grip on its gas, the gas goes; the stars, which are not a fluid and feel no pressure, do not. The result is a spiral with no fuel, and it is the commonest kind of galaxy in a cluster.

galaxies · Clusters A slope, not an angle. Above: the polarisation angle of a background source against the square of the observing wavelength, at the five wavelengths a radio survey actually uses. The plane rotates as it passes through magnetised plasma, by an amount proportional to the integral of the electron density times the field along the path — and to λ². The intercept is the angle the source emitted at, which nobody knows, so a measurement at one wavelength contains no information whatever; the slope is the rotation measure, here 42 radians per square metre, and it needs no knowledge of the source at all. Below: the fractional polarisation that survives. A telescope beam covers many lines of sight with slightly different rotation measures, their angles disagree by more at longer wavelengths, and the vector sum collapses — which is why the useful band has a long-wavelength edge that has nothing to do with sensitivity. Divide the rotation measure by the dispersion measure of the same path, 26.8 in the usual units, and the electron density cancels: the mean line-of-sight field is 1.93 µG, obtained without knowing the distance, the density, or where along the path the field was.

A slope that needs no source

Polarised light passing through magnetised plasma has its plane rotated, by an amount proportional to the square of the wavelength. A single measurement of the angle is worthless, because nobody knows the angle the source emitted at. A measurement of the slope against wavelength squared does not need to know.

starlight · Faraday rotation The energy at which the sky begins to point. Gyroradius against energy for a singly charged particle, in three field strengths, with the thickness of the galactic disc and the size of its halo marked. A cosmic ray is not an image of anything: its path is a helix about a field line, and by the time it arrives the direction it came from has been erased. The erasure is quantitative. At 3 µG a proton's gyroradius equals the disc's half-thickness at 4.2·10¹⁷ electronvolts and the halo's radius at 4.2·10¹⁹, so below the first the particle is stored and stirred for tens of millions of years, and only above the second does it travel in something like a straight line. The measured spectrum has a break — the knee — at about 3×10¹⁵ eV, which is within a factor of a few of the first of those; the sky only starts showing structure above 10¹⁹, which is the second. Two features of a spectrum measured on the ground, both located by one straight line on this plot.

The energy at which a sky begins to point

A cosmic ray arrives from a direction that has nothing to do with where it came from. Its path is a helix about a galactic field line, and only above the energy at which that helix is bigger than the galaxy does the arrival direction start to mean anything — which is one particle per square kilometre per century.

galaxies · Cosmic rays A layer several times thicker than its heat can explain. The vertical density profile of the neutral gas layer, drawn twice. The narrow curve is what thermal pressure alone supports: an 8-kilometre-a-second sound speed against the vertical gravity of the stellar disc gives a scale height of 47 parsecs. The broad curve adds the three pressures that are not heat — turbulent motion, the magnetic field and the cosmic rays — which together roughly triple the total and, because the scale height goes as the square of the effective dispersion, thicken the layer by a factor of 3.1 to 145 parsecs. The observed half-thickness of the H I layer is about 150. The narrow curve is a real prediction and it is wrong, and what is missing from it is precisely the two terms that emit nothing: a field measured by Zeeman splitting and Faraday rotation, and a particle population measured by what it does to a detector on a mountain. A galaxy's gas disc is inflated by things that cannot be photographed, and the thickness is how the inflation is measured.

A disc held open by what cannot be photographed

Solve hydrostatic equilibrium for the galaxy's gas layer using its temperature and the disc's gravity, and the answer is a layer several times thinner than the one that is there. What is missing from the calculation is turbulence, a magnetic field and a population of cosmic rays — three pressures of comparable size, two of which emit nothing.

galaxies · Interstellar medium A source that erases its own polarisation. The polarised fraction of a uniform slab that both emits and Faraday-rotates, relative to its intrinsic value, against wavelength, for total Faraday depths of 10, 40, 150 rad m⁻². Light from the back of the slab is rotated by the whole depth and light from the front by none, so the polarisation vectors from different depths fan out and cancel. The fraction falls as |sin(Φλ²)/(Φλ²)| and vanishes altogether at λ² = π/Φ — 56.0 cm for 10, 28.0 cm for 40, 14.5 cm for 150 — then returns weakly and vanishes again. A source measured only at wavelengths beyond its first null looks unpolarised, and a source measured across the null shows a polarised fraction that depends on the wavelength in a way no foreground screen can produce. The shape of the fall is a measurement of how the rotating plasma is arranged along the line of sight.

A source that rotates its own light

The rotation-measure method assumes the plasma that turns the polarisation sits in front of the source. When it is mixed into the source instead, light from the far side is turned more than light from the near side, the contributions cancel, and the straight line in wavelength squared bends, halves its slope and then vanishes. The cure is to stop measuring in wavelength at all.

starlight · Faraday rotation One sight line, two spectra: emission peaks at 46 K while the absorption reaches τ = 1.10. The 21-centimetre line along one sight line through a cold cloud (5·10²⁰ atoms cm⁻² at 60 K) embedded in warm gas (3·10²⁰ cm⁻² at 6000 K, half in front and half behind), computed by radiative transfer. Above: the emission spectrum, brightness temperature against velocity — a broad pedestal from the warm gas (dashed, alone) with the cold cloud's narrow peak on top, capped at 46 K because the cloud is nearly opaque at line centre. Below: the same gas seen in absorption against a bright radio source behind it, the fraction of the source's light transmitted. The absorption shows the cold cloud and almost nothing of the warm gas, whose optical depth is a hundred times smaller per atom. Read in the optically thin approximation, the emission gives a column of 6.26·10²⁰ cm⁻² against a true 8·10²⁰.

A temperature that belongs to none of the gas

The hydrogen between the stars announces itself at 21 centimetres twice — in emission, which counts atoms whatever their temperature, and in absorption against a radio source behind, which counts atoms divided by their temperature. The ratio of the two is a temperature. Along any real sight line it is the harmonic mean of a cold phase and a warm one, a number no parcel of the gas actually has — and where the cold gas is thick enough, the emission stops counting it at all.

galaxies · Interstellar medium Atomic gas that stops growing: a cloud holds at most 10, 35, 104 M☉ pc⁻² of HI. The surface density of atomic hydrogen in a slab lit on both faces, against the slab's total gas surface density, both logarithmic, for metallicities of solar, 0.3 solar, 0.1 solar. A thin slab is atomic throughout and sits on the one-to-one line (grey). A thick one shields its interior and turns it molecular, so every gram added beyond the transition is a gram of H₂ and the atomic column stops at 10.1 M☉ pc⁻² for solar, 34.7 M☉ pc⁻² for 0.3 solar, 103.7 M☉ pc⁻² for 0.1 solar. The saturation is the same thing the 21-centimetre maps of nearby galaxies show: atomic gas surface densities that rarely exceed about ten solar masses per square parsec in metal-rich discs, however much gas there is, and that climb in metal-poor dwarfs.

An atomic ceiling set by the dust

Pile more gas into a galaxy's disc and the atomic hydrogen stops growing at about ten solar masses per square parsec; everything beyond that is molecular. The ceiling is the column a cloud needs to shield its interior from ultraviolet light, and because dust both makes the molecules and does the final shielding, it scales as the inverse of the metallicity — and hardly at all with the starlight, since the cold gas thickens in step with the field that would break it apart.

galaxies · Interstellar medium Molecules take longer to form than a cloud takes to fall. Three timescales for a shielded cloud of 100 hydrogen atoms per cubic centimetre, against its metallicity relative to the Sun's on a logarithmic scale, all in years on a logarithmic scale. Molecular hydrogen forms on dust grains, and the time to turn the cloud's atoms into molecules is inversely proportional to the dust, so to the metallicity: 5.3 million years at solar, 53 million years at a tenth, 530 million years at a hundredth. The cloud's free-fall time, 4.3 million years, does not depend on its metals. The two cross near solar metallicity: above it the molecules form as fast as the cloud can collapse, below it the cloud collapses before most of its hydrogen has become molecular. The dashed line is a galaxy's molecular depletion time, two billion years — the timescale that equilibrium arguments implicitly assume is short compared with everything else.

A molecule that forms too slowly to wait for

The atomic hydrogen in a galaxy's disc turns molecular wherever a cloud is thick enough to shield itself from starlight, and stars form where it does. That is an equilibrium statement, and equilibrium takes time. Molecular hydrogen forms on dust grains, so in gas with a tenth of the Sun's metals it forms ten times more slowly — slowly enough that a cloud can finish collapsing before most of its hydrogen has become molecular, and form its stars from atoms.

galaxies · Interstellar medium Two ways of pointing an aperture, and the fork between them. The gas-to-young-star flux ratio inside apertures of size l, relative to the whole galaxy's, for apertures centred on peaks of molecular gas (upper branch) and on peaks of Hα from young stars (lower branch), if clouds live 20 Myr, the young stars shine in Hα for 4.3 Myr, the two overlap for 2 Myr and independent regions are 150 pc apart. On large scales every aperture averages many regions at all stages and both branches return to one. On small scales an aperture holds one region at one stage, and the branches split: ×2.1 on the gas peaks and ×0.10 on the stars at 10 pc. With the young stars' phase known from stellar evolution, the upper branch gives the overlap, the lower branch the clouds' lifetime, and the scale where the fork closes the regions' separation.

A lifetime read from how gas and stars sit apart

No molecular cloud has been watched for long enough to see it age, and every cloud looks the same whether it lives for one free-fall time or for ten. But a galaxy holds thousands of clouds at every stage at once, and how often molecular gas and young stars appear in the same place — measured in apertures of shrinking size, centred first on one and then on the other — turns a single snapshot into a clock, calibrated by how long the young stars shine.

galaxies · Molecular clouds

Named alongside it

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

Star formationSynchrotron radiationCold neutral mediumCosmic raysDepolarisationFaraday rotationFree-fall timeInterstellar dustMagnetic fieldMetallicityMolecular cloudsMolecular hydrogen

All concepts