Astronomy & Celestial Mechanics
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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.

Assumes Extinction, Ionisation and Opacity.

16 min read 8 figures Measuring the unreachableScales that defeat intuitionLight is the only messenger

The space between the stars is not empty, and it is not uniform either. A sight line out of the galaxy this one is being observed from inside passes through material at eighty kelvin and material at eight thousand and material at a million, in that order or in some other, and the astonishing thing about that list is not its range but that the entries are separated. There is gas at eighty kelvin and gas at eight thousand and there is almost nothing at eight hundred.

That absence is the subject of this essay, and it has a cause that is a good deal more interesting than the observation. Nothing sorts the gas. No boundary is imposed, no container holds the cold material apart from the warm, and the two are in direct mechanical contact everywhere. They are separate because thermal balance, in a gas heated the way this one is heated and cooled the way this one is cooled, has more than one solution — and because one of the solutions is a state that cannot survive being touched.

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.
Fig. 1 Thermal balance for interstellar gas, as pressure against density. Every point on the curve is a temperature at which cooling exactly cancels heating, and the curve is not monotonic: it rises, turns over, falls, and rises again. A horizontal line at the pressure of the local medium therefore meets it three times. The three crossings are a warm phase near half a particle per cubic centimetre, a cold phase near sixty, and one in between, drawn dashed because it does not last. The two survivors differ by a factor of a hundred and twenty in density and by exactly the same factor in temperature — necessarily the same factor, since the product of the two is the pressure they are both held at.

Why balance is a curve at all

A parcel of interstellar gas gains heat and loses it, and the two processes do not depend on the same things.

The gain is almost entirely photoelectric heating. A far-ultraviolet photon from some hot star, tens or hundreds of parsecs away, strikes a dust grain; the grain ejects an electron; the electron carries away a surplus of a few electronvolts and shares it with the gas through collisions. What matters for everything below is that this rate depends on the ultraviolet radiation field and on how much dust there is, and hardly at all on the temperature or the density of the gas receiving it. Each grain photoelectron is delivered to roughly one atom, so the heating per unit volume goes as the first power of the density.

The loss is radiative, and radiation from a dilute gas is a collisional process: an atom is excited by a collision with another particle and then radiates, so the rate per unit volume goes as the square of the density. It also depends violently on temperature, because an excitation with a threshold cannot happen below that threshold — the same reason an average over wavelength is dominated by wherever the gas is most transparent rather than by wherever it emits most.

Set the two equal and the density cancels once:

n Λ(T)  =  Γ.n\,\Lambda(T) \;=\; \Gamma .

Every temperature therefore has exactly one density at which the gas is in balance, and that correspondence is the curve above — plotted, because pressure rather than density is what neighbouring parcels have to agree on, as P=nTP = nT against nn.

Two cooling lines, and the temperature step they produce. Above: what interstellar gas radiates, per hydrogen nucleus per unit density, against temperature. The total is the sum of two lines with very different thresholds. The 158 micron fine-structure line of singly ionised carbon has an upper level only 92 K above its ground state, so it radiates at every temperature drawn here and is the only thing that works in the cold; Lyman α needs 118,000 K worth of excitation and is therefore absent below a few thousand degrees and dominant above 6400 K, where the two change places. Below: the same balance read as temperature against density. It is not a slope but a step — the near-vertical section is the unstable branch, and a medium whose density is anywhere along it has no equilibrium temperature it can hold. Removing the carbon from the gas would delete the lower line, and with it the entire cold phase; the interstellar medium has two states because it has two coolants with thresholds four orders of magnitude apart.
Fig. 2 The two lines that do all the cooling, and the temperature step they produce. Above: what the gas radiates per particle per unit density, against temperature. The 158 micron fine-structure line of singly ionised carbon has an upper level only 92 K above its ground state, so it works at every temperature drawn; Lyman α needs a hundred and eighteen thousand kelvin of excitation energy and is therefore absent below a few thousand degrees and overwhelming above. Below: the same balance read as equilibrium temperature against density. It is not a slope but a step.

The shape of the equilibrium curve is inherited from that second panel. Cooling has two thresholds, four orders of magnitude apart in the energy required, and between them the gas has to make do with whichever line it can still excite. A gas containing no carbon would have no lower branch, no step, and — as the rest of this essay argues — no cold phase at all.

Three solutions, and the one that cannot last

The interesting content of the first figure is that a horizontal line crosses it three times. Three densities are in thermal balance at the same pressure, and since mechanical contact between parcels is pressure contact, all three could in principle sit side by side indefinitely.

They cannot, and the reason is a sign.

Three equilibria at one pressure, and the arrows that keep two of them. The net rate at which a parcel of interstellar gas loses heat, plotted against its density while its pressure is held at 3000 K cm⁻³ — so its temperature is 3000/n and the whole balance is a function of one variable. It is plotted in units of the heating rate, so the value is the ratio of cooling to heating less one and the curve is bounded below by minus one; the runaway at the left, where the gas is at nine thousand kelvin and Lyman α is cooling it twenty times faster than anything can heat it, runs off the top of the frame. It crosses zero three times, at 0.47, 1.9, 57 particles per cubic centimetre, and those three densities are the ones in thermal balance. Above the axis the parcel is cooling, and a parcel cooling at fixed pressure shrinks, so it moves to the right; below the axis it is being heated and expands to the left. The arrows are those directions. They converge on the outer two crossings and flee the middle one: the cold and warm phases are stable to an isobaric squeeze and the state between them is not, so gas prepared there does not stay, and the medium ends up with two densities rather than a continuum of them.
Fig. 3 The net rate at which a parcel loses heat, plotted against its density while its pressure is held fixed — so its temperature is the pressure divided by the density, and the whole balance becomes a function of one variable. The curve crosses zero three times, and those three densities are the ones in thermal balance. Above the axis the parcel is cooling, and a parcel cooling at constant pressure contracts, so it moves to the right; below the axis it is gaining heat and expands to the left. The arrows are those directions. They converge on the outer two crossings and flee the middle one.

Squeeze a parcel sitting on the middle branch. Its density rises, its temperature falls, and — this is the whole of it — at that temperature the gas radiates more efficiently than before, so it loses heat faster than the heating replaces it, so it cools further, so it contracts further. Nothing brings it back. The same parcel expanded rather than squeezed radiates less, heats up, and expands further. The middle solution is an equilibrium in the sense that a pencil balanced on its point is an equilibrium.

This is Field’s criterion, and in the form drawn here it is a statement about the slope of one curve: an equilibrium is stable when the net-loss curve crosses zero going downwards. Written the way the original paper writes it, it is the condition that the net loss decrease with temperature at constant pressure, which is the same statement with the axis reversed.

So a medium prepared with a continuous range of densities does not keep one. Gas at the intermediate densities drains, over a cooling time, into one of the two states that hold. What is left is a two-phase medium: cold dense clouds embedded in warm rarefied material, at the same pressure, with a thermally forbidden gap between them. Nobody separated them and nothing keeps them apart. They are the two stable roots of one equation.

The width of the band, and what sets it

The pressure at which three solutions exist is not any pressure. Above the maximum of the equilibrium curve only the cold branch is available; below its minimum, only the warm one.

Two densities in thermal balance at one pressure, 141 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 4200 K cm⁻³ of the local medium the three crossings are a warm phase at 0.71 cm⁻³ and 5890 K, a cold phase at 101 cm⁻³ and 42 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 141 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.
Fig. 4 The same construction at a higher pressure. The three crossings survive but they have moved: the warm solution is denser and cooler, the cold one is denser still, and the two are further apart in density than before. Push the pressure above the curve’s maximum and the warm branch has no solution at all — every parcel finds itself on the cold branch and the medium has one phase again. That is not an abstraction: it is what happens behind a supernova blast wave, and it is why compression makes cold gas rather than merely making gas.

The band is roughly sixteen hundred to five thousand kelvin per cubic centimetre in the solar neighbourhood, and the mean pressure there is about three thousand — comfortably inside it, with about a factor of two of room on each side. That is a coincidence in the same sense that a planet’s surface temperature being near the triple point of water is a coincidence: it is not one, because the same star formation that supplies the ultraviolet also supplies the supernovae that set the pressure, and the two are yoked — the biggest stars deliver both, and quickly. But it is not a theorem either, and in a galaxy with much less dust — which means much less photoelectric heating per unit ultraviolet — the band sits somewhere else.

The phase that fills the volume and the phase that holds the mass

The two-phase argument accounts for the neutral gas. The real medium has more in it, and the extra components arrived in the theory by a different route: not from thermal balance but from supernovae, whose energy is almost all delivered as motion rather than as light and which heat gas to a million kelvin, at which temperature it cools so slowly that it simply stays.

Five named states of one medium, across 5 decades of density. The named states of the interstellar medium placed on the plane of density against temperature, both logarithmic, with three lines of constant pressure running across it. They are spread over 5 decades in density and five in temperature, and yet four of the five sit within a factor of 3.8 of one another in pressure — they lie nearly along one diagonal, because that is what mechanical contact between them requires. The exception is the molecular gas, which is over-pressured because it is held together by its own gravity rather than by the medium around it, and that exception is what makes star formation possible. The two numbers to read against each other are in the labels: the hot phase fills half the volume of the disc and holds one per cent of its mass, while the cold and molecular gas together hold half the mass in under four per cent of the volume. A map of the interstellar medium weighted by volume and one weighted by mass are pictures of different objects.
Fig. 5 The five named states on the plane of density against temperature, with lines of constant pressure across it. They span five decades in density and five in temperature, and four of the five sit within a factor of about four of each other in pressure — they lie nearly along one diagonal, which is what mechanical contact between them requires. The molecular gas is the exception, over-pressured because it is held together by its own gravity rather than by the medium around it. The area of each disc is its share of the volume of the disc near the Sun.

The numbers in that figure are worth reading twice, because they say something no picture of the interstellar medium conveys. The hot ionised phase fills about half the volume and holds about one per cent of the mass. The cold and molecular gas together hold half the mass in under four per cent of the volume. A map of the interstellar medium weighted by volume and a map weighted by mass are pictures of different objects, and almost every argument about the medium is really an argument about which of the two is meant.

The same disagreement runs through the observations. A twenty-one centimetre survey sees neutral hydrogen in emission and is therefore weighted by mass, so it sees mostly cold and warm neutral gas. An X-ray survey sees the hot phase and nothing else. An absorption measurement towards a background source — composition read from what is missing — samples whatever is on that particular sight line, weighted by nothing at all, which is why absorption and emission surveys of what appears to be the same gas return systematically different temperatures.

The dust, which is doing two jobs at once

Nothing above works without grains. They supply the photoelectrons that heat the gas, and they are also the only reason the medium can be seen at all along most sight lines — a magnitude of extinction is a column of dust, and a column of dust is a column of gas at a ratio that holds to a factor of two across the galaxy. The energy the grains take out has to go somewhere, and where it goes is the other half of the same budget.

The light dust removes at 0.56 µm comes back at 124 µm. One energy budget drawn twice, on a wavelength axis spanning four and a half decades. The upper curve is starlight from a 6500 K photosphere; the shaded region under it is the part removed by a magnitude of visual extinction, computed from the same CCM law the other modes here draw, and weighted towards the ultraviolet exactly as that law says. The curve on the right is what the grains do with it: a modified blackbody at 20 K with an emissivity index of 1.8, normalised so that the energy under it equals the energy under the shaded region. Integrating the two curves actually drawn returns a ratio of 1.000. The starlight peaks at 0.56 microns and the re-emission at 124, a factor of 220, so nothing about the two is recognisable as the same photons and everything about them is the same joules. The practical consequence is a rule about arithmetic: a galaxy's ultraviolet luminosity and its far-infrared luminosity are not two independent measurements of how many young stars it has. One is the light that escaped and the other is the light that did not, and adding them without noticing counts part of the population twice.
Fig. 6 One energy budget drawn twice. The shaded region is the starlight a magnitude of visual extinction removes, weighted to the ultraviolet by the law in the previous figure; the curve on the right is what the grains do with it — a modified blackbody at twenty kelvin, normalised so that the energy under it equals the energy under the shaded region. Integrating the two curves as drawn returns a ratio of one. The starlight peaks near half a micron and the re-emission near a hundred and twenty-four, so nothing about the two is recognisable as the same photons and everything about them is the same joules.

Twenty kelvin is a temperature the grains reach, and it is nothing like the temperature of the gas they sit in. There is no contradiction: the grains are in radiative equilibrium with starlight and the gas is in thermal balance with its own line emission, and the two systems exchange energy far too slowly for either to drag the other. A parcel of the cold neutral medium contains dust at twenty kelvin and hydrogen at eighty, and both numbers are right.

Where the ionisation comes from

The list of phases has two warm entries at the same temperature, one neutral and one ionised, and the reason they share a temperature is not a coincidence either. The warm ionised medium is not warm neutral gas that got hotter. It is gas that was ionised by ultraviolet photons escaping from hot stars, and which sits at nearly the same temperature for the unrelated reason that photoionised gas always sits near ten thousand kelvin — the balance a spectrum’s second reading depends on: the energy per photoionisation is set by the stellar spectrum, the cooling is set by the same lines, and the balance between them is remarkably insensitive to everything else. Two of them at eight thousand kelvin, arrived at by two different arguments.

The other pressures

Everything so far has treated pressure as nkTnkT, and in the interstellar medium that is only about a third of the story. The magnetic field contributes a pressure, and so do the cosmic rays, and to within the accuracy anybody can measure the three are comparable. The rough equality of thermal, magnetic and cosmic-ray pressure is called equipartition, and it is honestly more an observation than a result: nobody has a satisfying argument for why three quantities with such different sources should agree to within a factor of two. What it does mean is that the two-phase picture drawn here is the thermal part of a larger balance, and that a cloud can be supported against its own gravity by a field it took no account of, much as a stellar system can be supported by disorder rather than by rotation.

Where the cold gas goes

The cold neutral medium is not the end of the sequence. It is dense enough to shield its own interior from the ultraviolet that heats it, and shielded gas can form molecules, and molecular gas cools to ten or twenty kelvin — at which point a new question becomes urgent.

The critical mass falls as the cloud contracts, with a slope of −0.50. The Jeans mass — the least mass of molecular gas that its own pressure cannot support — against number density, for gas at 10, 20, 50 K, both axes logarithmic. The curves are straight because the mass goes as T^(3/2) ρ^(−1/2), and the slope measured off the drawn 10 K curve is −0.500 against the −0.5 that exponent requires. The consequence is the one that matters and it is a matter of sign: a cloud collapsing at constant temperature moves to the right along one of these lines, so the mass it takes to be unstable keeps falling, and sub-regions that were individually stable when the collapse began become individually unstable during it. A giant molecular cloud at 100 particles per cubic centimetre has a Jeans mass of 99 solar masses; a dense core at 10⁵ has one of 1.70. That is why a cloud of ten thousand solar masses makes a cluster rather than a star, and why the question about star formation is not what makes gas collapse but what stops the fragmenting.
Fig. 7 The least mass of molecular gas that its own pressure cannot support, against density. The curves are straight because the critical mass goes as temperature to the three-halves over the square root of density, and the consequence is a matter of sign: a cloud collapsing at constant temperature moves to the right along one of these lines, so the mass required to be unstable keeps falling. At the density of the cold neutral medium the number is thousands of solar masses; in a dense core it is under two.

That is where this ladder goes next, and it is worth noticing what has changed. Everything in this essay is a balance between heating and cooling in which gravity plays no part whatever — the gas is held up by the pressure of the gas around it, and the phases are decided by atomic physics and a radiation field. From the molecular phase onwards gravity is the whole story, and the interstellar medium stops being a medium and starts being a set of objects.

How the two states are told apart

The theory predicts two stable temperatures; establishing that both exist requires measuring the temperature of gas that is neither resolved nor localised, and the technique is a comparison of one line seen two ways.

Atomic hydrogen radiates at 21 centimetres, from the transition between the two orientations of the electron’s spin relative to the proton’s. The same transition also absorbs, so a cloud in front of a bright radio source removes some of that source’s continuum at the same wavelength.

The two measurements weight the gas differently, and that is the whole method.

Emission from an optically thin cloud is proportional to the number of atoms along the line of sight and is nearly independent of their temperature — hot and cold gas contribute alike, so the emission gives the total column.

Absorption is proportional to the number of atoms divided by their excitation temperature, because a warm population has nearly as many atoms in the upper state as in the lower and so absorbs very little. Cold gas absorbs strongly and warm gas hardly at all.

Take the ratio and the temperature falls out. Observe a bright background source, measure the absorption spectrum through it, then measure the emission from a nearby direction where the source is not, and the comparison gives the temperature of the absorbing gas directly.

The answers cluster where the theory says they should: absorption features at 40 to 100 kelvin, and a diffuse emission component with no detectable absorption at all, implying temperatures of thousands. The bimodality is measured rather than assumed, and the fraction of gas in each phase — roughly a third cold by mass in the solar neighbourhood — comes from the same comparison.

The residual difficulty is that the two lines of sight are not the same line of sight. The background source is a point and the emission comparison is taken from an annulus around it, so any structure in the cloud on those angular scales contaminates the difference — which is the dominant systematic in every such measurement and the reason the surveys observe hundreds of sources rather than a few good ones.

There is also a phase the technique is blind to. Gas at temperatures between the two stable branches absorbs and emits like a mixture of both, so a line of sight containing a little unstable gas is indistinguishable from one containing rather more cold gas — which means the measured fraction of gas in the intermediate state is an upper limit rather than a detection, and the claim that the intermediate state is rare rests partly on the theory it is being used to test.

Separating the two would need a tracer sensitive to the intermediate temperatures alone, and the candidates — fine-structure lines of carbon and oxygen — are themselves sensitive to the density and the radiation field, so the ambiguity moves rather than closing.

Where the picture stops

Three things are missing from the account above, and each is the subject of an active argument.

The medium is not in equilibrium. Everything drawn here is a steady state, and the actual medium is stirred by supernovae on a timescale comparable with its own cooling time. Gas is constantly being moved off the equilibrium curve and constantly relaxing back, so the phases are not sharp: surveys find a substantial fraction of neutral hydrogen at temperatures in the supposedly forbidden gap, which is not a refutation of the argument but a measurement of how hard the medium is being shaken.

The filling factors are contested. The hot phase’s half of the volume comes from a model of how supernova remnants overlap, and the answer depends on quantities — the porosity of the disc, how much hot gas escapes vertically — that are known to a factor of a few at best. Estimates in the literature run from twenty per cent to eighty.

And the heating rate is the weakest number in the chain. Photoelectric efficiency depends on grain size, on grain charge, and on the abundance of the very smallest grains, none of which is measured directly. The equilibrium curve’s shape is robust; the pressure at which it turns over is not, and it is that pressure the two-phase argument compares against.

One more pressure shows how narrow the range in which both stable states coexist actually is.

Three equilibria at one pressure, and the arrows that keep two of them. The net rate at which a parcel of interstellar gas loses heat, plotted against its density while its pressure is held at 4200 K cm⁻³ — so its temperature is 4200/n and the whole balance is a function of one variable. It is plotted in units of the heating rate, so the value is the ratio of cooling to heating less one and the curve is bounded below by minus one; the runaway at the left, where the gas is at nine thousand kelvin and Lyman α is cooling it twenty times faster than anything can heat it, runs off the top of the frame. It crosses zero three times, at 0.71, 1.3, 1.0e+2 particles per cubic centimetre, and those three densities are the ones in thermal balance. Above the axis the parcel is cooling, and a parcel cooling at fixed pressure shrinks, so it moves to the right; below the axis it is being heated and expands to the left. The arrows are those directions. They converge on the outer two crossings and flee the middle one: the cold and warm phases are stable to an isobaric squeeze and the state between them is not, so gas prepared there does not stay, and the medium ends up with two densities rather than a continuum of them.
Fig. 8 The stability analysis at a pressure of 4,200 rather than 3,000. The unstable branch is still there and its extent has changed, so the two-phase coexistence survives a factor in the pressure — which it has to, because the interstellar pressure varies by more than that across the Galaxy.

Where this ladder goes next

Later rungs on this anchor: the twenty-one centimetre line itself, which is both an emission measurement weighted by mass and an absorption measurement weighted by nothing, and the reconciliation of the two; the hot phase and how a galaxy vents it, which is where the gas budget of a whole disc stops balancing without a fountain; the transition from atomic to molecular hydrogen, which is a shielding calculation rather than a thermal one; turbulence, and what it means for a medium to have a pressure that is mostly kinetic; and the chemistry, which is the strangest part of all — a gas at ten kelvin and a millionth of a laboratory vacuum builds molecules of ten atoms, on grain surfaces, over a million years.

Where this goes next

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. The Balmer maximum is at 9,870 K, and it is a maximum in temperature. What two absorption lines actually count, each normalised to its own maximum. The first curve is the fraction of all hydrogen sitting in n = 2 — the only hydrogen a Balmer line can absorb — which is a Boltzmann factor climbing with temperature multiplied by the neutral fraction falling with it. The product peaks at 9,870 K, where 35.2% of the hydrogen is still neutral and only 8.73·10⁻⁶ of all of it is in n = 2 at all. Below the peak there is plenty of hydrogen and almost none of it excited; above it there is plenty excited and almost none of it neutral. The second curve is the fraction of calcium that is singly ionised, which is what the Ca II K line counts, and it peaks at 6,335 K — cooler, because calcium gives up its first electron at 6.113 eV. At 6,000 K the Balmer curve is at 0.1% of its own maximum while Ca II is near its peak, and calcium is 4.5·10⁵ times rarer than hydrogen in the same gas. A spectrum in which Ca II K is the strongest line is not a spectrum of a calcium star. Reading it as one is precisely the error that had the Sun made of iron until 1925. Why hydrogen's lines are strongest where hydrogen is not A Balmer line counts the hydrogen atoms sitting in one particular excited state, and that population peaks near 10,000 K — where a third of the hydrogen has already been ionised away. The strength of a line is a thermometer, and reading it as an abundance put hydrogen at one per cent of the Sun until 1925. The star-formation law, and the clock inside it. 46 model discs on the Kennicutt–Schmidt plane, built from Σ_SFR = 2.5e-4 Σ_gas^1.4 with 0.28 dex of scatter, with the exponent then fitted back off the drawn points at 1.42. The diagonal dashed lines are constant depletion times: gas divided by the rate consuming it. Every disc on this plane consumes its gas within a few gigayears, and a galaxy that has been forming stars for ten of them therefore cannot have been working from the gas it started with. The slope steeper than one is what makes the depletion time shorter where the gas is richer, which is the opposite of the intuition that a full tank lasts longer. The gas runs out before the galaxy does Divide a disc's gas by the rate it is turning that gas into stars and the answer is about two billion years — a seventh of the age of the disc. Every spiral still forming stars is therefore being fed from outside, and the star-formation law says the richer the disc, the sooner it starves.

What this makes readable

Essays that name this one as a prerequisite.

What links here

The 8 of 13 essays linking to this one that name the most of the same objects.

The objects this essay names

Each one links to every other essay that touches it.

Cold neutral mediumCooling functionField criterionFine-structure coolingHot ionised mediumInterstellar mediumPhotoelectric heatingPressure equilibriumThermal instabilityTwo-phase mediumVolume filling factorWarm neutral medium