Gravity versus pressure

Foundations

Empty, until you add it up

Look at the space between the stars and it seems the emptiest thing there is. On average it holds about one atom in every cubic centimetre, a vacuum far better than any laboratory on Earth can make. So where could new stars possibly come from?

The answer is that space is very large, and a very thin gas spread through a very large volume adds up. The Milky Way holds several billion Suns’ worth of gas between its stars, and the gas is not spread evenly. Gravity, turbulence and the shock waves of exploding stars gather it into clouds, and the densest of those clouds, a million times thicker than the average, are where every star you can see was born. The nearest big one, the cloud behind the Orion Nebula, is making stars tonight.

The cold, dark clouds

A star-forming cloud is not like the glowing nebulae in photographs. It is cold, about ten to twenty degrees above absolute zero, and dark, because it is laced with dust that blocks visible light. It is so cold that hydrogen atoms have paired up into molecules, which is why astronomers call them molecular clouds. A giant one spans a hundred light-years and holds a hundred thousand times the mass of the Sun, in knots and filaments, threaded by magnetic fields, churning slowly.

The contest

Inside such a cloud, two forces are at war. Gravity pulls every part toward every other part. Pressure, from the warmth of the gas, pushes outward. In 1902 James Jeans worked out who wins: gravity, if the cloud is massive enough, dense enough and cold enough; pressure, otherwise. A warm, thin cloud of a thousand solar masses will sit for ever. A cold, dense knot of a few solar masses cannot hold itself up, and falls.

That is why stars form in the coldest, densest places. And it is why the first stars, in lesson 1.6, were giants: their gas could not cool, so only huge knots could collapse. Today’s clouds, seeded with the carbon and oxygen and dust of earlier generations, cool easily, and they fragment into many small stars instead of a few enormous ones.

Slower than it should be

Left to gravity alone, a dense knot would collapse in a few hundred thousand years. Real clouds take far longer, and turn only about one percent of their gas into stars in that time. Something resists. Turbulence, the chaotic swirling of the gas, holds the cloud up much as pressure would. Magnetic fields stiffen it. And the moment a star forms, its light and wind begin to push the remaining gas away. Star formation is not a flood but a slow leak.

Falling in

When a knot does fall, the first thing that happens is that it stays cold. The gas radiates away the heat of compression, through its dust and molecules, as fast as it is made. Then the centre becomes dense enough to trap its own light. The heat has nowhere to go, the temperature climbs, and pressure finally pushes back. A protostar has formed: a hot, glowing, shrinking ball that shines not by fusion but by falling in on itself.

The cloud was spinning, slightly, as everything in the galaxy is. As it falls, it spins faster, like a skater pulling in her arms, and the spin flattens the infalling gas into a disc around the protostar. Gas spirals inward through the disc; some is flung out along the poles in jets that can be seen light-years away. In 2014 the ALMA telescope in Chile photographed such a disc around a star called HL Tau, less than a million years old, and found it already carved into rings and gaps, the first signs of planets. That disc is where the next chapter but one begins.

Ignition

The protostar shrinks and heats for millions of years. At about a million degrees it begins to fuse the trace of deuterium left from the first three minutes, a brief flicker. At about ten million degrees, hydrogen itself begins to fuse, releasing enough energy to hold the star up without any further shrinking. The collapse stops. The star has arrived on what astronomers call the main sequence, and it will stay there, in balance, for most of its life. For a star like the Sun the journey from cloud to ignition takes about thirty million years; for a star of fifteen solar masses, about a hundred thousand.

Below about eight percent of the Sun’s mass the core never gets hot enough. The object glows dimly from its own contraction, then cools for the rest of time: a brown dwarf, a star that did not quite make it.

What comes out

A single cloud makes stars of all sizes at once, but not equally. For every star like the Sun it makes several smaller and fainter ones, and only occasionally one much larger. The Milky Way as a whole turns about one and a half Suns’ worth of gas into stars each year: a modest rate, sustained for ten billion years.

Deeper

The Jeans criterion

For a spherical cloud of temperature T and density ρ, gravity wins when the mass exceeds the Jeans mass, which scales as T to the power three halves divided by the square root of ρ. Put in ten kelvin and ten thousand molecules per cubic centimetre, typical of a dense core, and the Jeans mass comes out at a few solar masses. Raise the temperature to a hundred kelvin and it rises thirty-fold; that is why warm gas does not form stars. The free-fall time, the time to collapse if nothing resists, scales as one over the square root of Gρ and is about three hundred thousand years at that density.

Why collapse is inefficient

Molecular clouds live for tens of millions of years, many free-fall times, and convert only a few percent of their mass into stars. Supersonic turbulence provides most of the support: the random motions in a cloud are several times the speed of sound in it, and the resulting ram pressure holds the cloud up on large scales while creating, in the collisions of gas streams, the dense knots that collapse on small scales. Magnetic fields add support and slow the infall. Once stars form, their radiation, winds and eventually supernovae disperse the parent cloud. The balance between these processes sets the star formation rate of the whole galaxy, and it is still not fully understood.

The stages of collapse

The first phase is isothermal: the gas radiates through molecular lines and dust emission and stays near ten kelvin while its density rises by many orders of magnitude. When the central density reaches about ten to the minus thirteen grams per cubic centimetre the core becomes opaque, and collapse becomes adiabatic: temperature rises with compression and a first hydrostatic core forms at a few hundred kelvin. When it reaches about two thousand kelvin, hydrogen molecules dissociate, absorbing energy, and the core collapses again to form the true protostar at a temperature of tens of thousands of kelvin and a size of a few solar radii. It then contracts on the Kelvin–Helmholtz timescale, radiating its gravitational energy, while the disc feeds it and the jets carry away angular momentum.

The pre-main-sequence clock

The Kelvin–Helmholtz time is roughly the gravitational binding energy divided by the luminosity. For the Sun’s mass and radius that is about thirty million years; for a fifteen-solar-mass star, whose luminosity is tens of thousands of times greater, about a hundred thousand years. Massive stars reach the main sequence while still buried in their birth cloud, which is why they are seen mostly by the glowing gas they ionise around them.

Where the mass goes

The initial mass function, the distribution of masses at birth, peaks at a few tenths of a solar mass and falls steeply above one solar mass: a cloud makes roughly ten times fewer stars at ten solar masses than at one. Objects below about 0.075 solar masses cannot sustain hydrogen fusion and become brown dwarfs; those below about thirteen Jupiter masses cannot even fuse deuterium. The dividing line between the largest planets and the smallest stars is a matter of physics, not of where an object formed.

Frontier

The recipe

Why the initial mass function has the shape it does, and whether it is the same in every galaxy and every epoch, is an open problem with real consequences: the mass distribution of stars sets how much light a galaxy makes, how many elements it forges, and how fast it uses its gas. Simulations that follow turbulence, magnetic fields, radiation and chemistry together are beginning to reproduce the observed function, but the ingredients that matter most are still argued over. Active research.

Watching it happen

The Webb telescope sees through the dust that hides collapsing cores from visible light, and ALMA maps the discs and jets at millimetre wavelengths. Together they are turning the stages above from theory into a photographed sequence, with surprises: discs that fragment into companion stars, planets forming earlier than models allowed, and streams of gas feeding discs from outside. The sequence is right; the timing and the detail are being rewritten.

Transcript and shot list

Target runtime about 5 minutes. Built as follow one cloud: a single knot of cold gas from thin haze to ignition, with the argument between gravity and pressure settled at every step. Shot types: ANIM is rendered from code with Manim, AI is a generated shot from Higgsfield with the shared style reference, REAL is agency imagery with credit, CAM is the narrator.

[00:00] S01 · REAL · The Orion Nebula, wide field (NASA, ESA, Hubble or Webb; confirm credit line).

One atom per cubic centimetre. You could not build a vacuum that good in any laboratory on Earth. And that is what stars are made out of. This is the Orion Nebula, thirteen hundred light-years away, and it is making stars as you watch it.

[00:21] S02 · ANIM · Cosmic calendar; a marker at 5 January labelled “first stars” and a bar running to midnight on 31 December labelled “still going”.

Star formation started around the 5th of January on the cosmic calendar, and it has never stopped.

[00:29] S03 · ANIM · A galaxy’s gas as faint haze; it gathers into filaments and dark clouds; a temperature readout shows 10 K; hydrogen atoms pair into molecules.

A thin gas spread through a very large volume adds up. The Milky Way holds billions of Suns’ worth of gas between its stars, and gravity, turbulence and the shocks of exploding stars gather it into clouds. The densest are cold, ten degrees above absolute zero, and dark, full of dust that blocks light. So cold that hydrogen atoms pair up into molecules. A giant one spans a hundred light-years and holds a hundred thousand Suns’ worth of gas.

[01:05] S04 · ANIM · A cloud with two arrows: gravity inward, pressure outward; sliders for mass, density and temperature; the cloud collapses when the cold, dense setting is reached.

Inside the cloud, two forces are at war. Gravity pulls everything inward. Pressure, from the warmth of the gas, pushes out. In 1902 James Jeans worked out who wins. Gravity, if the cloud is massive enough, dense enough and cold enough. Pressure otherwise. A warm, thin cloud sits for ever. A cold, dense knot of a few solar masses can’t hold itself up. It falls.

[01:35] S05 · ANIM · A cloud collapsing in slow motion; a clock runs past a free-fall time; turbulence and field lines hold it; only a small fraction turns into stars.

Left to gravity alone, a knot would collapse in a few hundred thousand years. Real clouds take far longer, and turn only about one percent of their gas into stars in that time. Turbulence holds them up. Magnetic fields stiffen them. And the moment a star forms, its light pushes the remaining gas away. Star formation isn’t a flood. It’s a slow leak.

[02:04] S06 · ANIM · A knot falls; it stays cold and dark; the centre becomes opaque; the temperature readout climbs; a glowing protostar appears.

When a knot does fall, it stays cold at first, radiating away the heat of compression through its dust. Then the centre grows dense enough to trap its own light. The heat has nowhere to go. The temperature climbs, and pressure finally pushes back. A protostar: hot, glowing, shrinking, shining not by fusion but by falling in on itself.

[02:31] S07 · ANIM · The infalling gas spins up and flattens into a disc; jets shoot from the poles.

The cloud was spinning slightly, as everything in the galaxy is. As it falls, it spins faster, like a skater pulling in her arms, and the spin flattens the gas into a disc. Gas spirals inward through the disc. Some is flung out along the poles in jets you can see light-years away.

[02:56] S08 · REAL · The ALMA image of the HL Tau disc with its rings and gaps (ALMA, ESO, NAOJ, NRAO; confirm credit line).

In 2014 the ALMA telescope in Chile photographed such a disc around a star called HL Tau, less than a million years old. It was already carved into rings and gaps: the first signs of planets. That disc is where a later chapter begins.

[03:16] S09 · ANIM · The protostar shrinks; a temperature dial passes one million, then ten million; fusion lights; the shrinking stops.

The protostar shrinks and heats for millions of years. At a million degrees it briefly burns the trace of deuterium left from the first three minutes. At ten million, hydrogen itself begins to fuse, and the energy is enough to hold the star up. The collapse stops. The star has arrived on the main sequence, in balance, where it will spend most of its life. For a star like the Sun that journey takes thirty million years. For a star of fifteen solar masses, a hundred thousand.

[03:56] S10 · ANIM · A small object below the fusion threshold glows dimly and fades; label: brown dwarf, 8 percent of the Sun’s mass.

Below about eight percent of the Sun’s mass, the core never gets hot enough. The object glows faintly from its own contraction, then cools for the rest of time. A brown dwarf. A star that didn’t quite make it.

[04:14] S11 · ANIM · One cloud producing a spray of stars: many small, a few medium, one giant; a counter for the Milky Way: 1.65 Suns per year.

A single cloud makes stars of every size at once, but not equally. For every Sun it makes several smaller, fainter stars, and only rarely a giant. The whole Milky Way turns about one and a half Suns’ worth of gas into stars each year. A modest rate, kept up for ten billion years.

[04:39] S12 · ANIM · Labels: ESTABLISHED for the physics of collapse; ACTIVE RESEARCH for what sets the recipe of masses.

The scorecard. That stars form when gravity beats pressure in cold, dense clouds, and how the collapse proceeds: established, and now photographed stage by stage. Why the recipe of masses comes out the way it does, and why the process is so inefficient: active research.

[05:00] S13 · AI into ANIM · Back to the Orion Nebula; a single new star brightens inside it; the calendar returns.

So the space between the stars isn’t empty. It’s the raw material, and it’s still being used. Somewhere in Orion tonight, a knot of cold gas is losing its argument with gravity. Next lesson: what a star actually is, and why it doesn’t blow itself apart.

Shot list

One AI shot, ten code-rendered shots, two agency images. Estimated Higgsfield use: 2 to 4 generations including retries.