Astronomy & Celestial Mechanics
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Molecular clouds — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    The cloud that cannot hold itself up

    A cold cloud collapses when gravity beats pressure, and the mass at which that happens falls as the square root of the density — so the collapse makes the condition for collapse easier, over and over, until the gas can no longer get rid of the heat. That is why a cloud of ten thousand solar masses makes a cluster and not a star.

    part 1 · galaxies
  2. The one number a cloud cannot change by squeezing. The mass-to-flux ratio in units of its critical value, against column density, for clouds threaded by fields of 3, 10, 30, 100 microgauss. λ below one is subcritical, and the field alone holds the cloud up, and no amount of compression changes that, because squeezing raises the magnetic and the gravitational energy at the same rate and leaves their ratio exactly where it was. λ above one is supercritical and the field is irrelevant to whether the cloud collapses. Each line has slope exactly one because λ is proportional to the column density at fixed field, and each crosses the boundary at 3.9·10²⁰ cm⁻² for 3 µG, 1.3·10²¹ cm⁻² for 10 µG, 3.9·10²¹ cm⁻² for 30 µG, 1.3·10²² cm⁻² for 100 µG. The Jeans mass is a threshold a cloud can cross by contracting; this one is a label it is born with, and the only way past it is to let the field leak out.

    Support that cannot be squeezed away

    A cloud held up by pressure can always be defeated by compressing it, because gravity gains faster than heat does. A cloud held up by a magnetic field cannot — squeezing raises both energies at exactly the same rate, so the ratio a cloud is born with is the one it keeps, and the only way out is to let the field leak.

    part 2 · galaxies
  3. Turbulence stops being supersonic at 0.04 parsecs. The velocity dispersion of molecular gas against the size of the region it is measured over, from σ = 1 (R/pc)^0.5 km/s, with the isothermal sound speed of 10 K gas drawn flat beneath it. The two cross at 0.035 parsecs, which is solved for here rather than quoted: below that scale the motions are subsonic and the gas is supported by its own pressure, above it they are supersonic and nothing thermal is relevant. At ten parsecs the Mach number is 17 and at a hundredth of a parsec it is 0.53. The crossing is the scale at which turbulent support runs out, and it is within a factor of two of the size of the dense cores that actually form stars — which is either the most important coincidence in the subject or the reason cores are the size they are.

    The support and the seed are the same motions

    A molecular cloud's lines are ten times wider than its temperature allows, and the width grows with the size of the region measured. The motions that widen them hold the cloud up as a whole and make the dense lumps inside it — so the same turbulence that delays star formation is what decides where it happens.

    part 3 · galaxies
  4. 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.

    part 4 · galaxies

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