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Milky Way Galaxy

Molecular Cloud Collapse

Molecular clouds collapse to produce the stars we see.  The nature of this collapse is uncertain, and two theories for how a molecular cloud collapses dominate the scientific investigations.

Molecular clouds are susceptible to gravitationally collapse, because gas pressure alone cannot counteract the gravitational force a cloud exerts on itself.  The stability of a gas cloud against gravitational collapse is given by the Jean's length λJ, which is proportional to (T/ρ)1/2, where T is the gas temperature relative to absolute zero and ρ is the gas density.  If the Jeans length of a cloud is smaller than the scale of a cloud, the gravitational force is stronger than the gas pressure, and the cloud shrinks.  As a cloud of mass M shrinks, its scale R decreases, its density increases as M/R3, and its Jeans length changes proportionally as M −1/2T1/2R3/2This last relationship shows that if the temperature rises less rapidly than R−1/2, is constant, or is falling as the cloud shrinks, the Jeans length shrinks faster than the scale of the cloud, the scale of the cloud continues to exceed the Jeans length, and the cloud continues its collapse.

A molecular cloud's temperature is set by the balance of heating from ultraviolet radiation and cosmic rays against cooling by the emission of infrared radiation.  When a cloud contracts, its gas density rises, which increases the rate at which it generates infrared radiation.  At the same time, the higher density of dust within the cloud blocks more starlight, which slows the heating of the cloud.  These effects cause the temperature of a cloud to drop as the cloud shrinks from the 100°K seen in the cool interstellar medium and in the outer layers of molecular clouds to the 10°K found in the cores of molecular clouds.  This drop in temperature as the molecular cloud shrinks ensures that the Jeans length remains less than the scale of the cloud; the cloud must collapse if only gas pressure provides support against the force of gravity.  The nature of this collapse, the inability of gas pressure to rise faster than the force of gravity as the cloud collapses, is similar to the collapse of a massive star to a neutron star or a black hole.

One effect of the rapidly-shrinking Jeans length is that a cloud tends to fragment into smaller and smaller high-density clouds.  If the temperature remained constant, the ratio of the Jeans length to the cloud size would change proportionally as R1/2, so if the cloud decreases by a factor of 4, the ratio of the Jeans length to the cloud size would fall by a factor of 2, and cloud would fragment into of order 8 smaller clouds.  These smaller clouds would then in turn fragment as the Jeans length continued to shrink faster than the sizes of the fragments.  This behavior fits the belief that a molecular cloud fragments into numerous low-mass stars when it gives birth to stars.

Other factors, however, complicate this simple picture of a gravitationally collapsing cloud.  Both magnetic fields and supersonic turbulence within a molecular cloud are sources of pressure that can counteract gravity, and both are seen within molecular clouds.

The magnetic field in a molecular cloud is tied to the ions and electrons within the cloud.  When the ionized gas moves, it carries the magnetic  field with it, and if it is sheared or compressed, the magnetic field it carries is also sheared and compressed, causing the strength of the magnetic field to increase.  Because of this, one expects the magnetic field B to increase as a cloud shrink and as turbulence within the cloud shears the magnetic field.  The magnetic field exerts a pressure on the ionized gas that is proportional to B2.  If the magnetic field becomes strong enough, it can exert a pressure on the ionized gas that counters the force of gravity.

But a magnetic field cannot bring the collapse of a cloud to a halt.  The magnetic field acts directly only on ions and electrons, not on the neutral atoms and molecules that constitute most of a molecular cloud's bulk.  The force exerted by the magnetic field on neutral particles is indirect, through collisions between them and the ions and electrons.  Gravity pulls the neutral molecules through the ions—a process called ambipolar diffusion—and the friction between these two gas components sets the timescale for the cloud's collapse.

Turbulence is a mechanism for converting kinetic energy into thermal energy.  The energy that drives the supersonic turbulence within a molecular cloud can come from the gravitational potential energy of the cloud or from the motions of the gas that formed the cloud.  This energy is first manifested as large-scale motion, but the kinetic energy gradually flows to smaller and smaller-scale turbulent motions, until friction and shock waves on the smallest scales convert this kinetic energy into thermal energy.  The kinetic energy of the turbulence can counteract the self-gravity of a molecular cloud.

The two theories that describe molecular-cloud collapse differ in how they regard magnetic fields and turbulence.[1]  The older of the two theories give precedence to the magnetic fields, while the younger gives precedence to turbulence.  In the older theory, a cloud acquired mass from its surrounding and from other clouds until it becomes gravitationally unstable and collapses.  As it collapses, it generates turbulence and a magnetic field that eventually stabilize it.  The cloud becomes quasi-static, with its contraction governed by ambipolar diffusion.  In the newer theory, molecular clouds form when Galactic winds collide.  The turbulence created when these winds interact is sufficient to prevent the cloud from collapsing; in fact, most of the cloud is gravitationally unbound under this theory.  Within the turbulent gas, regions of high density and low velocity form.  These stagnation points are unstable to gravitational collapse, and they collapse in free-fall, creating stars.  These two theories are similar from the standpoint of molecular cloud longevity, because the collapse timescale in the older theory is only a couple times the collapse timescale for the newer theory.  These theories state that molecular clouds collapse on a time scale of order 10 million years.

One final complication in these theories is that the stars created within a molecular cloud influence the collapse of the molecular cloud.  The new stars heat the molecular cloud sufficiently to increase the gas pressure within the cloud.  This not only can stop the collapse of a molecular cloud, it can cause the molecular cloud to expand.  The creation of stars in a cloud therefore provide feedback that slows the rate of star creation.

The one observational point that both theories must account for is the low stellar birth rate within our galaxy.   The rapid global collapse of molecular clouds would produce stars too rapidly, which is why a theory relying only on gas pressure is untenable.  For the theory that relies on magnetic fields, the slowing of a cloud's collapse by a magnetic field and turbulence and the feedback of star formation on the cloud provide the mechanisms that bring the theory into agreement with the observed star formation rate.  For the theory that relies on turbulence, the star formation rate is limited by the rate at which stagnation points form within the turbulent cloud and by the feedback of star formation.  In both theories, the stars control their own birth rate.

[1]McKee, Christopher F, and Ostriker, Eve C. “Theory of Star Formation,” in  Annual Review of Astronomy and Astrophysics, vol. 45.  Palo Alto: Annual Reviews, 2007: 565–687.

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