Milky Way Galaxy

Cold Clouds in the Warm Gas

Looking across the Galactic plane, we see cool, dense clouds floating in a warm, tenuous gas.  The contrast between these two states of the interstellar medium is striking.  There is no gently transition from the below 100 Kelvin temperatures of the cool clouds to the several thousand degree Kelvin temperatures of the warm gas. The change from several tens of atoms per cubic centimeter of the cool clouds to the 1 atom per cubic centimeter of the warm gas is abrupt.  But despite these rapid changes with temperature and density, the pressure within the cool clouds is about the same as the temperature within the surrounding warm gas.  Why does the interstellar medium simultaneously have two very different temperatures and densities while having a single pressure?  The current answer relies on a feedback loop involving the creation of massive stars.

In both the cool clouds and the warm gas, radiative heating is balanced by radiative cooling.  The predominant source of heat is ultraviolet radiation from the most massive main-sequence stars.  These O and B stars are born together in small groups called OB associations; The bright stars in the Orion nebula are a prime example of such an association.  The radiation released by these short-lived stars is absorbed by dust grains.  When an ultraviolet photon strikes a dust grain, it kicks an electron off of the grain.  The energy carried by this free electron is then distributed among the gas atoms through collisions that excite the electrons bound within the atoms.

The heating of the gas is offset by the radiative cooling of hydrogen, helium, and trace elements.  At low temperatures, the radiation is predominantly line radiation (light released with a characteristic wavelength when an electron drop from a high quantum state to low quantum state within an atom) from hydrogen and oxygen. In this regime, small changes in temperature lead to large changes in the rate at which energy is emitted.  At high temperatures, the cooling is predominately from Si II (singly-ionized silicon) and again small changes in temperature cause large changes in the cooling rate.^[1]  Between the low temperature and high temperature regimes is a regime where hydrogen and oxygen are unimportant radiation emitters compared to Si II and the rate at which Si II emits radiation is insensitive to temperature; in this regime, large changes of temperature cause only small changes in the cooling rate of a gas.  It is this rather esoteric fact of physics that allows the interstellar gas to display simultaneously the two states we see.

At very low densities and at very high densities, the equilibrium pressure of interstellar gas rises as the density rises; the temperature is stable in these regimes.  In these density regimes, a small rise in temperature causes a large rise in the cooling rate, which drives the gas back to the equilibrium temperature.  But over an intermediate range of densities, between about 1 particle per cm³ and 10 of particles per cm³ for the amount of ultraviolet radiation in the local Galactic disk, the pressure drops when the density rises.  This is the regime where Si II dominates the cooling while being insensitive to temperature changes.  Gas in this regime is thermally unstable.  If the temperature is slightly above the equilibrium temperature, the cooling rate falls below the heating rate, and the temperature keeps increasing.  If the temperature is slightly below the equilibrium temperature, the cooling rate exceeds the heating rate, and the temperature drops further.  This means that if the density of the interstellar gas is in this unstable regime, the gas will not be thermally stable until in reconfigures itself into two states.^[2]  For the amount of ultraviolet radiation in the local Galactic disk, the warm gas is thermally stable for densities below 1 particle per cm³, and the cool gas is thermally stable for densities of several 10s of particles per cm³.  With an average density a little over 1 atom per cm³, we are at the lower end of the unstable regime, so the gas segregates into thermally-stable low-density and high-density regions.

It may seem odd that we just happen to live in a galaxy in this special regime of cool clouds floating in a warm gas.  This environment, however, is not thought to be a consequence of luck, but rather a consequence of a feedback loop involving star formation.

The density range over which a gas is thermally unstable depends on the amount of ultraviolet radiation in the Galactic disk.  Increase the amount of ultraviolet radiation by a factor of ten, and the density range of thermal instability shifts upward by a factor of ten.  But the ultraviolet radiation is predominately from short-lives stars.  An OB association only produces large amounts of ultraviolet radiation for about 15 million years.  The Galactic disk contains large amounts of ultraviolet radiation only if new stars are continually born.  But where are stars born?  They are born in cold molecular clouds such as those of the Orion nebula, which form from the cool clouds.  Without the cool clouds, star formation should cease.

It is this association of star formation with cool clouds that provides the feedback loop that gives us what we see.  Let us imagine that the interstellar gas had a density that is below the range of thermal instability.  In this regime, the gas would be warm and tenuous, so it could not give birth to new stars.  As the large O and B stars ceased generating ultraviolet radiation as they age, the rate at which interstellar gas is heated would fall, causing the temperature to fall.  Because the gas is supporting itself against the gravitational force of the Galactic disk?the gas is effectively an atmosphere in the disk?the density of the gas would rise.  At the same time, the density range for thermal instability would shift to lower densities.  Eventually these changes would cause the interstellar gas to become thermally unstable.  When this happens, cool, dense clouds would form, and new stars would be born from them.  These new stars would emit enough ultraviolet radiation to balance radiative cooling and to keep the gas in its two-state configuration.

On the other hand, if there were low amounts of ultraviolet radiation in the Galactic disk, so that the interstellar medium would be in a single, thermally-stable state with a density above the regime of thermal instability, prodigious number of stars would precipitate out of the gas.  These stars would increase the amount of ultraviolet radiation, raising the temperature and lowering the density of the interstellar gas, and shifting the density range for thermal instability to higher values.  The interstellar gas would become thermally unstable, so part of the gas would become warm and tenuous.  Again, the interstellar gas would find itself in the two-state regime.  In this state, the rate of star formation would slow until radiative heating and cooling were in balance.  In short, the cool clouds exist with the warm gas because the cooling of the gas is in equilibrium with the star formation rate.

All of this depends on the elements created by stars and supernova shock waves over billions of years.  Without carbon and silicon to form dust and atoms of oxygen, and without silicon to cool the gas, the heating and cooling of the interstellar medium would be quite different from what we see.  The Galaxy of the past, when the interstellar medium was nearly devoid of elements heavier than helium, would have looked quite different from the Galaxy of today.