Self-Regulation of Star Formation in Disk Galaxies

Many different physical processes contribute in shaping galactic "ecosystems."  To understand galactic structure, morphology, and evolution, a key question is what regulates the star formation rate.  Star formation converts gas - the original "raw material" of the universe - into stars. Because stars impact their environment, the rate at which gas can collapse to make new stars is affected by the previous generation of star formation.

Here, we introduce the "actors" in the galactic pageant, and describe new research that has begun to explain how star formation regulates itself.

As seen in both the contemporary, nearby Universe and looking back to early epochs,
star formation
takes place primarily in disk galaxies.

These galaxies are flat, and when seen "face-on" often show twin-armed spiral patterns that swirl outward from the galactic center. Views of these arms with optical and ultraviolet telescopes (as in M83, right and below) show concentrated clumps of luminous star-forming regions.

Star-forming regions (red clumps in the M83 image below) host clusters containing thousands of stars, including many stars 10 or more times as massive as our own Sun. These massive stars emit prodigious radiation, which heats and ionizes the surrounding gas, creating "HII regions" locally.  

A substantial amount of radiation also escapes from star-forming regions, to heat the interstellar medium (ISM).

M83 (HST)


M83 (NGC 5236)
the Southern Pinwheel galaxy     
(courtesty of ESO)

              Trapezium (VLT)

Low mass, low-luminosity stars like our Sun are the most common in galaxies.
Because massive stars have short lifetimes (10 Myr) compared to low-mass stars (1000 Myr or more), high mass stars are concentrated in young, star-forming regions (like the Trapezium cluster in the Orion constellation, left). Over time, dispersal of clusters distributes the surviving low-mass stars throughout the galactic disk.  

Forming star clusters are surrounded by dense clouds of molecular gas and dust.  The stars in the cluster originate as the densest portions of the cloud, which collapse under their own weight.

The Trapezium cluster
(above) is also shown in the image to the right, where it is embedded in its birth cloud. This cloud, part of the Orion A molecular cloud in the southern part of the constellation Orion (below), is observed by the Spitzer Space Telescope (right) and the IRAS telescope (below) in the infrared radiation from warm dust.


  Orion IR

The giant molecular clouds (GMCs) where star formation takes place are the densest, coldest parts of the interstellar medium (ISM).  Because most of the gas is only about 10 degrees Kelvin above absolute zero, it is invisible in optical images.  With radio telescopes that can detect emission from the molecules at mm wavelengths, the cold gas comes into view.

Molecular gas is concentrated in the spiral arms of galaxies, as seen in the maps of the Whirlpool Galaxy (M51/NGC 5194) below. In most galaxies, the atomic medium is the main reservoir of interstellar gas.  The atomic medium is typically more spatially distributed than the molecular medium.


  Multiwavelength M51 (image courtesty S. Vogel/UMD)


Orion giant molecular cloud seen in CO emission, along with an optical image of the same region (image credit: CfA, Tom Dame)

When massive stars die, they explode as supernovae (SNe). The explosion blasts into the surrounding interstellar gas, with shock waves heating and accelerating the gas to hundreds of km/s.  Over time, the expanding supernova remnant shares its energy with gas over the whole thickness of the galactic disk. The shocked gas eventually cools and returns to the normal temperature of the ISM (100-10,000 K), but the momentum imparted by the supernova makes the gas continue to expand outward.  The energy from many expanding supernova blasts combines to generate turbulence in the interstellar medium. 

Cass A SNR

Cassiopeia A supernova remnant, as seen in X rays (Credit: NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.)

To model the ISM and star formation theoretically, we must consider how the gas in a galaxy evolves.  Gas is vertically distributed throughout the disk, but the ISM is far from uniform. Images of our own Milky Way (below) show what the emission from the gas, dust, and stars in the disk looks like "edge-on".

      milky way

We use computational models to follow the evolution of gas in a galaxies like the Milky Way. 

In our numerical models, we consider a small section of the disk, so that we have enough resolution to follow the details of the gas motions.

The movie below shows an example of gas evolution for conditions similar to those in the "Solar neighborhood" in our own Milky Way. The total duration of the animation represents approximately two galactic orbits, or ~500 Myr. The movie shows a radial-vertical slice through the interstellar medium (1kpc radial x 500 pc vertical dimensions).

In the simulation, we initially start with smooth conditions and a uniform temperature.  However, due to a process called thermal instability (see here for a description of our research on this topic), the gas rapidly separates into a distribution of cold, dense clouds surrounded by a warm, diffuse intercloud medium.  The cold clouds are overdense by a factor of 100, so they sink (like a stone!) toward the midplane of the galaxy.  As soon as a thin, dense layer collects at the midplane, the gravity of the cold, dense gas causes it to collapse gravitationally. Since collapse leads to star formation and star formation leads to energy injection from high-mass stars (see above), energy is injected into the gas in the surroundings of these star formation sites.  The feedback energy disperses both the cold, dense gas and the warm, diffuse gas vertically and horizontally, driving turbulence.

As the movie shows, the result is a cycle that is repeated over and over -- although never exactly the same: dispersed gas collapses to the midplane, which leads to star formation in the densest regions, which leads to energy injection from supernovae,  which disperses the gas once again.

Evolution of a radial-vertical slice through the interstellar medium

credit: Kim, Kim, & Ostriker (2011), the Astrophysical Journal

Based on many "numerical experiments" like the one illustrated above, we are able to determine how the detailed properties of star formation and the interstellar medium are expected to depend on the total amount of gas and stars that are present in a local region of a galaxy.

Properties that we can measure in our computational models include the star formation rate, the average velocity dispersion of the turbulent motions, and the proportions of gas in warm and cold phases.  The results from these numerical models are in good agreement with a theory we have developed for "self-regulated" star formation. In this theory, we show that in order for thermal, turbulent, and dynamical equilibrium all to be simultaneously satsified, star formation must continually inject energy into the interstellar medium. The conditions in the interstellar medium and the star formation rate mutually adjust until the rate of energy input from feedback offsets the rate of energy losses. 

The dissipation of turbulent energy heats the interstellar gas, and the gas is also heated by starlight. Energy is lost from the interstellar medium when the atoms, molecules, and dust radiate away the energy they have acquired. This "cooling" radiation (from nearby and distant galaxies) is observed using optical, infrared, and radio telescopes.

The star formation rates, turbulence levels, and balance of phases predicted by the theory and found in our computational models also agree with observations of the Milky Way and other nearby spiral galaxies.

Turbulent vertical velocity dispersion in diffuse gas (top), total (turbulent+thermal) vertical velocity dispersion in diffuse gas (middle), total velocity dispersion in all gas (bottom). Velocity dispersions are independent of the star formation rate because driving and dissipation rates scale together.

Credit: Kim, Kim, & Ostriker 2011, The Astrophysical Journal

Star formation rate per unit area vs. gas surface density per unit area, based on numerical simulations (colored points).  Different numerical "series" correspond to different ratios for the mass of old stars/mass of interstellar gas in the input galaxy model.

Greyscale in background shows observations of star formation vs. gas in a sample of nearby disk galaxies, with properties similar to the numerical simulations. Grey contours show observed star formation and gas in far outer disks (which have weaker stellar disks than we adopt for our numerical models). Observational data is from Bigiel et al (2011).

Credit: Kim, Kim, & Ostriker 2011, The Astrophysical Journal

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    This material is based upon work supported by the National Science Foundation (NSF) under Grant No. AST-0908185. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.