Basic Notions of Star Formation Theory

Stars form from the contraction of large, cold, low density gas and dust clouds which exist between the area between the stars (the Interstellar Medium, ISM) in our Galaxy. This is a rather amazing process in that it takes a cloud whose temperature is 10 - 50 Kelvins, whose density is thousands to millions of particles per cubic centimeter, and whose radius is initially around 1 parsec (3.26 light years), and shrinks it down to form a Main Sequence star -- objects with central temperatures of millions of Kelvins, central densities on the order of 10**26 particles per cubic centimeter, and radii of a million or so kilometers (10**(-7) parsec or 3 light-seconds!).

The process is driven by gravity.

• The clouds have low pressures due to their low densities and temperatures===>clouds will easily get out of hydrostatic equlibrium. When gravity wins, the clouds contract.

  • We can find a simple criterion for collapse by examining the hydrostatic equilibrium. Consider a cloud with central pressure P, mass M, radius R, where the individual gas molecules have a mass m, density N x m, and temperature T.
    • In equilibrium, DP/DR = -GM x density /R**2

      So, for collapse to occur the r.h.s must win. To get a rough feel for this criterion, note that density = N x m ~ M/R**3 ===> R ~ (M/N)**1/3 so that the criterion is

      M**(2/3) > P / N**(4/3) / (G m**[4/3]) ===> M > around M(Sun)

      for T ~ 10 - 50 Kelvin, N ~ 1,000 - 1,000,000 per c.c., and m ~ 1.7 x 10**(-24) grams.

      That is, for a given pressure and density, a cloud must have a mass greater than the above limit in order to become graviationally unstable and form a star. The above limit on the mass is known as the Jeans' Mass

  • In general, ISM clouds are in equilibrium and some sort of trigger is required to start the collapse. The trigger works to increase the density of the cloud by compressing it which increases the inward pull of gravity.

    • Various triggers have been proposed:
      • spiral arms of galaxies
      • shock waves generated by dying stars (supernovae)
      • winds and radiation from massive young stars
      • ..., ?

  • Once the collapse begins, the star keeps collapsing for roughly a free-fall time. The collapse does not slow down because the density of the cloud is so low that the energy released by the collapse (compression) is able to freely escape and so the cloud does not heat up!!
  • The initial collapse only slows after the cloud becomes dense enough to start trapping the heat generated by compression.
  • After this point, the star contracts more slowly (on a thermal (heat loss) time scale); increasing the pressure and density in its core.
  • The slow contraction continues until a temperature of a few million degrees is reached in its core whereupon hydrogen burning is ignited. and the cloud becomes a star (settling onto its place on the Main Sequence

  Some Comments on the General Process

  The preceding discussion concerned the formation of single stars. However, more than 50 % (and perhaps up to 80 %) of all stars are in mulitple (double star, triple star, quadruple star, ... ) star systems and thus an important point to try and understand is how do we form multiple star systems. Do binary star systems form by captures of random stars or do the stars in the systems form at the same time from the same cloud?

  • P(orbital) > 100 years, M(1)/M(2) is roughly the same as for indiviual stars observed in the Galaxy ===> stars probably form as individual stars, either because the binary system is so large that they form essentially as individual stars or because they formed in different regions and simply were captured into the binary system.
  • P(orbital) < 100 years, M(1)/M(2) ~ 1 ===> the stars in short orbital period binary star systems probably form as a unit.
  The theory of how individual stars form is in fairly good shape. The details of how binary stars form is much less secure (for example, see the Durisen and Tohline filmstrip).