Astronomy

The Birth of Stars

• Gravitational Collapse
  • The Jeans Mass
  • Protostar Formation
  • Mass Considerations in Protostar Formation
• Optional Website Reading

Gravitational Collapse

Study the picture and description of NGC 6745, the remnant of a two-galaxy collision. Note how the passage of the smaller galaxy along the edge of the larger spiral galaxy has left behind a trail of newly-formed bright-white O and B stars. While the initiating factor of gravitational collapse in this case was direct collision, the result is the same as when gravitational collapse starts more "gently" from the simple proximity of enough dense matter: we get stars.

The Jeans Mass

In a cloud of gas or matter, higher temperatures can create hydrostatic equilibrium, where the thermal energy from collisions create a sufficient outward expanding pressure to create stability against gravitational pull. For gravitational collapse to occur, the gravitational forces must be greater than the radiation pressure, which is why we see proto-stars forming in the cooler clouds of dark nebula. There actually is a formula for the hydrostatic equilibrium of the gas cloud: $$\frac{\delta P}{\delta r}=-\frac{G\rho M_{\mathrm{enc}}}{r^2}$$

Here, P is the pressure, ρ is the density of the enclosed mass M_enc, and r is the overall radius of the cloud. Any change in pressure δP must be countered by a change in radius δr so that the ratio expressed by -GρM_enc/r² remains in equilibrium.

Pressure can be simulated or measured by the rate at which sound travels across the radius of the cloud. A sound wave bouncing from one side to the other creates the outward pressure, moving the radius of the cloud outward by a small amount δP. At the same time, gravity attempts to collapse the cloud by some amount δr. If the sound waves can bounce back and forth and push the cloud outward more than it can collapse under gravity in the same period of time, the cloud remains stable or expands. However, if gravity can collapse the cloud more in the period of time it takes to bounce the restoring sound wave back-and-forth, the cloud will begin to collapse with runaway contraction: t_g < t_sound is the condition for collapse. A cloud is unstable and will undergo runaway contraction, beginning the process of stellar formation, if its mass is greater than a certain amount, called the Jeans mass after Sir James Jeans, who first estimated it as

Most star formation models are now "verified" by computer simulators. The Star Formation page at the University of Arizona shows how some computer simulations align with actual observations.

Protostar Formation

Star formation begins where there is sufficient matter distributed through space (making up the interstellar medium but dense enough to undergo gravitational collapse. We find matter in nebulae, clouds, which generally fall into one of these categories:

• emission nebulae: These clouds are made up of hydrogen and helium gas which have been energized by nearby stars emitting ultraviolet (UV) light. The high energy light hits a hydrogen atom's electron, kicking it up several levels. The electron falls back to a more stable low energy state in several steps, and at each step, it emits some (not all) of the energy it has absorbed from the UV light. Nebulae where the hydrogen retains its electron and remains un-ionized is an H I (H - one) region. If the UV light has a very short wavelength, it will have enough energy to kick the electron entirely out of its atom, leaving the proton and electron as isolated particles, a hydrogen ion H+, and the electron e-. Nebulae with ionized hydrogen are H II regions, and are characterized by light emission in the red visual range that occurs when a free electron loses energy to recombine with a proton and form a hydrogen atom. In general, these clouds are active and hot, and lack the density ρ required to begin gravitational collapse.
• reflection nebulae: These clouds contain dust particles that reflect incoming light without changing its wavelength. Since short wavelength (blue) light scatters more than longer wavelength light (red), these reflection nebula often appear blue or blue-white.
• absorption nebulae: These clouds contain molecules and dust particles that absorb energy but do not emit radiation in the visible range; instead, they act as blackbodies and re-emit energy in thermal (infrared or IR) ranges. These clouds may be both cool enough and dense enough for gravitational collapse to begin and form protostars. Dark nebulae that can form stars take the form of
  • Barnard objects: Dark nebulae with 10 - 100 solar masses of material with dense cores.
  • Bok globules: Dark nebulae with 5-10 solar masses of material, densely packed with dust particles (1%), helium atoms (25%) and hydrogen (74$) molecules.

Nebulae may exist in a stable hydrostatic situation where the internal temperature provides sufficient pressure to prevent gravitational collapse over a long period of time. Several events can, however, create a shock wave that partially condenses a particular area of the cloud, so that a runaway gravitational collapse begins. Trigger events may be:

• A nearby supernova explodes. In this case, the expanding shock wave of material collides with the edge of a nebula, creating a local dense region that begins to collapse.
• Collision of two clouds, which appears to happen in the denser interstellar medium of spiral galaxy arms.
• Nebulae affected by stellar winds from active giant and supergiant stars.

Mass Considerations in Stellar Formation

The amount of mass available in the nebula dictates how many stars may form, and for each star, the mass dictates the internal structure of collapse, heat formation and light emission.

Protostars with sufficient mass to transition to thermonuclear energy generation but with low mass (< 3 M_☉) will not be able to retain all of the mass of their outer layers against the internal heat pressure. These τ Tauri stars expel gases back into the interstellar medium. When the gases hit the surrounding dust clouds that have not yet joined in the collapse, we again have compression which may heat up sufficiently to glow, creating Herbig Haro objects.

Optional Readings

• For further discussion of stellar formation, take a look at Professor Gene Smith's UCSD Astronomy Class lectures.

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