Astronomy 218 Building Stars out of Gas clouds Star-Forming Regions Star formation is an ongoing process in galaxies. It is concentrated in a number of star-forming regions throughout these galaxies. Star-forming regions are associated with dark & emission nebulae. Collapsing Clouds The association with nebulae is causal, star formation occurs when part of a dust cloud contracts under its own gravitational force. Typical density in the dense core of a molecular cloud is 12 −3 nmc ~ 10 molecules m .

This equates to a mass density of ρmc = μ mp nmc. −15 −3 −12 −3 ρmc = 1.7 × 10 μ kg m = 2.9 × 10 μ M☉ AU Clearly, tremendous compression must occur to reach the −3 densities of stars. For example, ρ☉ = 1400 kg m . A molecular cloud core of a solar mass would have a radius 6 Rmc ~ 10 R☉ = 4000 AU = 0.02 pc. Collapse Time An estimate of the collapse time can be calculated from Kepler’s law. For a gas particle with orbital semimajor axis a, where M(r) is the mass interior to the particle's position. If the entire cloud is collapsing, M(r) is constant and we can consider the molecule to be on a very eccentric orbit. Then a = r0/2 and the time to reach the center, tff ~ P/2. Note that the result does not depend on the size of the cloud, r0, only the initial cloud density, ρ0. Sound Waves

This estimate of tff indicates how long collapse takes once it starts, but how does collapse start? The gas cloud is in hydrostatic equilibrium, with pressure balancing gravity. Any external push on the cloud is met by pressure waves, which travel at the speed of sound, The travel time for a wave of increased pressure to reach the surface and balance the external push is tpress ~ r0/cs.

If tpress < tff the pressure can respond to a perturbation and maintain hydrostatic equilibrium, but if tpress > tff, the equilibrium is unstable. Jean’s Length

The relationship tpress > tff leads to a limit of the size a cloud that is stable, which depends on density and temperature. A cloud larger than the Jean’s length, rJ, is prone to collapse when perturbed. For molecular hydrogen, μ = 2 & γ = 7/5. The corresponding mass is the Jean’s mass, MJ. Horsehead Nebula The Horsehead Nebula (Barnard 33), ~1 pc across and with a mass of 1000 M☉, is too large to collapse into a single star.

Instead small dense cores, with M ~ MJ within the nebula that will individually form stars. Fragmentation The first stage of star formation is the contraction of a large interstellar cloud, probably triggered by a shock or pressure wave from a nearby star. As it contracts, opacity and turbulence and gravitational instability cause the cloud fragments into smaller pieces with M ~ MJ. Star Clusters As a result of this fragmentation, stars don’t form individually, but in clusters of hundreds to thousands, like this star-forming region in the Orion Nebula Angular momentum At the large sizes of molecular gas clouds, even small rotational velocities produce significant angular momentum. For example, the Horsehead nebula as a −1 whole is rotating at ʋrot ~ 1 km s . The dense cloud core −1 rotate more slowly, ʋrot ~ 0.1 km s During the cloud’s collapse, conservation of angular momentum magnifies ʋrot

6 5 −1 ≈ 10 ʋ0 ≈ 10 km s Observations have not revealed any young stars with rotation rates as rapid as 105 km s−1, indicating that something is removing angular momentum from stars as they form. Protoplanetary Disk The collapsing cloud’s million-fold decrease in radius is altered by the attendant increase in rotational velocity, turning the cloud into a disk. For matter orbiting in the disk, gravity balances the centripetal acceleration

This limits the collapsing disk to β Pictoris, a radius Beuzit, et al. Grenoble/ESO until it can shed its angular momentum. Transferring L⃗ Angular momentum can not be “lost”, it can only be transferred. In the disk, inner regions are moving more quickly than outer regions, thus viscosity will tend to drag the outer regions forward. This increases the outer regions velocity, transferring angular momentum outward.

Magnetic fields in the disk, which were organized and concentrated during the collapse, provide a magnetic equivalent of viscosity. A wind from the disk, streaming along the magnetic field can also carry away angular momentum. Protostar As individual fragments collapse, their density rises, making them opaque. This raises the temperature and inhibits further fragmentation. By the time the fragment has collapsed to 100 AU, n ~ 1018 −3 m , Tc ~ 10,000 K. Over ~100,000 years, the protostar will collapse further in radius to 1 24 −3 AU, with n ~ 10 m , 6 Tc ~ 10 K. The protostar appears on the H–R diagram as its surface nears 3000 K. Disk & Wind Even before a protostar is really a star, they have very strong winds. These winds clear out the gas from the nebular disk over a volume roughly the size of the solar system, leaving the debris disk to form planets.

0.1 pc In the crowded surroundings of a star forming region, sometimes winds from neighboring stars interact. Herbig-Haro Objects The polar jets from a protostar carry significant mass, energy and angular momentum into the molecular cloud. Collisions between the jets and gas cloud produce Herbig–Haro objects. Seeing Protostars It is very difficult to see protostars directly through their shroud of gas and dust. The thickness of the protoplanetary disk, 0.001 parsec ~ 200 AU, is comparable to the diameter of the protostar.

0.001 pc 0.001 pc

The protostar is gradually revealed as its winds disperse the gas in the disk. Pre-Main Sequence Once the cloud has become a protostar, it is in hydrostatic equilibrium. A protostar’s luminosity results from gravitational contraction and the timescale of its contraction, the Kelvin-Helmholtz timescale. Once accretion onto the star stops, stabilizing its mass, the star is considered a pre-main sequence star. Hayashi & Henyey

The remainder of the star’s Hayashi lifecycle will play out on the track H–R diagram. Henyey track Initially the protostar is convective throughout and it follows the Hayashi track in the H-R Diagram as it contracts. Over ~106 yrs it reaches 28 −3 10 R☉, with n ~ 10 m , 6 Tc ~ 5 × 10 K. 7 7 Over ~10 yrs, Tc → 10 K and the core becomes radiative. From here, contraction follows the Henyey track. Nuclear Burning

6 Near the top of the Hayashi track, as Tc → 10 K, deuterium burning (2H + 1H → 3He + γ) commences. Deuterium burning establishes steep temperature gradients, maintaining convection. Convection brings deuterium-rich matter to the core until deuterium is exhausted throughout the star. Later, once the core reaches 10 million K, hydrogen burning begins, though it initially provides insufficient energy to fully balance gravity. The star therefore slowly contract, its radius decreasing by ~25% over 30 million years, until it reaches equilibrium with 7 Tc = 1.5 × 10 K. The star has reached the main sequence. Formation of Sun-like Stars This table summarizes the stages that a sun-like star goes through in the process of forming from an interstellar cloud. Note the increase of the timescale with density and the extreme rise of the central temperature. Stars of Other Masses This H–R diagram shows the evolution of stars of different masses.

For stars M < ½M☉, the core remains convective, so these stars follow the Hayashi track all the way to the main sequence.

For stars M > 3 M☉, the core becomes radiative much earlier, transitioning to the Henyey track sooner. This inhibits 2H exhaustion. Failed Stars Not all collapsing molecular cloud cores produce stars. Some fragments are too small for fusion ever to begin. While they initially radiate gravitational energy from their collapse, they quickly cool off and become dark. A protostar must have 0.08 solar masses (~ 80 times the mass of Jupiter) in order to become dense and hot enough that fusion via the pp-chain can begin, allowing the star a long luminous life. For collapsing clouds of mass between 12-80 Jupiter masses, deuterium burning allows a brief luminous phases, lasting < 108 years. These “failed star” are called brown dwarves. Observing Brown Dwarves

As with extra-solar planets, brown dwarves are difficult to observe directly, as they are very dim. These images show binary-star systems believed to contain a brown dwarf. The difference in luminosity between the star and the brown dwarf is apparent. Clearing Clouds With hundreds to thousands of stars produced in close proximity from a single interstellar cloud, formation of a star cluster has a tremendous effect on the local environment. Star Formation provoked Star formation can trigger a chain reaction within a molecular cloud. Shock waves from nearby star formation can provide the push needed to start the collapse process in another interstellar cloud. Other triggers: Planetary nebulae Supernovae Density waves in galactic spiral arms Galaxy collisions Construction by Destruction This is the part of the Carina Nebula, where newly formed stars are tearing apart their natal molecular cloud. The forces of stellar winds and radiation are not wholly destructive, forming stars in the compressed cloud. Here 2 pair of Herbig-Haro objects jetting from the cloud attest to new born stars within. Next Time Life of the Sun