Star Formation in Molecular Clouds : Observation and Theory Frank H. Shu, Fred C. Adams, Susana Lizano 1987 Simon DeDeo, 20 September 2004 “Greatest Hits” Seminar

A “fine tuning” problem? Range of scales important in star formation: But the majority of stars are roughly: Two generic solutions: hierarchical fragmentation of clouds that “happen” to end up in this range or “bottom-up” accretion halted by onset of burning. Three Teasers : 1

The Initial Mass Function In 1987, rather imperfectly known. However, we still rely, in general discussion, on the Salpeter Mass Function of 1955: For stars between 0.4 and 10 solar masses. A power-law has no features! But, by 1986, features in the IMF were suggested at 0.3 and 1.2 solar masses. Is this evidence for different modes of star formation? Three Teasers : 2

Bimodal Star Formation? Briceno et al., 2003 Taurus Star-forming Region Hillenbrand, 2004 Later work has confirmed the high mass end of the Salpeter mass function; the low mass end has proved to have a great deal of structure. Three Teasers : 2

Binary Star Formation For binary systems with periods > 100 years: no correlation between primary and secondary masses. When periods are < 100 years, there are disproportionate numbers of high mass ratios (i.e., nearly equal mass companions.) Fission versus fragmentation scenarios: do the companions form during a state of dynamical equilibrium, or as part of a dynamically collapsing background? Three Teasers : 3

Star Formation Efficiency Star formation rate: Rate of return to ISM: Our galaxy is irreversibly converting the ISM into stars on a timescale of roughly. Is this a problem? There are many variables to consider, but the real lesson is that we either have ISM replenishment (galactic infall), or large-scale changes in the star formation rate history. Something to ponder!

Properties of Molecular Clouds “Orion-like” giant molecular clouds (GMCs.) Large amount of clumpiness: These clumps resemble the “dark clouds” found throughout the disk, e.g., Taurus, Ophiuchi (even denser)...

The Stability of Molecular Clouds Giant Molecular Clouds have short lifetimes, on the order of : dispersed as they cross the spiral arms. Dwarf Molecular Clouds (majority of Milky Way molecules) can survive multiple galactic rotation periods, and live up to ten times longer. GMCs are not necessarily in mechanical equilibrium. DMCs necessarily are: if the DMCs were in the process of collapse: extreme star formation rates.

The DMC Stability Problem The Jeans Mass Thermal pressure cannot balance gravitational attraction or Signal takes longer than free-fall time to cross system The Jeans mass for the clumps found in molecular clouds is a few solar masses; DMCs should be exploding with star formation as entire clouds collapse and fragment. The major question of this talk!

How to support a DMC 1. Rotation? (But no large scale motions seen: observed ~km/s/pc angular velocities insufficient for support in early stages.) 2. Turbulence! : a source of non-thermal pressure. 3. Magnetic fields! : particles don’t cross field lines.

Turbulent Support? Measured CO linewidths suggest sufficient turbulent support — but in the absence of magnetic fields, turbulence should be dissipative: However:.... i.e., we need to regenerate turbulence.

Static magnetic fields I Unlike turbulence, magnetic fields are not easily dissipated. Using virial theorem, or more detailed arguments, one finds a new “Magnetic Jeans” mass: Observational evidence for (and larger!) fields from Zeeman splitting of OH at high column densities....magnetic fields play a key role in supporting DMCs!

Static magnetic fields II Collapse along field lines is not suppressed, however: Jeans-like contraction until thermal pressure can balance gravity again: Static fields alone would lead to molecular pancakes, not molecular clouds! (Observations show relatively ordered fields.) B field

Static magnetic fields III Consider this “Magnetic-Jeans” critical mass again: As the cloud collapses along the field lines, R decreases; the critical mass thus decreases, and fragmentation can occur perpendicular to the field lines. The pancake crumbles.

MHD Waves in Molecular Clouds Take a wave traveling perpendicular to z-axis: The force per unit volume will be: This averages out over one cycle to: Comparable to static field support when: Induced current force along static field line

Magnetic Fields and Turbulence Magnetic fields are the key ingredient in explaining the observed turbulence. We see from CO lines that there is a significant amount of turbulence in a molecular cloud — enough to support the cloud against collapse. But, naive arguments show that turbulence should dissipate rapidly. MHD waves provide a way for turbulence to be constantly regenerated!

Stellar winds? Cloud Collisions? Expanding HII regions? Supernovae? One important criterion: more sources inside the cloud than outside — otherwise, the cloud would compress! Further discussion of these issues, and other interesting phenomena (e.g., Magnetic braking) left to another class. Sources of MHD Waves

Ionization Fractions Need to couple the molecular cloud to the field lines! Cosmic ray ionization is balanced by two body recombination in the dense cores. Putting this together, and including dust grains, we find a typical ionization fraction of: i.e., totally tiny! The way in which the ions couple to the bulk of the material will be a crucial factor in determining how magnetic fields influence evolution.

Ambipolar Diffusion Neutrals are supported against gravity only by the frictional drag they experience against the ions. “Terminal velocity” is reached when the Lorentz force is balanced by the drag force Ions scatter rarely and are tied to the field. The terminal velocity is roughly: Hence, ambipolar diffusion happens slowly relative to dynamical processes.

What we have so far: DMCs must be in mechanical equilibrium, but Are much larger than their Jeans mass. Static and dynamic magnetic fields are the crucial ingredients; they lead to a new “Magnetic-Jeans” mass much larger than the thermal Jeans. Ambipolar Diffusion is a crucial part: the ionization fractions for molecular clouds are tiny! This sets the scale for “slipping” against the field. (without Ambipolar diffusion, clouds can never collapse!)

How DMCs fragment Two regimes: Supercritical: surface mass density is high enough to lead to contraction anyway. Generally associated with high-mass star production as in Orion. Subcritical: more commonly seen in the DMCs. Collapse timescales are governed by the rate of ambipolar diffusion. Star formation rate is significantly slower. AD support may continue until very high densities, when ions finally disappear.

Onset of Gravitational Collapse At high enough densities, magnetic and thermal support finally becomes unimportant. Treatment of the next stage of star formation is thus relatively simple. Expanding “collapse front” Infalling material “Inside out” collapse:

Density Profiles Accretion onto the central instability generically leads to a singular isothermal sphere profile: where a is the isothermal sound speed, The system has a definite temperature, but the density is a power law. Expansion proceeds self- similarly, depending only on the dimensionless parameter:...sound speed modified by turbulence and static fields.

Infall Rate The expanding isothermal sphere has no characteristic mass scale; instead, we have a characteristic accretion rate: Can be “derived” intuitively by considering scales, and assuming that the cloud was marginally supported just before collapse begins (i.e., sound speed was virial):

The Effects of Rotation Observed rotation rates are unimportant for initial support; but as cloud contracts, angular momentum can become significant. A circumstellar disk may form inside the centrifugal radius: For observed km/s/pc rotation rates, we find disks of sizes roughly AU for a half solar mass star.

Joining the Main Sequence? The Kelvin-Helmholtz Timescale: Says how long the protostellar object takes to radiate its gravitational binding energy (i.e., achieve thermal equilibrium.) Remember: infall rate is independent of the mass. Hence, divergent behaviour for high and low mass stars. High mass stars have a shorter K-H, and thus join the main sequence before the end of accretion.

Evolution of Low Mass Stars What halts the accretion process? Shu’s generic story: Protostar is initially a radiative envelope (accreting material of greater and greater entropy.) At around 0.03 solar masses, deuterium ignition; the star becomes convective. Convection & differential rotation lead to a dynamo effect; energy stored in rotation released as a stellar wind: infall reversed. Massive stars do not go convective on D burning.

Empirical Evidence for Deuterium Burning Switch-off Upper envelope: start of deuterium burning

The Post-infall World I (Briefly) Very energetic, bipolar outflows are seen: Herbig-Haro objects (lumps in the outflows) often seen. Presumably not associated with the stellar winds. Collimation is generated by the geometric properties of disk accretion.

The Post-infall World II (Briefly) T Tauri Stars: first optical appearance of low mass stars. High surface activity: the star is still settling down to the main sequence on a convective track. The IR excess found in T Tauri stars suggests a dusty nebular disk of ~100 AU. Passive disk: dust reprocessing stellar light. Active disk: could very high IR excess be produced by intrinsic disk luminosity?

Conclusions & Summary The stages of star formation: Slowly rotating cloud cores: subcritical clumps collapse as the magnetic field leaks out. Supercritical may flatten and fragment. Asymptotic approach to isothermal sphere; onset of inside-out free fall collapse, formation of protostellar disk consistent with observations. Ignition of Deuterium over 0.03 solar masses; under 2 solar masses, convection begins and stellar winds halt accretion: explains (roughly) the turnover in the IMF.

How to Write a 1000-cite Paper Kick off with some teasers (even if you can’t answer them by the end.) Large-scale order, small-scale convenience (cross reference.) Observational stories are more compelling than theoretical ones. Do not get too wrapped up in contemporary battles. Cherry pick the best debates. Mix up deep and shallow coverage.