- aake aake Aug 20, 2007 Please feel free to add more comments and alternative answers below!

0. What is the nature of supersonic MHD turbulence in weakly ionized plasmas?

  • -Why does Lighthill's (1955) hypothesis, which implies

  • has Kolmogorov scaling, work so well?

  • ÅN: Perhaps because the hypothesis is correct :-?

  • -How do the density distributions depend on the macroscopic turbulence properties?

  • ÅN: For a non--gravitating, non-magnetized isothermal gas the density PDF is an exact lognormal, with the width proportional to the Mach number. As long as the forcing is per unit mass, there is no dependence on the mean density anywhere in the equations, since both the continuity equation and the equations of motion may be written entirely in terms of the gradient of ln(rho).

  • In the real situation there are three main effects that break the assumptions above: 1) Non-isothermal behavior -- can be both heating and cooling, near barotropic, or not. 2) Selfgravity, and 3) Magnetic fields. All three of these affect primarily the (small) fraction of space where compression is high, leaving the rest of the volume still essentially inertial. This helps to reduce the effects in all three cases, so statistical properties that sample the volume uniformly (e.g. velocity power spectra) are affected only weakly.

  • 1) Equation of state effects primarily act to stretch or compress the wings of the density PDF; if the effective gamma is less than one, for example, the right-hand-side of the PDF is extended relative to the isothermal case, since it becomes easier to compress the gas. 2) Selfgravity also makes it easier to compress the gas, and can also induce collapse, thus stretching out the high-density wing also. 3) Magnetic fields, of strengths typical of star forming regions (as judged by simulations comparing diagnostics, rather than taking point measurements at face-value) tend to dominate the pressure at high density, thus suppressing the high-density wing of the density PDF -- the opposite effect relative to the other two.

1. What maintains the turbulence in molecular clouds?

  • -Is this turbulence almost universal?

  • ÅN: Yes, that is the great advantage of turbulence; it obeys nearly universal scaling laws. Similar (only slightly modified) scaling laws apply to supersonic turbulence and subsonic turbulence (cf. Boldyrev-She-Leveque).

  • -What leads to deviations from universal behavior, such as in regions of high-mass star formation?

  • ÅN: Selfgravity, and a non-isothermal equation-of-state (or rather an active energy equation). But note that the location where this happens, and the amount of mass found at or near (and heading for) that location may still be determined largely by the statistics of turbulence. Massive stars don't form there because God decided to make a deep potential well there; the potential well is deep because turbulence by chance brought a lot of mass there. Remember that observations show that already the cores are massive; this excludes competitive accretion as the reason for the high mass of the final star -- the mass of the core is high because large scale converging flows brought a lot of mass there, and the potential well became deep as a result of this, not as a cause of it!

  • -How does the level of turbulence determine the structure of molecular clouds?

  • ÅN: Larger levels of turbulence (higher sonic and Alfvénic Mach numbers) lead to larger compression, which leads to smaller and less massive cores (under the assumption that shock sheets fragment into structures with aspect ratios that are reasonably independent of the Mach numbers). The inertial motions in most of the volume is NOT affected by the Mach numbers; these motions proceed in the same manner, just faster.

  • -Are internal sources of energy shared throughout a cloud?

  • ÅN: Numerical simulations (e.g. by de Avillez & Breitschwert) show that SN-bubbles expand very rapidly into the ISM space between the cold and dense structures. Because of this, the energy is effectively and rapidly transferred into large scales, from which it can act to compress and massage the cold intervening clouds and maintain turbulence in these structures. Whether a similar mechanism enables the energy from protostellar jets and outflows to spread throughout MCs is less clear. These flows are much less energetic, and much less hot.

  • The scale-free nature of the turbulent power spectra (cf. Larson's v-relation and the paper by Ossenkopf and MacLow) provides strong indirect evidence to the effect that local driving of MCs is of less importance than the turbulent cascade of energy from larger scales

  • Or, to put it differently: The unambiguous presence of turbulent energy at large scales (certainly at least up to scales comparable to the thickness of the galactic disk -- cf. Larson's original 1981 paper) implies that there MUST be a cascade to smaller scales. Such a high-Re flow cannot just stop in "mid-air" (at mid-k), but must continue (as is observed) down to scales smaller than the smallest ones observed. It thus seems that small scale energy sources are either of less importance, or else must have input spectra tuned very carefully as a function of k, so as not to become conspicuous.

  • In this connection it is worth pointing out that one should be careful with the concept of a "sonic scale". The power spectrum (which is normally used to derive at which k the velocity drops below the sound speed) is a spatial average over a very intermittent velocity field, and probably represents a mean of larger velocities (or velocity differences!) near dense structures, and large volumes with very small velocity differences.

2. What is the role of magnetic fields in star formation?

  • -How do magnetic fields affect the rate of star formation?

  • ÅN: 1) By changing the compression ratios and thus the core initial core masses. 2) By providing a coupling to the gas that acts as rubber bands connecting distant patches of gas. This tends to accelerate the gas relative to the star / sink particle, which tends to shut off the B-H accretion, by increasing the velocity of the gas relative to the stars. 3) By (at least momentarily) counteracting collapse. However, this (classical) mechanism is not very effective, since the compression of magnetic fields in shocks tends to leave a lot of gas conveniently lined up for collapse along magnetic field lines.

  • -What is the role of magnetic fields in mass and angular momentum transfer in circumstellar disks, both due to the MRI and protostellar winds?

  • ÅN: 1) The EXTERNAL m.f. is important as a means of obtaining a large effective alpha from MRI in disks; it has been shown that the alpha is proportional to the magnetic field (or its energy density?) in the disk, largely independent of if the field is only generated by the MRI, or if an external source contributes more (perhaps much more) on top. Recent results indicating that the MRI gets weaker with increasing numerical resolution applies ONLY to the case with no external field. 2) The EXTERNAL m.f. is also crucial in the context of the launching of jets and outflows, which probably carry away a lot of angular momentum (and a fair amount of mass).

  • -Why do stars have such small magnetic fluxes?

  • ÅN: Magnetic fields can diffuse out through the cloud as it contracts, and through the disk, both as a result of small scale turbulence and in the disk because the m.f. is actively involved in the MRI, and in the launch of jets.


3. What sets the rate of star formation?

  • -Is the rate different in galactic bulges and in elliptical galaxies from that in disks? (This would imply an evolution with redshift.)

  • BE: I think the evidence indicates that all SF is in disks or pieces of disks: that bulges and ellipticals are mixed up disks, globular clusters form in disks, etc., so we only have to consider SF in the disk environment (ApJ 658 763)


  • ÅN: The reason that most (not all) star formation seems to occur in disks is that it occurs in COLD gas, which has a small vertical scale height. Star formation could possibly also occur in clouds condensing out of the hot coronae that must surround galaxies. Cooling flows in galaxy clusters could result in similar condensations, on a much larger scale. The "absence" of cooling flow evidence is partly a myth; there are examples where it can be seen.

  • -How much does the mean SFE vary with cloud mass, and why is the SFE dispersion so large?

  • BE: the total SFE pretty consistently increases with local density and that is simply a result of hierarchical structure. Since mass varies inversely with density by Larson-laws, the SFE decreases with increasing cloud mass.


  • ÅN: A contributing factor is probably also that the larger the cloud, the more sensitive it is to feedback from hot stars (UV, winds, SNe), since the dynamical time scales of larger clouds become long compared to the time scales of for example SNe from the most massive stars. In addition, the larger the cloud, the more massive are their most massive stars.

  • -How long do GMCs live in different environments?

  • BE: The cores where stars form seem to evolve from start to finish in only a few instantaneous crossing times (at low density this crossing time is long in absolute terms and at high density it is short). GMC envelopes can evolve much more slowly than cores even relative to the crossing time because the envelopes seem to be magnetically subcritical. However, most envelopes are forced to evolve more quickly than this as a result of compression and disruption from SF in the cores (astroph/07072252)

  • ÅN: The controversy over GMC lifetimes seems to a large extent to be a question of words ("a few", "several", ...). Is the difference between a factor of 2-3 and 4-6 dynamical times (which may again have various definitions), or is it really significantly larger than that? In what context can one most easily turn the difference of opinion into numbers? Orion?

4. What determines the IMF?

  • -What determines the characteristic stellar mass?

  • BE: I have not seen any theory for this which get the characteristic stellar mass as constant as it seems to be: considering the large variations in both gas and dust temperatures in different environments. The characteristic mass cannot just be the result of a characteristic density for certain physical processes.

  • ÅN: I would like to see that claim substantiated. ARE the stellar masses really that similar in different contexts? A more robust measure than just a subjective perception of similarity should be used, and one should take care to use homogeneous data (if such exist). Since low mass (BD and VLM) stars are notoriously difficult to detect, and completeness may vary, it may be better to use the median of mass; the mass below (and above) which half of the mass in a sample resides. Since the claim is that the distributions are so surprisingly similar, one should be able to pick any suitable measure, and of course the more robust ones are then to be preferred.

  • As for reasons why the median stellar masses may be rather insensitive to different environments there is an important cancellation effect in the scaling of the turbulent Bonnor-Ebert mass (cf. PP's 'Blackboard Lunch' talk Aug. 20, 2007); it scales with the inverse square root of density and with the inverse of the Mach number (actually Mach number to the -1.1 if taken from numerical simulations). This means that in regions of different size that follow the Larson scaling relations (density inversely proportional to size and Mach number proportional to size to the 0.4), the two effects cancel to a large extent, and leave only a very weak dependence on density.

  • A prediction from that scaling would be that regions with both a low mass density and a low Mach number should have larger typical stellar masses (did anyone say 'Taurus' ?-).

  • BE: The point is that the temperature should vary a lot with position and this affects the BE mass. The Larson laws are just the virial theorem with a constant pressure. And writing the BE mass in terms of pressure (not density or velocity dispersion), all that is left is T. And for dust heating or other processes, the T should vary with position or SF activity. You need a heating and cooling equilibrium from molecules to give a T dependence on density such that the BE mass stays constant. I discussed this in ApJ 1997 486, 944, and quote it here:

  • "Note that the total pressure in a molecular cloud is somewhat constant with time because it equals the weight per unit area of the whole overlying gas cloud in its own gravitational potential. The total pressure is also nearly the same in different regions of the Galaxy because the pressure boundary condition for the cloud comes from the background interstellar pressure, which depends primarily on the weight of the gas layer in the disk. There should be a radial dependence for this pressure because the layer column density decreases exponentially with Galactocentric distance, and the pressure varies approximately as the square of the column density. Thus the background pressure in the Galaxy should vary by a factor of ~2 between ~5 kpc from the center and the solar neighborhood. This would lead to a 50% increase in M_J if T were constant. The molecular cloud thermal temperature should also decrease with Galactocentric radius, however, so M_J might not actually vary much. Typically, the rate of molecular cloud cooling scales approximately with T^2 (Neufeld, Lepp, & Melnick 1995), and this cooling energy ultimately comes from the background radiation and cosmic-ray field. The background field varies approximately as the local column density of stars in a galaxy. The square root of pressure in the denominator of M_J also scales approximately with the local column density. Thus the ratio of T^2/P^½ might not vary much with Galactocentric radius, or it might vary either way by a small amount. Such a variation should show up only in the value of the star mass at which the IMF flattens out (on a log-interval plot). Since observations of this flattening tend to be limited to local regions because of the faintness of the stars there, observations cannot yet constrain the possible variation of M_J with radius in the Milky Way. Other galaxies could show a significantly higher M_J if T is very large (as may be the case in a starburst) and P is not larger than the local value in proportion to T^4."

  • ÅN: I agree, mostly; the lack of evidence is probably partly a result of cancellation effects. In practice it is also difficult to measure the position of the peak of the IMF accurately, so this also contributes to masking remaining dependencies.


  • -Does the IMF of stars today vary with physical conditions?

  • ÅN: Surely it must vary with physical conditions, the question is only "how much", and to what extent there are cancellation effects.

  • -In particular, brown dwarfs may be exponentially sensitive to initial conditions (e.g., the theory of Padoan and Nordlund)

  • BE: the physical condition that makes the most sense is density: high density environments (e.g., dense cluster cores) somewhat correlate with more massive stars (flatter IMFs).

  • ÅN: Such a statement does not seem consistent with the belief that the IMF depends very little on the environment. According to our (PP & ÅN) scaling and reasoning, larger density makes it easier to form low mass stars, so should move the characteristic mass towards lower mass, as should a higher Mach number. A higher density also implies that the very same converging motion scoops up more mass, but this only leads to a shift of the power law (when tagged with individual stars), which does not change the slope (nor can this be used to conclude that the peak shifts to the right). Note that the relative constancy of the (non-dimensional) SFR implies that denser environments have to have an aggregate conversion rate that scales as the square root of the density, for otherwise similar conditions (same size, Mach number and temperature).

5. How do massive stars form?

  • -How do they overcome radiation pressure?

  • ÅN: This has been largely answered by the UCB group's simulations

  • -What are the initial conditions that lead to massive star formation?

  • ÅN: Sufficiently large mass in the cloud, so the IMF extends to massive stars. In any cloud that forms massive stars, the particular location where massive stars will form is singled out by turbulence; these are the locations where the turbulent motions happen to collect a lot of mass

  • -Why are massive stars always formed as part of clusters?

  • BE: there seems to be good evidence that a few percent of O stars do not form in clusters, and this fraction is what you'd get from the cluster mass function if you go down to a 100 Msun cluster; i.e., the O star as a 100 Msun cluster (de Wit et al. 2005; Parker & Goodwin 2007)

  • ÅN: Really?? I find it hard to believe that there are circumstances where O stars form in splendid isolation.

  • -What is the nature of disks and outflows in massive protostars?

  • ÅN: This has been partly answered by the UCB group's simulations, but magnetic fields need to be included in the modeling as well

6. How do star clusters form?

  • -What determines the initial cluster mass function?

  • BE: only the hierarchical structure of clouds is needed to explain the ICMF (hierarchical structure comes from turbulence + self-gravity).

  • ÅN: plus the absence of any other effect depending strongly on size. In this respect the ICMF differs (somewhat) from the IMF

  • -Is the distribution of stellar masses within a cluster established prior to cluster formation, or after the cluster has begun forming stars?

  • BE: the IMF appears to be independent of the cluster environment: e.g., it is the same in Scaled OB associations (unbound) as in super starclusters having the same total mass -- a point made by Deidre Hunter long ago.

  • ÅN: If the IMF is indeed largely determined by turbulent fragmentation then the distribution is determined prior to cluster formation, and even the locations and sizes of clusters is "built-in" (encoded in the initial velocity structure).

7. How do cores collapse and disks accrete at various stages?

  • -what is the resolution of the luminosity problem in low mass star formation? (are early infall rates higher than current predictions?)

  • ÅN: Is there really a problem? Standard accretion scaling is with the square of the mass, which implies that it starts out slowly, and accelerates towards the end. So, since observations are biased towards seeing the more slowly evolving phases the most likely thing to observe is an envelope (with a few solar masses, say) containing a low mass or very low mass protostellar object near the center.

  • -Are purely hydrodynamic (non-self-gravitating) processes important to disk accretion?

  • ÅN: Probably not; disk accretion is probably self-regulating (marginally critical). If the disk is non-selfgravitating it can probably not accrete fast enough to cope with the most rapid phases of infall from the envelope. It's mass then grows, until it becomes self-gravitating, which leads to the growth of non-liner waves and correspondingly increased effective alpha.

  • -How does planet formation affect the evolution of disks and the accretion process?

  • ÅN: A radical idea is that it shuts off / terminates / wipes clean / the disks. In this heretic view the famous 3-10 Myr disks are the FAILED systems that did NOT make planets, while the systems with planets quickly loose their disks, or develop major holes in their disks.


OTHER QUESTIONS

  • A. How do stars form in the Galactic Center?


  • ÅN: The larger temperatures increases the characteristic mass. The higher UV-intensities also require somewhat higher densities before MCs become self-shielded (so they can cool), but this is not a large effect, since optical depth increases exponentially with column density.

  • B. How do binaries form?


  • ÅN: Through fragmentation of collapsing protostellar cores, which typically leads to 1-3 stars per core. The reason that the mass ratio approaches unity for very low mass stars and BDs may be essentially due to the rapidly decreasing likelihood of obtaining sufficient compression for collapse of much lower mass companions.