Journal Club. Review of; “Rapid formation of molecular clouds and stars in the solar neighborhood” Hartmann et al (2001). Nathan Mayne. Where are the post-T Tauri stars? or

Plan: Currently two opposing paradigms of star formation. Slow Star Formation (SSF)Rapid Star Formation (RSF) 1.Basic Intro/discussion of SSF theory 2.Photometric constraints on SF. 3.RSF, the answer? 4.Post-T Tauri stars (PTTS) in the Taurus complex. 5.Dynamical molecular cloud formation. 6.Discussion of age spreads in CMD space. 7.RSF theory and discussion.

7(a). Hypothesis 7(b). Problems with RSF 7(c). Observational support. 7(d). Local/non local triggering. 7(e). Cloud accumulation: Molecular gas shielding, Gravitational instabilities, Collapse timescale, Turbulence, Magnetic fields. 7(f). Simulation of cloud formation. 7(g). RSF summary. 7(h). Discussion. 7(I). Conclusion.

SSF Theory. Shu (1977) and Shu et al. (1987) Giant Molecular Cloud (GMC) are long lived. Supported by magnetic field. Neutral particles carry flux away by slow diffusion through magnetic field-ambipolar diffusion. Ionisation fraction???TIM If M cl > M cr (M cl is mass of cloud, M cr is a critical mass). Large cores and dilute magnetic fields, OB associations. If M cl < M cr small core development, T associations. Timescale of 5-10Myrs for ambipolar diffusion.

Photometric dataCHECK. Timescale for core formation and dispersal of GMC ~ 5-10Myrs. Star forming regions should show age spreads comparable to this, with significant population of older stars. Many more PTTS stars should be found. Young associations should still be embedded in molecular material, due to large dispersal times. Data suggests much smaller age spreads. Distinct lack of PTTS. Most young regions lack significant H 2 density.

Photometry of Taurus star forming region.

RSFCHECK. GMC, large scale turbulent flows. No magnetic field dominance. Supersonic decays rapidly and rapid gravitational collapse ensue. Timescales <3Myrs. Discussed recently in: Ballasteros-Parades et al 1999 Elmegreen 2000 Pringle et al 2001 Hartmann 2001 Hartmann et al 2001 Bunringham et al 2005

PTTS? Star formation is SSF, why are there not many more older objects found with younger PMS populations. Ballasteros-paredes et al 1999 Propose large scale flows of HI atomic gas, 5-10 kms -1 shocking to form dense filamentary H 2 clouds. Star formation takes <3Myr after MHD numerical simulations. Using HI and CO mapping of Taurus and the MHD code, showed that velocity dispersion of HI flow is important factor, not the molecular ‘static’ medium. The density quickly drops and the molecular clouds disperse/become ‘invisible’.

Dynamical molecular cloud formation. Can exist large agglomerations of HI gas, rapidly form H 2 clouds, at high density, collapse and then expand to form HI rapidly. Elmegreen (2000), studied many star forming regions. Found that the formation time was comparable to the t cross of the parent cloud. Support from studies of embedded clusters, retained herachichal structure and time scales not consistent with SSF. Shows structure frozen in on large scale, formed through large scale transient events.

Pringle et al (2001), also explores the problem. Additional problem exist that ambipolar diffusion refers to the slow collapse of only one core, most stars form as binary or multiple systems. From studies of Allen et al of spiral arm gas densities. Shows stars formed in areas of high H 2 density, with the resulting stars disassociating and later ionizing the gas ‘downstream’ to HI and HII. Could be more H2 in ISM, due to deficiencies in CO mapping (local effects) and traditional decay is UV flux. This is measured near the sun, being in a bubble of relatively low density ISM. In addition the H 2 could be shielded by dust an A V ~0.5 is needed for shielding to be effective. This could be present in spiral arms, as the light from emerging stars has to travel longditudinally in the ISM present in the arms. Supported by HI clouds out at high galactic lattitude, translucent ‘cirrus’, at T~8K and densities of n~10 4 cm -3.

“GMC’s appear as the tip of the iceberg..” Hot areas of larger regions of H2, shocks heat up the ISM and it becomes self gravitating. Rapid star formation ensues, no magnetic field effects, with the stars subsequently introducing radiation, leading to rapid dispersal of cloud. If this hypothesis is true should leads to following conclusions; 1.Star Formation in H 2 occurs in t~1-2×t cross 2.Lifetimes of H 2 clouds are short. 3.H 2 clouds do not appear in dynamical equilibrium. 4.Onset time for star formation is << ambipolar diffusion. 5.Most stars are formed in binary or multiple systems, no current ambipolar models of these systems. Understanding and observation of the cold H 2 phase is required.

Errors in Age spread. The main argument for the RSF model is the low age spread assigned to many star forming regions. Two papers have investigated how valid this is. The age spread could still support SSF. The age spread is cannot currently confirm either model. Hartmann 2001 Investigates binarity and includes a general discussion of the error budget with reference to discerning star formation histories. Finds binarity effect is too small to explain observed spread. Burningham et al (2005) Investigates, binarity, photometric errors and photometric varability on the timescale ~ few years. Finds all have small effect on age spread.

RSF Theory. Problems posed: 1.Short disc lifetimes 2.Short GMC lifetimes 3.Small age spread in star forming regions, but observed apparent age spread is still too large. Therefore put forward RSF. Here generally discussed and coupled with numerical simulations.

Key tenets of the hypothesis. 1.Much accumulation and dispersion of gas is done in the atomic phase. 2.Once column density of GMC is high enough to form H 2 and CO, the gravitational force is >> interstellar pressure forces-RSF and turbulent dissipation in limited areas of the cloud complex. 3.Magnetic fields are not strong enough to support cloud and prevent rapid formation of centrally condensed cores. 4.Rapid dispersion after stars form from shock waves and a reduction of shielding by small expansion of cloud. This limits the length of the stars formation epoch and GMC lifetime.

Region a(Myr)Molecular Gas?Ref. (age) Coalsack......Yes... Orion Nebula...1Yes1 Taurus... 2Yes1, 2, 3 Oph... 1Yes1 Cha I, II...2Yes1 Lupus... 2Yes1 MBM 12A...2Yes4 IC Yes1, 4, 5, 6 NGC Yes1 Upper Sco...2-5No1, 6, 7 Sco OB No8 TWA...? 10No9 ? Cha...? 10No10 References.— (1) Palla & Stahler (2) Hartmann (3) White & Ghez (4) Luhman (5) Herbig (6) Preibisch & Zinnecker (7) Preibisch et al (8) de Geus et al (9) Webb et al (10) Mamajek, Lawson, & Feigelson 1999.

Problems with RF. How do star form so quickly? Why does the magnetic field not slow the collapse? Try to show that the conditions to form H 2 from HI in the ISM are similar to the conditions for gravitational collapse: High density. Low temperatures. Low Magnetic fields. Low turbulent support. To show that GMC supercritical.

Observational Data/Support pc across with, velocity dispersion~2kms -1.  t cross =10-20Myrs Ages of all stars <4Myrs (Palla and Stahler 2000).  need an external trigger. Not a lateral propagation at the velocity dispersion. Large scale supersonic atomic flows colliding and forming post shock regions, as before. Coherence set by large scale velocity field, meaning relevant length is shortest not longest. Stellar energy input drives flows over 100pc scales and feeds the turbulence at small scales, local bubbles expand and interact leading to complicated morphology. Taurus cloud complex;

Local/Non Local triggering. Interacting flow-complicated morphology. Local triggering mechanisms cannot explain spatially extended groups. Cloud dormant for long time. Non-local triggering suggest molecular cloud formation and SF at the same time. BHV 99, simulations show HI clouds can form quickly.  Need to consider formation of H 2 from HI and subsequent collapse.

Cloud Accumulation: Molecular gas shielding. Need high column density, shield H 2 and CO from photo dissociation. n H (min)~1-2×10 21 cm -3 A V (min)~0.5-1 Can take long time to build up HI gas, then when H 2 formed-SF. Detailed calculations in E Bergin et al (2001). Using Wolfire et al (1995), HI eqbr in ~10 5 yrs (instantaneous).

Need to find post shock temperature where shielding is important. For average densities, shielding keeps temp<30K, cosmic background heating to ~10K.  expect T~10-30K. Grain effect from private communication. Need < 15K for rapid H 2 formation, observations of grain temperatures, 13-22K. If T grain ~20K, need A V ~0.8 to lower T~15K, for dust to catalyse HI to H 2. Given a sticking fraction, find (Bergin et al 2001), rapid formation of H 2 once HI densities ~10 3 cm -3.

Gravitational instabilities. Model post shock region as infinite, planar, nearly isothermal and relatively static. P c =P e + (  2 G)/2 (P c =central pressure, P e =ext pressure,  =total column density) Column density of self gravity in H 2 cloud is ~ to ext pressure of column density of H atoms. N H ~1.5×10 21 (P e /k) 4 ½ cm -2 Or A V ~0.8(P e /k) 4 ½ ((P e /k) 4 in units of 10 4 cm -3 K) This is comparable to density needed for H 2 formation. So clouds form primed for collapse.

Collapse timescale. From (Spitzer1978), for model situation neglecting ext pressure, critical wave number for stability. k c =(G  )/c s 2 Leads to Jeans length. c =(2  )/k c =0.7T 10 N pc. (N 21 =column density in units of cm -2, T 10 =temperature in units of 10K) Max growth rate,  max (  min =1/  max at 2 c.(Simon 1965) Times of 1-3 Myr valid over wide range of masses and length scales, once shielding conditions are met. Rotations and expansions don’t appear to be limitations at these densities.

Turbulence. Accepted that small scale turbulence, leads to internal pressure support. Typ ~2kms -1  1.Pressures must be 2 orders of magnitude larger than typical interstellar pressures. 2.Turbulent motions damp rapidly. 3.These motions are not purely, or even mostly small scale turbulence. Large scale turbulence aids formation of objects, Klessen et al(200). Even where (1) not applicable (2) and (3) lead to RSF. These measured turbulences contain large scale turbulent energy. LOS.

Magnetic fields: compression and the “Flux Problem”. Pressure from magnetic fields could stop post shock densities rising. True for oblique shocks. Recently Mac low and Klessen (2001), high densities can form at ‘kinks’ in field lines. Left: Field geometry for 1-D steady MHD oblique shock model. Field increasingly tangential as post shock gas cools,  magnetic pressure limits compression. Right: Geometry of clouds in numerical simulations, magnetic fields in~ equipartition strength with turbulent gas pressure. Clouds form in kinks in field lines, dense regions in post shock gas arise where the tangential magnetic field becomes small.

This effect with weak or intermediate magnetic fields from the numerical simulations delays but does not prevent rapid H 2 formation. Collapse to cores, from Nakano and Nakamura 1978); G  c 2 >B 2 /(4  2 ) multiply by area and take square root (4  2 G) 1/2 M c >  B ( M c =mass cloud, and  B = magnetic flux threading) Clouds satisfying these are supercritical, otherwise subcritical. Standard model clouds subcritical. Leads to the large timescale, solution is for clouds to be initially supercritical or close to margin, only small amounts of flux need to be removed (Hartmann 1998, Nakano 1998). Observations support this in even dense cores (Bourke et al 2001).

Super/sub criticality depends heavily on boundary conditions. PVP95, numerical simulations. Condensation in both cases, but collapse only when supercritical. A subcritical ‘box’ will always remain subcritical. Meaning if the magnetic fields initially provide support they can halt the collapse, otherwise can only delay. The size of the region determines whether sub/supercritical, from accumulation length (Mestel 1985). Typ ~ 400pc. Means GMC from this size area are formed supercritical. Williams, Blitz and McKee (2000), show formation of GMC 10 6 M solar from 1cm -3 needs volume ~400pc.

Again assuming sheetlike geometry. P t > B 2 /(8  ) (P t =tangential pressure to confine B, perpendicular to sheet). P t is ~ P e (pressure normal to sheet) else sheet compressed in other direction. Using column densities satisfying H 2 formation conditions. (G  2 )/2>P e  For clouds satisfying H 2 formation have: (G  2 )/2>P e >P t >B 2 /(8  ) This satisfies the collapse condition of (Nakano and Nakamura 1978). Meaning the cloud tends to be supercritical at column densities required for H 2 formation.

Simulation of Cloud Formation. Used numerical simulations of PVP95 of ISM by 1000 pc Initiated by small random velocity map. Self gravity, Magnetic fields, Coriolis force, Galactic shear, diffuse heating, cooling and stellar energy input. The latter when densities >30cm -3 flux~O star is turned on for 6Myr. Support hypothesis, particularly with large scale flows re- aggregating at later times and some distance away. Leads to star formation, temporally and spatially distributed as expected from model.

4 frames from simulation. Vectors, magnetic field directions and strengths. Gray scale, density in logarithmic units. "Clouds," regions where the density exceeds 15 cm-3, are, black isocontours. After ~10 Myr, “SF" occurs (Local densities ~threshold level), adding energy to the simulation. Clouds built up by flows several hundreds of parsecs, concentrating most of mass into a small fraction of the computational region.

RSF Summary. To explain, Small age spreads of spatially extended SF regions, contested with other data and authors. RSF where, Large scale flows forming large clouds. Clouds become molecular at densities comparable to those favorable to gravitational collapse. At least in restricted regions. Clouds are supercritical at formation due to large accumulation lengths. Ambipolar diffusion unnecessary.

Discussion. Large scale structures, needed for GMC. Observations of H 2 gas clouds far out of galaxy. Various studies show could be the case in Orion. Flows initially atomic, shocks from spiral arms help increase density. Most applicable in solar circle where HI ratio higher.

Supercritical star formation, SF in Dark clouds, as densities higher than HI phase. Not as favourable for ambipolar diffusion. GMC form in supercritical state,  ionisation and diffusion effects limited. Has been argued SF in subcritical units. More plausible that collapse starts in supercritical regions. Efficiency and Galactic SF rates Low SF rate not due to slowing by ambipolar diffusion Low efficiency in converting gas to stars. Cloud rapid dispersal aids this view. Sne and stellar winds more likely to eject distant low density gas, natal dense material much more difficult to remove.

Protostellar collapse, H 2 formed instantly susceptible to collapse. Large scale flows unlikely to produce hydrostatic structures, protostellar cores often modeled as. RSF, dynamical SF and rapid hydrostatic eqbr, due to cooling times << free fall times. Shocks in GMC, unlikely to be in hydrostatic eqbr. Protostellar cores generally prolate, easier if cores not in hydrostatic eqbr. Triaxiality lends itself to flow driven mechanism. Large scale flows form cores and give rise to clustered SF

Conclusions. Observational evidence suggest SF fast and dispersal of GMC rapid, claimed in this paper. Showed can be explained by RSF, with large scale flow in ISM. Need to understand HI to H 2 conversions. Column densities of conversion similar to that required for collapse. Require that magnetic fields have small effect. Numerical simulations favour this mechanism. Much left, Can outflows disperse GMC rapidly enough. Rapid dispersion of small scale turbulence needed. Higher masses and densities need to be considered.

(left)-SF-expanding shell-self-gravitating. Densities in shell achieve similar values over very large scales.  SF coordinated t < t cross (radius bubble /vel shell ). Velocity dispersion among SF can be small, << vel shell, over regions small in comparison with radius bubble. (center) As the  ISM  uniform on large scales,   shell  uniform,  SF  simultaneous over entire shell-range of SF epochs. (right) If clouds rapidly dispersed by SF, lifetime of H 2 can still be short. The large-scale numerical simulations of the ISM by PVP95, BHV99, etc., ->most clouds formed from interactions of flows from distinct SF sites. Schematic view of large-scale triggered star formation.