Lecture 3 Properties and Evolution of Molecular Clouds

Lecture 3Properties and Evolution ofMolecular CloudsSpitzer space telescope image of Snakemolecular cloud (IRDC G11.11-0.11

The Galaxy in COThe CfA CO Survey (488,000 spectra 7’ resolutionII I IV IIIQuadrantshttp://cfa-www.harvard.edu/mmw/MilkyWayinMolClouds.html2MASS Near-IR Survey

The OrionGiantMolecularCloudComplexTotal mass200,000 MsunCO map of Wilson et al. (2005) overlaid on image of Orion4

Cloud Mass FunctiondN/dlog(m) = kM -0.81M upper = 5.8 x 10 6 MsundN/dlog(m) = kM -0.67M upper = 5.8 x 10 6 MsunMass is weighted towardthe most massive cloudsWilliams & McKee 1997ApJ 476, 166.

Size-Linewidth RelationshipSolomon 1987 ApJ 319, 730

Are Clouds Bound?

Are Clouds Bound?

Are Clouds Bound?Larson 1981VirialBoundNote: σ is 3-D velocity distribution

Using Galactic Ring DataVirialBoundNote: alpha may beunderestimatedHeyer et al. 200912

The Stability of Clouds: Jeans InstabilityWe start with the basic equations for fluid motions:13

The Stability of Clouds: Jeans Instability14

The Stability of Clouds: Jeans Instability15

The Stability of Clouds: Jeans Instability16

The Stability of Clouds: Jeans Instability17

The Stability of Clouds: Jeans Instability18

The Stability of Clouds: Jeans Instability19

Are Clouds Stable to Fragmentation?For n(H2) = 40 cm -3 λJ = 6 pc MJ = 450 Msun (cloud size)For n(H2) = 100 cm -3 λJ = 4. pc MJ = 350 Msun (cloud size)For n(H2) = 1000 cm -3 λJ = 1.2 pc MJ = 100 Msun (clump size)Cloud masses and lengths exceed Jeans length masses.From clouds in the inner galaxy from Heyer et al. 200920

Molecular Clouds areFilamentary and ClumpyOrionUnits in ParsecsOphiuchusTaurus21

Star Formation EfficiencyTypical cloud efficiencies are a few percent for molecular cloudsFrom Evans et al. 200922

Lifetimes of Nearby Clouds

The Lifetimes of CloudsSurvey of CO toward 24 Clusters: Leisawitz, Bash & Thaddeus 1989 ApJS 70, 731

5 MyrOB Associations10 Myr20 MyrUnbound groups ofOB stars plus many(usually undetected)low mass stars.Near associationsinclude Sco OB2 andOrion OB1.Associations havesubgroups of differentages.Only one residual cloud in Upper ScoSubgroups with ages >5 Myr typically don’thave residual gas.Slides from Thomas Prebisch (MPIFR)1-10 Myr

Timescales• Star formation lifetime < 5 MyrStar formation timescale comparable to cloud free-fall time andlarger than crossing time.t = length/σ26

A Proposed Picture for StarFormation in the Nearby Galaxy27

The Formation of Molecular HydrogenThe rate of H 2 formation in the gas phase is very low.H 2 can form on the surfaces of dust grains (from Stahler & Palla):Collision rate with grains: 1/t coll = n HI σ d V thH moves around grains through quantum tunneling, may find defect in lattice andstick. When another H comes along, the two atoms bind. Some of that energy kicksthe H 2 off the grain.Formation rate: R H2 = 1/2 γ H n d / t coll= 1/2 γ H n d n HI σ d V thγ H is the sticking probability, n d is density of grains, n HI is density of hydrogen, σ d iscross section of grains, V th = thermal velocity of gas

Dissociation of Molecular Hydrogen1. Absorption of UV photons with energies of 4.48-13.6 ev2. The photons raises molecule to excited electronic state.3. This energy can be exchanged to vibrational and rotational modes.4. A fraction of these excited molecules will dissociate into two H.Two prevent dissociation, molecules must be shielded from UVradiation from external starlight. This is done by dust and selfshielding of the molecule.

PDRs: Photodissociation Regionsor Photon Dominated Regions from FUVRadiationSpitzer Image ofCep OB3

PDRsPhotons with13.6 ev > hϖ > 4.48 ev cannotionize H2, but can dissociate H 2D. J. Hollenbach & A. G. G. M. Tielens ARAA 35, 179

Heating and Cooling in PDRsTemperature determined by balanceof heating and cooling ratesD. J. Hollenbach & A. G. G. M. Tielens ARAA 35, 179

Collapse vs CompressionHow do we create a cloud with N(H2) = 2 x 10 21 cm -3 (2 AV)3d collapse of spherical cloud1d compression of elongated cloudτ = κρ 2Rρ = M/(4/3πR 3 )τ = [κ3/(4π)]R -2τ = κρΔxρ = M/(AL)τ = kM/AThe time to collapse from an HIcloud with density of 10 cm -3Would take 6 Myr to sweep up from10 cm -3 with a 10 kms -1 motion

Converging FlowsHI flow (from bubble as example)H 2HI flow (from bubble as example)Heitsch et al. In press

Formation of Clumps (Heitsch et al. 2008 in press)

The Destruction of Molecular CloudsM16

Photoevaporative Flows due to EUV Ionizing Radiation (hν > 13.6 ev)Hester et al. 1996 AJ 111, 2349

Cepheus BubbleThe Rocket EffectGlobule Moving atup to 20 km s -1CO (1-0) mapPatel et al. 1998 ApJ 507, 241Ionized Gas Movingat up to 20 km s -1Kent Wood

Gravity also plays an important role in forming clouds39Yang et al. 2007

SummaryMolecular clouds are typically massive objects with masses of 10 4 - 10 6 solar massesThey tend to follow Larson’s laws: N(H 2 ) = 1 x 10 21 cm -2 , σ = k R 0.5They tend to have approximately equal kinetic and potential energies.They are unstable to fragmentationLifetimes are a few million years, comparable to free-fall time, less than crossing time.Picture of star formation:•Gas swept up into opaque sheets.•Gravity forms filaments and clumps•Gas fragments to form stars•Stars (particularly massive stars) quickly dissipate the gas.

Sizescales100 pc < 0.1 pc10 MyrCloud complexes OB associationsTimescales1 MyrIndividual CloudsClusters and ClumpsCores and Protostars

Supersonic Motions in CloudsSound speed in molecular cloudsc s = (kT/m H2 ) 1/2c s = 0.35 km s -1Linewidths were a few km s -1 , thus motionsare supersonic