Chapter 4 : Molecular clouds

Transcription

1 Chapter 4 : Molecular clouds 4.1 Introduction! 4.2 Properties of molecular clouds! 4.3 Surveys of molecular clouds! 4.4 Mass determination! 4.5 Probes for physical conditions! 4.6 Thermal balance! 4.7 Cloud stability ; onset of star formation 1

2 4.1. Introduction Typical characteristics of GMCs:! - Mass = M! - Distance to nearest GMC = 140 pc (Taurus)! - Typical size = pc! - Size on the sky of nearby GMCs = 5-20 x full moon! - Average temperature (in cold parts) = K! - Typical density = cm -3! - Typical (estimated) life time ~10 7 year! - Star formation efficiency ~1-10% Composition of material (by mass):! Properties of the gas:! - 99% gas: 0.9 H 2 /H, 0.1 He, 10-4 CO, 10-5 other molecules (by number)! - 1% solid sub-micron particles (dust) : Mostly silicates + carbonaceous (< "m in size) - Gas mostly in molecular form: H in H 2, C in CO, O in O 2 (?), N in N 2 (?).! - At the edges of molecular clouds: transition to atomic species. Photo-Dissociation Regions (PDRs).! - H 2 not directly observable need a tracer (e.g., dust, CO). 2

3 4.1. Introduction! Nearby well-studied GMCs Taurus (dist 140 pc, size 30 pc, mass 10 4 M ): Only low mass stars (~105), quiet slow star formation, mostly isolated star formation.! Ophiuchus (dist 140 pc, size 6 pc, mass 10 4 M ): Low mass stars (~78), strongly clustered in western core (stellar density 50 stars/pc), high star formation efficiency! Orion (dist 400 pc, size 60 pc, mass 10 6 M ): Cluster of O-stars at center, strongly ionized GMC, O-stars strongly affect the lowmass star formation! Serpens, Chamaeleon... 3

4 4.2 Properties of molecular clouds! Relations Virial equilibrium:! Mvir D σ 2 σ n D (D = cloud diameter, σ=σ 1D = velocity dispersion)! Density-size ( condensation ) relation: n = 3900 D -1.2 cm -3! Turbulence law: σ1d = 1.2 D 0.3 km s -1! These relations were first noted by Larson (1981) and subsequently confirmed by surveys to hold for clouds 0.1<D<100 pc. Only 2 of the 3 relations are independent. Note that σ D 1/3 (Kolmogorov law) expected for turbulent energy cascade from larger to smaller scales in idealized incompressible fluid. 4

5 4.2 Properties of molecular clouds! Structure of GMCs Two descriptions : Clump picture : hierarchical structure! - Clouds ( 10 pc)! - Clumps (~1 pc) : Precursors of stellar clusters! - Cores (~0.1 pc) : High density regions which form individual stars or binaries! ~1 pc 10 pc ~0.1 pc Fractal picture : clouds are scale-free ; suggested by power-law fits to relationships between cloud parameters. Limits: self-gravitating systems are not selfsimilar (e.g. self-similarity breaks down at ~ pc in Taurus Williams 1998) Example of a fractal object: f(z) = z 2 +c, (z,c) Z, c= i 5

6 4.2 Properties of molecular clouds! Lifetimes, formation GMC Lifetimes: controversial! Long estimates: >10 8 yr based on z-distribution and presence GMCs in interarm regions! Short estimates: ~2x10 7 yr because OB stars destroy GMC rapidly and GMCs mostly confined to spiral arms! GMC Formation: random collisions of smaller clouds or spiral density wave? This image is from a simulation which includes the thermodynamics of the ISM, a 2 armed spiral potential, self gravity and stellar feedback. Black/white = total gas column density! Blue/yellow = molecular gas.! Simulations of GMC formation in a spiral galaxy appear to show that smaller clouds (present in the gas due to thermal instability) coalesce into more massive GMCs as they pass through spiral shocks in a galaxy. Self gravity aids GMC formation and produces more dense, massive GMCs. Stellar feedback then disrupts the clouds within a timescale of ~10 Myrs. 6

7 4.2 Properties of molecular clouds! Ionization Ions play a central role in gas-phase chemistry of molecular clouds! UV do not penetrate (dense) molecular clouds ionization via CR! Degree of ionization: x ' CR k rec n 1/2 ' 10 5 p n with ζ CR = primary CR ionization rate ~ s -1 k rec = recombination rate ~ s -1 Figure (Fig of Tielens)

8 4.3 Surveys of molecular clouds Because H2 is not observable directly in dense, cold clouds, surveys generally use trace molecules like CO! Most surveys done in 12 CO J = 1 0 at 2.6 mm! Advantages: 12 CO second most abundant molecule, small dipole moment easily excited even in relatively low-density gas! Disadvantages: 12 CO lines optically thick difficult to infer column densities, biased towards warmer clouds, T A ( 12 CO) T 8

9 4.3 Surveys of molecular clouds Recall: for diffraction-limited telescope,! b ( ) = 0.25 (µm) D(m) = (GHz) D(m) Thus at d = 100 pc, can resolve pc at d = 1 kpc 0.26 pc at d = 10 kpc 2.6 pc surveys of the Milky Way concentrate only on the largest molecular structures! Overview of surveys (2000 status) Name Telescope size Type of spectra # of spectra Beam size UMASS/FCRAO 14m 12 ~1,700, Bell laboratories 7m 13 ~60, Nagoya/NANTEM Twin 4m 12 ~1,000, CfA/Cerro Tololo Twin 1.2m 12 ~460,

10 4.3 Surveys of molecular clouds! Results Velocity-Integrated Spatial Map Galactic Latitude Beam Galactic Longitude G S212 0 W3 NGC7538 Cas A r e a Tau-Per-Aur Complex Cyg OB7 Cyg X W51 f W Coal Sack Galactic Center G317 4 R CrA R Ori A & B Fa ul ar r m Ri p a r Carin a Ar m log T mb dv (K km s 1 ) 180 e r s e u +260 s A r Vela CMa OB1 Carina Tangent ng S Maddalena s Mon Cloud Gem OB1 OB d in g A rm +180 Norma Tangent 0 Galactic Longitude Longitude-Velocity Map +240 m Centaurus Tangent n 60 A x r O u t e FIG. 2. Velocity-integrated CO map of the Milky Way. The angular resolution is 9 over most of the map, including the entire Galactic plane, but is lower (15 or 30 ) in some regions out of the plane (see Fig. 1 & Table 1). The sensitivity varies somewhat from region to region, since each component survey was integrated individually using moment masking or clipping in order to display all statistically significant emission but little noise (see 2.2). A dotted line marks the sampling boundaries, given in more detail in Fig. 1. S147 i n g 240 P E m A r 120 ec c 180 ol Aquila Rift Cyg X Cas A e r s e u s W44 p W3 W51 W50 Cyg OB7 k 100 P Mon R2 S. Ori Filament S235 Gum Nebula Chamaeleon Gem OB1 Rosette λori +280 M Lindblad Ring & Local Arm Mon OB1 CMa OB1 Orion Complex Scutum Tangent Sagittarius Tangent S147 Vela Carina Nebula 0 Galactic Longitude Maddalena s Cloud Lupus Aquila Rift Aquila South Pegasus LSR radial velocity ( km s 1 ) i R t t Lacerta Per OB2 20 Ophiuchus Hercules Disk Galactic Latitude Polaris Flare Cepheus Flare CTA-1 S147 S235 Nuclear Ursa Major Cam Resolution LSR radial velocity ( km s 1 ) Galactic Longitude Galactic Longitude log T 330 Dame et al ; mb db 0.0 (K arcdeg) FIG. 3. Longitude-velocity map of CO emission integrated over a strip ~4 wide in latitude centered on the Galactic plane (see 2.2) a latitude range adequate to include essentially all emission beyond the Local spiral arm (i.e., at v > 20 km s 1). The map has been smoothed in velocity to a resolution of 2 km s 1 and in longitude to a resolution of 12. The sensitivity varies somewhat over the map, since each component survey was integrated individually using moment masking at the 3-σ level (see 2.2). 10

11 4.3 Surveys of molecular clouds! Results About 90% of H2 mass in 5000 complexes with size > 20 pc; M>10 5 M! About 50% of H2 mass in 1000 complexes with size > 50 pc, M>10 6 M! About 90% of H2 mass inside solar circle (vs. 33% H I mass)! Mass spectrum clouds, for M= M :! Cloud population:! dn cloud dm cloud / 1.7 Mcloud warm clouds (T>10 K) : associated with H II regions found in spiral arms! cold clouds (T<10 K) : found throughout the disk M 11

12 4.4. Mass determination! H 2 tracers : dust From last lecture: F = apple B d 2 M d ) M d = F ( )d2 B(, T d )apple (Bergin & Tafalla 2007) κν = dust emissivity (cm 2 g -1 ) ν β Figure 4.3 Figure 1: Top Panel: Photographic image of the Taurus Molecular Cloud taken by E. E. Barnard (Barnard 1919). His notes state that, very few regions of the sky are so remarkable as this one. Indeed the photograph is one ofthemostimportant of the collection, and bears the strongest proof of the existence of obscuring matter in space. Courtesy of the Observatories of the Carnegie Institution of Washington. Bottom Panel: 13 CO J=1 0 integrated emission map of the same region obtained using the Five College Radio Astronomy Observatory. Crosses mark the location of known protostellar objects and the emission color scale ranges from K km s 1. Image kindly provided by PF Goldsmith in advance of publication. Cloud mass = Md / fd fd = dust-to-gas ratio = 0.01 Good sensitivity of detectors at temperature of molecular clouds ( 40 K mm/submm)! Dust optically thin at these λ! κ ν not well known 12

13 4.4. Mass determination! H 2 tracers : (CO) line emission (Bergin & Tafalla 2007) Consider CO J J-1 line: EJ = J(J+1) K AJ,J-1 = J 4 (2J+1) s -1 gj = 2J+1 νj = 115 J GHz Assume LTE and τ 1 N J = J 2 (2J + 1) Z T mb dv cm 2 Depletion! Partition function N(CO) Density ratio(*) N(H2) Figure 4.4 Figure 7: A deep optical image of the dark globule Barnard 68 (top left; Alves, Lada & Lada 2001) along with contour maps of integrated intensityfrom molecular emission lines of N 2 H + (contour levels: by 0.3 K km s 1 ), C 18 O( by0.1Kkms 1 ), and 850µm dustcontinuumemission(10 70 by 10 mjy beam 1 ). Molecular data, with an angular resolution of 25,are from Bergin et al. (2002) and dust emission (angular resolution of 14.5 )from Bianchi et al. (2003). Can estimate ng, Tg (if multi-line) (*) CO/H2 = CO/H2 = C 18 O/H2 = Opacity and depletion can lead to complex analysis 13

14 4.4. Mass determination! CO/H 2 conversion factor (= X factor) More generally, determination of cloud mass from CO as tracer of H2 requires a relation between the observed integrated CO intensity, I CO = T A (V)dV = 1.06 T A V, and H 2 column density! Various methods used to calibrate this relation Measure ICO for regions with high A V! Determine AV from star counts or extinctions toward stars! Use NH /A V from diffuse clouds! Assume all hydrogen is molecular: N(H)=2N(H2 ) Problems:! Method 1 : I CO vs A V N(H 2 )/I CO cm 2 (K km s 1 ) 1! AV from star counts inaccurate! Dust properties different in dense and diffuse clouds; NH /A V may also be different 14

15 4.4. Mass determination! CO/H 2 conversion factor (= X factor) Method 2 : 13 CO vs A V Determine AV as in method 1! Measure 13 CO line intensity! Assume 13 CO optically thin, 12 CO optically thick! Assume Tex ( 13 CO) = T ex ( 12 CO)! Assume 12 CO/ 13 CO τ ( 13 CO) N( 13 CO) from LTE analysis N(H 2 ) = (5.0 ± 2.5) 10 5 N LTE ( 13 CO) cm 2 N(H 2 )/I CO = (3 5) cm 2 (K km s 1 ) 1! Problems:! Determination of AV inaccurate! Often Tex ( 13 CO) < T ex ( 12 CO) N( 13 CO) as a function of A V in Taurus and ρ Oph. Open circles are lower limits. The 13 CO abundance is influenced by isotopic enhancement and saturation effects, so that its functional dependence on A V varies from source to source. The dashed lines are the relationships determined by Dickman (1978) from a large sample of dark clouds. 13 C 18 O data scaled by 500 are also indicated.! (Frerking et al. 1982) 15

16 4.4. Mass determination! CO/H 2 conversion factor (= X factor) Method 3 : Virial method Can show that: N(H2 ) /I CO n(h 2 ) / T A! N(H2 ) /I CO = (10 K/T A ) (n(h 2 )/1000 cm 3 ) 1/2 cm 2 (K km s 1 ) 1! Notes:! Does not assume any value for n(co)/n(h2 )! Method can be applied to any molecule! Conversion factor depends on T and n in the cloud should be different for cold dark clouds and giant molecular clouds! Problems:! Assumes virial equilibrium! Measures only mass within τ = 1 surface! Practical difficulties in determining 12 CO line width 16

17 Assumes virial equilibrium 4.4. Mass determination! ss within ' = 1 surface sures on Meafactor CO/H2 conversion (=lyxma factor) 12CO line w g nin mi ter de in ies Practical difficult Surveys Properties CO/H2 Diagnostics Radiation transport Therm Size linewidth relation Virial mass LCO rela 17

18 4.4. Mass determination! CO/H 2 conversion factor (= X factor) Method 4 : γ rays Interaction of cosmic rays with interstellar gas produces γ-rays:! CR-e - + gas!! γ! CR-p + + gas, 0 γ! Gamma-ray flux is a measure of total gas mass! Comparison with ICO gives conversion factor! Iγ = ε [ N(H) + 2{N(H 2 )/I CO }I CO ] + I IC + I bg!! { N(H2 ) /I CO cm 2 (K km s 1 ) 1! X Inverse Compton Problems:! Calibration γ-ray fluxes! Value only refers to large scale structures such as entire GMCs 18

19 4.4. Mass determination! CO/H2 conversion factor (= X factor) Method 5 : IRAS 100.m vs HI and H2 User IRAS 100.m + HI 21 cm surveys to calibrate NHI/I100 in regions without CO emission! Assume Ntot/I100 NHI/I100! Measure I100, ICO and NHI where CO detected; use Ntot/I100 and measured H I to determine N(H2)! Surveys Properties CO/H2 Diagnostics Radiation transport Thermal balance Star formation 20 cm 2 (K km s 1) 1 at b > 5 N(H2) /ICO = (1.8±0.3) 10 X from IRAS 100 µm Dame et al

20 4.4. Mass determination! CO/H 2 conversion factor (= X factor) Summary Various methods agree remarkably well, in spite of problems associated with each method:! Conversion factors! X ~ cm 2 (K km s 1 ) 1! apply to global scale (~1 ), not locally! give no information on N(H2 ) / N(CO)! depend on T and n! Conversion factor derived for Galactic Disk is not valid for galactic nuclei (including Galactic Center region) or metal-poor systems! 20

21 4.4. Mass determination! Clump mass spectrum Interesting for predicting the stellar masses of the newborn stars.! Similar to stellar IMF (Salpeter 1955: dn/dm M ) for M < 0.5 M : for M > 0.5 M : Fig Deep 1.3 mm continuum map of ρ Ophiuchi (d = 140 pc) at 0.01 pc (= 2000 AU) resolution. (Motte et al. 1998) Fig Frequency distribution of masses for 60 small-scale clumps extracted from the mosaic of Fig. 1 (solid line). The dotted and longdashed lines show power laws of the form N/ m m 1.5 and N/ m m 2.5, respectively. The error bars correspond to N counting statistics. 21

22 4.5. Probes for physical conditions! Overview of molecular probes Figure 4.8 (Figure 10.9 of Tielens) 22

23 4.5. Probes for physical conditions! Molecules as temperature probes For molecule in LTE, Tex = T kin in RJ limit with τ 1, T A T kin - T bg antenna temperature is direct measure of T kin! Examples of thermometers: 12 CO (J=1-0, 2-1,...), symmetric top molecules (NH 3, CH 3 CN), asymmetric top molecules (H 2 CO) 23

24 4.5. Probes for physical conditions! Molecules as density probes Critical density : ncr = A ul /γ ul! ncr depends on: dipole moment. : A ul. 2 Examples: n Molecules with larger. sample denser regions! Transitions with different J info on n rotational quantum number J: A ul J 3!. (Debye) CS

25 4.5. Probes for physical conditions! Molecules as density probes nc = critical density ; neff = density needed to produce a 1 K line at typical column density 25

26 4.5. Probes for physical conditions! Molecules as density probes CS compared to 13 CO in diffuse and dense clouds CS has a high critical density and thus traces high volume density! 13 CO traces column density 26

27 4.6. Thermal balance! Heating UV photons do not penetrate dense clouds heating mostly caused by cosmic rays! Minor heat sources: gas-grain collisions and hydrodynamical/ turbulent processes! CR heating: X + CR* X + + e - * + CR! CR ionizes X and transfers energy to e- (up to 35 ev) ; elastic collisions between e - * and other species transfers energy! low energy CR (~1-10 MeV) are most efficient! CR erg s 1 cm 3 CR heating rate: CR = n ζ CR = primary ionization rate (Note : the total ionization rate, ξ CR, depends on ζ CR and e - fraction) 27

28 4.6. Thermal balance! Heating (Fig 3.8 of Tielens) 28

29 2 H2 2 J J 2) J J 2) J Thermal balance! H Cooling H2 Effective cooling processes are those satisfying the following criteria:! n(co) 10 5 n(h2 ) 1. frequent collisions, i.e. abundant collision partner! excitation energy kinetic energy, i.e. Etransition ~ Tcloud! 3. large probability of excitation during collision (function of σul and Aul)! 4. emission of a photon before another collision occurs! 5. emitted photon is not re-absorbedj (gas thin for cooling radiation)! = 0 optically 1 Most carbon converted into CO [C II] cooling not important (1)! N Cooling dominated by molecular lines, in particular CO : ECO(1-0) = 5.5 K CO should be effective coolant down to T of this order (2). However, CO may become an efficient absorber of its own photons (5) H2 O not satisfied, efficiency much reduced, more minor molecules contribute 18 (OH, C18O...) 1 e 0 = CO cooling rate:! CO 4 B( J,J 1, T ) J,J 1 J 1 At highest densities H2O may become important H2 H2 O SiO 0 29

30 Surveys Properties CO/H2 Diagnostics Radiation transport Thermal balance Star formation 4.6. Thermal balance! Cooling as a function of T and n Cooling as function of T and n (Fig 2.11 of Tielens) 30

31 4.7 Cloud stability ; onset of star formation Condition for collapse (cloud with thermal support only) : MC > M J M J = Jeans mass 1/2 5kB T M J = Gµm H 3/2 3 4 Free-fall timescale for uniform density sphere: Free-fall timescale for uniform density sphere : 3 1/2 t = 32G 0 1 = n H2 1/2 2(G ) 1/ cm yr 3 t yr for n 10 4 cm 3 t yr for n 10 2 cm 3 31

32 4.7 Cloud stability ; onset of star formation! Star-formation efficiency Milky Way cloud mass ~ M (spread in clouds with mass > 10 4 M, i.e. very unstable)! Above tff applies theoretical star formation rate M cloud /t ff > 300 M /yr Observed star formation rate across the MW ~ 3 M /yr!!! Observed star formation rate inside star forming regions between 3 6% (Taurus, Ophiuchus,...) and 30-40% (Orion)! Explanations:! Clouds are supported against free collapse (support is not only thermal: B-field, turbulence)! Star formation is inefficient in turning mass into stars 32

33 4.7 Cloud stability ; onset of star formation! Bonnor-Ebert spheres (Shu 1977) Previously assumed uniform density ; problem: center feels greater gravitational force requires greater pressure (i.e. greater density) to balance it. Solve momentum equation and equation of state: Dv Dt = OP O P = c2 s cs = isothermal sound speed ξ -2 Leads to Lane-Emden equation : 1 d 2 2 du =e u d d ξ = β -1/2 ρc 1/2 r ; β = cs 2 /4πG ; u = -ln(ρ/ρc) Family of solutions depending on central density 33

34 4.7 Cloud stability ; onset of star formation! Bonnor-Ebert spheres At point A, equilibrium becomes unstable: small increase in external pressure decrease in volume (hence in radius) reduction of the internal boundary pressure further reduction in volume... collapse (curve spirals round singular point) Rcrit occurs for ξ~6.5 (Emden s table) and it follows (Bonnor 1956, Shu 1977): Rcrit = 0.49cs(Gρcrit) -1/2 and Mcrit = 1.18cs 4 G -3/2 Pext -1/2 34

35 4.7 Cloud stability ; onset of star formation! Example of a Bonnor-Ebert sphere : B68 Left: deep B,V,I band (0.44, 0.55, 0.90 µm) image (7' 7') of the dark molecular cloud Barnard 68 taken with ESO's Very Large Telescope. Right: deep B,I,K band (0.44, 0.90, 2.2 µm) image of the cloud. The K band image was obtained with ESO's New Technology Telescope. The red circles show the data points for the averaged profile of a sub-sample of the data that do not include the cloud's southeast prominence. The open circles include this prominence. The solid line represents the best fit of a theoretical Bonnor Ebert sphere to the data. The close match of the data with theory indicates that the internal structure of the cloud is well characterized by the equations for a self-gravitating, pressure-confined, isothermal sphere and thus Barnard 68 seems to be a distinct dynamical unit near a state of hydrostatic equilibrium, with gravity balanced by thermal pressure. 35 (Alves et al. 2001, Nature)

36 Summary of molecular clouds Mass ~ M ; size ~ pc ; T ~ K ; n ~ cm -3! Mostly H2 ; CO/H 2 ~ 10-4 ; other molecules 10-5! Fractal in nature (except for self-gravitating systems), but often described with hierarchical picture.! Traced by dust (drawback: dust emissivity not well known) or CO (drawback: opacity, depletion)! CO/H2 conversion factor (global scale, T&n dependence) : X ~ cm 2 (K km s 1 ) 1! Clump mass spectrum similar to stellar IMF : dn/dm Mγ, γ~ -2.5 ; -1.5! Heating mostly from cosmic-rays ; cooling from CO, H2 O, C I, O 2 (depending on T and n)! Site of star-formation: actual rate theoretical rate B-field, turbulence

37 37

38 Properties of molecular clouds GMC Lifetimes: controversial! Long estimates: >10 8 yr based on z-distribution and presence GMCs in interarm regions! Short estimates: ~2x10 7 yr because OB stars destroy GMC rapidly and GMCs mostly confined to spiral arms! GMC Formation: random collisions of smaller clouds or spiral density wave?! Fractal structure: M D 2 rather than D 3! Hierarchical structure observed on all scales! Fractal index interstellar clouds very similar to that of clouds in the Earth s atmosphere 38

39 Clump mass spectrum Orion B: First GMC systematically surveyed for dense gas and embedded YSOs by E. Lada 1990 Survey of gas clumps: clumps in range M = M dn dm " M #1.6 dln M " M #0.6 M dn d ln M " M 0.4 Most of mass in massive clumps 39

40 4.4. Probes for physical conditions Physical conditions from line ratios Line ratios are sensitive probes of the density and temperature of the gas in the range between the critical densities and excitation energies of the levels involved. e.g., CO 3-2/6-5! CO 3-2 : ncr ~ cm-3, Eup ~ 35 K! CO 6-5 : ncr ~ cm-3, Eup ~ 115 K! Figure 4.9 (Figure of Tielens) 40