Dinamica del Gas nelle Galassie II. Star formation

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1 Dinamica del Gas nelle Galassie II. Star formation Overview on ISM Molecular clouds: composition and properties. Plasmas Charge neutrality, infinite conductivity; Field freezing; Euler equation with magnetic force; Magnetic Pressure and tension; Magnetic virial theorem; Shocks with magnetic field. Stability of clouds Isothermal sphere, Lane-Emden equation; Bonnor-Ebert sphere and mass; Analysis of stability; Effect of rotation; Effect of magnetic field; Hydromagnetic waves; The role of turbulence. Collapse of clouds Free-fall time; Self-similar collapse; Ambipolar diffusion, magnetic braking. - The Formation of Stars, Stahler & Palla, Wiley-VCH - The Physics of Astrophysics, F. H. Shu, University Science Books 1

2 Molecular clouds 2

3 Location of GMCs Strahler & Palla, 2006, W-VCH 3

4 IR allsky Cygnus Ophiucus Rosette Taurus Orion IRAS micron 5

5 Orion nebula Distance from Sun ~ 400 pc CO map outer contours dots = CO peaks Shaded loop = UV emission Maddalena et al

6 CO J=2-1 Orion A Optical multicolor Maddalena et al

7 Rosette cloud CO J=3-2 peak emission map. O stars are shown as triangles. Squares show the locations of the outflows found in the region. Dent et al. 2009, MNRAS 8

8 Dense cores T ~ K, n ~ 2x103-2x105 cm-3, sizes < 1 pc More than 50% have associated IR sources 9

9 Properties of molecular complexes Type n (cm -3 ) L (pc) M (M O ) T (K) c s (km/s) σ obs (km/s) v rot (km/s/ pc) B (µg) v A (km/s) GMCs < Dark clouds < Dense cores <~1 ~30 ~0.4 10

10 2 50 10 5 15 0.25 2 <0.05 10 1.5 Dark clouds 10 3 1-10 10 2-4 10 0.

10 Composition of MCs 11

11 Composition of MC A ul = radiative de-exitation coefficient Strahler & Palla, 2006, W-VCH For n >> n crit -> LTE 12

12 Orion B - CO vs CS CO - moderately high density CS -> High density regions Lada et al

13 Dense cores Elongated (mostly prolate) whether or not they harbour an embedded star Myers et al

14 HI envelops Rosette MC CO J=1-0 + HI envelop (dashed) Blitz & Thaddeus 1980, ApJ 15

15 Heating & cooling 16

16 H 2 formation and maintenance Strahler & Palla, 2006, W-VCH 17

17 Cooling inside MCs Rotational transitions: 12 CO, 13 CO O 2, H 2 O etc. Tielens 2005, CUP 18

18 Heating of MC vs CNM CR = cosmic ray ionization decay of turbulence grav = gravitational heating ambipolar diffusion d-g = collision with dust-grains Tielens 2005, CUP pe = photo-electric effect CR = cosmic ray ionization CI = photoionization of Carbon X-ray ionization 19

with dust-grains Tielens 2005, CUP pe = photo-electric effect CR =

19 Stability of clouds 20

20 MCs are rather stable t ff ~ (G ρ) -1/2 MC blown away by stellar winds O stars From the stellar cluster age 21

21 Bonnor-Ebert mass Boyle s law: stable unstable Bonnor 1956 Strahler & Palla, 2006, W-VCH 22

22 Coalsack G2 dense core Extinction map Bonnor-Ebert sphere with ξ=5.8 Lada et al. 2004, ApJ 23

23 Barnard 68 Alves et al. 2001, Nature 24

24 Equilibrium of rotating clouds β = Ω 0 2 R 03 / 3GM Ω 0, R 0 of the initial sphere from which the cloud has contracted Along R Along z Isothermal sphere Strahler 1983, ApJ 25

25 Critical mass with rotation For comparison: Bonnor-Ebert sphere β = Ω 0 2 R 03 / 3GM unstable unstable Strahler 1983, ApJ 26

26 A clear case L1495 Velocity gradients? Typical β = 0.02 (very low) Gradient ~ 3 km/s/pc Goodman et al. 1993, ApJ 27

27 Magnetostatic equilibrium Dinamica del gas AA Strahler & Palla, part 2006, 2 W-VCH 28

28 Critical mass with Magnetic field α = B 0 2 / 8 π P 0 B 0, P 0 of the initial homogenous sphere from which the cloud has contracted Tomisaka et al. 1988, ApJ Strahler & Palla, 2006, W-VCH 29

29 Problems with Magnetic field Magnetic field orientation non coherent (evidence for MHD waves?) Dense cores are not too elongated but probably prolate! Loren 1989, ApJ Goodman et al. 1990, ApJ Myers et al

30 Large velocity dispersion CO J=1-0 Taurus cloud complex Channel maps at different velocities Mizuno et al σ oss ~ 1-2 km/s 31

31 Non-thermal kinetic energy Equilibrium between non-thermal kinetic energy (T) and gravitational energy (W) 2 o Larson s law GM ~ σ 2 L α vir ~ 1 log K turb / W Larson 1981; Stahler & Palla 2006, W-VCH 32

32 Turbulence achievements Supersonic turbulence predicts σ L 1/2 1 o Larson s law σ (velocity dispersion) S 0.4 (size) If dense cores are the products of turbulence then one expect a power-law spectrum Clumps in Rosette MC Solomon et al Williams & Blitz 1994, ApJ 33

33 Pre-stellar cores and IMF Ward-Thompson & Whitworth, CUP 34

34 Different IMFs 35

35 Summary SF & turbulence McKee & Ostriker 2007, ARA&A 36

36 Collapse of clouds 37

37 Dense cores with and without stars R = radius of the cloud Benson & Myers 1989, ApJS 39

38 Self-similar isothermal collapse Basic equations a = c s (sound speed) Self-similarity Solution Shu 1977, ApJ 40

39 Inside-out collapse Similarity variables: x = r / c s t v(x) = u(r,t) / c s a b Shu 1977, ApJ 41

40 Simulations of collapse Mass accretion ( core = protostar) Non-dimentional variables: Density profile ρ / ρ c Foster & Chevalier

41 Deformation of field lines Initial field is rather uniform NGC 1333 IRAS 4A B 0 ~ 0.5 mg t coll ~ few 10 4 yr Frau et al. 2011, A&A 43

42 From dense cores to stars Optical-IR spectral energy distribution i = 0 i = 0 i = 90 i = 90 i = 0 i = 90 i = inclination along the line of sight Lada 1999, Kluwer Hogerheijde

43 Formation of protostars Strahler & Palla, 2006, W-VCH 45

44 SF on the large scale 46

45 Star formation indicators Kennicutt et al

46 SFR vs galaxy type Kennicutt 1998, ARA&A 48

47 HI distribution vs optical/uv Sancisi et al. 2008, A&ARv 49

48 HI and Molecular clouds in M33 Engargiola et al

49 The Kennicutt-Schmidt (K-S) law Kennicutt

50 Local K-S law Leroy et al

51 Local K-S law 21 galaxies THINGS Slope change? 53

Heating & Cooling in Molecular Clouds

Lecture 8: Cloud Stability Heating & Cooling in Molecular Clouds Balance of heating and cooling processes helps to set the temperature in the gas. This then sets the minimum internal pressure in a core