ISM Structure: Order from Chaos
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1 ISM Structure: Order from Chaos Philip Hopkins with Eliot Quataert, Norm Murray, Lars Hernquist, Dusan Keres, Todd Thompson, Desika Narayanan, Dan Kasen, T. J. Cox, Chris Hayward, Kevin Bundy, & more
2 The Turbulent ISM IMPORTANT ON (ALMOST) ALL SCALES LMC Ø Ø Ø Ø Ø Ø Gravity Turbulence Magnetic, Thermal, Cosmic Ray, Radiation Pressure Cooling (atomic, molecular, metal-line, free-free) Star & BH Formation/Growth Feedback : Massive stars, SNe, BHs, external galaxies, etc.
3 Number The ISM YET THERE IS SURPRISING REGULARITY Stars & Pre-Stellar Gas Cores: Giant Molecular Clouds: Number (dn/dm) Bastian Chabrier MW LMC SMC M33 M31 IC10 Blitz, Rosolowski et al. Mass [M ]
4 Number The ISM YET THERE IS SURPRISING REGULARITY Stars & Pre-Stellar Gas Cores: Giant Molecular Clouds: Number (dn/dm) Bastian Chabrier dn dm / M 1.8 MW LMC SMC M33 M31 IC10 / M 2.2 Blitz, Rosolowski et al. Mass [M ]
5 Number The ISM YET THERE IS SURPRISING REGULARITY Stars & Pre-Stellar Gas Cores: Giant Molecular Clouds: Number (dn/dm) Bastian Chabrier dn dm / M 1.8 MW LMC SMC M33 M31 IC10 DM Halos?! / M 2.2 Blitz, Rosolowski et al. Mass [M ]
6 LMC Extended Press-Schechter / Excursion-Set Formalism Ø Press & Schechter 74: Ø Ø r Fluctuations a Gaussian random field Know linear power spectrum P(k~1/r): variance ~ k 3 P(k)
7 LMC Extended Press-Schechter / Excursion-Set Formalism Ø Press & Schechter 74: Ø Ø r Fluctuations a Gaussian random field Know linear power spectrum P(k~1/r): variance ~ k 3 P(k) Ø Count mass above critical fluctuation: Halos Ø Turnaround & gravitational collapse (< R 1/k) > crit
8 LMC Extended Press-Schechter / Excursion-Set Formalism Ø Press & Schechter 74: Ø Ø r Fluctuations a Gaussian random field Know linear power spectrum P(k~1/r): variance ~ k 3 P(k) Ø Count mass above critical fluctuation: Halos Ø Turnaround & gravitational collapse (< R 1/k) > crit Ø Generalize to conditional probabilities, N-point statistics, resolve cloud in cloud problem (e.g. Bond et al. 1991)
9 Turbulence BASIC EXPECTATIONS Velocity: E(k) / k p (ke(k) u t (k) 2 )
10 Turbulence BASIC EXPECTATIONS Velocity: E(k) / k p (ke(k) u t (k) 2 ) Density: Lognormal in r: dp(ln R) = 1 h (ln hln i) 2 i p exp 2 S(R) 2 S(R) Vasquez-Semadeni, Nordlund, Padoan, Ostriker, & others Text
11 Turbulence BASIC EXPECTATIONS Velocity: E(k) / k p (ke(k) u t (k) 2 ) Density: Lognormal in r: dp(ln R) = 1 h (ln hln i) 2 i p exp 2 S(R) 2 S(R) Vasquez-Semadeni, Nordlund, Padoan, Ostriker, & others Text S(R) = Z dlnks k W (k, R) 2
12 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h 1+ k h Chandrasekhar 51, Vandervoort 70, Toomre 77
13 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h Angular Momentum apple V disk R disk 1+ k h Chandrasekhar 51, Vandervoort 70, Toomre 77
14 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h 1+ k h Angular Momentum apple V disk R disk Thermal Pressure / r 2 Chandrasekhar 51, Vandervoort 70, Toomre 77
15 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h 1+ k h Angular Momentum apple V disk R disk Thermal Pressure / r 2 Turbulence / r p 3 r 1 r>r sonic : u 2 t >c 2 s Chandrasekhar 51, Vandervoort 70, Toomre 77
16 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h 1+ k h Angular Momentum apple V disk R disk Thermal Pressure / r 2 Turbulence / r p 3 r 1 r>r sonic : u 2 t >c 2 s Gravity Chandrasekhar 51, Vandervoort 70, Toomre 77
17 What Defines a Fluctuation of Interest? DISPERSION RELATION:! 2 = apple 2 + c 2 s k 2 + u t (k) 2 k 2 4 G k h 1+ k h Angular Momentum apple V disk R disk Thermal Pressure / r 2 Turbulence / r p 3 r 1 r>r sonic : u 2 t >c 2 s Gravity Mode Grows (Collapses) when w<0: > c (k) = 0 (1 + kh ) h (M 2 h + kh 1 p ) kh + 2 kh i Chandrasekhar 51, Vandervoort 70, Toomre 77
18 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Log[ Density / Mean ]
19 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Log[ Density / Mean ]
20 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER Averaging Scale R [pc] PFH 2011 Thermal+ Magnetic Log[ Density / Mean ] Angular Momentum Turbulence
21 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER Averaging Scale R [pc] PFH 2011 Thermal+ Magnetic Log[ Density / Mean ] Angular Momentum Turbulence
22 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER Averaging Scale R [pc] PFH 2011 Thermal+ Magnetic Log[ Density / Mean ] Angular Momentum Turbulence
23 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER Averaging Scale R [pc] PFH 2011 Thermal+ Magnetic Log[ Density / Mean ] Angular Momentum Turbulence
24 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Log[ Density / Mean ] First Crossing
25 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Log[ Density / Mean ] First Crossing GMCs
26 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Last Crossing Log[ Density / Mean ] First Crossing GMCs
27 Counting Collapsing Objects EVALUATE DENSITY FIELD vs. BARRIER PFH 2011 Averaging Scale R [pc] Last Crossing Log[ Density / Mean ] First Crossing GMCs Cores/IMF
28 Evolve the Fluctuations in Time CONSTRUCT MERGER/FRAGMENTATION TREES p( ) = 1 h p exp 2 S (1 exp [ 2 ]) ( (t = 0) exp [ ]) 2 2 S (1 exp [ 2 ]) i Time
29 Evolve the Fluctuations in Time CONSTRUCT MERGER/FRAGMENTATION TREES p( ) = 1 h p exp 2 S (1 exp [ 2 ]) ( (t = 0) exp [ ]) 2 2 S (1 exp [ 2 ]) i Time Fraction Collapsed Per Crossing Time Simulations (Cooling+Gravity+MHD) Padoan & Nordlund Vazquez-Semadeni PFH 2011
30 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS Number (>Mcloud) PFH 2011 log[ M cloud / M sun ]
31 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS r sonic r h S(r) S 0 Number (>Mcloud) PFH 2011 log[ M cloud / M sun ]
32 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS r sonic r h dn S(r) S 0 dm / M e (M/M J ) Number (>Mcloud) PFH 2011 log[ M cloud / M sun ]
33 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS r sonic r h dn S(r) S 0 dm / M e (M/M J ) Number (>Mcloud) 2+ (3 p)2 MJ 2 Sp 2 ln M log MJ M PFH 2011 log[ M cloud / M sun ]
34 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS r sonic r h dn S(r) S 0 dm / M e (M/M J ) Number (>Mcloud) 2+ (3 p)2 MJ 2 Sp 2 ln M log MJ log M MJ M PFH 2011 log[ M cloud / M sun ]
35 The First Crossing Mass Function VS GIANT MOLECULAR CLOUDS r sonic r h dn S(r) S 0 dm / M e (M/M J ) Number (>Mcloud) 2+ (3 p)2 MJ 2 Sp 2 ln M log MJ log M MJ M PFH 2011 log[ M cloud / M sun ]
36 The Last Crossing Mass Function VS PROTOSTELLAR CORES & THE STELLAR IMF PFH 2012
37 The Last Crossing Mass Function VS PROTOSTELLAR CORES & THE STELLAR IMF PFH 2012
38 Void Abundance VS HI HOLES IN THE ISM PFH 2011 Don t need SNe to clear out voids
39 Structural Properties of Clouds LARSON S LAWS EMERGE NATURALLY
40 Structural Properties of Clouds LARSON S LAWS EMERGE NATURALLY
41 Clustering PREDICT N-POINT CORRELATION FUNCTIONS PFH (r M) hn[m r0 <r]i hn[m]i First Crossing: GMCs & new star clusters Predicted
42 Clustering PREDICT N-POINT CORRELATION FUNCTIONS 1+ (r M) hn[m r0 <r]i hn[m]i PFH 2012b Text Last Crossing: Cores & Stars
43 Clustering PREDICT N-POINT CORRELATION FUNCTIONS 1+ (r M) hn[m r0 <r]i hn[m]i PFH 2012b Text Last Crossing: Cores & Stars
44 Clustering PREDICT N-POINT CORRELATION FUNCTIONS 1+ (r M) hn[m r0 <r]i hn[m]i PFH 2012b Why is Star Formation Clustered? Text S ln M(k) 2 ln r 3 p Last Crossing: Cores & Stars
45 Clustering of Stars: Predicted vs. Observations PREDICT N-POINT CORRELATION FUNCTIONS
46 Testing the Analytics vs. NUMERICAL SIMULATIONS v z Power spectra Correlation Function/Clustering Hansen, Klein et al. log( E[k] ) 2 p=2 0 Intermittency Exponents (ln[rho]) k [kpc -1 ] Bournaud & Elmegreen Linewidth-Size Relation Liu & Fang compilation (30 sims) Fragmentation Rate (per Dynamical Time) Simulations (Cooling+Gravity+MHD) Number of GMCs Excursion Set PFH Padoan & Nordlund Vazquez-Semadeni
47 General, Flexible Theory: EXTREMELY ADAPTABLE TO MOST CHOICES Densities Ø Complicated, multivariable gas equations of state Lognormal Ø Accretion Not-so Lognormal Ø Magnetic Fields Ø Time-Dependent Background Evolution/Collapse Core MFs GMC MFs Ø Intermittency Ø Correlated, multi-scale driving
48 Variation in the Core Mass Function VS NORMAL IMF VARIATIONS PFH 2012 Weak variation with Galactic Properties Near-invariant with mean cloud properties (up to sampling)
49 Variation in the Core Mass Function VS NORMAL IMF VARIATIONS PFH 2012 Weak variation with Galactic Properties Near-invariant with mean cloud properties (up to sampling) M sonic M( crit R sonic ) c2 s R sonic G
50 Variation in the Core Mass Function VS NORMAL IMF VARIATIONS PFH 2012 Weak variation with Galactic Properties Near-invariant with mean cloud properties (up to sampling) M sonic M( crit R sonic ) c2 s R sonic G M T min 10 K R sonic 0.1pc
51 Variation in the Core Mass Function VS NORMAL IMF VARIATIONS PFH 2012 Weak variation with Galactic Properties Near-invariant with mean cloud properties (up to sampling) M sonic M( crit R sonic ) c2 s R sonic G M T min 10 K R sonic 0.1pc / T 2 min R cl 2 cl
52 Variation in the Core Mass Function VS NORMAL IMF VARIATIONS PFH 2012 Weak variation with Galactic Properties M sonic M( crit R sonic ) c2 s R sonic G M T min 10 K R sonic 0.1pc / T 2 min R cl 2 cl
53 BUT, What About Starbursts? PFH 2012 MW: T cold 10 K gas 10 km s 1 (Q 1 for gas 10 M pc 2 ) Text
54 BUT, What About Starbursts? PFH 2012 MW: T cold 10 K gas 10 km s 1 (Q 1 for gas 10 M pc 2 ) Text ULIRG: T cold 70 K gas 80 km s 1 (Q 1 for gas 1000 M pc 2 )
55 BUT, What About Starbursts? PFH 2012 Core Mass Function MW: T cold 10 K gas 10 km s 1 ULIRG (Q 1 for gas 10 M pc 2 ) Text MW ULIRG: T cold 70 K gas 80 km s 1 (Q 1 for gas 1000 M pc 2 )
56 BUT, What About Starbursts? BOTTOM-HEAVY: TURBULENCE WINS! PFH 2012 Core Mass Function MW: T cold 10 K gas 10 km s 1 ULIRG (Q 1 for gas 10 M pc 2 ) MJeans is bigger but MSonic is smaller (bigger clouds with more fragmentation) Text MW ULIRG: T cold 70 K gas 80 km s 1 (Q 1 for gas 1000 M pc 2 ) Mach number in ULIRGs: M & 100
57 BUT, What About Starbursts? BOTTOM-HEAVY: TURBULENCE WINS! PFH 2012 Core Mass Function MW: T cold 10 K gas 10 km s 1 ULIRG (Q 1 for gas 10 M pc 2 ) Van Dokkum & Conroy (nearby elliptical centers) MJeans is bigger but MSonic is smaller (bigger clouds with more fragmentation) MW Text Kroupa Chabrier ULIRG: T cold 70 K gas 80 km s 1 (Q 1 for gas 1000 M pc 2 ) Mach number in ULIRGs: M & 100
58 Open Questions: 1. What Maintains the Turbulence?
59 Open Questions: 1. What Maintains the Turbulence? Efficient Cooling: P diss M gas v turb t crossing
60 Open Questions: 1. What Maintains the Turbulence? Efficient Cooling: P diss M gas v turb t crossing 2. Why Doesn t Everything Collapse?
61 Open Questions: 1. What Maintains the Turbulence? Efficient Cooling: P diss M gas v turb t crossing 2. Why Doesn t Everything Collapse? Top-down turbulence can t stop collapse once self-gravitating Fast Cooling: Ṁ M gas t freefall
62 Summary: * ISM statistics are far more fundamental than we typically assume * Ø Turbulence + Gravity: ISM structure follows Ø Lognormal density PDF is not critical Ø ANALYTICALLY understand: Ø GMC Mass Function & Structure ( first crossing ) Ø Core MF ( last crossing ) & Linewidth-Size-Mass Ø Clustering of Stars (correlation functions) Ø Feedback Regulates & Sets Efficiencies of Star Formation Ø K-S Law: enough stars to offset dissipation (set by gravity) Ø Independent of small-scale star formation physics (how stars form) Ø
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