ISM Structure: Order from Chaos Philip Hopkins with Eliot Quataert, - PowerPoint PPT Presentation

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 Thursday, August 16, 12

The Turbulent ISM LMC IMPORTANT ON (ALMOST) ALL SCALES  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. Thursday, August 16, 12

The ISM YET THERE IS SURPRISING REGULARITY Giant Molecular Clouds: Stars & Pre-Stellar Gas Cores: MW Bastian LMC Chabrier SMC M33 M31 Number (dN/dM) IC10 Number Blitz, Rosolowski et al. Mass [M � ] Thursday, August 16, 12

The ISM YET THERE IS SURPRISING REGULARITY Giant Molecular Clouds: Stars & Pre-Stellar Gas Cores: MW Bastian LMC Chabrier d N SMC d M ∝ M − 1 . 8 M33 M31 Number (dN/dM) IC10 Number ∝ M − 2 . 2 Blitz, Rosolowski et al. Mass [M � ] Thursday, August 16, 12

The ISM YET THERE IS SURPRISING REGULARITY Giant Molecular Clouds: Stars & Pre-Stellar Gas Cores: MW Bastian LMC Chabrier d N SMC d M ∝ M − 1 . 8 M33 M31 Number (dN/dM) IC10 Number DM Halos?! ∝ M − 2 . 2 Blitz, Rosolowski et al. Mass [M � ] Thursday, August 16, 12

Extended Press-Schechter / Excursion-Set Formalism LMC  Press & Schechter ‘74: r Fluctuations a Gaussian random field   Know linear power spectrum P(k~1/r): variance ~ k 3 P(k) Thursday, August 16, 12

Extended Press-Schechter / Excursion-Set Formalism LMC  Press & Schechter ‘74: r Fluctuations a Gaussian random field   Know linear power spectrum P(k~1/r): variance ~ k 3 P(k)  “Count” mass above critical fluctuation: “Halos”  Turnaround & gravitational collapse ρ ( < R ∼ 1 /k ) > ρ crit ¯ Thursday, August 16, 12

Extended Press-Schechter / Excursion-Set Formalism LMC  Press & Schechter ‘74: r Fluctuations a Gaussian random field   Know linear power spectrum P(k~1/r): variance ~ k 3 P(k)  “Count” mass above critical fluctuation: “Halos”  Turnaround & gravitational collapse ρ ( < R ∼ 1 /k ) > ρ crit ¯  Generalize to conditional probabilities, N-point statistics, resolve “cloud in cloud” problem (e.g. Bond et al. 1991) Thursday, August 16, 12

Turbulence BASIC EXPECTATIONS ( k E ( k ) ∼ u t ( k ) 2 ) E ( k ) ∝ k − p Velocity: Thursday, August 16, 12

Turbulence BASIC EXPECTATIONS ( k E ( k ) ∼ u t ( k ) 2 ) E ( k ) ∝ k − p Velocity: h � (ln ρ � h ln ρ i ) 2 1 i Lognormal in r : Density: d p (ln ρ | R ) = exp p 2 S ( R ) 2 π S ( R ) Vasquez-Semadeni, Nordlund, Padoan, Ostriker, & others Text Thursday, August 16, 12

Turbulence BASIC EXPECTATIONS ( k E ( k ) ∼ u t ( k ) 2 ) E ( k ) ∝ k − p Velocity: h � (ln ρ � h ln ρ i ) 2 1 i Lognormal in r : Density: d p (ln ρ | R ) = exp p 2 S ( R ) 2 π S ( R ) Vasquez-Semadeni, Nordlund, Padoan, Ostriker, & others Text Z d ln k S k | W ( k, R ) | 2 S ( R ) = Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Angular Momentum κ ∼ V disk R disk Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Angular Momentum Thermal Pressure κ ∼ V disk ∝ r − 2 R disk Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Angular Momentum Thermal Turbulence Pressure ∝ r p − 3 ∼ r − 1 κ ∼ V disk ∝ r − 2 u 2 t > c 2 R disk r > r sonic : s Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Angular Momentum Thermal Gravity Turbulence Pressure ∝ r p − 3 ∼ r − 1 κ ∼ V disk ∝ r − 2 u 2 t > c 2 R disk r > r sonic : s Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

What Defines a Fluctuation of Interest? DISPERSION RELATION: s k 2 + u t ( k ) 2 k 2 − 4 π G ρ | k | h ω 2 = κ 2 + c 2 1 + | k | h Angular Momentum Thermal Gravity Turbulence Pressure ∝ r p − 3 ∼ r − 1 κ ∼ V disk ∝ r − 2 u 2 t > c 2 R disk r > r sonic : s Mode Grows (Collapses) when w<0: 2 h i ( M − 2 + | kh | 1 − p ) kh + ρ > ρ c ( k ) = ρ 0 (1 + | kh | ) h | kh | Chandrasekhar ‘51, Vandervoort ‘70, Toomre ‘77 Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Log[ Density / Mean ] Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Log[ Density / Mean ] Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Thermal+ Magnetic Log[ Density / Mean ] Turbulence Angular Momentum Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Thermal+ Magnetic Log[ Density / Mean ] Turbulence Angular Momentum Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Thermal+ Magnetic Log[ Density / Mean ] Turbulence Angular Momentum Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Thermal+ Magnetic Log[ Density / Mean ] Turbulence Angular Momentum Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Log[ Density / Mean ] First Crossing Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Log[ Density / Mean ] First Crossing GMCs Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Last Crossing Log[ Density / Mean ] First Crossing GMCs Thursday, August 16, 12

PFH 2011 “Counting” Collapsing Objects EVALUATE DENSITY FIELD vs. “BARRIER” Averaging Scale R [pc] Last Crossing Log[ Density / Mean ] Cores/IMF First Crossing GMCs Thursday, August 16, 12

Evolve the Fluctuations in Time CONSTRUCT “MERGER/FRAGMENTATION” TREES − ( δ − δ ( t = 0) exp [ − τ ]) 2 1 h i p ( δ | τ ) = exp p 2 S (1 − exp [ − 2 τ ]) 2 π S (1 − exp [ − 2 τ ]) Time Thursday, August 16, 12

Evolve the Fluctuations in Time CONSTRUCT “MERGER/FRAGMENTATION” TREES − ( δ − δ ( t = 0) exp [ − τ ]) 2 1 h i p ( δ | τ ) = exp p 2 S (1 − exp [ − 2 τ ]) 2 π S (1 − exp [ − 2 τ ]) Time Fraction Collapsed Per Crossing Time Simulations (Cooling+Gravity+MHD) Padoan & Nordlund Vazquez-Semadeni PFH 2011 Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS Number (>M cloud ) PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS r sonic ⌧ r ⌧ h S ( r ) ∼ S 0 Number (>M cloud ) PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS r sonic ⌧ r ⌧ h S ( r ) ∼ S 0 Number (>M cloud ) d n d M ∝ M − α e − ( M/M J ) β PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS r sonic ⌧ r ⌧ h S ( r ) ∼ S 0 Number (>M cloud ) d n d M ∝ M − α e − ( M/M J ) β α ≈ − 2 + (3 − p ) 2 ⇣ M J ⌘ ln 2 S p 2 M ⇣ M J ⌘ ≈ − 2 + 0 . 1 log M PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS r sonic ⌧ r ⌧ h S ( r ) ∼ S 0 Number (>M cloud ) d n d M ∝ M − α e − ( M/M J ) β α ≈ − 2 + (3 − p ) 2 ⇣ M J ⌘ ln 2 S p 2 M ⇣ M J ⌘ ⇣ M J ≈ − 2 + 0 . 1 log ⌘ α ≈ − 2 + 0 . 1 log M M PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “First Crossing” Mass Function VS GIANT MOLECULAR CLOUDS r sonic ⌧ r ⌧ h S ( r ) ∼ S 0 Number (>M cloud ) d n d M ∝ M − α e − ( M/M J ) β α ≈ − 2 + (3 − p ) 2 ⇣ M J ⌘ ln 2 S p 2 M ⇣ M J ⌘ ⇣ M J ≈ − 2 + 0 . 1 log ⌘ α ≈ − 2 + 0 . 1 log M M PFH 2011 log[ M cloud / M sun ] Thursday, August 16, 12

The “Last Crossing” Mass Function PFH 2012 VS PROTOSTELLAR CORES & THE STELLAR IMF Thursday, August 16, 12