Direct Evidence for Two Fluid Effects in Molecular Clouds. Dinshaw Balsara & David Tilley University of Notre Dame

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1 Direct Evidence for Two Fluid Effects in Molecular Clouds Dinshaw Balsara & David Tilley University of Notre Dame 1

2 Outline Introduction earliest stages of star formation Theoretical background Magnetically regulated star formation Turbulence driven star formation New data showing that we might be tracing the dissipation scales New simulation efforts to bridge these models Can two fluid effects be identified? 2

3 Giant Molecular Clouds Composed primarily of molecular hydrogen 10% helium by number of atoms over 150 molecules and ions detected in trace amounts very complex chemistry! Sizes up to 50 pc; Mean densities of cm 3 peak densities can be many orders of magnitude larger due to shocks, turbulence, and collapse heavily extincted in visual light; some optically thin windows in the infrared, submillimeter and radio 3

4 Introduction 4

5 Prestellar Cores in Molecular Clouds Cores are individual bound clumps of material within a cloud Well studied distribution of masses identical to distribution of stellar masses Salpeter power law dn/dm ~ M 2.35 Classified according to slope of IR spectrum Olmi et al Mass spectrum in Vela D Class 0 No detectable central IR source Class I Thick envelope Thick disk Class II Minimal envelope Thick disk Class III No envelope Minimal disk 5

6 Critical Mass for Collapse M > 5 G R 2 B 3 M > 2.4 c 2 s G R v A = B 4πρ Caveat: Does not account for the increase in the 6 curvature of the magnetic field lines during collapse!

7 Properties of the Turbulence (Large Scales) Turbulence found to be supersonic (Mach 3 5) but mildly sub Alfvenic (Crutcher 1994) Magnetic pressure dominates gas pressure. Mass to flux ratios barely super critical in cores. Self similarity of line profiles/velocity dispersion on range of scales taken to be evidence for turbulence (Falgarone & coworkers; Ossenkopf & Mac Low 2002; Falcetta Gonsalves, Lazarian & Houde 2010) 7

8 Properties of the Turbulence (Small Scales) Turbulence is expected to form an energy cascade Li & Houde (2008) observed that the turbulent velocity of ions (HCO + ) was smaller than that of neutral (HCN) molecules (J=4 3) difference in the turbulence spectrum? Li et al. (2010): M17, DR21(OH), NGC 2024 show similar trends 8

9 Understanding the Small Scale Results Ambipolar diffusion does not set the cutoff for neutrals Ions should have steeper spectral slope than neutrals at (the small) ambipolar diffusion scales Linewidth-size relation for neutrals & ions Black neutrals ; Red ions 9

10 Standard Model for Star Formation Focus on the 10 s of mpc scales where prestellar cores form The classic picture of star formation involves cores collapsing slowly gravitational forces nearly balance pressure & magnetic forces Magnetic field dragged in with collapse Collapse occurs faster parallel to the magnetic field magnetically supported discs 10

11 Magnetic Regulation of Star Formation Tension in curved magnetic field lines Magnetic fields coupled to ions Most of material in core is neutral Weak coupling magnetic field can drift Magnetic fields slowly leak out of core due to this ambipolar drift Key Challenges: Evolution occurs slowly (10 7 years) Why are km/s turbulent velocities observed? How do entire clouds achieve virial equilibrium 1 8π B2 1 4π B ( )B 11

12 Poloidal Magnetic Field Balsara

13 Midplane Density Balsara

14 Turbulence Driven Star Formation Focus on the pc scales where the turbulence is observed Cloud dynamics driven by internal stirring, not magnetic fields shock generated turbulence colliding molecular clouds supernovae shocks stellar winds & ionization fronts protostellar jets Key Challenges: Evolution occurs very quickly (10 5 years) How do molecular clouds survive over 10 7 years? How do prestellar cores (which are observed to collapse subsonically) regulate their collapse? 14

15 Problems with Turbulence Models In order to get collapse to occur, turbulence models with ideal physics must use weak magnetic fields otherwise, gravity cannot overcome magnetic forces observed magnetic fields within molecular clouds are very close to critical Tilley & Pudritz

16 Re introduce Ambipolar Diffusion Ambipolar diffusion can permit magnetic fields to escape from cores reduce barrier to formation of low-mass cores Methods: Single-Fluid Model efficient for low ionization fractions ignores momentum of ions high computational cost for highresolution simulations (diffusion term) Two-Fluid Model efficient for high-resolution includes ion momenta exactly high computational cost for low ionization fractions (hi v A in ions) Nakamura & Li

17 Wave Propagation in Partially Ionized Systems (Two fluid dispersion analysis with ionization fraction 10 6 shown) Fast Slow Alfvén Magnetosonic Waves Waves Balsara 1996 Tilley & Balsara 2010 long wavelength Sound waves Dissipation Scale Plasma Scale 17 short wavelength

18 Turbulence with Single Fluid Ambipolar Diffusion (dispersion analysis of two fluid with heavy ion approximation also done) Dissipation Scale Fast Slow Alfvén Magnetosonic Waves Waves Sound waves from Balsara

19 Our Simulations of Two Fluid Turbulence RIEMANN code Compare ionization fractions from 10 2 to 10 6 Continually driven by adding a spectrum of kinetic energy at large wavelengths Is there a difference in the character of the turbulence beneath the dissipation scale? 19

20 Energy Spectrum Well Ionized (10 2 ) (Energies normalized at k=2π/l; all waves survive) Energy injection Neutrals and ions follow each other very closely long wavelength 20 short wavelength

21 Energy Spectrum Less Ionized (10 3 ) (Alfven & fast magnetosonic waves drop out in the ionized fluid below dissipation scale) Energy injection Neutrals and ions spectrum begin to separate 21

22 Energy Spectrum Poorly Ionized (10 5 ) Energy injection Neutrals and ions spectrum becomes separated 22

23 Line Widths of Neutral and Ionized Species (Synthetic Line Profiles) ξ=10-2 Neutral Species (HCN) (Dashed Line Overlaps with solid) Ionized Species (HCO + ) (Solid Line) 23

24 Line Widths of Neutral and Ionized Species (Synthetic Line Profiles) ξ=10-5 Neutral Species (HCN) Ionized Species (HCO + ) Tilley & Balsara

25 Comparison at Different Ionizations Difference between ion and neutral linewidths increases at smaller ionization fractions ξ=10-2 ξ=10-4 ξ=10-5 Tilley & Balsara

26 Linewidth Size Relation Diamonds neutral line widths Squares ion line widths Diamonds & Squares slightly offset Tilley & Balsara

27 Linewidth Size Relation Our simulation results Measured line widths (Li & Houde 2008) (Note that the dissipation scale is at ~0.01 pc, or about 1 arcsec in this figure Black neutrals ; Red ions for both plots 27

28 Summary Theoretical models for star formation require strong turbulence and strong magnetic fields Gravitational collapse requires a mechanism that allows magnetic fields to disengage with the collapsing flow ambipolar / ion neutral drift New computational tools have been constructed that allow us to bridge the gap between the turbulently regulated models and the magnetically regulated models Two fluid ambipolar drift has quantifiable effects on the turbulent line widths that are measured. Observable handle on the ambipolar dissipation scale We now have simulations to back up the observations & 28 their interpretation.

29 Newton s Laws for Fluids vi 1 ρi + ρi( vi ) vi + Pi + ρi Φ+ B ( B) t 4π + αρ ρ = 0 n i i ( v v) vn ρn + ρn n n + n + ρn Φ+ αρnρi n i = t ( v ) v P ( v v ) 0 29

30 Wave Propagation with heavy ion approximation Tilley & Balsara