Formation and Collapse of Nonaxisymmetric Protostellar Cores in Magnetic Interstellar Clouds

Transcription

1 Formation and Collapse of Nonaxisymmetric Protostellar Cores in Magnetic Interstellar Clouds Glenn E. Ciolek Department of Physics, Applied Physics, and Astronomy & New York Center for Studies on the Origins of Life (NSCORT) Rensselaer Polytechnic Institute 1

2 Magnetic Support of Clouds Evidence for magnetic support of molecular clouds: 2

3 Magnetic Support of Clouds Evidence for magnetic support of molecular clouds: - Polarimetry. 2

4 Magnetic Support of Clouds Hildebrand et al. (2000) 3

5 Magnetic Support of Clouds NGC 1333 IRAS 4A (Girart, Rao, & Marrone 2006) 4

6 Magnetic Support of Clouds Further evidence: 5

7 Magnetic Support of Clouds Further evidence: - Modified Chandrasekhar-Fermi method. 5

8 Magnetic Support of Clouds Further evidence: - Modified Chandrasekhar-Fermi method. - Zeeman splitting. 5

9 Magnetic Support of Clouds Further evidence: - Modified Chandrasekhar-Fermi method. - Zeeman splitting. The measured magnetic fields yield mass-to-flux ratios M Φ B ( σ n B) that are within a factor 2 below or above the critical value for gravitational collapse (Crutcher 2004). 5

10 Theoretical Models & Observations Past decade: axisymmetric models of formation and collapse of protostellar cores in magnetically supported molecular clouds were developed. 6

11 Theoretical Models & Observations Past decade: axisymmetric models of formation and collapse of protostellar cores in magnetically supported molecular clouds were developed. Ciolek & Basu (2000) applied a model to the L1544 prestellar core. 6

12 Theoretical Models & Observations Past decade: axisymmetric models of formation and collapse of protostellar cores in magnetically supported molecular clouds were developed. Ciolek & Basu (2000) applied a model to the L1544 prestellar core. - Reproduced observed density and velocity profiles (Williams et al. 1999, Caselli et al. 2002) 6

13 Theoretical Models & Observations Past decade: axisymmetric models of formation and collapse of protostellar cores in magnetically supported molecular clouds were developed. Ciolek & Basu (2000) applied a model to the L1544 prestellar core. - Reproduced observed density and velocity profiles (Williams et al. 1999, Caselli et al. 2002) - Predicted magnetic field strength, confirmed by Zeeman measurements (Crutcher & Troland 2000). 6

14 Theoretical Models & Observations Past decade: axisymmetric models of formation and collapse of protostellar cores in magnetically supported molecular clouds were developed. Ciolek & Basu (2000) applied a model to the L1544 prestellar core. - Reproduced observed density and velocity profiles (Williams et al. 1999, Caselli et al. 2002) - Predicted magnetic field strength, confirmed by Zeeman measurements (Crutcher & Troland 2000). Problem: clouds and cores usually not axisymmetric. 6

15 Theoretical Models & Observations L1544 Prestellar Core (Williams et al. 1999) 7

16 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless initial mass-to-flux ratio for a self-gravitating object: µ 0 M Φ B M Φ B 0 crit where ratio. M Φ B crit 0 17 G is the critical mass-to-flux 8

17 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless initial mass-to-flux ratio for a self-gravitating object: µ 0 M Φ B M Φ B 0 crit where ratio. M Φ B crit 0 17 G is the critical mass-to-flux µ 0 1 Subcritical, magnetically supported. 8

18 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless initial mass-to-flux ratio for a self-gravitating object: µ 0 M Φ B M Φ B 0 crit where ratio. M Φ B crit 0 17 G is the critical mass-to-flux µ 0 µ Subcritical, magnetically supported. Supercritical, gravitational collapse. 8

19 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless neutral-ion collision time: τ ni 0 neutral ion collision time gravitational contraction timescale cm n n x i 7 where x i n i n n is the degree of ionization. 9

20 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless neutral-ion collision time: τ ni 0 neutral ion collision time gravitational contraction timescale cm n n x i 7 where x i n i n n is the degree of ionization. τ ni 0 1 Ineffective neutral-ion coupling. 9

21 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless neutral-ion collision time: τ ni 0 neutral ion collision time gravitational contraction timescale cm n n x i 7 where x i n i n n is the degree of ionization. τ ni 0 τ ni Ineffective neutral-ion coupling. Some coupling of neutrals with ions & magnetic field. 9

22 Magnetic Fields & Star Formation: Fundamental Parameters Dimensionless neutral-ion collision time: τ ni 0 neutral ion collision time gravitational contraction timescale cm n n x i 7 where x i n i n n is the degree of ionization. τ ni 0 τ ni Ineffective neutral-ion coupling. Some coupling of neutrals with ions & magnetic field. For typical cloud conditions, τ ni

23 Modeling Nonaxisymmetric Collapse Model Cloud Schematic z Z(x,y) x B P ext 10

24 Modeling Nonaxisymmetric Collapse We numerically integrate the coupled nonlinear partial differential equations for the system of neutral and ion fluids, and the magnetic field in Cartesian geometry. These include: Continuity of mass. 11

25 Modeling Nonaxisymmetric Collapse We numerically integrate the coupled nonlinear partial differential equations for the system of neutral and ion fluids, and the magnetic field in Cartesian geometry. These include: Continuity of mass. Force equations of neutrals and ions. 11

26 Modeling Nonaxisymmetric Collapse We numerically integrate the coupled nonlinear partial differential equations for the system of neutral and ion fluids, and the magnetic field in Cartesian geometry. These include: Continuity of mass. Force equations of neutrals and ions. Maxwell s equations. 11

27 Modeling Nonaxisymmetric Collapse We numerically integrate the coupled nonlinear partial differential equations for the system of neutral and ion fluids, and the magnetic field in Cartesian geometry. These include: Continuity of mass. Force equations of neutrals and ions. Maxwell s equations. Poisson s equation. 11

28 Modeling Nonaxisymmetric Collapse We numerically integrate the coupled nonlinear partial differential equations for the system of neutral and ion fluids, and the magnetic field in Cartesian geometry. These include: Continuity of mass. Force equations of neutrals and ions. Maxwell s equations. Poisson s equation. Full formulation presented in Ciolek & Basu (2006). 11

29 Linearized and Fourier-Analyzed System Assume small-amplitude perturbation δ f for any physical variable f in the system of equations governing the evolution of a model cloud: δ f x y t exp i k x x k y y ωt 12

30 Linearized and Fourier-Analyzed System Assume small-amplitude perturbation δ f for any physical variable f in the system of equations governing the evolution of a model cloud: δ f x y t exp i k x x k y y ωt Resulting dispersion relation can be solved for the complex frequency ω k x ky. 12

31 Linearized and Fourier-Analyzed System Assume small-amplitude perturbation δ f for any physical variable f in the system of equations governing the evolution of a model cloud: δ f x y t exp i k x x k y y ωt Resulting dispersion relation can be solved for the complex frequency ω k x ky Gravitationally unstable modes exist if I ω The growth time for the instability is. is positive. τ g 1 I ω 12

32 Timescale for Gravitational Instability 10 3 ~ τ ni,0 = µ 0 = τ g λ 13

33 Lengthscale of Maximum Growth Rate λ g m 10 3 ~ τ ni,0 = 0.04 λ g,m µ 0 14

34 Numerical Simulations of Nonaxisymmetric Core Formation 15

35 Numerical Simulations of Nonaxisymmetric Core Formation 15

36 Numerical Simulations of Nonaxisymmetric Core Formation 15

37 Numerical Simulations of Nonaxisymmetric Core Formation 15

38 Numerical Simulations of Nonaxisymmetric Core Formation 15

39 Dynamical Infall of Protostellar Cores Basu & Ciolek (2004) 16

40 Dynamical Infall of Protostellar Cores Basu & Ciolek (2004) 16

41 Dynamical Infall of Protostellar Cores Basu & Ciolek (2004) 16

42 Summary We have developed models of protostellar core formation and nonaxisymmetric collapse in magnetic interstellar clouds. 17

43 Summary We have developed models of protostellar core formation and nonaxisymmetric collapse in magnetic interstellar clouds. From a linear analysis of the models, determined the lengthscale of maximum gravitational instability λ g m and its dependence on the parameter µ 0. λ g m has a resonance for clouds near the critical state µ

44 Summary We have developed models of protostellar core formation and nonaxisymmetric collapse in magnetic interstellar clouds. From a linear analysis of the models, determined the lengthscale of maximum gravitational instability λ g m and its dependence on the parameter µ 0. λ g m has a resonance for clouds near the critical state µ 0 1. Nonlinear simulations verify that the fundamental fragmentation scale is λ g m. 17

45 Summary We have developed models of protostellar core formation and nonaxisymmetric collapse in magnetic interstellar clouds. From a linear analysis of the models, determined the lengthscale of maximum gravitational instability λ g m and its dependence on the parameter µ 0. λ g m has a resonance for clouds near the critical state µ 0 1. Nonlinear simulations verify that the fundamental fragmentation scale is λ g m. Clouds with µ 0 2 have cores with large-scale infall velocities that are excluded by observations. 17