Magnetized turbulence and cosmic ray transport in the
Magnetized turbulence and cosmic ray transport in the interstellar medium A. Marcowith (L. U. P. M) COSMIS Kick-off meeting
Great variety of transport A very complex problem: processes • • CR random walk = parallel perpendicular transport to the mean MF (Schlickeiser’ 02, Shalchi’ 09) • Parallel & perpendicular transport: r. L – Magnetic fluctuations at scales > r. L (= E/Ze. B): • magnetic mirroring/focusing (see Marco’s talk), 3 D chaotic behavior induces a perpendicular transport. – At scales < r. L: • scattering off magnetic field fluctuations (parallel/perpendicular transport, second order Fermi acceleration). – Other transports: advection, shocks (Bykov’ 01) – The ISM is inhomogeneous/time dependent/partially ionized 12/11/2021 COSMIS Kick-off meeting • Cosmic ray transport rely on calculations of 3 D transport (parallel perpendicular) + Mean 2 MF
Two fluid calculations • MHD+ fluid of CRs: – Prescribed diffusion coefficients but … – Back-reaction included: dynamical, heating, ionization effects. • Used in a great variety of problems – In most of cases: analytical calculations. – Galactic magnetic dynamo (Parker instability): Hanasz+09 • PIERNIK code (free access, interesting for tests, Michal ready to help). – Galactic winds (CR driven): Breitschwerdt+91 – Molecular cloud collapse: thermal instability Wagner+05, Shadmehri’ 09 – Adiabatic/Radiative shocks Cox & Boulares’ 83, 12/11/2021 COSMIS Kick-off meeting 3 Wagner+07
Transport effects Cosmic ray density versus time in two sourc One in magnetic field flux tube / One out • Snodin et al’ 06 Effect of the CR diffusivity Þ Depends on the diffusion coefficients // and & on the properties of the turbulence Þ What does import in fluid dynamics is the CR pressure gradient = the force exerted on the magnetised fluid. • Never really considered in the case of the ISM (to my knowledge). 12/11/2021 COSMIS Kick-off meeting 4
Kinetic calculations • Diffusion coefficients calculations. 12/11/2021 COSMIS Kick-off meeting 5
Diffusion coefficients recipes 1. Definitions: Mean B along z v//= v 2. Fokker-Planck Diffusion Relation v(t)-B(t): 3. Magnetic tensor: x(t) particle trajectory 4. Specific models for P(k, t) isotropic A(k)=specific spectrum 12/11/2021 Goldreich-Sridhar COSMIS Kick-off meeting anisotropic 6
Diffusion coefficients recipes 1. Definitions: Mean B along z v//= v 2. Fokker-Planck Diffusion Relation v(t)-B(t): 3. Magnetic tensor: x(t) particle trajectory 4. Specific models for P(k, t) isotropic A(k)=specific spectrum 12/11/2021 Goldreich-Sridhar COSMIS Kick-off meeting anisotropic 7
Some solutions • Quasi-linear theory (QLT): treat CR trajectory as unperturbed (ie x(t) produced by Bz) (Schlickeiser’ 02) • Non-linear analytical theories (NLT) (Shalchi’ 09) – Use different approximations (resonance broadening, second ordrer trajectory calculations …. ) for different ISM phases. – Goldreich-Sridhar (Yan & Lazarian’ 08): • In incompressible MHD: bad confinement by Alfvén waves by gyroresonance (kr. L = 1) slow waves help through transit-time damping (Tcherenkov resonance). 12/11/2021 COSMIS Kick-off meeting D vs Incompressible case: Scattering by slow modes but gyroresonance limits // at small pitch-angles 8
Propagation into a multi-phase ISM • Calculations in the compressible limit: several constraints (Yan & Lazarian’ 04’ 08) – Three types of waves: Aflvén, slow/fast magnetosonic (S/F M) – Forcing at large scales L + turbulent cascade cut-off at scales lc < L due to different processes (viscous, Landau, ion-neutral …). • Some results: – NLT: FM waves control the CR mean free path in the WIM and halo (very hot ISM). * rebound of mfp around 100 Ge. V in the WIM phase: viscous damping reduces available FM waves to those slab modes. 12/11/2021 COSMIS Kick-off meeting CR // 9 mean free path vs Energy
Numerical simulations • Numerical simulations – From a prescribed turbulent model (eg isotropic): we specify A(k) (Giacalone & Jokipii’ 99, Casse+02, Candia & Roulet ‘ 04, A. M+06) – From MHD solutions (Reville+08, Beresnyak+10) … COSMIS project 12/11/2021 COSMIS Kick-off meeting 10
Numerical solutions: incompressible limit • Analytical/numerical calculations: Beresnyak+10 3 D incompressible MHD solved using pseudospectral method (Cho+00) over a periodic box size 2. = * Beresnyak => Elsasser variables Runge-Kutta + predictor-corrector schemes Normalized in a way that in principle both non-relativistic and relativistic limits can be handled. 12/11/2021 Kick-off Forcing = stochastic v spectrum. COSMIS k [2, 3. 5] withmeeting outer scale L = /2 11
Particle diffusive motion for different Larmor radii (energies) r. L [0. 1, 1] (x 2 ) x parallel to the background MF B 0 Parallel diffusion rl rl 2 Perpendicular diffusion rl 2 rlr 2 2 l Dxx is constant at low energies and scales as rl beyond 0. 1 L 12/11/2021 rl ! Several drawbacks: * Perpendicular and parallel wrt to B 0 not with the mean COSMIS Kick-off meeting 12 MF
Conclusions • Two fluid calculations: – Rely on prescribed diffusion coefficients. – Important to handle dynamical coupling between CRs and MHD. • Kinetic calculations: – Rely on prescribed turbulence models (eg Goldreich. Sridhar). – Only in test particle limit (for the moment). – MHD-kinetic approach still very limited wrt to analytical calculations. 12/11/2021 COSMIS Kick-off meeting 13
Cosmis in short MHD simulations (RAMSES, Hennebelle+08 and/or Heracles) Magnetic field Forcing by converging flows (? ) (high resolution simulations, task 1) or random Supernovae explosions (large scale simulations, task 2). Cases 1 & 2: 12/11/2021 Cosmic ray propagation (task 3) in: 1. Snapshots as test particles 2. Time dependent simulations as test particles 3. Cosmic rays as a fluid with diffusion coefficients inputs COSMIS Kick-off meeting 14 from (1) and (2): back reaction.
Discussion Cosmic Rays, Turbulence & Supernova remnants 12/11/2021 COSMIS Kick-off meeting 15
COSMIS project: task 3 • Task 3. 1: propagation of cosmic rays in the test-particle approximation in the ISM (R. Cohet, A. M. , C. Vigh)* – – – Incompressible case: reproduce Beresnyak’s results. Simulation set 1: high resolution simulations (task 1) Extend the results by Beresnyak to the compressible case. Try to explore the case of low energy cosmic rays (connection with task 3. 2). Simulation set 2: large scale simulations including forcing by supernova remnants (task 2) • Task 3. 2. 1: dynamical effect of cosmic rays will be investigated through a two fluid approach (explicit schemes) (C. Vigh, A. M. , R. Cohet) – – • Dynamical impact of low energy CRs in high resolution simulations (task 1) To be used in supernova remnant modelling (task 2) Large scale dynamical impact using simulation set 2 (task 2) Explore the case of high energy cosmic rays (including backreaction connection with task 3. 1): gamma-ray emission. Task 3. 2. 2: ionization by CRs (C. Vigh, A. M. , R. Cohet) – Evaluate the ionization impact using simulation set 1 (task 1). 12/11/2021 COSMIS Kick-off meeting * Men at work in Montpellier 16
Other related topics for task 3 • Cosmic ray escapes from sources (Stefano’s talk): – Injection term in the coupled kinetic-MHD equations. • Propagation of low energy CRs (Marco’s talk): – Influence of sources distribution (Cesarsky’ 75). – Coupling CRs and MHD: dynamical effects can be handled. – Position of CRs can determined and ionization derived: one needs to separate electrons/ions (two fluids MHD): requires some developments in the MHD code. 12/11/2021 COSMIS Kick-off meeting 17
Discussion: needs 1. MHD turbulence -CRs : – Propagation properties at multi-scales: CR physics, diffuse radiation (CRp, Cre). 2. MHD turbulence - SNRs & CRs: – – Local influences of sources on ISM through CRs ? Dynamical effects. 3. Chemistry- MHD turbulence & CRs: – Ionization and heating: both effects have to be accounted at once in chemical models. 12/11/2021 COSMIS Kick-off meeting 18
Back up slides 12/11/2021 COSMIS Kick-off meeting 19
CR random walk • Type of random walk probed by the mean square deviation (msd) 0<a<1 sub-diffusion a=1 diffusion 1<a<2 super-diffusion a=2 ballistic NB: Pure diffusion (a=1) is a particular case that is expected in developed turbulence (no intermittency effects) at scales/times sufficiently large … etc 12/11/2021 COSMIS Kick-off meeting 20
Models of MHD turbulence • Models of Pij – Separated dynamical effects: magnetostatic case: =1 1/ Isotropic turbulence: A=spectrum+geometry 2/ Cases of anisotropic axisymmetric turbulence with no helicity Turbulence models A(k//, k ) Slab S(k//) (k )/ k 2 D S(k ) (k//)/ k Goldreich-Sridhar S(k )f(k///k 2/3) 12/11/2021 COSMIS Kick-off meeting S(k): L-1<k<ld-1 Schlickeiser’ 02 Chandran’ 00 21
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