picard & galactic cr propagation

Picard & Galactic CR Propagation

CRISM 2014 – Ralf Kissmann

Montpellier 2014 June 27.

Ralf Kissmann CRISM 2014

Reminder: Description of CR Transport

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial / momentumdiffusion

Spatial convection

(Adiabatic) energy changes

Inter-species reactions

Loss terms

Result

CR-distribution ψ

→ input for gamma rays

Solution

Simplifications → analytical

General case → numerical

Propagation Transport Equation

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Individual Terms

CR sources

Spatial convection

Loss terms

Result

CR-distribution ψ

Solution

Galactic Propagation Codes

Major Codes

semi-analytical:

fully numerical

Galprop

Dragon

Other Approaches

Busching et al.

Effenberger et al.

Hanasz et al. (Piernik)

Transport in ISM

(by Heinz & Sunyaev (2002))

Propagation Codes

Major Codes

semi-analytical:

fully numerical

Galprop

Dragon

Other Approaches

Busching et al.

Effenberger et al.

Transport in ISM

Propagation Codes

Major Codes

semi-analytical:

fully numerical

GalpropDragon

Other Approaches

Busching et al.

Effenberger et al.

Transport in ISM

Propagation Codes

Major Codes

semi-analytical:

fully numerical

GalpropDragon

Other Approaches

Busching et al.

Effenberger et al.

Transport in ISM

Propagation Codes

Major Codes

semi-analytical:

fully numerical

GalpropDragon

Other Approaches

Busching et al.

Effenberger et al.

Transport in ISM

Propagation Codes

Physics in Numerical Propagation Codes

Transport Processes

Convection

Diffusion

Momentum diffusion

Propagation Modelling

Transport Processes

Convection

Diffusion

Momentum diffusion

Galaxy Model

Matter distribution

Magnetic field

Hydrogen Distribution

(From Galprop website)

Transport Processes

Convection

Diffusion

Momentum diffusion

Galaxy Model

Matter distribution

Magnetic field

Interaction with ISM

Spallation cross sections

Energy loss processes

Nuclear network

Hydrogen Distribution

Transport Processes

Convection

Diffusion

Momentum diffusion

Galaxy Model

Matter distribution

Magnetic field

Nuclear network

Secondaries

Secondary CRs

Gamma rays

Transport Processes

Convection

Diffusion

Momentum diffusion

Galaxy Model

Matter distribution

Magnetic field

Nuclear network

Secondaries

Secondary CRs

Gamma rays

Solution Process

CR source distribution

⇓Transport solver

⇓CR distribution

⇓Gamma ray emission

Transport Processes

Convection

Diffusion

Momentum diffusion

Galaxy Model

Matter distribution

Magnetic field

Nuclear network

Secondaries

Secondary CRs

Gamma rays

Solution Process

CR source distribution⇓

Transport solver

⇓CR distribution

Transport Processes

Convection

Diffusion

Momentum diffusion

CR Distribution

Secondaries

Secondary CRs

Gamma rays

Solution Process

Transport solver⇓

CR distribution

Transport Processes

Convection

Diffusion

Momentum diffusion

Gamma Ray Emission

Secondaries

Secondary CRs

Gamma rays

Solution Process

Transport solver⇓

CR distribution⇓

Gamma ray emission

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Physics as parameters

Constant in timeConstant in space

→ Parameter tuning

Diffusion

Convection

Halo height

Propagation Issues

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Diffusion

Convection

Halo height

Transport Parameters

Source distribution q(r, p)

Diffusion tensor DMomentum diffusion Dpp

Spatial convection v

Energy losses p

Spallation τf

Propagation Issues

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Diffusion

Convection

Halo height

Energy losses p

Spallation τf

Propagation Issues

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Diffusion

Convection

Halo height

Energy losses p

Spallation τf

Propagation Issues

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Diffusion

Convection

Halo height

Technical Issues

Solver

Local structure ↔ spatialresolution

Consistency

Propagation Issues

Issues in Galprop

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Physics Issues

Diffusion

Convection

Halo height

Technical Issues

Solver

Local structure ↔ spatialresolution

Consistency

Propagation Issues

Example I: Diffusion

Diffusion in Galprop

Isotropic

No spatial variation

Alternatives:

Dragon, PicardEffenberger et al.

CRs Inside the Heliosphere

(From Ulysses website)

Propagation Issues

Isotropic

Alternatives:

Propagation Issues

Isotropic

Alternatives:

Field Aligned Diffusion

D‖ 0 0

0 D⊥,1 00 0 D⊥,2

Propagation Issues

Isotropic

Alternatives:

Diffusion in Cartesian Coordinates

D‖ cos2 ψ +D⊥ sin2 ψ

(D‖ −D⊥

)sinψ cosψ 0(

D‖ −D⊥)

sinψ cosψ D‖ sin2 ψ +D⊥ cos2 ψ 0

0 0 D⊥

Propagation Issues

Isotropic

Alternatives:

Boundary conditions?

Diffusion ↔ advection

Energy dependence

Galprop:

Restricted to boxψ = 0 at boundary

The Galaxy

(artist sketch by NASA)

Propagation Issues

Example II: Consistency

Propagation

Azimuthally symmetric

Gamma Ray Computation

Ring-distribution for gas

Gas for Propagation

Gamma Ray Emission

(Picard results for 100GeV gamma rays)

Propagation Issues

Propagation

Gas for Propagation

Gamma Ray Emission

Propagation Issues

Propagation

Gas for Propagation

Gamma Ray Emission

Propagation Issues

Propagation

Gas for Propagation

Gamma Ray Emission

Propagation Issues

Propagation

But: CR distribution

20 15 10 5 0 5 10 15 2020

Gamma Ray Emission

Propagation Issues

Solving the Transport Equation

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Diffusion-advectionequation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Solve multiple time stepsCharacteristic time-scalesConvergence to steadystate

→ Time-integration solver

Propagation Issues

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Propagation Issues

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Propagation Issues

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Propagation Issues

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Propagation Issues

Transport Equation

∂t= q(r, p) +∇ · (D∇ψ − vψ) +

∂pp2Dpp

p2ψ −

{pψ −

3(∇ · v)ψ

τfψ −

Type of Equation

Abbreviation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Possible Solutions

Time-dependent

Steady state

Standard Approach

Time integration

Propagation Issues

Standard Approach via Time-Integration

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Start with empty Galaxy

Integrate until convergence

Problem

Characteristic timescales

Convergence timescales

Propagation Steady State

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

Explicit

Implicit

Solution Approach

Problem

Explicit schemes

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Easy to solve

Time step restriction

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Explicit schemes

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Easy to solve

Implicit schemes∂ψ

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Coupled matrix equation

Larger time step

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Explicit schemes

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Easy to solve

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Larger time step

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Explicit schemes

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Easy to solve

∂t= f(ψ)→

ψn+1 − ψn

∆t= f(ψ

Larger time step

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Time Evolution of Spectrum

E [MeV]

102 103 104 105 106 107 108 109 10101024

steady state time: 200 myr time: 60 myr time: 20 myr time: 6 myr time: 2 myr

Possible Solvers

SDEs / Monte Carlo

(Pseudo-) particles

Grid-based

ExplicitImplicit

Solution Approach

Problem

Time Evolution of Spectrum

E [MeV]

102 103 104 105 106 107 108 109 10101024

steady state time: 200 myr time: 60 myr time: 20 myr time: 6 myr time: 2 myr

Characteristic time: ∼50 yrs

The Galprop solver

Numerical Implementation

Crank-Nicolsondiscretisation

Time-integration

Dimensional splitting

Decreasing timesteps

Problems

Check for convergence?

Timestep control

Problem dependent?

Nuclear reaction network

Galprop

→ Let’s do better

Propagation Galprop

The Galprop solver

Time-integration

Problems

Timestep control

Problem dependent?

Galprop

Propagation Galprop

The Galprop solver

Time-integration

Problems

Timestep control

Problem dependent?

Galprop

Propagation Galprop

The Galprop solver

Time-integration

Problems

Timestep control

Problem dependent?

Galprop

Propagation Galprop

The Galprop solver

Time-integration

Problems

Timestep control

Problem dependent?

Galprop

Propagation Galprop

The Galprop solver

Time-integration

Problems

Timestep control

Problem dependent?

Galprop

Propagation Galprop

How to do better

A Different Approach

Solve steady state problem

Simplified Transport Equation∂ψ

∂t= s(r, p) +∇ · (D∇ψ − vψ) +

Difficulty

Discretisation

→ Coupled matrix equation

→ Band-diagonal matrix

Iterative solver

MultigridBICGStab

Propagation Alternative

How to do better

Simplified Transport Equation

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

Discretisation in 1D

∇D∇ψ =Dxx∂2ψ

'Dxxψi+1 − 2ψi + ψi−1

→ aiψi−1 − biψi + ciψi+1 = −si ∀i

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

→ Coupled matrix equation→ Band-diagonal matrix

Iterative solver

MultigridBICGStab

Descretisation in 2D

∂x2+Dyy

∂2ψ

'Dxxψi+1,j − 2ψi,j + ψi−1,j

+Dyyψi,j+1 − 2ψi,j + ψi,j+1

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

Descretisation in 2D

∂x2+Dyy

∂2ψ

'Dxxψi+1,j − 2ψi,j + ψi−1,j

+Dyyψi,j+1 − 2ψi,j + ψi,j+1

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

Multigrid Illustration

How to do better

0 = s(r, p) +∇ · (D∇ψ − vψ) +ψ

Difficulty

Discretisation

Iterative solver

MultigridBICGStab

Multigrid Illustration

Multigrid Implementation

Red-black Gauss-Seidel

Alternating planeGauss-Seidel

Cosmic Particle Transport:

Features of Picard

Solver

Steady-state solution

Explicit time integrator

MPI-parallel

→ High resolution

Improved nuclear network

Example Simulation Results

x [kpc]

y[kpc]

Example results:Milkyway as spiral galaxy

Picard Features

Features of Picard

Solver

MPI-parallel

→ High resolution

Example Resolution

Standard Galprop

→ 2D (1 kpc × 100 pc)

Picard

→ 3D (up to ∼75 pc3)

x [kpc]

y[kpc]

Picard Features

Features of Picard

Solver

MPI-parallel

→ High resolution

Physics

3D source distributions

Anisotropic diffusion

tbd...

x [kpc]

y[kpc]

Picard Features

Features of Picard

Solver

MPI-parallel

→ High resolution

Physics

3D source distributions

Anisotropic diffusion

tbd...

x [kpc]

y[kpc]

Picard Features

Milkyway as a Spiral Galaxy

Model setup

Spiral arm source dist.

Standard Galpropparameters

Electrons / protons↔ Nuclear network

Results

Different sourcedistributions

→ 1 TeV electrons

Differences ↔normalisation

↔ Vicinity of Earth

Secondaries

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Axi-symmetric Model

x20 15 10 5 0 5 10 15 204

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

NE-2001 Model

x20 15 10 5 0 5 10 15 204

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Other Four Arm Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Two Arm Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Two Arm Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

NE-2001 Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Other Four Arm Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Two Arm Model

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Distribution of Carbon

x [kpc]

y[kpc]

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

Distribution of Boron

x [kpc]

y[kpc]

Picard Applications

Model setup

Results

→ 1 TeV electrons

Secondaries

B/C Ration

kinetic Energy per nucleon

101 102 103 104 105 1060.00

0.40HEAO-3ACEATICCREAMAMS-1

Picard Applications

Gamma Rays with Picard

Axi-Symmetric Configuration

Preliminary Conclusion

Increase of IC component

Two-arm model excluded?

Axi-symmetric model?

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Four-Arm Configuration

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Two-Arm Configuration

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Axi-Symmetric Configuration

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Four-Arm Configuration

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Residual - Four Arm Configuration

Gamma Ray Data

100 MeV

100 GeV

Picard Applications

Conclusion

Inverse Compton & Spiral Arms

Application of Picard

Principal CR data X

GeV photons (X)

TeV photons

Electrons / DM

Galactic Propagation

New generation of models

Different improvementsunder way

Conclusion

Inverse Compton & Spiral Arms

Application of Picard

Principal CR data X

GeV photons (X)

TeV photons

Electrons / DM

Galactic Propagation

New generation of models

Different improvementsunder way

Conclusion

picard & galactic cr propagation

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