DiffusiveShockAccelerationModels.jl

This package provides a number of efficiency models for Diffuse Shock Acceleration (DSA). It provides a number of functions to calculate what fraction of the energy dissipated at a shock is used to accelerate Cosmic Rays (CRs). If you use this implementation in a publication please cite Böss et. al. (2023).

Install

As usual with Julia just run

] add DiffusiveShockAccelerationModels

Mach number dendent efficiency models

Different authors found a number of models that describe the acceleration efficiency of CRs at shocks dependent on the sonic Mach number. Here we implemented the following DSA models:

Implemented DSA models

DiffusiveShockAccelerationModels.Kang07 — Type

Kang07(X_cr::T=0.05, η_max::T=0.0348) where T

Efficiency model by Kang, Ryu, Cen, Ostriker 2007, http://arxiv.org/abs/0704.1521v1

Values

X_cr: Pcr / Pth defined in model for re-acceleration. Basis for interpolation between acceleration and re-acceleration efficiency.
η_max: Maximum efficiency defined in the model

source

DiffusiveShockAccelerationModels.KR13 — Type

KR13(X_cr::T=0.05, η_max::T=0.0348) where T

Efficiency model by Kang&Ryu 2013: ApJ, 764, 95.

Values

X_cr: Pcr / Pth defined in model for re-acceleration. Basis for interpolation between acceleration and re-acceleration efficiency.
η_max: Maximum efficiency defined in the model

source

DiffusiveShockAccelerationModels.CS14 — Type

    CS14(X_cr::T=0.05, η_max::T=0.5*0.2055) where T

Efficiency model by Caprioli&Spitkovsky 2014 efficiency.

Values

X_cr: Pcr / Pth defined in model for re-acceleration. Basis for interpolation between acceleration and re-acceleration efficiency.
η_max: Maximum efficiency defined in the model

source

DiffusiveShockAccelerationModels.Ryu19 — Type

    Ryu19(X_cr::T=0.05, η_max::T=0.0348) where T

Efficiency model by Ryu et al. 2019: https://arxiv.org/pdf/1905.04476v2.pdf.

Values

X_cr: Pcr / Pth defined in model for re-acceleration. Basis for interpolation between acceleration and re-acceleration efficiency.
η_max: Maximum efficiency defined in the model

source

DiffusiveShockAccelerationModels.P16 — Type

    P16(X_cr::T=0.05, η_max::T=0.5) where T

Constant efficiency as in Pfrommer+ 2016, doi: 10.1093/mnras/stw2941

source

Magnetic field angle dependent efficiency models

Another parameter in the acceleration efficiency is the shock obliquity. Here we used the results from Pais et. al. (2019) who fit a functional form to the data by Caprioli&Spitkovsky (2014).

DiffusiveShockAccelerationModels.η_B — Function

η_B(θ_B::Real, θ_crit::Real)

Calculate B angle dependent efficiency component following Pais et. al. 2018, eq. 7, https://arxiv.org/pdf/1805.00128.pdf

source

Ions

Ions are found to be accelerated primarily at quasi-parallel shocks. We provide two helper functions for this.

DiffusiveShockAccelerationModels.ηB_acc_p — Function

ηB_acc_p(θ_B::Real)

Magnetic field geometry dependent efficiency for protons at initial acceleration.

source

DiffusiveShockAccelerationModels.ηB_reacc_p — Function

ηB_reacc_p(θ_B::Real)

Magnetic field geometry dependent efficiency for protons at reacceleration.

source

Electrons

Electrons are found to be accelerated primarily at quasi-perpendicular shocks. We provide two helper functions for this.

DiffusiveShockAccelerationModels.ηB_acc_e — Function

ηB_acc_e(θ_B::Real)

Magnetic field geometry dependent efficiency for electrons at initial acceleration.

source

DiffusiveShockAccelerationModels.ηB_reacc_e — Function

ηB_reacc_e(θ_B::Real)

Magnetic field geometry dependent efficiency for electrons at reacceleration.

source

Usage

To use for example the mach number dependent model by Kang & Ryu (2013), combined with the shock obliquity model by Pais et. al. (2019)

using DiffusiveShockAccelerationModels

ηM_model = KR13()  # Mach number dependent model
Mach = 5.0         # we assume a Mach 5 shock
θ_B  = 0.1π        # angle between shock normal and magnetic field vector
X_cr = 0.0         # X_cr = P_cr / P_th -> in this case no pre-existing CRs

# magnetic field angle dependent acc. efficiency
ηB   = ηB_acc_p(θ_B)  

# Mach number dependent acc. efficiency
ηM   = η_Ms(ηM_model, Mach, X_cr)

# total efficiency
η_tot = ηB * ηM