SynchrotronKernel.jl

This package computes the synchrotron kernel for a frequency ratio $x = \frac{\nu}{\nu_0}$ and its polarisation components.

kernels

Simple interface

If you simply need to calculate the synchrotron kernel and the polarisation components you can use the following functions

Synchrotron Kernel

SynchrotronKernel.synchrotron_kernel — Function

synchrotron_kernel(x::Real)

Computes the first synchrotron function and the polarisation components at a given frequency ratio $x = \frac{\nu}{\nu_0}$. Returns a tuple (K_tot, K_ort, K_par).

K_tot = F(x)
K_ort = 0.5 * (F(x) + G(x))
K_par = 0.5 * (F(x) - G(x))

Synchrotron Functions

$F(x) = x \int_x^\infty K_{\frac{5}{3}}(t) dt$

$G(x) = x K_{\frac{2}{3}}(x)$

source

Intensity

SynchrotronKernel.synchrotron_intensity — Function

synchrotron_intensity(x::Real)

Computes the total synchrotron kernel, without polarisation components. Wrapper for F.

$F(x) = x \int_x^\infty K_{\frac{5}{3}}(t) dt$

source

Polarisation

SynchrotronKernel.synchrotron_polarisation — Function

synchrotron_polarisation(x::Real)

Computes the second synchrotron function at a given frequency ratio $x = \frac{\nu}{\nu_0}$. Returns a tuple of (K_ort, K_par).

K_ort = 0.5 * (F(x) + G(x))
K_par = 0.5 * (F(x) - G(x))

Synchrotron Functions

$F(x) = x \int_x^\infty K_{\frac{5}{3}}(t) dt$

$G(x) = x K_{\frac{2}{3}}(x)$

source

Synchrotron Functions

If you need to access the individual synchrotron functions you can use the direct interface.

First Function

SynchrotronKernel.ℱ — Function

ℱ(x::Real)

Computes the first synchrotron function at a given frequency ratio $x = \frac{\nu}{\nu_0}$.

$F(x) = x \int_x^\infty K_{\frac{5}{3}}(t) dt$

Wrapper for F.

source

SynchrotronKernel.F — Function

F(x::Real)

Computes the first synchrotron function at a given frequency ratio $x = \frac{\nu}{\nu_0}$.

$F(x) = x \int_x^\infty K_{\frac{5}{3}}(t) dt$

source

Second Function

SynchrotronKernel.𝒢 — Function

𝒢(x::Real)

Computes the second synchrotron function at a given frequency ratio $x = \frac{\nu}{\nu_0}$.

$G(x) = x K_{\frac{2}{3}}(x)$

Wrapper for G.

source

SynchrotronKernel.G — Function

G(x::Real)

Computes the second synchrotron function at a given frequency ratio $x = \frac{\nu}{\nu_0}$.

$G(x) = x K_{\frac{2}{3}}(x)$

source