tardis.energy_input.util module

tardis.energy_input.util.angle_aberration_gamma(direction_vector, position_vector, time)

Angle aberration formula for photons in 3D

Parameters:

direction_vectorarray

position_vectorarray

timefloat

Returns:

array

New direction after aberration

tardis.energy_input.util.compton_theta_distribution(energy, sample_resolution=100)

Calculates the cumulative distribution function of theta angles for Compton Scattering

Parameters:

energyfloat

sample_resolutionint

Returns:

theta_anglesOne dimensional Numpy array, dtype float

norm_theta_distributionOne dimensional Numpy array, dtype float

tardis.energy_input.util.convert_half_life_to_astropy_units(half_life_string)

Converts input half-life to use astropy units

Parameters:

half_life_stringstr

Half-life as a string

Returns:

astropy Quantity

Half-life in seconds

tardis.energy_input.util.doppler_factor_3d(direction_vector, position_vector, time)

Doppler shift for photons in 3D

Parameters:

direction_vectorarray

position_vectorarray

timefloat

Returns:

float

Doppler factor

tardis.energy_input.util.euler_rodrigues(theta, direction)

Calculates the Euler-Rodrigues rotation matrix

Parameters:

thetafloat

angle of rotation in radians

directionOne dimensional Numpy array, dtype float

x, y, z direction vector

Returns:

rotation matrixTwo dimensional Numpy array, dtype float

tardis.energy_input.util.get_index(value, array)

Get the index that places a value at array[i] < array <= vec[i+1]

Parameters:

valuefloat

Value to locate

arrayarray

Array to search

Returns:

int

Index

tardis.energy_input.util.get_perpendicular_vector(original_direction)

Computes a random vector which is perpendicular to the input vector

Parameters:

original_directionarray

Returns:

numpy.ndarray

Perpendicular vector to the input

tardis.energy_input.util.get_random_phi_photon()

Get a random phi direction between 0 and 2 * pi

Returns:

float

Random phi direction

tardis.energy_input.util.get_random_theta_photon()

Get a random theta direction between 0 and pi

Returns:

float

Random theta direction

tardis.energy_input.util.get_random_unit_vector()

Generate a random unit vector

Returns:

array: random unit vector

tardis.energy_input.util.klein_nishina(energy, theta_C)

Calculates the Klein-Nishina equation

https://en.wikipedia.org/wiki/Klein%E2%80%93Nishina_formula

\[\]

rac{r_e}{2} [1 + kappa (1 - cos heta_C)]^{-2} left( 1 + cos^2 heta_C + rac{kappa^2 (1 - cos heta_C)^2}{1 + kappa(1 - cos heta_C)} ight)

where \(\kappa = E / (m_e c^2)\)

Parameters:

energyfloat

Packet energy

theta_Cfloat

Compton angle

Returns:

float

Klein-Nishina solution

tardis.energy_input.util.normalize_vector(vector)

Normalizes a vector in Cartesian coordinates

Parameters:

vectorOne-dimensional Numpy Array, dtype float

Input vector

Returns:

One-dimensional Numpy Array, dtype float

Normalized vector

tardis.energy_input.util.solve_quadratic_equation(position, direction, radius)

Solves the quadratic equation for the distance to the shell boundary

Parameters:

positionarray

directionarray

radiusfloat

Returns:

solution_1float

solution_2float

tardis.energy_input.util.solve_quadratic_equation_expanding(position, direction, time, radius)

Solves the quadratic equation for the distance to an expanding shell boundary

Parameters:

positionarray

directionarray

timefloat

radiusfloat

Returns:

solution_1float

solution_2float

tardis.energy_input.util.spherical_to_cartesian(r, theta, phi)

Converts spherical coordinates to Cartesian

Parameters:

rfloat64

Radius

thetafloat64

Theta angle in radians

phifloat64

Phi angle in radians

Returns:

array

x, y, z coordinates