Module diskchef.physics.ionization
This module contains parametrizations of ioniaztion rates
Expand source code
"""
This module contains parametrizations of ioniaztion rates
"""
import diskchef.engine.other
import numpy as np
from scipy.interpolate import interp2d
DENSITIES = np.logspace(20, 25, 6)
TEMPERATURES = np.array([3e6, 1e7, 3e7, 1e8, 3e8])
BRUDERER_TABLE = np.array( # from Bruderer+2009 Table3
[
[4.8e-11, 2.4e-11, 1.0e-11, 3.4e-12, 1.2e-12],
[4.2e-12, 4.5e-12, 2.5e-12, 9.8e-13, 3.7e-13],
[6.9e-14, 3.7e-13, 4.0e-13, 2.2e-13, 1.0e-13],
[6.9e-17, 9.6e-15, 3.9e-14, 4.5e-14, 3.3e-14],
[6.8e-22, 4.5e-17, 2.0e-15, 9.4e-15, 1.4e-14],
[1.8e-30, 8.6e-22, 1.7e-17, 1.4e-15, 6.4e-15]
]
)
"""Array representing Bruderer+09 table 3"""
INTERPOLATED_LOG_BRUDERER_TABLE = diskchef.engine.other.unsorted_interp2d(
np.log10(DENSITIES), np.log10(TEMPERATURES), np.log10(BRUDERER_TABLE.T), kind='cubic'
)
"""Interpolated table 3 of Bruderer+09"""
def bruderer09(column_density, temperature=3e6):
"""Return x-ray ionization rate as of Bruderer+09 table 3
https://iopscience.iop.org/article/10.1088/0067-0049/183/2/179/pdf
Args:
column_density: number of protons + neutrons from the source, cm**-2 (1e20..1e25)
temperature: plasma temperature of the source, K (3e6..3e8)
Returns:
ionization rate (float, in 1/s) for Fx = 1 erg/s
"""
log_column_density = np.log10(column_density)
log_temperature = np.log10(temperature)
out = 10 ** INTERPOLATED_LOG_BRUDERER_TABLE(
log_column_density, log_temperature, assume_sorted=False
)
if len(out) == 1:
return out[0]
return out
def padovani18l(logdens):
"""Return galactic cosmic ray ionization rate as of Padovani+18 App. F model L
https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf
Args:
logdens: log10 of number density in g/cm**2 from the source
Return:
ionization rate, in 1/s
"""
logdens = np.where(logdens < 19, 19, logdens)
logdens = np.where(logdens > 27, 27, logdens)
return 10 ** (
-3.331056497233e6 +
logdens * 1.207744586503e6
- logdens ** 2 * 1.913914106234e5
+ logdens ** 3 * 1.731822350618e4
- logdens ** 4 * 9.790557206178e2
+ logdens ** 5 * 3.543830893824e1
- logdens ** 6 * 8.034869454520e-1
+ logdens ** 7 * 1.048808593086e-2
- logdens ** 8 * 6.188760100997e-5
+ logdens ** 9 * 3.122820990797e-8
)
def padovani18h(logdens):
"""Return galactic cosmic ray ionization rate as of Padovani+18 App. F model H
https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf
Args:
logdens: log10 of number density in g/cm**2 from the source
Return:
ionization rate, in 1/s
"""
logdens = np.where(logdens < 19, 19, logdens)
logdens = np.where(logdens > 27, 27, logdens)
return 10 ** (
1.001098610761e7 +
- logdens * 4.231294690194e6
+ logdens ** 2 * 7.921914432011e5
- logdens ** 3 * 8.623677095423e4
+ logdens ** 4 * 6.015889127529e3
- logdens ** 5 * 2.789238383353e2
+ logdens ** 6 * 8.595814402406e0
- logdens ** 7 * 1.698029737474e-1
+ logdens ** 8 * 1.951179287567e-3
- logdens ** 9 * 9.937499546711e-6
)Global variables
var BRUDERER_TABLE-
Array representing Bruderer+09 table 3
var INTERPOLATED_LOG_BRUDERER_TABLE-
Interpolated table 3 of Bruderer+09
Functions
def bruderer09(column_density, temperature=3000000.0)-
Return x-ray ionization rate as of Bruderer+09 table 3
https://iopscience.iop.org/article/10.1088/0067-0049/183/2/179/pdf
Args
column_density- number of protons + neutrons from the source, cm**-2 (1e20..1e25)
temperature- plasma temperature of the source, K (3e6..3e8)
Returns
ionization rate (float, in 1/s) for Fx = 1 erg/s
Expand source code
def bruderer09(column_density, temperature=3e6): """Return x-ray ionization rate as of Bruderer+09 table 3 https://iopscience.iop.org/article/10.1088/0067-0049/183/2/179/pdf Args: column_density: number of protons + neutrons from the source, cm**-2 (1e20..1e25) temperature: plasma temperature of the source, K (3e6..3e8) Returns: ionization rate (float, in 1/s) for Fx = 1 erg/s """ log_column_density = np.log10(column_density) log_temperature = np.log10(temperature) out = 10 ** INTERPOLATED_LOG_BRUDERER_TABLE( log_column_density, log_temperature, assume_sorted=False ) if len(out) == 1: return out[0] return out def padovani18h(logdens)-
Return galactic cosmic ray ionization rate as of Padovani+18 App. F model H
https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf
Args
logdens- log10 of number density in g/cm**2 from the source
Return
ionization rate, in 1/s
Expand source code
def padovani18h(logdens): """Return galactic cosmic ray ionization rate as of Padovani+18 App. F model H https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf Args: logdens: log10 of number density in g/cm**2 from the source Return: ionization rate, in 1/s """ logdens = np.where(logdens < 19, 19, logdens) logdens = np.where(logdens > 27, 27, logdens) return 10 ** ( 1.001098610761e7 + - logdens * 4.231294690194e6 + logdens ** 2 * 7.921914432011e5 - logdens ** 3 * 8.623677095423e4 + logdens ** 4 * 6.015889127529e3 - logdens ** 5 * 2.789238383353e2 + logdens ** 6 * 8.595814402406e0 - logdens ** 7 * 1.698029737474e-1 + logdens ** 8 * 1.951179287567e-3 - logdens ** 9 * 9.937499546711e-6 ) def padovani18l(logdens)-
Return galactic cosmic ray ionization rate as of Padovani+18 App. F model L
https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf
Args
logdens- log10 of number density in g/cm**2 from the source
Return
ionization rate, in 1/s
Expand source code
def padovani18l(logdens): """Return galactic cosmic ray ionization rate as of Padovani+18 App. F model L https://www.aanda.org/articles/aa/pdf/2018/06/aa32202-17.pdf Args: logdens: log10 of number density in g/cm**2 from the source Return: ionization rate, in 1/s """ logdens = np.where(logdens < 19, 19, logdens) logdens = np.where(logdens > 27, 27, logdens) return 10 ** ( -3.331056497233e6 + logdens * 1.207744586503e6 - logdens ** 2 * 1.913914106234e5 + logdens ** 3 * 1.731822350618e4 - logdens ** 4 * 9.790557206178e2 + logdens ** 5 * 3.543830893824e1 - logdens ** 6 * 8.034869454520e-1 + logdens ** 7 * 1.048808593086e-2 - logdens ** 8 * 6.188760100997e-5 + logdens ** 9 * 3.122820990797e-8 )