1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
|
# Copyright (c) 2016 Weitian LI <liweitianux@live.com>
# MIT license
"""
Utilities for conversion among common astronomical quantities.
"""
import numpy as np
import astropy.units as au
import numba
def Fnu_to_Tb(Fnu, omega, freq):
"""Convert flux density to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
Parameters
----------
Fnu : `~astropy.units.Quantity`
Input flux density, e.g., `1.0*au.Jy`
omega : `~astropy.units.Quantity`
Source angular size/area, e.g., `1.0*au.sr`
freq : `~astropy.units.Quantity`
Frequency where the flux density measured, e.g., `1.0*au.MHz`
Returns
-------
Tb : `~astropy.units.Quantity`
Brightness temperature, with default unit `au.K`
References
----------
- Brightness and Flux
http://www.cv.nrao.edu/course/astr534/Brightness.html
- Wikipedia: Brightness Temperature
https://en.wikipedia.org/wiki/Brightness_temperature
- NJIT: Physics 728: Introduction to Radio Astronomy: Lecture #1
https://web.njit.edu/~gary/728/Lecture1.html
- Astropy: Equivalencies: Brightness Temperature / Flux Density
http://docs.astropy.org/en/stable/units/equivalencies.html
"""
equiv = au.brightness_temperature(omega, freq)
Tb = Fnu.to(au.K, equivalencies=equiv)
return Tb
def Sb_to_Tb(Sb, freq):
"""Convert surface brightness to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
Parameters
----------
Sb : `~astropy.units.Quantity`
Input surface brightness, e.g., `1.0*au.Jy/au.sr`
freq : `~astropy.units.Quantity`
Frequency where the flux density measured, e.g., `1.0*au.MHz`
Returns
-------
Tb : `~astropy.units.Quantity`
Brightness temperature, with default unit `au.K`
"""
omega = 1.0 * au.arcsec**2
Fnu = (Sb * omega).to(au.Jy) # [Jy]
return Fnu_to_Tb(Fnu, omega, freq)
@numba.jit(nopython=True)
def Sb_to_Tb_fast(Sb, freq):
"""Convert surface brightness to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
This function does the calculations explicitly, and does NOT rely
on the `astropy.units`, therefore it is faster. However, the input
parameters must be in right units.
Tb = Sb * c^2 / (2 * k_B * nu^2)
where `SB` is the surface brightness density measured at a certain
frequency (unit: [ Jy/rad^2 ] = [ erg/s/cm^2/Hz/rad^2 ]).
Parameters
----------
Sb : float
Input surface brightness, unit [ Jy/deg^2 ]
freq : float
Frequency where the flux density measured, unit [ MHz ]
Returns
-------
Tb : float
Calculated brightness temperature, unit [ K ]
"""
# NOTE: `radian` is dimensionless
rad2_to_deg2 = np.rad2deg(1.0) * np.rad2deg(1.0)
Sb_rad2 = Sb * rad2_to_deg2 # unit: [ Jy/rad^2 ] -> [ Jy ]
c = 29979245800.0 # speed of light, [ cm/s ]
k_B = 1.3806488e-16 # Boltzmann constant, [ erg/K ]
coef = 1e-35 # take care the unit conversions
Tb = coef * (Sb_rad2 * c*c) / (2 * k_B * freq*freq) # unit: [ K ]
return Tb
@numba.jit(nopython=True)
def Fnu_to_Tb_fast(Fnu, omega, freq):
"""Convert flux density to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
This function does the calculations explicitly, and does NOT rely
on the `astropy.units`, therefore it is faster. However, the input
parameters must be in right units.
Parameters
----------
Fnu : float
Input flux density, unit [ Jy ]
omega : float
Source angular size/area, unit [ deg^2 ]
freq : float
Frequency where the flux density measured, unit [ MHz ]
Returns
-------
Tb : float
Calculated brightness temperature, unit [ K ]
"""
Sb = Fnu / omega
return Sb_to_Tb_fast(Sb, freq)
|
