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
|
# Copyright (c) 2016-2017 Weitian LI <weitian@aaronly.me>
# MIT license
"""
Utilities for conversion among common astronomical quantities.
"""
from .units import (UnitConversions as AUC, Constants as AC)
def Sb_to_Tb(Sb, freq):
"""
Convert surface brightness to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
Tb = Sb * c^2 / (2 * k_B * nu^2)
where `Sb` is the surface brightness density measured at a certain
frequency, in units of [Jy/arcsec^2].
1 [Jy] = 1e-23 [erg/s/cm^2/Hz] = 1e-26 [W/m^2/Hz]
NOTE
----
It is very easy to use ``astropy.units`` for the conversion:
equiv = au.brightness_temperature(omega, freq)
Tb = Fnu.to(au.K, equivalencies=equiv)
WARNING:
Using `astropy.units` for the conversion may be much slower.
This can be used as a cross check for the calculation.
Parameters
----------
Sb : float
Input surface brightness
Unit: [Jy/arcsec^2]
freq : float
Frequency where the flux density measured
Unit: [MHz]
Returns
-------
Tb : float
Calculated brightness temperature
Unit: [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
"""
# NOTE: [rad] & [sr] are dimensionless
arcsec2 = AUC.arcsec2rad ** 2 # [sr]
Sb /= arcsec2 # [Jy/arcsec^2] -> [Jy/sr]
coef = 1e-35 # unit conversion coefficient
Tb = coef * (Sb * AC.c**2) / (2*AC.k_B * freq**2) # [K]
return Tb
def Fnu_to_Tb(Fnu, omega, freq):
"""
Convert flux density to brightness temperature, using the
Rayleigh-Jeans law, in the Rayleigh-Jeans limit.
Avoid using `astropy.units` to optimize the speed.
Parameters
----------
Fnu : float
Input flux density
Unit: [Jy] = 1e-23 [erg/s/cm^2/Hz] = 1e-26 [W/m^2/Hz]
omega : float
Source angular size/area
Unit: [arcsec^2]
freq : float
Frequency where the flux density measured
Unit: [MHz]
Returns
-------
Tb : float
Calculated brightness temperature
Unit: [K]
"""
Sb = Fnu / omega # [Jy/arcsec^2]
return Sb_to_Tb(Sb, freq)
def JyPerPix_to_K(freq, pixelsize):
"""
The factor that converts [Jy/pixel] to [K] (brightness temperature).
Parameters
----------
freq : float
The frequency where the flux density measured.
Unit: [Jy]
pixelsize : float
The pixel size.
Unit: [arcsec]
"""
factor = Fnu_to_Tb(Fnu=1.0, omega=pixelsize**2, freq=freq)
return factor
|
