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# Copyright (c) 2016-2018 Weitian LI <weitian@aaronly.me>
# MIT license
"""
Utilities for conversion among common astronomical quantities.
"""
import numpy as np
from .units import (UnitConversions as AUC, Constants as AC)
from ..share import COSMO
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
def flux_to_power(flux, z, index=1.0):
"""
Calculate the (spectral) power from the measured flux density at
the same frequency with K-correction taking into account, if the
spectral index is given.
Parameters
----------
flux : float
The measured flux density at a frequency.
Unit: [mJy]
z : float
The redshift to the source.
index : float, optional
The spectral index (α) of the source flux: S(ν) ∝ ν^(-α)
If given, the K-correction is taken into account.
Returns
-------
power : float
The calculated (spectral) power at the same frequency as
the flux density measured.
Unit: [W/Hz]
"""
flux *= 1e-29 # [mJy] -> [W/Hz/m^2]
DL = COSMO.DL(z) * AUC.Mpc2m # [m]
power = 4*np.pi * DL**2 * (1+z)**(index-1) * flux # [W/Hz]
return power
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