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A quick guide to intensity and temperature conversion for the black body radiation and in particular the cosmic microwave background (CMB).

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cmb_units

A quick guide to intensity and temperature conversion for the black body radiation and in particular the cosmic microwave background (CMB). Check out the tutorial.ipynb for a demonstration of the formulas and the code.

The module lib/unit_conversion.py has a convenient unit conversion function called convert_units_of that takes in a map/pixel with a certain unit and returns a map/pixel in another unit.

Here's an example of how it can be used to convert a temperature fluctuation dT around the mean value of T_0 to intensity fluctuations dI_nu at three frequency channels of 100, 143, and 217 GHz:

from lib.unit_conversion import convert_units_of

T_0 = 2.7255 # [K]
dT = 1E-5 # [K]

frequencies = [100,143,217] # [GHz]

dI = convert_units_of(dT, from_units="T", to_units="I",
                          at_nu=frequencies,
                          with_map_avg=T_0,
                          is_differential=True)

Depending on the input map and the given frequencies, the output dI will have the shape: (#frequency channels, #pixels).

The valid keywords for from_unit and to_unit are:

Variable [units] keyword
Brightness Temperature [K] "T", "T_b", "T_cmb", "T_CMB", "K", "K_CMB"
Specific Intensity [MJy/sr] "I", "I_nu", "MJy/sr"
Rayleigh_Jeans Temperature [K_RJ] "T_RJ", "T_rj", "s_nu", "K_RJ", "K_rj"

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A quick guide to intensity and temperature conversion for the black body radiation and in particular the cosmic microwave background (CMB).

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