Optical Magnitudes and Related Definitions

The absolute calibration of the Johnson System of magnitudes

Filter BandCentral WavelengthAbsolute flux density for mag=0.00
U0.364.35 10-121.88 10-23
B0.447.20 10-124.44 10-23
V0.553.92 10-123.81 10-23
R0.701.76 10-123.01 10-23
I0.908.30 10-132.43 10-23
J1.253.40 10-131.77 10-23
Ha1.65 1.18 10-13 1.14 10-23
K2.23.90 10-146.30 10-24
L3.48.10 10-153.10 10-24
M5.02.20 10-151.80 10-24
N10.21.23 10-164.30 10-25
a The H band does not originally belong to the Johnson system, I have taken the calibration from A. Tokunaga's section on infrared astronomy in Astrophysical Quantities (it will be in the 4th edition of AQ, still to be published). Note that I have corrected the zero magnitude of the H band by a factor derived from the band in common between Johnson's system and Tokunaga's table which is the list of flux from Vega. In principle Vega is defined to have m=0 at all bands but in some systems, it is 0.02 or 0.03.

The definition of the calibration system

Here I explain my understanding of how the flux densities corresponding to m=0 are established. A main calibrator, a star, is chosen and assumed to have m=0 at all wavelengths. This "star" is also chosen such that it has a black-body emission which peak is located at a much shorter wavelength than that of interest. This assumption corresponds to .

As a result the spectral density of the calibrator is:

This way the zero-magnitude fluxes at two different frequencies are linked by:

What is red and what is blue?

A color is the difference of two magnitudes of an object. Given that magnitudes include the log function and a minus sign, it is not always obvious to remember what is red and what is blue. The graph below summarizes that:

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