Magnitude Zero Points

The following discussion of zero points is taken from "Evolution of the "Real" Visual Magnitude System" by Ron Zissell (ZRE). It was published in JAAVSO Volume 26, Number 2 (1998). The complete scanned article can be found through the ADS.

In the original magnitude system of Hipparcus, the stars were divided into six brightness classes. The brightest stars were put into the first class and the faintest into the sixth class. These sorting bins of brightness were called "magnitudes" which meant "size". There was no "Zero Point" in this original system.

When photometry had developed to the point where brightness ratios of ten percent or less could be measured, the old system of brightness classes gave way to a continous scale of brightnesses (the correct term should be Flux not brightness) still loosely coupled to the old magnitude steps. Which star of Hipparcus is 4.5 magnitude? The average of all stars in the fourth magnitude class will not be 4.5 since there are more fainter forth magnitude stars than brighter ones.

Pogson suggested that a magnitude difference of one, represented a fixed ratio of flux. We still use his suggested ratio constant today. Two stars that have observed Flux F1 and F2 will mave a magnitude difference dm defined by:

          dm = m1 - m2 = -2.50*LOG(F1/F2)                (1)

          m1 =  -2.50*LOG(F1/F2) + m2                    (2)

Equation 1 will allow an observer to accurately measure the magnitude Difference between two stars. It will not give the magnitude of star 1 unless one first knows the magnitude of star 2 as shown in equation 2.

Equation 2 is used to give local magnitudes in preliminary reductions. F1 and F2 are measures of the flux in units of milli- amperes on a current meter, volts on a voltmeter, mm of deflection on a chart recorder, photon counts from a pulse amplifier, or ADUs from a CCD apperture photometry reduction program.

If one assumes that F2 has a value of 1.000, and m2 has a value of 0.000, then :

       m1 = -2.50* LOG(F1)                               (3)

The values of m1 from equation 3 are on a Local magnitude scale. One can calculate magnitude differences from the local system that would compare with those differences measured by others. If observer A uses photon counts and observer B uses ADUs, their local magnitudes will be quite different but their magnitude differences would be the same. ( we are not taking into account extinction corrections or filter tranformations in this discussion)

Local magnitudes can be converted into standard magnitudes by the addition of a Zero Point, Zp in Equation 4. Zp is a function of the units used to measure flux, amplification factor of instrument, size of telescope, atmospheric extinction, etc.

    
       m1 = -2.50*LOG(F2) + Zp                           (4)

Which one of Hipparcus's stars of the first magnitude is really 1.000 magnitude? Given that star, all the other stars could be calibrated by use of equation 1 or 4. Even if one picked a particular star and assigned a defining magnitude to it, what assurance is there that the star would remain constant over time or be above the horizon at the time of observation?

When Argelander visually produced the BD catalog he assigned magnitudes to the stars recorded to one decimal place. The magnitudes roughly followed Hipparcus's steps. The significant difference being that Argelander's system used continous real numbers while Hipparcus's was quantized in integers.

The Harvard Photometry project by Pickering used a measuring device to perform photometry on four thousand stars. He defined the zero point of the Harvard system by observing a number of stars in the fifth magnitude range from the BD each night and assuming their average magnitude. Thus, the systems were tied together by the average of many stars; not by a single stars.

The V magnitude of Sirius is given as -1.45 while Alcor is 4.03. The magnitude difference is 5.48 . One could define Sirius to be 1.00 which would make Alcor 6.48 . The magnitude difference is the same in either case. Only the Zero Point has been shifted.

When Johnson and Morgan produced their Photoelectric catalog in 1953, they were measuring to two decimal places. They had to assign a zero point to their photometric system that would make it similar to previous systems. The V magnitudes assigned to their primary standards were chosen so as to match the International System then in use.

The Johnson V PEP magnitudes differ from The Harvard visual photometry by about 0.1 magnitude. The Harvard photometry has been the basis of the visual magnitudes on the AAVSO charts. Comp star extrapolations to fainter magnitudes introduced large systematic errors which plague our older charts to this day. CCD chips have a large dynamic range and can extend sequences to fainter limits with better accuracy than by earlier methods.

For this reason we have chosen to adopt the V magnitudes of Johnson as defining the Zero Point of our visual magnitude system for future charts.

More details can be found in the following papers:

Zissell, R.E. "Evolution of the "Real" Visual Magnitude System". 1998 JAAVSO 26 No 2, 151

Johnson, J.L. and Morgan, W.W. "Fundamental stellar photometry for standards of spectral type on the revised system of the Yerkes spectral atlas" 1953 APJ 117, 3, 313