# A question about stellar magnitude and the pogson's equation

Well surely the eye has different sensitivity to various wavelengths... Will the Pogson's equation not be affected if say I compare Betelgeuse and Rigel (both having a marked difference in spectral lines)...

Also, how can we ever draw a standard in stellar magnitude observed if both location and individual visual acuity?

Does atmosphere also have any effect??

Please refer some good resources for further study in this topic.

• The first paragraph of en.wikipedia.org/wiki/Apparent_magnitude answers most of your questions: "The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth, adjusted to the value it would have in the absence of the atmosphere. The brighter the object appears, the lower the value of its magnitude. Generally the visible spectrum (vmag) is used as a basis for the apparent magnitude". Adding my own note: photographic magnitude is also an important concept and is included in star catalogs like Tycho-2/NOMAD
– user21
Oct 14, 2014 at 2:47
• @barrycarter Please convert this into an answer. Feb 21, 2018 at 16:44

Pogson's equation
Pogson's equation for magnitude $$m$$, given in modern form in terms of the base-10 logarithm: $$m = m_{ref} - 2.5\log_{10}\frac{I}{I_{ref}}$$ where $$m_{ref}$$ is the magnitude of a reference object, $$I$$ is the intensity of the object in question, and $$I_{ref}$$ is the intensity (brightness) of the reference object. Intensities are in units of power density (for example Watts per square meter). (see Wikipedia Apparent magnitude)

Visual Magnitude
This of course leaves out the frequency band over which the magnitude is measured resulting in numerous magnitudes depending on the region of the spectrum specified. Previously there was a notion of visual magnitude, $$m_{vis}$$, based on how objects appear to the eye. As this is subjective and individuals vary, visual magnitude was supplanted by magnitude measured through a standard V-band filter. The V-band filter response is typically centered at 551 nm and has a half-power width of 88 nm. This is in contrast to bolometric magnitude, $$m_{bol}$$, where total received power over all wavelengths is considered. Image from UBV photometric system at Wikipedia.

0 Magnitude
To anchor the scale it is also necessary to select what constitutes 0 magnitude. Traditionally, Vega has been selected as the 0 magnitude reference (see The Stellar Magnitude System from Sky & Telescope). A more precise definition is typically used such as the one found in JHKLM Photometry: Standard Systems, Passbands, and Intrinsic Colors. In this system, Vega has a V magnitude of 0.03.

Impact of Observer
With the subjective version of visual magnitude the characteristics of an individual's eyes and observing experience with factor into magnitude estimations. In addition, while the magnitude scale is linear, perceived brightness is not. Quoting from the above referenced Sky & Telescope link:

The resulting stellar magnitude system is logarithmic, in neat agreement with the 1850s belief that all human senses are logarithmic in their response to stimuli. The decibel scale for rating loudness was likewise made logarithmic. Alas, it's not quite so, not for brightness, sound, or anything else. Our perceptions of the world follow power-law curves, not logarithmic ones. Thus a star of magnitude 3.0 does not in fact look exactly halfway in brightness between 2.0 and 4.0. It looks a little fainter than that. The star that looks halfway between 2.0 and 4.0 will be about magnitude 2.8. The wider the magnitude gap, the greater this discrepancy.

Impact of Atmosphere
The atmosphere can indeed reduce the apparent brightness of objects, but this is not included in the definition of magnitude as the reduction is a function of location, time, and elevation angle. A correction can be applied to estimated magnitudes such as the one contained in Correcting for Atmospheric Extinction.