Instrumental magnitude refers to an uncalibrated

apparent magnitude Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's li ...

, and, like its counterpart, it refers to the

brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...

of an astronomical object seen from an observer on

Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...

, but unlike its counterpart, it is only useful in relative comparisons to other astronomical objects in the same image (assuming the photometric calibration does not spatially vary across the image; in the case of images from the Palomar Transient Factory, the absolute photometric calibration involves a zero point that varies over the image by up to 0.16 magnitudes to make a required illumination correction). Instrumental magnitude is defined in various ways, and so when working with instrumental magnitudes, it is important to know how they are defined. The most basic definition of instrumental magnitude,

m

, is given by :

m = -2.5 \log_(f)

where

f

is the intensity of the source object in known physical units. For example, in the paper by Mighell, it was assumed that the data are in units of electron number (generated within pixels of a

charge-coupled device A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a ...

). The physical units of the source intensity are thus part of the definition required for any instrumental magnitudes that are employed. The factor of 2.5 in the above formula originates from the established fact that the human eye can only clearly distinguish the brightness of two objects if one is at least approximately 2.5 times brighter than the other. The instrumental magnitude is defined such that two objects with a brightness ratio of exactly 100 will differ by precisely 5 magnitudes, and this is based on Pogson's system of defining each successive magnitude as being fainter by

100^

. We can now relate this to the base-10 logarithmic function and the leading coefficient in the above formula: :

100^=(10^2)^=10^=10^ = 2.51188643 \cdots

The approximate value of 2.5 is used as a convenience, its negative sign assures that brighter objects will have smaller and possibly negative values, and tabulated values of base-10

logarithms In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

were available more than three centuries before the advent of computers and calculators.

References

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Publications of the Astronomical Society of the Pacific ''Publications of the Astronomical Society of the Pacific'' (often abbreviated as ''PASP'' in references and literature) is a monthly peer-reviewed scientific journal managed by the Astronomical Society of the Pacific. It publishes research and ...

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