Limiting magnitude

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Limiting magnitude is the faintest apparent magnitude detectable or detected by a given instrument.

In some cases, limiting magnitude refers to the utter threshold of detection. In more formal uses, limiting magnitude is specified along with the strength of the signal, e.g., "10th magnitude at 20 sigma." Sometimes limiting magnitude is qualified by the purpose of the instrument, e.g., "10th magnitude for photometry;" this statement recognizes that a photometric detector can detect light far fainter than it can reliably measure it.

The International Dark-Sky Association has been vocal in championing the cause of limiting skyglow and light pollution / photopollution.

[edit] Limiting Magnitude in Amateur Astronomy

In amateur astronomy, limiting magnitude frequently refers to the faintest stars that can be seen with the unaided eye near the zenith on clear moonless nights. The quantity is most often used as an overall indicator of sky quality, in that light polluted and humid areas generally have brighter limiting magnitudes than remote desert or high altitude areas.

There is even variation within metropolitan areas. For those who live in the immediate suburbs of New York City, the limiting magnitude is approximately 4.0. This corresponds to roughly 250 visible stars, or one-tenth the number that can be perceived under perfectly dark skies. From the outer boroughs of New York City (Brooklyn, Queens, Staten Island and the Bronx), the limiting magnitude is approximately 3.0, suggesting that at best, only about 50 stars might be seen at any one time. From brightly-lit Midtown Manhattan, the limiting magnitude is approximately 2.0, meaning that from the heart of New York City only approximately 15 stars will be visible at any given time.

From relatively dark suburban areas, the limiting magnitude is frequently closer to 5 or somewhat fainter, but from very remote and clear sites, some amateur astronomers can see nearly as faint as 8th magnitude. Many basic observing references quote a limiting magnitude of 6, as this is the approximate limit of star maps which date from before the invention of the telescope.

Ability in this area, which requires the use of averted vision, varies substantially from observer to observer, with both youth and experience being beneficial. At higher altitudes, breathing pure oxygen is an advantage; and there is much anecdotal evidence as well that the herb bilberry can generally improve night vision.

[edit] Calculating the Limiting Magnitude Using a Telescope

Ignoring relatively minor complicating factors, the gain in magnitudes of a telescope is 5 * Log₁₀(D₁/D₀), where D₁ is the diameter of the telescope's primary light gathering component, and D₀ is the diameter of the eye's dark adapted pupil. Both quantities must be measured in the same units. D₀ varies from person to person but is typically 6-7mm (~1/4").

A 10-inch (D₁=254mm) telescope therefore provides a gain of about 8 magnitudes beyond what could be observed without it. Thus, if one is at a site where the naked eye limiting magnitude is 5, the telescope will allow one to see stars as faint as about magnitude 13.