Limiting magnitude

In astronomy, limiting magnitude is the faintest apparent magnitude of a celestial body that is 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 reducing skyglow and light pollution.

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 brightness, 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 lives in the immediate suburbs of New York City, the limiting magnitude might be 4.0. This corresponds to roughly 250 visible stars, or one-tenth the number that can be perceived under perfectly dark skies. From the New York City boroughs outside Manhattan (Brooklyn, Queens, Staten Island and the Bronx), the limiting magnitude might be 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 possibly 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.

Limiting magnitude is traditionally estimated by searching for faint stars of known magnitude. In 2013 an app was developed based on Google's Sky Map that allows non-specialists to estimate the limiting magnitude in polluted areas using their phone.[1]

Calculating limiting magnitude

Limiting magnitude can be calculated by using a telescope.

As a first approximation, the gain in magnitudes of a telescope is $5 \cdot \log_{10}(\frac{D_1}{D_0})$, 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 6–7 mm (~1/4").

A 10-inch (D1 = 254mm) telescope therefore would provide 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 (NELM) is 5, the telescope will allow one to see stars as faint as about magnitude 13.

In real a telescope allows one to see much fainter stars because at higher powers the background is darkened and contrast increased. A typical 10-inch scope at high power (250× or more) will easily reach magnitude 15. See the Telescope Limiting Magnitude Calculator. Derived from this site the formula is

$m \cdot v=m_{naked eye}-2+2.5 \cdot \log_{10}(D \cdot P \cdot t)$

where
D = objective or main mirror diameter in mm
P = power or magnification
t = transmission factor, usually 0.85–0.9.