Limiting magnitude
The International Dark-Sky Association has been vocal in championing the cause of reducing skyglow and light pollution.
From the boroughs of New York City 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 about 15 stars will be visible at any given time.
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.
Earth's sky is never completely black – even in the absence of light pollution there is a natural airglow that limits what can be seen.
Curtis reported his naked-eye limit as 6.53, but by looking at stars through a hole in a black screen (i.e. against a totally dark background) was able to see one of magnitude 8.3, and possibly one of 8.9.
[5] Naked-eye magnitude limits can be modelled theoretically using laboratory data on human contrast thresholds at various background brightness levels.
Andrew Crumey has done this using data from experiments where subjects viewed artificial light sources under controlled conditions.
at the darkest sites, consistent with the traditionally accepted value, though substantially poorer than what is often claimed by modern amateur observers.
To explain the discrepancy, Crumey pointed out that his formula assumed sustained visibility rather than momentary glimpses.
He reported that "scintillation can lead to sudden 'flashes' with a brightening of 1 to 2 mag lasting a hundredth of a second.
If the latter, then the individual's concern with limiting magnitude may be to maximise it, whereas for science a main interest should be consistency of measurement."
He recommended that "For the purposes of visibility recommendations aimed at the general public it is preferable to consider typical rather than exceptional performance... Stars should be continuously visible (with direct or averted vision) for some extended period (e.g. at least a second or two) rather than be seen to flash momentarily.
"[8] Crumey's formula, stated above, is an approximation to a more general one he obtained in photometric units.
[9] He obtained other approximations in astronomical units for skies ranging from moderately light polluted to truly dark.
measured by a sky quality meter), and establishes their actual limiting magnitude, they can work out their own
Crumey recommended that for accurate results, the observer should ascertain the V-magnitude of the faintest steadily visible star to one decimal place, and for highest accuracy should also record the colour index and convert to a standard value.
One reason is that as magnification increases, the exit pupil gets smaller, resulting in a poorer image – an effect that can be seen by looking through a small pinhole in daylight.
Another reason is that star images are not perfect points of light; atmospheric turbulence creates a blurring effect referred to as seeing.
A third reason is that if magnification can be pushed sufficiently high, the sky background will become effectively black, and cannot be darkened any further.
This happens at a background surface brightness of approximately 25 mag arcsec−2, where only 'dark light' (neural noise) is perceived.
as a function of the sky surface brightness, telescope magnification, observer's eye pupil diameter and other parameters including the personal factor
Choosing parameter values thought typical of normal dark-site observations (e.g. eye pupil 0.7cm and
[13] Crumey obtained his formula as an approximation to one he derived in photometric units from his general model of human contrast threshold.
[14] As an illustration, he calculated limiting magnitude as a function of sky brightness for a 100mm telescope at magnifications ranging from x25 to x200 (with other parameters given typical real-world values).
More generally, for situations where it is possible to raise a telescope's magnification high enough to make the sky background effectively black, the limiting magnitude is approximated by
As well as vindicating the theoretical model, Crumey was able to show from this analysis that the sky brightness at the time of Bowen's observations was approximately 21.27 mag arcsec−2, highlighting the rapid growth of light pollution at Mount Wilson in the second half of the twentieth century.
[19] Telescopes at large observatories are typically located at sites selected for dark skies.
Most 8 to 10 meter class telescopes can detect sources with a visual magnitude of about 27 using a one-hour integration time.
Automated astronomical surveys are often limited to around magnitude 20 because of the short exposure time that allows covering a large part of the sky in a night.
