# Sky brightness

Airglow made visible from aboard the ISS (NASA)

The fact that the sky is not completely dark at night can be easily observed. Were the sky (in the absence of moon and city lights) absolutely dark, one would not be able to see the silhouette of an object against the sky.

The intensity of the sky varies greatly over the day and the primary cause differs as well. During daytime when the sun is above the horizon direct scattering of sunlight (Rayleigh scattering) is the overwhelmingly dominant source of light. In twilight, the period of time between sunset and sunrise, the situation is more complicated and a further differentiation is required. Twilight is divided in three segments according to how far the sun is below the horizon in segments of 6°.

After sunset the civil twilight sets in, and ends when the sun drops more than 6° below the horizon. This is followed by the nautical twilight, when the sun reaches heights of -6° and -12°, after which comes the astronomical twilight defined as the period from -12° to -18°. When the sun drops more than 18° below the horizon the sky generally attains its minimum brightness.

Several sources can be identified as the source of the intrinsic brightness of the sky, namely airglow, indirect scattering of sunlight, scattering of starlight, and artificial light pollution.

## Airglow

When physicist Anders Ångström examined the spectrum of the aurora borealis he discovered that even on nights when the aurora was absent its characteristic green line was still present. It was not until the 1920s that scientists were beginning to identify and understand the emission lines in aurorae and of the sky itself and what was causing them. The green line Angstrom observed is in fact an emission line with a wavelength of 557.7 nm caused by the recombination of oxygen in the upper atmosphere.

Airglow is the collective name of the various processes that occur in the upper atmosphere that result in the emission of photons with the driving force being primarily UV-radiation from the sun. Several emission lines are dominant, a green line from oxygen at 557.7 nm, a yellow doublet from sodium at 589.0 and 589.6 nm, and a red lines from oxygen at 630.0 and 636.4 nm.

The sodium emissions come from a thin sodium layer approximately 10 km thick at an altitude of 90 - 100 km, above the mesopause and in the D-layer of the ionosphere. The red oxygen lines originate at altitudes of about 300 km, in the F-layer. The green oxygen emissions are more spatially distributed. How sodium gets to mesospheric heights is not yet well understood, but it is believed to be a combination of upward transport of sea salt and meteoritic dust.

In daytime sodium and red oxygen emissions are dominant, and are roughly 1000 times more luminous than nighttime emissions because in daytime the upper atmosphere is fully exposed to solar UV radiation. The effect is however not noticeable to the human eye since it totally fades in the glare of directly scattered sunlight.

## Indirect scattering of sunlight

Amount of air still illuminated after sunset, at the horizon. Normalized so that zenith is 1 airmass

Indirectly scattered sunlight comes from two directions. From the atmosphere itself, and from outer space. In the first case, the sun has just set but still illuminates the upper atmosphere directly. Because the amount of scattered sunlight is proportional to the number of scatterers (i.e. air molecules) in the line of sight, the intensity of this light decreases rapidly as the sun drops further below the horizon and illuminates less of the atmosphere.

When the sun's altitude is < -6° 99% of the atmosphere in zenith is in the Earth's shadow and second order scattering takes over. At the horizon, however, 35% of the atmosphere along the line of sight is still directly illuminated, and continues to be until the sun reaches -12°. From -12° to -18° only the uppermost parts of the atmosphere along the horizon, directly above the spot where the sun is, is still illuminated. After that, all direct illumination ceases and astronomical darkness sets in.

A second source sunlight is the zodiacal light, which is caused by reflection and scattering of sunlight on interplanetary dust. Zodiacal light varies quite a lot in intensity depending on the position of the earth, location of the observer, time of year, and composition and distribution of the reflecting dust.

## Scattered light from extraterrestrial sources

Not only sunlight is scattered by the molecules in the air. Starlight and the diffuse light of the milky way are also scattered by the air, and it is found that stars up to V magnitude 16 contribute to the diffuse scattered starlight.

Other sources such as galaxies and nebulae don't contribute significantly.

## Light pollution

Light pollution is an ever increasing source of sky brightness in urbanized areas. In densely populated areas that don't have stringent light pollution control the entire night sky is regularly 5 to 50 times brighter than it would be if all lights were switched off, and very often the influence of light pollution is far greater than natural sources (including moonlight). This article is about natural sky brightness, for more information about light pollution please visit the light pollution article.

## Twilight

When the sun has just set the brightness of the sky decreases rapidly thereby enabling us to see the airglow that is caused from such high altitudes that they are still fully sunlit until the sun drops more than about 12° below the horizon. During this time, yellow emissions from the sodium layer and red emissions from the 630 nm oxygen lines are dominant, and contributes to the purple-ish color sometimes seen during civil and nautical twilight.

After the sun has also set for these altitudes at the end of nautical twilight, the intensity of light emanating from earlier mentioned lines decreases, until the oxygen-green remains as the dominant source.

When astronomical darkness has set in the green 557.7 nm oxygen line is dominant, and atmospheric scattering of starlight occurs

## Relative contributions

The following table gives the relative and absolute contributions to night sky brightness at zenith on a perfectly dark night at middle latitudes without moonlight and in the absence of any light pollution.

Night sky brightness
Cause Surface brightness [S10] Percentage
Airglow 145 65
Zodiacal light 60 27
Scattered starlight ~15 7

(The S10 unit is defined as the surface brightness of a star whose V-magnitude is 10 and whose light is smeared over one square degree, or 27.78 mag arcsec-2).

The total sky brightness in zenith is therefore ~220 S10 or 21.9 mag/arcsec² in the V-band. Note that the contributions from Airglow and Zodiacal light vary with the time of year, the solar cycle, and the observer's latitude roughly as follows:

${\rm Airglow}/{\rm S}_{10} = 145+108(S-0.8)$

where S is the solar 10.7 cm flux in MJy, and various sinusoidally between 0.8 and 2.0 with the 11-year solar cycle, yielding an upper contribution of ~270 S10 at solar maximum.

The intensity of zodiacal light depends mainly on the observer's ecliptic latitude, which is geographical latitude +- 23.5° (the inclination of the ecliptic plane), and varies as

${\rm ZodiacalLight}/{\rm S}_{10} = 140 - 90\sin(|\beta|)$

where β is the ecliptic latitude and is smaller than 60°, in other cases the contribution is that given in the table.

In extreme cases natural zenith sky brightness can be as high as ~21.0 mag/arcsec², roughly twice as bright as nominal conditions.