# Surface brightness

The surface brightness (Engl. Surface Brightness ) is a luminance . It is used in astronomy to record the brightness of astronomical objects with large areas such as comets , nebulae or galaxies . ${\ displaystyle B}$

## observation

During visual observations, the surface brightness in the telescope cannot be greater than that of the free-eyed . It is maximum when the exit pupil AP of the eyepiece corresponds to the pupil diameter of the dark-adapted eye .

Dark adaptation is hardly possible near the city because of the light pollution . Therefore, the observation of astronomical objects is only possible up to a certain surface brightness. This mainly affects faint galaxies and gas nebulae .

## calculation

The surface brightness is the ratio of the apparent brightness  H to the surface  F :

${\ displaystyle B = {\ frac {H} {F}}}$

or logarithmic in magnitudes:

${\ displaystyle B _ {\ text {mag}} = - 2 {,} 5 \ cdot \ log {\ frac {H} {F}}}$

If the apparent brightness of the object is replaced by the apparent brightness  m in magnitudes, it follows:

${\ displaystyle B _ {\ text {mag}} = m + 2 {,} 5 \ cdot \ log F}$

## units

The surface brightness is measured in  cd / m². The unit mag / arcsec² is common in astronomy  ; The unit S 10 describes the brightness as the number of stars of brightness 10 mag within one square degree .

Conversions:

• ${\ displaystyle B = 1 {,} 084 \ cdot 10 ^ {5} \ cdot 10 ^ {- 0 {,} 4 \ cdot X}}$
With
• ${\ displaystyle B}$ in cd / m²
• ${\ displaystyle X}$ in mag / arcsec²
• 1 S 10 = 0.69 · 10 −6  cd / m².

Example: Lowest brightness of the night sky under optimal conditions: 21.6 mag / arcsec² = 2.5 · 10 −4  cd / m² = 370 S 10 .

## Individual evidence

1. Other notation:${\ displaystyle B = 1 {,} 084 \ cdot 10 ^ {5} \ cdot e ^ {- 0 {,} 92104 \ cdot X}}$
2. Converter cd / m² - mag / arcsec²