# Absolute brightness

The absolute brightness is an auxiliary variable in astronomy and astrophysics , in order to be able to compare the actual brightness (thus the luminosity of self-luminous objects ) of celestial objects in visible light.

## definition

The absolute brightness differs from the apparent brightness that is actually measured for an object from the earth ; the latter depends on the one hand on its luminosity (for self-luminous objects such as stars ) or its reflectivity (for non-self-luminous objects) and on the other hand on its distance and is additionally influenced by interstellar matter for objects outside the solar system .

The absolute brightness is the brightness that an observer would measure from a uniform distance; this is determined as follows:

• for self-luminous objects : 10  parsecs (32.6  light years ). For stars that are less than 10 parsecs away, the apparent brightness is therefore greater (i.e. its numerical value smaller) than the absolute brightness and vice versa.
• for reflective objects of the solar system ( planets , comets and asteroids ): an astronomical unit  (AU). It is assumed that the object is 1 AU away from the sun and at the same time 1 AU away from the observer and is in full opposition (i.e. being observed from the location of the sun).

## Unity and magnitude

Like apparent brightnesses, absolute brightnesses are specified in magnitudes (mag). A smaller numerical value means greater luminosity.

The brightest fixed stars achieve absolute brightness of about −9 mag (300,000 times the luminosity of the sun ), while the faintest stars reach +17 mag (less than one ten thousandth of the sun's luminosity).

In older works on astronomy in particular, one often finds the spelling with a superscript M above the decimal point, for example with a star of the third (absolute) magnitude. The use of the capital letter makes it clear that it is an absolute brightness. ${\ displaystyle 3 {\ stackrel {\ text {M}} {,}} 0}$

## Bolometric brightness

Bolometric brightness indicates the brightness of a star not only in visible light, but in the entire electromagnetic spectrum . The correction required for this depends on the sensitivity range of the measuring device and the spectral type of the object in question.

The photographic brightness of the sun (in visible light) is , on the other hand, the bolometric brightness . ${\ displaystyle 5 {\ stackrel {\ text {M}} {\ text {,}}} 16}$${\ displaystyle 4 {\ stackrel {\ text {M}} {\ text {,}}} 74}$

## Distance module

The difference between the apparent brightness  m and the absolute brightness  M is called the distance module, because it is closely related to the distance  r . From the definition of the brightness levels it follows:

{\ displaystyle {\ begin {aligned} {\ frac {r} {10 \, \ mathrm {pc}}} & = 10 ^ {\ frac {mM} {5 \, \ mathrm {mag}}} \\\ Leftrightarrow mM & = 5 \, \ mathrm {mag} \ cdot \ log _ {10} \ left ({\ frac {r} {10 \, \ mathrm {pc}}} \ right) \ end {aligned}}}

If the distance measure is given as a dimensionless number, the distance module can be written as: ${\ displaystyle r ^ {*} = r / \ mathrm {pc}}$

{\ displaystyle {\ begin {aligned} mM & = 5 \, \ mathrm {mag} \ cdot (\ lg r ^ {*} - \ lg 10) \\ & = - 5 \, \ mathrm {mag} +5 \ , \ mathrm {mag} \ cdot \ lg r ^ {*} \ end {aligned}}}

From the definition of the parallax second, the relationship between the distance measure and the annual parallax π (as a dimensionless number in arc seconds ) follows: ${\ displaystyle r ^ {*}}$

${\ displaystyle r ^ {*} = {\ frac {1} {\ pi}}}$

This then gives:

{\ displaystyle {\ begin {aligned} mM & = - 5 \, \ mathrm {mag} -5 \, \ mathrm {mag} \ cdot \ lg \ pi \\ & = - 5 \, \ mathrm {mag} \ cdot (1+ \ lg \ pi) \\\ Leftrightarrow \ pi & = 10 ^ {{\ frac {mM} {- 5 \, \ mathrm {mag}}} - 1} \\\ Leftrightarrow r ^ {*} & = 10 ^ {1 - {\ frac {mM} {- 5 \, \ mathrm {mag}}}} \ end {aligned}}}

With the help of these important for astronomy formula for stars whose luminosity is known (eg. B. Cepheid or supernovae , the type Ia), the distance can be calculated luminosity distance . In this way, the distance of the Andromeda nebula could be determined in 1923 .

The difference between apparent and absolute brightness is partly based on the interstellar extinction , i.e. H. the partial absorption of radiation by interstellar dust . This must be taken into account by an additional term, the extinction parameter , in the equation for the difference in brightness: ${\ displaystyle A}$

${\ displaystyle mM = 5 \, \ mathrm {mag} \ cdot (\ lg \, r ^ {*} - 1) + A}$
m - M distance m - M distance
Parsec Light years Parsec Light years
- 5th 1, 00 3.26 +5.5 125.89 410.61
−4 1.58 5.17 +6.0 158.49 516.93
−3 2.51 8.19 +6.5 199.53 650.78
−2 3.98 12.98 +7.0 251.19 819.28
−1 6.31 20.58 +7.5 316.23 1,031.41
00 10, 00 32.62 +8.0 398.11 1,298.47
+1 15.85 51.69 +8.5 501.19 1,634.68
+2 25.12 81.93 +9.0 630.96 2,057.94
+3 39.81 129.85 +9.5 794.33 2,590.80
+4 63.10 205.79 +10, 0 1,000, 00 3,261.62
+ 5 100, 00 326.16 + 25, 0 1,000,000, 00 3,261,619, 00

## Examples

### Self-luminous objects (stars)

star Apparent
brightness
( noun )
Absolute
brightness
( M )
Distance
module
( m - M )
distance
Sun −26.73 mag 0+4.84 mag −31.57 1 AE
Sirius 0−1.46 mag 0+1.43 mag 0−2.89 002.64 pc
Vega 0+0.03 mag 0+0.58 mag 0−0.55 007.75 pc
Pollux 0+1.15 mag 0+1.08 likes 0+0.07 010.34 pc
Spica 0+1.04 mag 0−3.51 mag 0+4.55 081.3 0 pc
Rigel 0+0.12 mag 0−6.78 mag 0+6.90 240 , 00 pc
Deneb 0+1.25 mag 0−7.24 mag 0+8.49 499 , 00 pc

### Reflective objects of the solar system

object (Maximum) apparent
brightness
( m )
Absolute
brightness
( H )
Distance to the sun
Venus - 04.9 mag - 04.4 mag 0.7 AU
Jupiter - 02.9 mag - 09.4 mag 4.9-5.5 AU
Eros + 07 , 0likes +11.2 mag 1.1-1.8 AU
Apophis <+15 , 0mag
(year 2029 up to +3 mag)
+19.7 mag 0.75-1.1 AU
Ceres + 06.6 mag + 03.3 mag 2.6-3.0 AU
Pluto +13.7 mag - 00.8 mag 30 - 49 AU
Sedna +21 , 0likes + 01.5 mag 76 - ≈900 AU
2018 VG 18 +24.6 mag + 03.3 mag currently 120 - 130 AU