Apparent magnitude

The apparent magnitude is how bright a celestial body - in particular a fixed star - appears from Earth. The apparent brightness is expressed as a number, it carries the additional magnitude ( referred to as " like ", formerly m), size class or just size. The smaller the number, the brighter the star.

Today's scale for measuring the apparent brightness goes back to the Greek astronomer Hipparchus (ca. 190-120 BC) and Ptolemy (ca. 100-175 AD) back, which the stars according to their ( perceived with the naked eye ) Brightness one rushed into six size classes. The brightest stars, were attributed to the first variable, the weakest of the sixth magnitude. Later, the scale has been expanded out to both sides to brighter objects as well as both - according to advent of the telescope - to classify fainter objects can. The brightness scale is logarithmic in 1850 defined by Norman Pogson, so that a first magnitude star exactly 100 times as bright as a star sixth size. Stars of the first size are a factor ( about 2.5 ) as a bright star of the second size. The calibration of the scale was carried out on so-called standard stars.

• Very large telescopes ranging up to about the 22 size, modern astrophotography to 25 size, which is about a candle flame on the moon. The Hubble Ultra Deep Field galaxies are still having a brightness of 29 may be seen.
• Brighter objects than 0 Size obtain a negative sign, such as the Venus -4.4 or like the sun like -26.

The apparent brightness of a star depends on the observation band (filter). For scientific observations a number of different filter systems are defined, are comparable with the observations with different telescopes and instruments.

Spellings

Polaris has an apparent brightness ( "Magnitude " ) of about two. The following notations are usual for this:

• 2.0 m
• 20
• 2.0 may
• 2 magnitude
• M = 2.0
• 2 star size
• Size class 2
• Second size class

Definition

After Norman Robert Pogson a difference in brightness of 1:100 corresponds to a difference of five size classes and 5 likes. The magnitude scale is logarithmic, as well as sensations of man in the Weber- Fechner law are proportional to the logarithm of the stimulus.

Physically, the brightness scale by the energy of the incident light is defined ( bolometric luminosity ). If m is the magnitude and the measured flux density of each star that applies to their difference in brightness

Assuming for the luminous flux of an object the size class 0, we obtain the brightness of the first object

For small variations in brightness approximately

And the numbers are. The former figure shows the relationship to define clearly.

The ratio of the brightness of the class m to the brightness of the class ( m 1)

For example, corresponds to a relative difference in brightness of 1 ppm of a class brightness difference of about 1.1 μmag.

Power limit

Under urban conditions, the dark-adapted eye detects objects up to 4 may, under ideal conditions in the mountains up to 6 mag. By monitoring devices more stars are visible. The apparent brightness of the faintest stars that can just make an observation unit still defined its intrinsic size.

Considering a pupil diameter of the eye of d = 7 mm based on the output can increase by optical instruments with the opening D from the definition equation of the size classes derive. The factor of 2 arises from the fact that the intensity of a quadratic function of the diameter of:

And with the above sizes:

The relationship can be further simplified (for 5 · log ( 1/7) = -4.2 ):

A pair of binoculars with the opening of 20 mm expanded visibility up to a magnitude 8 likes, a telescope of 70 mm to 11 mag and a like from 200 mm to 13. Large telescopes penetrate with CCD sensors to size classes of 30 before like.

The current instrumentation of the Hubble Space Telescope sees stars of magnitude 31, which roughly corresponds to the brightness of a candle on the moon. With the future of the ESO 42- meter reflecting telescope E -ELT is computationally an observation of celestial bodies of the 36th magnitude possible.

Photometric zero point

With the beginning of the photometry, the individual classes were further subdivided, for modern measuring instruments to an almost arbitrary refinement is possible. An accurate reference value was necessary. Initially, the scale on the Polarstern with 2.1 like was aligned, until it turned out that its brightness varies slightly. As a reference, therefore, is traditionally the star Vega, whose brightness was set at a magnitude of zero. For calibration of modern photometric systems today is a set of well- measured reference stars near the celestial pole, the so-called " Polsequenz ". The commonly used UBV system is calibrated in such a way, for example. This results for Vega in the UBV system an apparent magnitude of V = 0.03 mag. Color indices are defined such that stars of type A0V have ( to this Wega heard ) the average color index 0.00. Brightness systems with this property are called " Vega - brightness " means.

Moreover, the apparent brightness depends on the wavelength of light. Therefore, in observational astronomy, the apparent brightness is often given for the visual spectral range around 550 nanometers. It is characterized by the V symbol.

Overall brightness of multiple stars

The overall brightness of a multiple star is calculated from the luminous fluxes of the individual components:

In the case of a double star (n = 2) with the luminances of the individual components M1 and M2 are obtained:

Examples

Permanent objects

The apparent brightness of the sun, planets, and our moon varies greatly partly among other things because the very variable distance from the Earth. Even more, however, the magnitude of the moon is affected by its phase ( crescent moon ). Because of these strong fluctuations are usually classified in only stars to apparent magnitude. The naked- eye stars are distributed as follows:

Uncommon Objects

In addition to the "classical" objects in the sky there are some other objects that appear only briefly or in eye-catching appearance only at certain places on earth can be seen. You can even surpass the brightness of Venus.

Comets

The apparent brightness of comets can be described by:

Where:

M0 and n are fitting parameters that are derived from measurements and allow a comparison of the comet with each other. For example, could the brightness profile of the comet Tempel 1 with the parameters m0 = 5.5 mag and n = 25 are quite well reproduced.

Demarcation

The apparent brightness depends on the distance of the observer (or the Earth) from the observed object and - if not self-luminous objects (planets, dwarf planets, asteroids, TNOs, etc.) - in addition to the phase and distance from the central star. Thus the moon appears due to its proximity much brighter than distant stars, although these light billions of times stronger.

An independent on the distance variable is the absolute brightness.

It was originally understood by those apparent magnitude, as it appears to the eye. Today it is called visual magnitude - in contrast to the photographic magnitude, which corresponds to a slightly different spectral sensitivity.