The Concept of Magnitude in Astrophysics

In Astrophysics, often the terms like Apparent magnitude, Absolute magnitude and Bolometric magnitude are encountered. Ever wondered what are these terms and how much are they important in Astronomy? Well, a lot.The concept of magnitude is very important to understand for an amateur astronomer or a science enthusiast.

Magnitude is basically the ” brightness” of an astronomical object. There are numerous objects visible in the night sky. These objects vary in distance from earth and hence they also vary in their brightness. We shall first discuss the concept of Apparent magnitude.

Apparent Magnitude

The apparent magnitude is the brightness of an object as visible through the naked eye. In 2nd Century BC, Hipparchus first classified the stars according to their apparent brightness of apparent magnitude and cataloged some 1000 stars into 6 groups. The group 1 stars were the brightest, group two stars were fainter than the group 1 and so on. The 6th group stars were the faintest. In 2nd Century AD, Ptolemy also used the same approach and classified the stars into his own catalog.

98,Sir William Herschel,by Lemuel Francis Abbott
William Herschel

In 1830, British Astronomer William Herschel discovered that the stars of group 1 were 100 times brighter than stars of group 6. Later in 1856, N.R. Pogson developed a scale in which he assumed that the ratio of the brightness of objects in two successive groups is same.

This led to the conclusion that a first magnitude star is 2.5 times brighter than the second magnitude star and so on for the next ratios.Mathematically, if B(m) and B(n) are the brightnesses of two stars with magnitudes m and n ( n>m ), then

B(m)/B(n) = (2.5)^ n-m

This equation has something very important to tell. According to this equation, the brighter the object, lesser is its magnitude. This means that an object with magnitude -4 is brighter than the object with magnitude, say +2.

Example: The apparent magnitude of Sun is -26.74 and that of the brightest star in the night sky is -1.74 So according to the above equation, Sun turns out to be more than 10 billion times brighter than Sirius. The image below illustrates the concept briefly.

appmag

Absolute Magnitude

The apparent magnitude depends upon the luminosity of an object or the total amount of energy radiated from it per second. Besides this, it also depends upon a very crooked parameter, the distance. Since the distances vary largely, the apparent magnitude of an astronomical object does not provide the actual brightness or luminosity. So the new term introduced was the Absolute Magnitude.

In the concept of absolute magnitude, we fix the distance of an object to some standard distance. The chosen distance is 10 parsec (32.6 light years). So the absolute magnitude of an object is actually the apparent magnitude of an object if it were 10 parsec away. We assume the objects to be placed at this distance and compare their luminosity. Mathematically, if m is the apparent magnitude of an object, M is its absolute magnitude and d is its distance from earth then,

m – M = 5 log (d) – 5

The quantity m – M only depends on the distance and hence its known as the distance modulus. The equation represents a relation between an object’s absolute and apparent magnitude and its distance from us.

The absolute magnitudes of most of the stars lie between -20 to + 10. The absolute magnitude of the sun is +4.8 which shows that our sun turns out to be an average star in the stellar population.

Photovisual Magnitude:

When stars are observed visually, it is termed as visual magnitude. Our retina is insensitive to a wide range of the electromagnetic spectrum. A star can be photographed using different filters and the magnitudes so obtained are termed as Photovisual magnitudes.

Bolometric Magnitude

All the magnitudes defined so are cover only limited regions of stellar spectrum. The stellar magnitude based on the radiations measured over the entire range of electromagnetic spectrum is known as the Bolometric magnitude. bolometric-mag

But since no single detector is sensitive to all the wavelengths of the stellar spectrum, to convert any other other magnitude into bolometric magnitude, some corrections need to be applied. In particular, the difference between the bolometric magnitude and photovisual magnitude is termed as Bolometric correction ( BC).

The BC for sun is -0.11 The BC is always a negative quantity. The importance of this magnitude can be understood from a simple example. There is an orange giant star Arcturus, in  the constellation of Bootes. It is about 110 times brighter than the Sun. But in the infrared spectrum, the star is 180 the star is 180 times more powerful than the Sun. So the total ( bolometric ) output of Arcturus is far more greater than its apparent output.

img017

So the bolometric magnitude represents the total luminosity ( power output ) of a star.

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