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Stars and Steller Evolution : Lecture 11

Organisation of Stars

Apparant Magnitude

This is a measure of how bright a star appears in the sky from Earth. It is a numerical rating which increases as the star becomes dimmer. It may be positive or negative. There is a standard star (which is a theoretical star rather than a real star) whose brightness is given as 0.0. (The closest star to this is Arcurus in the constelation Bootes.) If a star is 1/2.514 as bright as this it has an apparent magnitude of +1.0. If it is 2.514 brighter it would have an apparent magnitude of -1.0.
Brightness Apparant Magnitude
1 0.0
1/2.514 +1.0
1/2.5142 +2.0
1/2.5143 +3.0
1/2.5144 +4.0
1/2.5145=1/100=10-2 +5.0
10-4 +10.0
10-6 +15.0
10-8 +20.0
The scale uses a standard brightness B0 which is close to, but not exactly that of Vega. In terms of this the formula is

Note that B has a technical meaning which I wont give here.

Absolute Magnitude

When comparing stars it is useful to be able to compare them properly. To do so we introduce the concept of absolute magnitude . Quite simply this is what a stars apparent magnitude would be IF it were exactly 32.6 (10 parsecs) away from us. We can look at the table of stars and see that the absolute magnitude of some stars is very large - Rigel is -7.1 and Betalguse -5.6. These very powerful stars are actually far away but appear bright because they are extremely powerful. Under this scale our Sun would have absolute magnitude 4.8.

The absolute magnitude scale is what we need to compare stars. To calculate it we need a stars apparant magnitude and distance from us.

We compute the absolute magnitude, M, from the apparant magnitude, m, and the distance (in parsecs), DL , using

Spectral Type

The nature of Light

We only know about stars because of the light which reaches us. This however contains a great deal of information provided we can use it. To do so we must understand the nature of light.

Light is a Wave It is a wave of the electric and magnetic fields. The different type of light can be characterised by the wavelength - the distance between peaks of the waves. In order of decreasing wavelength the type of light include, Radio waves, microwave, infra-red, red visable light, blue visable light, ultra-violet, x-rays, .. White light is a mixture of all wavelengths. Splitting light into the different wavelengths is enormously important in Astronomy.

Hot objects emit light in all wavelengths. However the "profile" of wavelengths changes as the object's temperature increases. At low T's the object will mainly radiate in the infra-red. As the temperature is increased the object emits more total light and the profile changes - shorter wavelengths become more dominant. As T increases the object appear red - it is red-hot. If T increases further the object is brighter and the colour shifts towards white. Further temperature increases make the light have a blue tinge. It is important that we can look at a stars colour and decide its temperature.
Temperature Maximum Wavelength Corresponding type of light
290K 0.001 cm Infrared
1000K 0.00029 Infrared
5800 0.00005 Visable
10,000 0.000029 Ultraviolet
1,000,000 0.00000029 X-rays

Spectra of Stars

We can examine the spectra of the star, Using the light we can define a star's Spectral Type . This is basically the colour and hence the temperature. The types are as follows
Spectral Type Colour T (C) Examples
O Blue-Violet 28,000-50,000 Mintaka (delta-Ori)
B Blue-White 10,000-28,000 Rigel
A White 7,500-10,000 Sirius
F Yellow-White 6,000-7,500 Procyon
G Yellow 5,000-6,000 Sun
K Orange 3,500-5,000 Albebaron
M Red-Orange 2,500-3,500 Betalguese
The classification spectra can be seen here

© Dave Dunbar 2020