Luminosity is a measure of the total energy given output by a star at all wavelengths from gamma radiation to radio waves. For example the Sun gives out about 500 million million million MJ of energy every second so its luminosity is 500 million million million MJ.
The luminosity depends on:
(a) the size of the star
(b)
the temperature of the star
(a) for a star with a certain surface temperature the
bigger the star the more energy it gives out. A star with double the radius of another one will
have an area four times as great and so have a luminosity four times greater than the first
star
(b) for a star of a certain size the hotter the star the more energy it gives out and
so the greater its luminosity. A star with a temperature of double another one will have a
luminosity sixteen times greater.
The brightness is
how bright a star appears when seen from the Earth. This depends on:
(a) the actual
luminosity of the star
(b) the distance of the star from the observer on the
Earth
If we have two stars of the same luminosity with one star double the distance
of the other from the Earth the closer star will look four times brighter. It obeys the inverse
square law.
The photograph shows the Pleiades star cluster. The brighter stars look
about the same brightness – in fact they are. They are all part of the cluster and about the
same distance from the Earth. However some of the background stars may be just as bright
– they don't look it because they are much further away.
The luminosity depends on the surface area
of the star. The surface area (A) of a star of radius R is 4pR2. A star with a radius of 2R will therefore have four times
the luminosity of a star of radius R if the stars are at the same temperature.
The
luminosity of a star also depends on its temperature. If we consider a star to be a perfect
black body then the radiation emitted per second (E) is given by the Stefan-Boltzmann
law.
Energy emitted per second (E) = sAT4
where sis Stefan's constant (5.7x10-8 Wm-
2K-4) and T is the absolute temperature of the star. (Strictly we should write
the difference in the temperature between the star and its surroundings but since the
temperature of a star is very large, as least a few thousand K and the temperature of space
is very low – about 3 K, this slight inaccuracy can be ignored).
We can calculate this
energy output for a star of the same size as our Sun. R = 6.96x108 m and T = 6000K.
Therefore E = 5.7x10-8x6.08x1018x60004 =
4.5x1026 J.
A star with a temperature twice that of our Sun would have an energy
output sixteen (24) times as great.
Consider a star like Rigel in Orion (on the right in the photo). The surface temperature of Rigel is 11600 K (1.9 times that of the Sun) and its radius is seventy times that of the Sun. The energy output of Rigel per second is therefore 702x1.94 = over 68000 times that of the Sun. In other words an enormous 3.08x1031 J. Altair in Aquila at nearly 17 light years away has an output of just less than ten times that of the Sun.
where lmaxA ,TA and lmaxB ,TB are the peaks of the energy wavelength
curve and the absolute temperature of two black bodies, in this case two stars.
Consider two
stars A and B whose energy-wavelength curves are shown in the diagram.
Star A has an energy peak nearer the blue
end of the spectrum and is at a higher temperature than star B that has an energy peak
towards the red end of the spectrum.
The brightness of a star seen from the Earth depends its intrinsic luminosity but also on its distance from the Earth. The observed brightness for a given star decreases inversely proportionally to its distance away. The presence of interstellar gas will further decrease the observed brightness.