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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 22.4 | Stars |
In these revision notes for Stars, we cover the following key points:
A star is a celestial body that produces energy by itself.
Scientific observations have proven that stars have different masses. They range from 1/10 to 200 times a solar mass. The dimensions of stars differ at even higher ranges; their radius may vary from a few kilometres to 10 billion kilometres. The temperature of stars outer surface varies from 2000 K to 40,000 K.
Like all the other light sources, the quantity used to evaluate the illumination of stars is the light flux, Φ, which represents the total light energy emitted by a light source in the unit time.
Another relevant parameter used when dealing with light illumination is illumination, b, otherwise known as illuminance (or brightness). It represents the light flux Φ incident on a given surface area, A. If the distance star-Earth (observer) is denoted by d (it represents the radius of light sphere formed when light is emitted from a star located at its centre), we obtain for illumination b of the given star:
The illumination of stars is measured in lux (1 lux = 1 lumen/m2 where 1 lumen = 1 candela/steradian. Hence, 1 lux = 1 cd/str·m2). Illuminaion is a quantitative indicator of which star is brighter and which is dimmer. However, scientists prefer to use the logarithm of illumination known as apparent magnitude, m, to estimate how bright a star is. Apparent magnitude m is a dimensionless quantity. Thus, according to this system, the apparent magnitudes m1 and m2 of two different stars relate to each other according the equation
Since antiquity, visible stars have been classified in 6 categories, these depend on the illumination they brought on Earth. Thus based on this classification, the brightest stars were considered as first class stars and the dimmer ones as sixth class stars.
Absolute illumination b0 is a reference unit. It corresponds to the illumination produced by a star that is 10 parsecs away from Earth [parsec (pc) is a unit of length used for astronomical distances outside the Solar System; 1 parsec = 3.26 light years = 3.086 × 1017 m].
Absolute magnitude M of a luminous object represents the apparent magnitude of this object if it was at a distance of 10 pc. Based on this approach, it is clear that the absolute magnitudes M1 and M2 of two stars 1 and 2 relate to their light fluxes Φ1 and Φ2 through the following formula:
The colour of a star is an indicator of the wavelength of EM radiation it emits. Based on the Wien's Law, we have for the relationship between the characteristic wavelength and temperature of a black body:
where b = 2.898 × 10-3 m · K is a constant (Wien's constant).
In astronomy, Hertzsprung-Russell diagram, also called H-R diagram, is a graph in which the luminosity values of stars (shown in the vertical axis) are plotted against their temperatures (shown in the horizontal axis). From this diagram, we can identify four groups of stars:
Main sequence stars. This is a zone which includes most stars of the Universe because they are in the longest and most stable stage of their life. This zone contains our Sun as well. Main sequence stars includes those starts in which the fusion reaction that converts hydrogen to helium takes place.
(Red) giant stars. This zone lies in the top-right section of main sequence stars and includes relatively cool stars that emit high amounts of radiation due to their large dimensions. These stars are colder than those in the main sequence; their temperatures vary from 3000 K to 6000 K. Nuclear reactions taking place in red giants are different from those occurring in the main sequence stars. The most common reaction in red giants involves the helium burning to produce carbon.
Red super giants. These stars are older than red giants as they have completed the cycle of helium-to-carbon conversion and now are in the stage of carbon burning to produce heavier elements such as oxygen and other chemical elements up to iron, where the conversion process terminates. Red super giants lie above red giants in Hertzsprung-Russell Diagram. This means they radiate even higher amounts of energy because radius of such stars may extend up to a few thousand times the solar radius.
White dwarfs. These stars lie in the bottom-left zone of Hetrzsprung-Rusell diagram. This means their temperature is very high but their brightness is very dim. The surface temperature of such stars is about 10 000 K and their radius is not more than a few thousand kilometres, i.e. about 100 times smaller than the radius of Sun. White dwarfs have very high densities reaching one billion times the water density. No nuclear reaction take place in them. The mass of white dwarfs is close to that of Sun but they never exceed the value of 1.4 times the solar mass.
Besides the four categories of stars explained above, which don't change their appearance with time, there also exist a variety of atypical stars known as variable stars. For several reasons, the illumination produced by such stars changes with time. Some types of stars belonging to variable stars category include:
Cepheids, which are stars whose illumination varies periodically with time. This period varies from a few days to a few weeks. Moreover, the illumination of such stars is proportional to the period of variation. This important feature allows astronomers to measure long distances in the Universe.
RR-Lyrae stars. These too are stars with periodical illumination but unlike cepheids, this period of variation ranges from a few hours to a few tens of hours.
Novae are stars the illumination of which changes in an explosive way. Thus, their illumination suddenly increases by 10 units apparent magnitude and then, it decreases gradually within a few months to the original state.
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