Stelar Characteristics & Evolution

Wien's displacement law represents the wavelength at which maximum intensity is radiated away from a star's surface depends on its temperature. As seen on the graph, 5000 K temperature is equivalent to 580nm intensity, meaning the star emits more radiation at longer visible wavelengths than shorter and thus has an overall white-yellow color.

When radiation is emitted from the hot core of a star, it passes the cooler layers which causes some wavelengths of the continuous spectrum to be absorbed and remitted in unpredictable directions. Passing the light coming from e.g. the sun can be passed through a diffraction grating or prism to identify elements from the star.


The main sequence stars follow the Mass-luminosity L M^3.5. For example if star A has twice the mass of star B makes star A 11 times more luminous meaning energy from nuclear fusion occurs 11 times more. But that also makes the lifetime of star A shorter in contrast to star B.



Hertzsprung–Russell diagram

The luminosity of a star depends on its mass and radius and thus the sizes of stars can be compared on the HR diagram by sing the lines of constant radius. Moving from the bottom right to the top left, the main sequence stars being the most common stars increase in size, temperature and luminosity. Other types of non-main sequence stars are indicated on the diagram as well. Once stars reach the end of their lifespan, the result becomes changes in their luminosity, known as pulsating variable stars such as Cepheid variables. Such stars are found in the instability strip.

Cepheid variables

These stars are often used to determine the distance from the earth to the galaxies in which they are located, thus given the name "Standard Candles". Their luminosity occurs in typical times of only a few days and their periods are directly related to their maximum (or average) luminosity. Period luminosity relationship follows a logarithmic scale and luminosity is given in multiples of the sun's luminosity. Luminosity can be measured from the graph and with the known brightness, distance can be measured following the equation b=L/4πd^2.

As luminosity is at its lowest, the outer layer of Cepheid variables gets an increase in ionized helium and thus the outer layer becomes less transparent making photons unable to escape. Photons are then absorbed, energy is transferred and the star expands. In turn, the outer layer cools, ionized helium decreases causing luminosity to increase causing gravitational forces to oppose the expansion and so the star oscillates under such conditions.


Evolution of main-sequence stars

Once the hydrogen in the core gets low, the lower energy release disturbs the pressure and gravitational equilibrium and so the star collapses inwards. Gravitational energy transfers into kinetic energy causing the temperature to rise and so hydrogen fusion becomes possible in the outer layers of the core turning the star into a "Red giant or Red supergiants". The star gains a larger size and reduced surface temperature. Even heavier elements become possible to fuse depending on the mass and temperature of the star at this stage.


Red giants are formed by main sequence stars of less than eight solar masses and if heavier evolve into red supergiants.

When no more fusion occurs in a red giant, its core collapses and the outer layer ejects around the star into a "Planetary nebula". The remaining core becomes a "White dwarf".

The electron degeneracy pressure of the white dwarf insures no further collapse will take place. The smaller size, lower luminosity, and higher temperature shifts the color into a white one.


The maximum mass of a white dwarf of 1.4 x solar mass is the Chandrasekhar limit. Within more massive red supergiants, the electron degeneracy pressure will not be enough to prevent collapse of the core causing a "Supernova". Depending on the size of the red supergiant, either a neutron star or a black hole will emerge.


A neutron star is tightly packed neutrons with high density = high temperature, and a small radius. The neutron star remains stable due to the neutron degeneracy pressure.


Black holes are regions of space with highly compressed matter that prevents even the escape of electromagnetic radiation including light. Its presence is detected by observing its effect on other matter and radiation.


The maximum mass of a neutron star of about 3 x solar masses is the Oppenheimer-Volkoff limit. If the core after a supernova has a lower mass than the limit, it will contract into a neutron star and otherwise into a black hole since the neutron degeneracy pressure will not be strong enough to resist further collapse.


Reference

Physics Book - John Allum and Christopher Talbot - Second Edition - Hodder 2017

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