IB Option E: Astrophysics: Stellar radiation and stellar types

the main energy source of stars

Stars are formed by interstellar dust coming together through mutual gravitational attraction. Loss in potential energy as this happens can (if the initial mass of the dust collection is sufficient) produce high temperatures necessary for fusion. The fusion process produces a radiation pressure that can then stop any further gravitational collapse.

The thermonuclear process produces a radiation pressure that is in equilibrium as the gravitational pressure.

The total energy emitted by the star per unit time.
this energy is emitted uniformly in all directions

The energy received per unit time per unit area at the Earth
b=L/4pi d^2

Attaching a radiation sensitive instrument known as a bolometer to a telescope. If the radius d is measured then the luminosity can be found.

If we regard stars to be black body radiation, then the luminosity L of a star is given by L=4π(R^2)(σ)(T^4)
R is radius of the star, T is surface temperature, σ is S-B constant

Relationship between the maximum value of wavelength emitted by a black body and its temperature. λ_max T=constant = 2.9X10^-3
We can use Wein law to find the temperature of a star from its spectrum. If we know temperature and luminosity, radius can be found.

The radiation reaching us from stars does not form a continuous spectrum. There is a series of black lines that correspond to missing wavelengths of light that have been absorbed by the cooler, outer laters of the star. Different stars have different spectrums

The wavelengths absorbed are characteristic of the atoms present. Hence the absorption spectrum can be used to identify the elements present in the outer layers of the star.
Using doppler effect, we can find the speed and direction of motion.

change in the apparent frequency of a wave as observer and source move toward or away from each other
Moving towards – frequency increases (wavefronts bunch up and wavelength shortened, increasing the frequency)

For surface temperature. The absorption spectrum of a particular star will depend on its surface temperature

Large and low surface temperature

Small, high surface temperature

Stars that have undergone gravitational collapse to such an extent that their core is effectively made up of just neutrons

When the core of a star can collapse no further, the other layers, which as still falling rapidly inwards, will be reflected back causing an enormous shockwave.

Rotating neutron stars. As they rotate they emit beams of electromagnetic radiation from the poles of the star.

suggested that certain stars that undergo gravitational collapse will reach a density and radius such that the gravitational field at the surface of the star will be strong enough to prevent electromagnetic radiation from escaping the surface.

two rotating stars about a common centre
The period of rotation depends on the sum of the masses of the two stars and the separation of the stars. By measuring the angular separation of the two stars as seen from Earth and knowing how far they are from Earth, we can calculate the linear separation. The period of revolution can be measured directly and hence the sum of the masses can be found.

stars whose luminosities vary regularly

Binary nature of the system can be deduced from the fact that the stars periodically eclipse each other.
As the stars orbit each other, one will block light from the other. The brightness of the system will vary periodically. This variation in brightness yields information as to the ratio of the surface temperature of the stars and also the relative size of the stars and the size of its orbit.

Star A is approaching us, so its spectral lines are in blue-shift. Star B is red-shift.

see textbook page 336