Astronomy subject
(This question might look long, but most of the sentences are hints actually, I believe it should not take too much time as these are just low points questions in my assignment)
1.)
Description:
Stars like the Sun can be considered to be supported by gas and radiation pressure. In other words, the star will collapse until the outward pressure of the gas and radiation it produces balances the inward attraction due to gravity. For a white dwarf star, which our Sun will become once it dies, the star is instead supported by electron degeneracy pressure. Material in a white dwarf star is incredibly densely packed together, further collapse under the influence of gravity is prevented by the pressure of the electrons repelling one another. Neutron stars, which are the end result of stars more massive than the Sun, are denser still. They are so tightly squeezed together that the protons and electrons within them have been pushed together to form neutrons. The collapse of a neutron star under the influence of gravity is prevented due to neutron degeneracy pressure (caused by the strong nuclear force).
Questions:
For an object 1.7 times the mass of the Sun (the Sun is 1.99 × 1030 kg), work out the radius it would have if it were a:
i) main sequence star, supported by gas and radiation pressure of 280 Pa m2 kg-1.
ii) a white dwarf, supported by electron degeneracy pressure of 3.6 × 106 Pa m2 kg-1.
iii) a neutron star, supported by a neutron degeneracy pressure of 9.2 × 1011 Pa m2 kg-1.
(all units in metre)
HINT:
Pressure = Force/Area, so if you consider the force due to gravity on a 1kg object of surface area 1 m2, and the object is in equilibrium, ie the force due to gravity balances the force due to the pressure then Pressure (in Pa m2 kg-1) = GM/r2.
2.)
Young white dwarfs are typically far hotter than stars like the Sun (e.g. Twd ≈ 42,000K; TSun ≈ 6,000 K). Despite this, they are also very, very faint. Given a white dwarf that is seven times hotter than a star, and using the radii (for the star and white dwarf) you calculated earlier in this question, calculate how much brighter (or fainter) that white dwarf would be than a star like the Sun.
L white dwarf = (Answer) ×L star ???
HINT: L is the luminosity, the power (P) radiated by the object. Right at the begining of the course (kettle topic) you saw that for radiation the power is given by:
L = P = σAeT4
in this equation e is the emisivity (1 for the Sun and a white dwarf), σ is Stefan's constant = 5.67 × 10-8 Js-1m-2K-4, A is the surface area in m2 and T is the temperature in K.