Template:ASTR508/Assignment8a

List and identify with a phrase or two 5 effects that modify the so-called Chandrasekhar Mass from the oft quoted value of 1.45 solar masses. Which effects cause increases and which cause decreases and which one or two are most important within the context of iron cores in massive stars? Which are important for accreting white dwarfs?
What two instabilities lead to the dynamic implosion of the iron core?
What two effects lead to the failure of the "prompt shock" in Type II supernovae?
Consider a sphere of initial radius $5\times 10^{8}$ cm and mass 1.4 solar masses, initially heated 10¹⁰K Assuming constant density, total ionization, Y_e = 0.5, homologous expansion ( $v\propto r$ ), and opacity due to electron scattering, calculate the radius the expanding sphere would have when it first became optically thin. (aside: the gas does not really remain totally ionized but the Doppler broadened forest of iron lines in a SN I provides an opacity comparable to electron scattering, use κ_e = 0.2 cm²g^-1 throughout) If the expansion were adiabatic as well as homologous what would be the temperature of the radiation at this point (assume that radiation entropy is separately conserved). Obviously this is too cold because you have left out the effect of radioactive decay.
For this same sphere, estimate the radius and time when the diffusion time for the radiation would be equal to the expansion time scale for the density. (hint: first show that for homologous expansion, $v\propto r$ , that $\rho /{\dot {\rho }}$ is just the elapsed time divided by 3) for an assumed surface expansion velocity of 10⁹ cm s^-1. If the supernova radiates 10⁴³erg s^-1 as a blackbody (not true!) what would be the effective temperature of the photosphere (assume for example that the photosphere lies at 1/2 the just computed for the edge of the sphere). Compare your answers to the characteristics of Type I supernovae.
Distinguish the terms "deflagration" and "detonation" in the context of the exploding white dwarf model for a Type I supernova. Which is the currently favoured mechanism for propagating the runaway? Why? What sets the peak value of temperature that is experienced behind the flame front? Describe what happens to each of the following (increase or decrease) as one crosses a a) detonation or b) deflagration front: density, pressure.