Physics 560

Midterm II: Suggested Study Problems, in no particular order

- Show explicitly that an isothermal, monatomic ideal gas will not be convectively unstable.
- Calculate the Luminosity-Core Temperature homology relations for UMS and LMS stars.
- Assume that the 1 solar mass core of a 10 solar mass star collapses to produce a Type II supernova. Assume further that all of the energy released by the collapsing core is converted to neutrinos and that 1% of the neutrinos are absorbed by the overlying envelope to power the ejection of the supernova remnant. Estimate the final radius of the stellar remnant if sufficient energy is to be liberated to just barely eject the remaining 9 solar masses to infinity.
- Estimate the gravitational binding energy of a neutron star with a mass of 1.4 solar masses and a radius of 10 km. Compare your answer with the amount of energy released in neutrinos during SN1987a.
- Use the exact expression for electron degeneracy pressure (for the nonrelativistic case) to derive the degeneracy condition discussed in lecture. Discuss the evolution of the Sun in the log(r)-log(T) plane.
- Suppose the Sun were to collapse into a neutron star. Find the resultant rotation period and magnetic field strength. Compare the rotation (before and after) to the breakup rotation period for the Sun.
- What is the transmitted intensity of light through a cloud in the optically thin and optically thick limits? How do these change if the cloud emits light as well as absorbs light?
- Use some or all of Kepler’s laws to estimate the free-fall time for a cloud collapse.
- An
external magnetic field contributes a pressure term to the Virial Equation
that can help induce the collapse of a cloud that would, in the absence of
the external pressure and magnetic field, be in hydrostatic balance. If the external magnetic pressure is
given by B
^{2}/8p, retrace the arguments for a maximum external gas pressure before cloud collapse (as in HW 4). How might this change if there is a uniform*internal*magnetic field that supports the cloud against collapse instead? - Derive an expression for the centrifugal radius of a slowly rotating cloud that collapses to form a protoplanetary disk. Given some typical parameter ranges, how big is the resulting protoplanetary disk for the protosun?