Homework 08 Solutions
Please answer at least 4 of the following 5 questions correctly for full
credit:
Question 1
How do main sequence stars generate the energy that makes them shine? Make
sure your answer is correct for the main sequence, but also is specific
enough not to simply apply to all proper stars.
Answer
By fusing Hydrogen into Helium, and only Hydrogen into Helium. Only after they
leave the main sequence will stars start burning heavier elements, starting
with fusing Helium into Carbon.
Question 2
Luminosity means energy is radiated off. In a protostar: Where does this
energy come from?
Answer
Purely from gravitational infall (gravitational contraction). The definition
of a protostar is that no fusion takes place (while the definition of a star
is that it creates energy through fusion!).
Question 3
Is it the interplay between internal temperature and pressure or between
surface temperature and luminosity that allows newborn stars to reach
equilibrium and become main sequence stars?
Answer
It is the interplay between internal temperature and pressure that establishes
equilibrium. For a given mass it will lead to a zero age main sequence
temperature and luminosity, but stability is determined by the profile of
temperatures and density that regulates reaction rates and energy transport
throughout the star. Page 13 of lecture 25 shows that solar mass and lower
than solar mass stars and lower pass through the upper region of the main
sequence on their way to the White Dwarf region. So there is a short period
where they have a higher mass star's main sequence surface temperature and
luminosity while they truly are dying stars on their way to White Dwarfdom.
Question 4
The relationship between pressure and temperature plays an important role in
regulating the rate of fusion at the center of a star. Does electron degeneracy
affect the temperature or the pressure when it undercuts the regulatory
function of this relationship?
Answer
Indeed it does. Once the core of a star is supported by electron (or neutron)
degeneracy, the pressure inside that degenerate region becomes independent of
temperature. Thus an increase in temperature no longer also leads to an
increase in pressure, which in turn would normally lead to expansion against
the force of gravity and its associated cooling...
Question 5 (the conceptual one...)
Which two energies must be stable in time and equal to each other for a star
to be in equilibrium, i.e. not to change size or luminosity?
Answer
The energy radiated off from its surface and the energy produced in its
interior. The latter may generally have two contributions: one from fusion,
and one from gravitational infall. If there is a contribution from
gravitational infall on top of that from fusion, the star is not considered
stable though: Gravitational infall means its structure is changing, and that
typically leads to ensuing adjustments in surface temperature and/or
luminosity in reaction to these internal changes.
The deadline for submitting solutions to this homework has passed.
Last modified: Fri Mar 28 10:21:24 MDT 2008