Download OUR UNIVERSE Problem Set 7 Solutions Question A1 Question A2

OUR UNIVERSE
Problem Set 7 Solutions
Question A1
PN
Log
Luminosity
AGB
HB RGB
MS
WD
Log T
Question A2
The early universe consisted of mainly hydrogen, a little helium, hence there was no iron, and stars
made out of these materials and went through their evolution where very large stars can fuse
elements up to Fe in their cores, releasing energy with each fusion reaction [1].
However, the fusion of iron results in the consumption (not release of energy), which results in a
massive core collapse. When the core mass exceeds Chandrasekhar's limit (1.44 Msun), a type II
supernova occurs [1].
The star explodes releasing the iron into space where is can go on to be involved in the formation of
new stars and solar systems [1]. Our solar system is one such system, so the presence of Fe in the
Earth's core can be explained as the solar system being made of material ejected from ancient TypeII supernova explosions [1].
Question A3
From the HR diagram, O-class stars have very high luminosities and high temperatures [1].
The high luminosity means that the star is large which gives rise to high densities in the cores of
these stars, and high temperature means the nuclei are moving very fast [1]. These two factors
combine to give a very high rate of collisions of nuclei in the cores which means that they burn up
their nuclear fuel very quickly and hence live for relatively very sort times [1].
Question B
This question was exactly as it appeared in the May 2011 exam. The suggested answer below is the
one supplied to the External Examiner when he reviewed the paper.
The questions may be answered in many different ways, the marker should take this into account.
The main thing is that the main points or each part are covered, and that they are done so in a
structured way.
(a) The hydrogen-burning main sequence phase,
As the proto-star collapses under its own gravity its atoms (hydrogen about 70 % and helium about
25 %) heat up because they exchange gravitational potential energy for kinetic energy, eventually
the atoms in the core reach temperatures of about 15 million K and nuclear fusion commences,
whereby hydrogen fuses to helium. At this point the new star settles onto the main sequence. The
radiation pressure from the fusing core is able to support the star halting the collapse. The star is
held to a reasonably constant size for ca 1010 years via self regulation. That is, if the star tries to
collapse under gravity it would result in an increased temperature and hence a higher rate of
hydrogen fusion (more collision per second) which increases the radiation pressure and blow the
star back up again. [5]
(b) hydrogen exhaustion and the red giant phase,
During its life on the main sequence the star continually converts hydrogen into helium. However,
the temperatures and the density in the star are never enough to fuse helium. Therefore, as helium is
more massive that hydrogen, the star slowly builds up a non-fusing heilium core surrounded by a
fusing hydrogen core. As such, the core becomes depleted in hydrogen and fusion rates slow
causing the core to begin to contract due to its gravity. This heats a shell just outside the core, where
hydrogen remains, initiating fusion of hydrogen to helium in the shell. The higher temperatures lead
to increasing reaction rates, producing enough energy to increase the star's luminosity by a factor of
about 1,000. The outer layers of the star then expand greatly, beginning the red giant phase of the
star's life. Due to the expansion of the outer layers of the star, the energy produced in the core of the
star is spread over a much larger surface area, resulting in a lower surface temperature and a shift in
the star's visible light output towards the red – hence red giant. [5]
(c) the helium flash and the horizontal branch phase,
The helium flash is the mechanism that ends the complete collapse of the core and the ascent up the
red giant branch depends on the mass of the star. For sun-like stars the core will become dense
enough that electron degeneracy pressure will prevent it from collapsing further. Once the core is
degenerate, it will continue to heat until it reaches a temperature of roughly 10 8 K, hot enough to
begin fusing helium to carbon via the triple-alpha process. Once the degenerate core reaches this
temperature, the entire core will begin helium fusion nearly simultaneously in a so-called helium
flash, which increases the size of the core such that the electrons are no longer degenerate. The
expanded core cools allowing the star to collapse further to below red giant size. The core helium
fusing phase of a star's life is called the horizontal branch (which is like the main sequence except
that the star's core consists of a helium fusing core surrounded by a hydrogen-fusing shell. The
higher core temperatures cause the star to be larger on the HB that is was on the MS. [5]
(d) the asymptotic giant branch phase, the planetary nebula phase,
The asymptotic giant stage is an analogue of the red giant stage referred to earlier, the only
differences being that the non-fusing core in this case is carbon and that it is the helium in the
fusing core that is becoming depleted - with their attendant higher temperatures, which again causes
fusion rates to slow leading to another core collapse and shell expansion until it is supported again
by electron degeneracy and the star expands greatly in a new red giant phase. However, this time
the temperature in a 1-solar mass star never reaches a high enough level to initiate a carbon flash
and a new HB carbon burning phase. Hence, the star continues to increase in size to diameter
commensurate with that of the orbit of Mars. The convective zone of the star are so far from the
core that they feel little gravitational attraction and becomes so weakly bound that becomes unstable
and breaks away expanding into space away from the core at about 20 km s –1 leaving a so-called
planetary nebula. [5]
(e) the white dwarf phase.
Following the planetary nebula stage the remnant which is primarily helium has a mass of about 0.5
solar masses. It contracts under gravity exchanging gravitational potential energy for kinetic energy
of the helium, which thereby increases in temperature ca 100,000 Kelvin; well below the 100
Megakelvin needed for helium fusion. Without a nuclear 'fire' in the centre the remnant continues to
collapse and only halts when the remnant is so small that all the electrons become degenerate,
yielding an electron degeneracy pressure that holds up the remnant from further collapse. Once the
collapse stops the remnant no longer heats up via gravitational collapse and without a nuclear fire
the remnant slowly cools over 10s of billions of years by radiating heat. [5]