Chapter 7 Flashcards
What is the structure of a sub-giant branch star?
H burning takes place in core and gets exhausted from inside out, leaving a H burning shell around the core
He rich core grows outwards and becomes larger and contracts to regain hydrostatic equilibrium (pressure goes up in core)
Expanding photosphere
What is the temperature of the core of the sub-giant branch?
2 x 10^7 K which is sufficient for surrounding H to burn via CNO cycle
T^16 dependence which lead to thin H burning shell
Why is the core of a star entering the sub-giant branch so hot?
In order to maintain pressure balance but this causes H-rich envelope to expand with L being constant and R increasing while T decreases
Where does the star move in the HR diagram to reach the sub-giant branch?
redwards
What are the central temperatures of sub giants still too low for?
Helium burning to occur in centre at this stage
When does the star move upwards in HR diagram to Red Giant Branch?
As surface layers cool due to expansion of envelope, the convection zone deepens into the star
Convection is more efficient at transporting the energy than radiation so L increases and T is now constant
What confirms the CNO cycle in red giant branch?
Enhanced 14N/12C and 13C/12C ratios observed in spectra of red giants
What kind of envelope does a red giant have?
An extensive fully convective envelope
When can the ideal gas law (P= rRT/μ) break down?
When pressure and density continue to increase in contracting He core and at a given temp
What do free electrons do as density increases?
The free electrons try to fill all available quantum states
Electrons are fermions with spin=1/2
What is Pauli’s exclusion principle?
A given quantum cell can have at most 2 electrons (oppositely directed spins)
What does not obey Pauli’s exclusion principle?
Helium nuclei as they have spin 0
What does the restriction on electrons from Pauli’s principle lead to?
A pressure greater than that for an ideal gas
What kind of electrons can co-exist in an orbital?
Only electrons of opposite spin
From Heisenberg’s uncertainty principle how many electrons are predicted to be able to occupy an “uncertainty” volume of 6-dimensional phase space?
At most 2 electrons which gives a volume of a quantum cell equal to h^3
What is volume occupied by particles with momentum equal to in spherical coordinates?
4pip^2dp
in 6D phase space: Vxyz x 4pip^2dp
When does the Maxwellian distribution violate the Pauli exclusion principle?
For a sufficiently high particle density at low momenta
first do so at p=0 when n (number density of electrons) is at its maximum
What happens as the core contracts?
Density increases for given T and the low momentum electrons hit the degeneracy limit first
What happens as degeneracy limit cannot be exceeded?
The electrons need to re-distribute to high momentum i.e higher pressure
When does degeneracy increase until?
Only the high momentum tail of the Maxwellian distribution is left
What happens to the quantum states are degeneracy increases?
All available quantum states will fill up to some maximum momentum p0 (Fermi momentum)
When is gas called completely degenerate?
When there are negligible number of electrons with p>p0
How can degeneracy be removed?
By increasing the temperature and hence average momentum of the electrons
What is the Fermi momentum?
The maximum momentum in a degenerate gas which depends on the density
What is pressure due to?
Degenerate electrons
Pressure is independent of temperature
What happens at the tip of RGB?
He core is completely degenerate and T reached 10^8K which leads to triple a reactions to start
What causes the runaway process, helium flash?
The pressure does not increase initially as RGB He core become completely degenerate, because pressure is only a function of density and not of temperature
What do runaway reactions cause?
The temperature to increase and it populates the Maxwellian electron distribution, starting with the high energy tail.
Degeneracy is lifted and pressure increases
What causes star to move from RGB to Horizontal branch after runaway reactions?
Core expands leads to envelope contraction so R decreases and T increases
Density and T in shell decrease so L decreases
In order to maintain pressure balance what happens to the envelope which is contracting?
The density of it goes up
What does the initial position on HB of Horizontal branch depend on?
Metallicity
RED END: metal rich (young Pop I)
BLUE END: metal poor (old Pop II)
What is the structure of a horizontal branch star?
He burning in core which CO in centre builds up
He intershell
H burning shell
envelope
How does star ascend from HB to Asymptotic Giant Branch (AGB)?
As the core contracts and envelope expands, T decreases and convection zone deepens
Efficient convection means L increases
What is the structure of AGB star?
CO core
He burning shell
H burning shell
H and He envelope
What usually dominates Ls on AGB?
H burning shell
This causes a thermal pulse (occurs with increasing frequency)
When do runaway reactions occur again(He flash)?
When there is a build up of pressure in he burning shell
What happens after He flash?
Envelope expands and cools, giving rise to less H burning, which increases when core is shrinking again
This slowly increases again as He flash dumped on core
What happens after thermal pulses?
Surface is now cool enough (T = 3000K) and dense enough for dust to form in atmosphere
What gives rise to dense stellar wind?
Combination of pulsation and radiation pressure on dust
How long does it take dense wind to eject envelope?
around 10^4 yrs
When does Teff rise rapidly?
When remnant H or He burning shell now very close to surface
Core continues to contract
When is a planetary nebula formed?
When Teff > 30,000K and the stellar remnant can ionize ejected envelope
What is the structure of the planetary nebula?
Nebula has an emission line spectrum
Abundances in nebula reflect CNO processed (enhanced He and N) and triple a process (enhanced C) material
What eventually happens to planetary nebula?
It expands and eventually disperses into the interstellar medium
(very few old PNe have been observed as they are so faint)
How long does it take a planetary nebula central star to run out of H or He in remnant shell?
Around 10^4-5 years
What happens after planetary nebula runs out of H and He?
Core contracts again
Central T and density never get high enough for C burning
Degenerate CO core then cools and L decreases
Surface is left either H or He rich
What is the expansion speed of the PN material?
Around 20-30km/s which should be at least as large as the escape speed
What is strange about the observed expanding material?
It’s speed is around 20 km/s so it couldn’t have been ejected from PN central star.
So PN material was probably ejected during an earlier phase
When do white dwarfs reach a maximum mass?
When all (degenerate) electrons are pushed to relativistic velocities Mass = 1.4Mo (known as Chandrasekhar mass)
Which type of stars go through the AGB and PN stages?
Low to intermediate mass stars (0.8 to 8 Mo)
What do stars that go through the AGB and PN stages return?
A large fraction of their mass to the interstellar medium enriched in heavy elements
What is the stellar remnant?
A CO white dwarf
