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
