Week 5 Stellar Stability

Question 1

what is the electron orbit equation

Answer 1

En = -13.6eV / n^2

Question 2

what does a change in energy level require

Answer 2

absorption or emission of energy

Question 3

what is the change in energy level equation

Answer 3

E = 13.6[ 1/n1^2 - 1/n2^2] eV

Question 4

what is the emission of an specific energy photon wavelength equation

Answer 4

1 / λ = R [ 1/n1^2 - 1/n2^2 ]

R is the Rydberg constant

Question 5

how do the wavelength of the emitted photons relate to the hydrogen line emission

Answer 5

The photon’s have discrete wavelength values depending on the energy level they started at and the change in energy level. Each of these transitions corresponds to a unique hydrogen line

Question 6

what are the names for the first 3 hydrogen line series and what section of the EM spectrum do each of them correspond to

Answer 6

Lyman from n=1 UV
Balmer from n=2 Optical
Paschen from n=3 Radio

Question 7

for a typical star the hydrogen lines are strongest in the middle of the spectral sequence what are the 2 effects that contribute to this

Answer 7

At high temp the hydrogen at the surface is ionised so can’t absorb a photon to produce a line
Balmer series require electrons @ n=2 which is not possible when H is ionised

Question 8

what is the procedure to find the dynamical time for a star

Answer 8

find the escape velocity
use t = R / vesc to find t
sub in the star's density for its mass 
simplify by removing the constant to get dynamical time 
tdyn ~ sqrt[ 1 / Gρ ]

Question 9

why is dynamical time not the correct time for a star’s collapse

Answer 9

it is too short since it doesn’t consider that gravity is counteracted by another force

Question 10

what is the force that counteracts gravity in a star

Answer 10

pressure gradient

Question 11

what is the hydrostatic equilibrium equation and why is it important

Answer 11

dP/dt = -Gm(r)ρ/r^2
it is important because stars must satisfy this equation to a very high accuracy because any deviation would lead to a huge instability in time scales

Question 12

what are the 2 Newton theorems involved in Hydrostatic Equilibrium

Answer 12

The gravitational force from a spherically symmetric mass distribution can be calculated as if the entire mass is located at the centre of the sphere
The gravitational force of a spherically symmetric shell on any object inside, regardless of the objects location within the shell is zero

Question 13

how do we find the potential energy of a star and what can be said about it

Answer 13

we use the hydrostatic equilibrium equation and integrate both sides wrt r
the total gravitational potential energy is proportional to the square of the mass

Question 14

what causes the pressure in stars and what are the 2 pressure equations

Answer 14

pressure is the result of the gas particles moving around at high speed
P = nkT
P = 1/3 nmv^2

Question 15

how does KE relate to the Pressure equations

Answer 15

We know that KE = 1/2nmv^2

this can be rearranged using the pressure equations to get KE = 3/2 nkT

Question 16

what is the Kelvin-Helmholtz scale and what is its equaiton

Answer 16

It tells us how long a star can power itself using its energy
tkh = -Ep / L ~= GM^2 / RL

Question 17

what must be true for a star to be stable against its own gravity and what is the name of this

Answer 17

Ep + 2KE = 0

this is the virial theorem