Astrophysics (option D)

Question 1

Two properties of stars

Answer 1

light and heat

Question 2

Apparent Brightness

Answer 2

How a star appears on Earth (Wm^-2)

Question 3

Luminosity

Answer 3

Power emitted from the star (W or Jsec^-1)

Question 4

Apparent Brightness Equation

Answer 4

b = L / 4pi d^2,

where
b = apparent brightness (Wm^-2),
L = luminosity (W or Jsec^-1),
d = distance to star (m)

Question 5

Light Year

Answer 5

The distance light travels in one year

Question 6

Luminosity of the Sun

Answer 6

Lo = 3.83 * 10^26 W

Question 7

Blackbody

Answer 7

Perfect emitter or absorber of radiation.

Question 8

Wien’s Displacement Law

Answer 8

lambda(max.) * T = 2.9 * 10^-3 mK,

where
lambda(max.) = wavelenth of the maximum intensity (m),
T = effective temperature / surface temperature (K)

Question 9

Stefan-Boltzmann Law

Answer 9

L = Stefan-Boltzmann constant * A * T^4,

where
L = Luminosity of the star (W),
o- Stefan-Boltzmann constant = 5.67 *10^-8,
A = surface are of the sphere = 4pi r^2 (m^2),
T = surface temperature of the star (K)

Question 10

Chandrasekhar Limit

Answer 10

Maximum mass of a white dwarf star. remnant mass (M) = 1.4 mass of the sun (Mo). If a star has M < 1.4Mo, it will end up as a white dwarf. Electron degeneracy pressure.

Question 11

Oppenheimer-Volkoff Limit

Answer 11

Maximum mass of a neutron star. Neutron degeneracy pressure. If a star has M = 1.5Mo - 3.0Mo, it will go supernova and end up as a neutron star / pulsars. M = remnant mass, Mo = mass of the sun

Question 12

Mass-Luminosity Relation

Answer 12

L is proportional to M^3.5,

where
L = the luminosity of a star,
M = its own mass.

L = kM^3.5

Question 13

Parallax Method

Answer 13

d = 1/p,

where
d = distance to the star (pc),
p = parallax angle (arc sec)

Question 14

Spectroscopic Parallax

Answer 14

1) Use spectrum of star to know where it sits on the colour/temperature axis
2) Use that to estimate L
3) Use equation (and L and b) to get distance

Question 15

Cepheid Variables

Answer 15

Stars tha vary regularly in size and luminosity

Question 16

Vampire Stars

Answer 16

Binary system, white dwarf (mass less than Chandrasekhar Limit) accretes material from companion star, goes above limit and explodes in a Supernova

Question 17

Red Shifted Galaxies

Answer 17

Galaxy spectral lines shifted to longer wavelengths (redder). This means galaxies moving away from us - Universe is expanding.

Question 18

Cosmic Microwave Background (CMB) Radiation

Answer 18

Universe expands and cools, wavelength increases, energy goes down.
Predicted CMB should be isotropic (same in all directions) - homogenous.
Peak temperature / peak wavelength = 2.76 K (blackbody temperature)

Question 19

Receding Galaxies

Answer 19

Z = delta lambda / lambda0 is approx. equal to v / c,
where
Z = red shift,
delta lambda = change in wavelength (m)
+ if wavelength increases (red shift)
- if wavelength decreases (blue shift)
lambda0 = emitted wavelength (m)
v = relative velocity of speed of light (ms^-1 OR _c)
c = speed of light (ms^-1)

Question 20

Scale Factor R

Answer 20

Z = (R/R0) - 1,

where
Z = red shift
R = scale factor, or ‘size’ of the Universe
R0 = ‘size’ of the Universe initially

Question 21

Hubble’s Law

Answer 21

Recession speed of galaxies is related to their distance from us.
v = Hod

where
v = speed (ms^-1)
H0 = hubble constant
d = distance (Ly, m, pc)

Question 22

Age of the Universe

Answer 22

t = 1/H0

where
t = time
H0 = hubble constant

Question 23

Jean’s Criterion

Answer 23

For a gas cloud to undergo gravitational collapse and produces protostars, the magnitude of the gravitational potential energy of the gas cloud must be strictly greater than the total kinetic energy of the particles in the gas cloud.

Cloud of hydrogen gas can collapse under its own gravity if M > Mj.

if the magnitude of the gravitational potential energy of the particles is greater than the
kinetic energy of the particles.

Question 24

Main Sequence Star

Answer 24

Stars spend vast majority of their lifetimes in this stage. Stars convert hydrogen to helium in its core (nuclear fusion). Star is in hydrostatic equilibrium (inwards gravity pressure = outwards radiation pressure)

Question 25

After Main Sequence

Answer 25

• Runs out of H in the core
• Core collapses - dense enough to fuse Helium to other stuff (C, N, …) This is called the Helium flash.
• Becomes a red giant - outer part expands and cools
  -Runs out of He in core, collapses, burns heavier and heavier elements, repeat repeat
• Depending on mass, it can go up to Iron. This is the limit. Can’t fuse any heavier, collapses.

Question 26

R-process (rapid)

Answer 26

Make elements heavier than iron? (star)

Neutron Capture

• element does not have time to decay
• ‘seed’ nuclei, can make heavier elements
• usually, you need Supernova explosion for R-process
  -also in thermonuclear explosions (discovery of Einsteinium and Fermium)

Question 27

S-process (slow)

Answer 27

Make elements heavier than iron? (star)

Neutron Capture

• ‘secondary’ nuclei (needs already existing heavy elements)

Question 28

Type II Supernovae (core collapse)

Answer 28

• Single star (high mass)
• Core collapses and makes supernova (since M > 1.4Mo)
• Tough to know exactly how much mass it had
• End result: Supernova + neutron star

Question 29

Density Equation

Answer 29

p = mass/volume

Question 30

Mass Equation

Answer 30

M = 3/4pi r^3 * p (density)

Question 31

Velocity Equation

Answer 31

v = square root of (4pi/3 * Gp) * r

where
v = velocity (ms^-1)
G = gravity
p = density
r = radius

**velocity is proportional to the radius

Question 32

Velocity (v^2) Equation

Answer 32

v^2 = (GM) / r

where
v = velocity
G = gravity
M = mass
r = radius

Question 33

Two Types of Dark Matter

Answer 33

• MACHOS (MAssive Compact Halo Objects)
• WIMPS (Weakly Interacting Massive Particles)

Question 34

Massive Compact Halo Objects (machos)

Answer 34

• Hidden
• Regular mass
  (failed brown stars, dwarves, etc)

Question 35

Weakly Interacting Massive Particles (wimps)

Answer 35

• More exotic particles
  (neutrinos, axions, supersymmetric)

Question 36

Cosmological Principle

Answer 36

• Homogeneous (same everywhere)
• Isotropic (same in all directions) (slight fluctuations in CMB - small anisotropies)

Question 37

Critical Density

Answer 37

Density of the Universe needed to completely stop the expansion

Question 38

Critical Density Equation

Answer 38

pc = (3 H0^2) / (8pi * G)

where
pc = critical density
H0 = hubble constant
G = gravity

Question 39

Density Parameter

Answer 39

omega0 = p / pc

Question 40

Differences between type Ia and type II supernova

Answer 40

• Ia have consistent maxima in their light curves but II vary
• Ia has a strong ionized SiII line but II has hydrogen lines in their spectra
• Ia was a white dwarf but II are massive stars
• Ia form from binary systems but II are the result of core collapse of a star
• Ia can be used as standard candles but II are not

Question 41

Type Ia supernova

Answer 41

Is a type of supernova that occurs in binary systems in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white dwarf. Physically, carbon–oxygen white dwarfs with a low rate of rotation are limited to below 1.44 solar masses.