Astrophysics (option D) Flashcards
Two properties of stars
light and heat
Apparent Brightness
How a star appears on Earth (Wm^-2)
Luminosity
Power emitted from the star (W or Jsec^-1)
Apparent Brightness Equation
b = L / 4pi d^2,
where
b = apparent brightness (Wm^-2),
L = luminosity (W or Jsec^-1),
d = distance to star (m)
Light Year
The distance light travels in one year
Luminosity of the Sun
Lo = 3.83 * 10^26 W
Blackbody
Perfect emitter or absorber of radiation.
Wien’s Displacement Law
lambda(max.) * T = 2.9 * 10^-3 mK,
where
lambda(max.) = wavelenth of the maximum intensity (m),
T = effective temperature / surface temperature (K)
Stefan-Boltzmann Law
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)
Chandrasekhar Limit
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.
Oppenheimer-Volkoff Limit
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
Mass-Luminosity Relation
L is proportional to M^3.5,
where
L = the luminosity of a star,
M = its own mass.
L = kM^3.5
Parallax Method
d = 1/p,
where
d = distance to the star (pc),
p = parallax angle (arc sec)
Spectroscopic Parallax
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
Cepheid Variables
Stars tha vary regularly in size and luminosity
Vampire Stars
Binary system, white dwarf (mass less than Chandrasekhar Limit) accretes material from companion star, goes above limit and explodes in a Supernova
Red Shifted Galaxies
Galaxy spectral lines shifted to longer wavelengths (redder). This means galaxies moving away from us - Universe is expanding.
Cosmic Microwave Background (CMB) Radiation
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)
Receding Galaxies
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)
Scale Factor R
Z = (R/R0) - 1,
where
Z = red shift
R = scale factor, or ‘size’ of the Universe
R0 = ‘size’ of the Universe initially
Hubble’s Law
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)
Age of the Universe
t = 1/H0
where
t = time
H0 = hubble constant
Jean’s Criterion
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.
Main Sequence Star
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)
After Main Sequence
- 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.
R-process (rapid)
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)
S-process (slow)
Make elements heavier than iron? (star)
Neutron Capture
- ‘secondary’ nuclei (needs already existing heavy elements)
Type II Supernovae (core collapse)
- 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
Density Equation
p = mass/volume
Mass Equation
M = 3/4pi r^3 * p (density)
Velocity Equation
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
Velocity (v^2) Equation
v^2 = (GM) / r
where
v = velocity
G = gravity
M = mass
r = radius
Two Types of Dark Matter
- MACHOS (MAssive Compact Halo Objects)
- WIMPS (Weakly Interacting Massive Particles)
Massive Compact Halo Objects (machos)
- Hidden
- Regular mass
(failed brown stars, dwarves, etc)
Weakly Interacting Massive Particles (wimps)
- More exotic particles
(neutrinos, axions, supersymmetric)
Cosmological Principle
- Homogeneous (same everywhere)
- Isotropic (same in all directions) (slight fluctuations in CMB - small anisotropies)
Critical Density
Density of the Universe needed to completely stop the expansion
Critical Density Equation
pc = (3 H0^2) / (8pi * G)
where
pc = critical density
H0 = hubble constant
G = gravity
Density Parameter
omega0 = p / pc
Differences between type Ia and type II supernova
- 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
Type Ia supernova
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.
