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)
