1. Introduction to Cosmological Observations Flashcards
What is cosmology?
- the study of the universe
- we aim to describe the past, explain the present and predict the future
- considering an ideal and model universe, galaxies are a small length scale
Units
Distance - 1AU
-the average distance of the Earth from the Sun
~1.5*10^11 m
Units
Distance - pc
-the distance of a star when the angle from the Earth-Sun line of sight is one arcsecond
~3.1*10^16
Units
Mass - M☉
-1 solar mass ~ 2*10^30kg
Units
Luminosity - L☉
-luminosity of the sun ~ 3.8*10^26W
Units
Energy
1eV = 1.602*10^(-19)J
Planck Length
lp = [Għ/c^3]^(1/2) ~ 1.6*10^(-35)m
Planck Mass
Mp = [ħc/G]^(1/2) ~ 2.2*10^(-8)kg
Planck Time
tp = [Għ/c^5]^(1/2) ~ 5.4*10^(-34)s
Planck Energy
Ep = mpc² ~ 1.210^(28)eV
Planck Temperature
Tp = Ep/k ~ 1.4*10^(-2)K
Length Scales
-we will consider length scales from lp to 10^4Mpc, the cosmological horizon
Olbers Paradox
- assuming an infinite universe, with average number density of stars n, average luminosity of star L, and flux f(r)=L/4πr²
- we then calculate the intensity of radiation reaching earth as infinite, but the night sky appears dark
- we have also assumed that the universe is infinitely old, if it is not (age to) and c is finite then we can only observe light from stars up to a distance c*to away
Isotropic Definition
-no preferred direction
Homogeneous Definition
-no preferred points
Cosmological Principle
-there is nothing special about our location in the universe
isotropy + cosmological principle => homogeneity
Galactic Redshift
redshift = z = (λob-λem)/λem
- when z<0, blueshift
- when z>0, redshift
Classical Doppler Effect
Equation
fobs = observed frequency fem = emitted frequency vr = speed of observer vs = speed of source vw = speed of wave
fobs = (vw+vr)/(vw+vs) * fem
Classical Doppler Effect
vs,vr «_space;vw
fobs = [1 + (vr-vs)/vw] fem Δf = fobs-fem = [(vr-vs)/vw]fem
Classical Doppler Effect
vs,vr «_space;vw
vr=0
Δf = -vs/vw fem
Classical Doppler Effect
for light
Δf = -vs/c fem
Hubble’s Law
Data
-in 1925 Hubble had measurements of z for ~40 galaxies
-most were redshifted but the local group were blueshifted
-plotted distance against cz and found a linear relationship
cz = Hor
Hubble’s Law
Relation Between v and r
-if v is the velocity of the galaxy moving away:
-Doppler effect => z=v/c
-observation => cz=Hor
=>
v = Ho*r
-where Ho is the Hubble constant
Ho = 70±7 km /s /Mpc
Scale Factor
-consider a three point triangle
-in order for the universe to be expanding both isotropically and homogeneously the increase in size of each side must be given by:
r(t) = a(t)r(to)
-the velocity of each side is then given by:
v = dr/dt = a’(t)r(to)
= a’(t) r(t)/a(t)
= a’(t)/a(t) r(t)
-let H(t) = a’(t)/a(t)
-so v(t) = H(t) r(t)
-so at any given time, v=Hor
Hubble Time
-if a galaxy is moving away at constant velocity v:
v=Hor
-at a previous time to it must have been a distance r away:
r=vto
-rearrange for time:
to = r/v = r/r*Ho = 1/Ho
-this is the Hubble Time, the approximate age of the universe, 14Gyr
Hubble Distance
-the distance that light has travelled since the start of the universe:
dh = c/Ho = c*to ~ 4300±300Mpc
Flux from a Galaxy
Fgal = nLc/Ho = 2*10^(-11)L☉ au^(-2)
Flux from the Sun
F☉ = 1L☉/4π(1au)^2 ~ 0.08L☉au^(-2)
-much brighter than a general point in the universe
Baryons
-protons and neutrons
Leptons
-electrons and neutrinos
Photons
-radiation, no mass, travel at the speed of light
E = hf = hc/λ
