1. Introduction to Cosmological Observations

Question 1

What is cosmology?

Answer 1

• 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

Question 2

Units

Distance - 1AU

Answer 2

-the average distance of the Earth from the Sun

~1.5*10^11 m

Question 3

Units

Distance - pc

Answer 3

-the distance of a star when the angle from the Earth-Sun line of sight is one arcsecond
~3.1*10^16

Question 4

Units

Mass - M☉

Answer 4

-1 solar mass ~ 2*10^30kg

Question 5

Units

Luminosity - L☉

Answer 5

-luminosity of the sun ~ 3.8*10^26W

Question 6

Units

Energy

Answer 6

1eV = 1.602*10^(-19)J

Question 7

Planck Length

Answer 7

lp = [Għ/c^3]^(1/2) ~ 1.6*10^(-35)m

Question 8

Planck Mass

Answer 8

Mp = [ħc/G]^(1/2) ~ 2.2*10^(-8)kg

Question 9

Planck Time

Answer 9

tp = [Għ/c^5]^(1/2) ~ 5.4*10^(-34)s

Question 10

Planck Energy

Answer 10

Ep = mpc² ~ 1.210^(28)eV

Question 11

Planck Temperature

Answer 11

Tp = Ep/k ~ 1.4*10^(-2)K

Question 12

Length Scales

Answer 12

-we will consider length scales from lp to 10^4Mpc, the cosmological horizon

Question 13

Olbers Paradox

Answer 13

• 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

Question 14

Isotropic Definition

Answer 14

-no preferred direction

Question 15

Homogeneous Definition

Answer 15

-no preferred points

Question 16

Cosmological Principle

Answer 16

-there is nothing special about our location in the universe

isotropy + cosmological principle => homogeneity

Question 17

Galactic Redshift

Answer 17

redshift = z = (λob-λem)/λem

• when z<0, blueshift
• when z>0, redshift

Question 18

Classical Doppler Effect

Equation

Answer 18

fobs = observed frequency
fem = emitted frequency
vr = speed of observer
vs = speed of source
vw = speed of wave

fobs = (vw+vr)/(vw+vs) * fem

Question 19

Classical Doppler Effect

vs,vr &laquo_space;vw

Answer 19

fobs = [1 + (vr-vs)/vw] fem
Δf = fobs-fem = [(vr-vs)/vw]fem

Question 20

Classical Doppler Effect
vs,vr &laquo_space;vw
vr=0

Answer 20

Δf = -vs/vw fem

Question 21

Classical Doppler Effect

for light

Answer 21

Δf = -vs/c fem

Question 22

Hubble’s Law

Data

Answer 22

-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

Question 23

Hubble’s Law

Relation Between v and r

Answer 23

-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

Question 24

Scale Factor

Answer 24

-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

Question 25

Hubble Time

Answer 25

-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

Question 26

Hubble Distance

Answer 26

-the distance that light has travelled since the start of the universe:
dh = c/Ho = c*to ~ 4300±300Mpc

Question 27

Flux from a Galaxy

Answer 27

Fgal = nLc/Ho = 2*10^(-11)L☉ au^(-2)

Question 28

Flux from the Sun

Answer 28

F☉ = 1L☉/4π(1au)^2 ~ 0.08L☉au^(-2)

-much brighter than a general point in the universe

Question 29

Baryons

Answer 29

-protons and neutrons

Question 30

Leptons

Answer 30

-electrons and neutrinos

Question 31

Photons

Answer 31

-radiation, no mass, travel at the speed of light

E = hf = hc/λ