1. Introduction to Cosmological Observations Flashcards Preview

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1

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

2

Units
Distance - 1AU

-the average distance of the Earth from the Sun
~1.5*10^11 m

3

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

4

Units
Mass - M☉

-1 solar mass ~ 2*10^30kg

5

Units
Luminosity - L☉

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

6

Units
Energy

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

7

Planck Length

lp = [Għ/c^3]^(1/2) ~ 1.6*10^(-35)m

8

Planck Mass

Mp = [ħc/G]^(1/2) ~ 2.2*10^(-8)kg

9

Planck Time

tp = [Għ/c^5]^(1/2) ~ 5.4*10^(-34)s

10

Planck Energy

Ep = mp*c² ~ 1.2*10^(28)eV

11

Planck Temperature

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

12

Length Scales

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

13

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

14

Isotropic Definition

-no preferred direction

15

Homogeneous Definition

-no preferred points

16

Cosmological Principle

-there is nothing special about our location in the universe
isotropy + cosmological principle => homogeneity

17

Galactic Redshift

redshift = z = (λob-λem)/λem
-when z<0, blueshift
-when z>0, redshift

18

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

19

Classical Doppler Effect
vs,vr << vw

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

20

Classical Doppler Effect
vs,vr << vw
vr=0

Δf = -vs/vw fem

21

Classical Doppler Effect
for light

Δf = -vs/c fem

22

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
c*z = Ho*r

23

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

24

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

25

Hubble Time

-if a galaxy is moving away at constant velocity v:
v=Ho*r
-at a previous time to it must have been a distance r away:
r=v*to
-rearrange for time:
to = r/v = r/r*Ho = 1/Ho
-this is the Hubble Time, the approximate age of the universe, 14Gyr

26

Hubble Distance

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

27

Flux from a Galaxy

Fgal = nLc/Ho = 2*10^(-11)L☉ au^(-2)

28

Flux from the Sun

F☉ = 1L☉/4π(1au)^2 ~ 0.08L☉au^(-2)
-much brighter than a general point in the universe

29

Baryons

-protons and neutrons

30

Leptons

-electrons and neutrinos