Flashcards in 1. Introduction to Cosmological Observations Deck (31)

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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

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##
Units

Energy

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

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## Planck Length

### lp = [Għ/c^3]^(1/2) ~ 1.6*10^(-35)m

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## Planck Mass

### Mp = [ħc/G]^(1/2) ~ 2.2*10^(-8)kg

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## Planck Time

### tp = [Għ/c^5]^(1/2) ~ 5.4*10^(-34)s

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## Planck Energy

### Ep = mp*c² ~ 1.2*10^(28)eV

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## Planck Temperature

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

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## 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

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## Isotropic Definition

### -no preferred direction

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## Homogeneous Definition

### -no preferred points

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## Cosmological Principle

###
-there is nothing special about our location in the universe

isotropy + cosmological principle => homogeneity

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## 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

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##
Classical Doppler Effect

vs,vr << vw

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

Δf = fobs-fem = [(vr-vs)/vw]fem

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##
Classical Doppler Effect

vs,vr << vw

vr=0

### Δf = -vs/vw fem

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##
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

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## 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

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## Hubble Distance

###
-the distance that light has travelled since the start of the universe:

dh = c/Ho = c*to ~ 4300±300Mpc

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## Flux from a Galaxy

### Fgal = nLc/Ho = 2*10^(-11)L☉ au^(-2)

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## Flux from the Sun

###
F☉ = 1L☉/4π(1au)^2 ~ 0.08L☉au^(-2)

-much brighter than a general point in the universe

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## Baryons

### -protons and neutrons

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