II. The Universe Around Us - Macquarie University - Faculty of Science...

II. The Universe Around Us

ASTR378 Cosmology : II. The Universe Around Us 23

Some Units Used in Astronomy

•  1 parsec distance at which parallax angle is 1”; 1 pc = 3.086×1016 m (≈3.26 light years; 1 kpc = 3.086×1019 m, 1 Mpc = 3.086×1022 m)

•  1 M = 1.989×1030 kg, 1L = 3.839×1026 W

•  1 Å = 10-10 m (0.1 nm) •  1 eV = 1.602×10-19 J


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≡

The Visible Universe •  Stars (Sun: 1 M, 1 L) •  Galaxies (MW: 1011 – 1012 M) •  Local Group (MW + M31 + ...): scale ~1 Mpc •  Clusters/superclusters of galaxies, voids: scale ~100 Mpc •  ~Smooth on larger scales...


Other Wavelengths of “Light”

•  Microwaves: the Cosmic Microwave Background (CMB), black body spectrum corresponding to 2.7°K

•  Radio, Infrared: can penetrate (IR can be emitted by) dust, see obscured star formation / objects at high redshift (+...)

•  X-ray: hot gas, important for measuring the mass of galaxy clusters (+...)


The Cosmological Principle Considering the largest scales in the Universe, we make the following fundamental assumptions:

1) Homogeneity: On the largest scales, the Universe has the same physical properties

Every region has the same physical properties (mass density, expansion rate, visible vs. dark matter, etc.)

2) Isotropy: On the largest scales, the Universe looks the same in any direction

We should see the same large-scale structure in any direction

3) Universality: The laws of physics are the same everywhere in the Universe

Cosmology : II. The Universe Around Us ASTR378 27

Homogeneity and Isotropy

•  Cosmological principle: on large scales the Universe is homogeneous and isotropic –  homogeneous (Universe looks the same at

each point) ≠ isotropic (Universe looks the same in all directions)

–  but isotropic at every point = homogeneous –  large scales: >≈ 100 Mpc

•  Perfect cosmological principle: the Universe is homogeneous and isotropic in space and time Steady State Universe (not true!)


CMB

Olbers’ Paradox

•  Heinrich Olbers (1826): Why is the night sky dark? –  n = mean number density of stars, L = mean stellar

luminosity

–  flux at Earth:

–  power (unit area)-1 (steradian)-1:

–  total intensity of starlight:

•  Yet the night sky is dark...?

ASTR378 Cosmology : II. The Universe Around Us 29 �

f (r) = L4πr2

dJ(r) = L4πr2

× n × r2dr

J = nL4π

dr =r= 0

∞∫ ∞

The Expanding Universe

•  Redshift z :


Blueshift

Redshift

�

z ≡ λobs − λemλem

z ≈vc (SR: )

�

1+ z( ) = 1+ v /c1− v /c

•  1920’s: Hubble (and Humason) discovered a proportionality between a galaxy’s redshift and its distance (Hubble Law)

�

z = H0

cr

�

v = H0r

The Hubble Constant •  Hubble found a value for the Hubble Constant

H0 ≈ 500 km s-1 Mpc-1 (bad calibration!) •  For decades H0 disputed (50 – 100); current

consensus H0 ≈ 70 km s-1 Mpc-1

•  Outside the Local Group, virtually every galaxy is moving away from us -- why doesn’t this violate the Cosmological Principle?

•  If no acceleration/deceleration, galaxies were together at time:


Original Hubble Diagram

More Recent Version

�

t0 = rv

= rH0r

= H0−1

H0 ≈ 70⇒ H0−1 ≈14 , c

H0

≈ 4300Gyr Mpc (Hubble Distance, or horizon distance)

(Hubble Time)

How can the Hubble Law be Isotropic? •  Three galaxies (1,2,3) in a triangular

configuration, with sides r12, r23, r31

•  Homogeneous, uniform expansion means shape preserved expansion law of form r12(t) = a(t)r12(t0)

•  a(t): scale factor; a = 1 @ t= t0 •  At time t, an observer in galaxy 1 will

see the other galaxies receding with velocity:


1 2

3

�

v12(t) = dr12

dt= ˙ a r12 t0( ) =

˙ a a

r12 t( )

v31(t) = dr31

dt= ˙ a r31 t0( ) =

˙ a a

r31 t( )

the velocity distance relation takes the linear form v = Hr, with H=å/a

What’s the Universe Made Of?


Particle Symbol Rest Energy (MeV) Charge

proton p 938.3 +1

neutron n 939.6 0

electron e- 0.511 -1

neutrino νe,νμ,ντ ?,?,? 0

photon γ 0 0

dark matter? ? ? 0

in the non-relativistic limit

Energy of a particle

Bar

yons

�

Eγ = hf hν( ) Energy of a photon

�

Etotal2 = m2c 4 + p2c 2

Etotal = mc 2 1+ p2

m2c 2⎛

⎝ ⎜

⎞

⎠ ⎟ 1/ 2

≈ mc 2 + 12p2

m

Sneak Peek: What is the Universe Made of?


0.6% in Stars

Blackbody Radiation

•  In thermodynamic equilibrium, photons have a energy densityεin the frequency interval df around frequency f given by the blackbody (BB) function:

•  The number density of photons is:


�

ε f( )df = 8πhc 3

f 3dfexp(hf /kBT) −1

εγ = αT 4 , α = π 2kB4

15h3c 3≈7.565×10-16 J m-3 K-4

�

nγ = βT 3, β = 2.404π 2

kB3

h3c 3 ≈2.03×107 m-3 K-3

Blackbody Radiation II

•  Peak frequency of BB distribution: fpeak ≈ 2.8kBT/h •  Peak energy of BB distribution: Epeak = hfpeak

≈2.8kBT •  Mean photon energy: Emean = hfmean ≈ 2.7kBT


The Cosmic Microwave Background •  Discovered in 1965 by

Penzias and Wilson, BB spectrum with T=2.725±0.001 K

•  Big Bang vs. Steady State

•  Once dipole (motion towards Hydra, 630 km s-1) and Galactic emission subtracted, extremely isotropic / homogeneous (10-5)


•  Note: ~1% of the static on TV is due to the CMB!

How is the CMB a Relic of the Big Bang? •  “Hot” Big Bang: Early

Universe very dense and very hot (T>>104 K) baryonic matter completely ionised, free electrons made Universe opaque to photons

•  As Universe expanded, T; when T~3000°K, neutral atoms formed, no longer many free electrons photons free to go

•  So why is the CMB a 2.7°K BB, not a 3000°K BB?

ASTR378 Cosmology : II. The Universe Around Us 38 �

V ∝ a t( )3, εγ = αT 4 , Pγ =εγ3

dQ = dE + PdV , dQ = 0, dEdt

= −P t( ) dVdt

E = εγV = αT 4V , P = Pγ = αT 4

3

α 4T 3 dTdtV + T 4 dV

dt⎛ ⎝ ⎜

⎞ ⎠ ⎟ = − 1

3αT 4 dV

dt1TdTdt

= − 13V

dVdt; V ∝ a t( )3 ⇒ d

dtlnT( ) = − d

dtlna( )

T(t)∝ a(t)−1

•  The CMB was a 3000°K BB when the Universe was ~1100× smaller!


Looking at the Last Scattering Surface

•  Today, at z = 0 the universe is fairly transparent

•  At higher redshift, z (looking backward in time) the universe was denser (ρ = ρ0×(1+z)3) and hotter (T=T0×(1+z))

•  At z ≈ 1100, the universe was so dense that T >≈ 3000°K

•  At z > 1100 there is a transition: the universe becomes completely ionised and opaque to visible light − the last scattering surface

•  The universe was ~350,000 years old at z≈1100


Should the CMB be Smooth ?

•  There are people, planets, stars, galaxies, galaxy clusters and galaxy superclusters today, so we expect some non-uniformities (wiggles, etc.) in the CMB


The Cosmic Background Explorer (COBE)

Objectives: •  Accurately measure the CMB

temperature •  Find expected CMB

fluctuations


Basic results from COBE


More Results from COBE

•  The Earth is moving with respect to the CMB detectable Doppler shift! –  Earth’s motion around the Sun –  Sun’s motion around the Galaxy –  the Galaxy’s motion w/rt other

galaxies (large scale flows)

•  Microwave emission from the Galaxy

•  Fluctuations in the CMB

The CMB Today

COBE (1990’s) WMAP (2000’s)


The Latest: Planck (2009 – )


Olbers’ Paradox Revisited

•  What are our assumptions? •  Unobstructed line of sight to every star in the Universe?

–  not true – some could be blocked by foreground stars, intervening dust – but still night sky should look like the surface of a star!

•  Number density n and mean luminosity L constant w/rt r ? •  Universe is infinitely large? (And filled with stars?) •  Universe is infinitely old? •  Flux from distant sources follows inverse square law?


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