Black is the Colour ......

So how did it all begin?

• In what follows:

  The smallest things we will talk about are galaxies: typically 10 billion (1010) stars and a size of 20 kpc (1020 m) M51 in Can Ven: HST picture

But most of the time we'll be talking about clusters of galaxies: this is Coma cluster. Typically 1 million billion (1015) Msun and a size of 2 Mpc (1022 m)

Jim Misti Misti Mountain Observatory

Redshift:

• The Doppler effect gives
  \color{red}{ z = \frac{{\lambda - \lambda _0 }}{{\lambda _0 }} = \frac{{\delta \lambda }}{{\lambda _0 }}}
• Velocity of recession: \color{red}{v = zc}

Hubble found vel. of recession ∝ distance \color{red}{v = Hd,H = 70{\rm{ km/s/Mpc}}} 1 Mpc (megaparsec) = 3x1022 m. Note although all galaxies are receding from us, does not imply we are at the centre: in the currant cake model all currants see all the others as receding

Big Bang (once over lightly)

RULE 1 in Physics 100: Never mix your units! \color{red}{ \begin{array}{l} H = 70 \times 1000/3 \times 10^{22} \approx 2 \times 10^{ - 18} s^{ - 1} \\ \Rightarrow \frac{1}{H} \approx 5 \times 10^{17} {\rm{ s }} \approx 17 \times 10^9 {\rm{ yrs.}} \\ \end{array}}

What does this time represent? Must be age of universe: if expansion does not change i.e. 17x109 yr. ago, all the galaxies were in the same place. Universe had a beginning, implied by the big bang. Can run Hubble expansion back: we would like to use this to predict what will happen in the end

Where was the Big Bang?

• 
• A 2-D analog is the surface of a balloon: Note the following:
• It has no centre in 2-D space. Deflating it reduces it to zero size: i.e. at the moment of the big bang, not only matter was created, but also space and time
• The galaxies are not receding from us: space is expanding
• We require a curved 2-D surface embedded in a 3-D volume.
• This is a positively curved universe: we can also construct negatively curved ones (harder to visualize)

What's going to happen in the end?

How can we tell if the universe will expand forever?

• As a model, consider this as an escape velocity problem. How hard do we need to throw a galaxy on the "outside" so that it escapes? Note: our calculation had better not depend on r! \color{red}{ \frac{1}{2}mv^2 - \frac{{GMm}}{r} = 0} but v = Hr and the total mass of the universe inside M = 4π/3 ρ r³

H²r² = 2G4π/3 ρ r²

• (we got lucky: the r cancels out!). We can turn this round and write it as an equation for ρ

• \color{red}{ \rho _0 = \frac{{3H^2 }}{{8\pi G}}}
• Hence the critical density

• ρ₀ ~ 9 x 10^-27 kg m^-3 ~ 6 Hydrogen Atoms m^-3 (Number is flaky).
• We'll use \color{red}{\Omega {\rm{ = }}\frac{\rho }{{\rho _0 }}} , because some errors cancel out.

The entire future of the universe is given by this one number!!!!!!!!!

So if Ω > 1: Universe come to nasty end in ~ 50 x 109 yr. Ω = 1: "critical universe")Universe expansion slows down asymptotically Ω < 1: Universe expands forever More important:we live forever if Ω ≤ 1, (well maybe).

So how do we weigh the universe?

• First Guess: What you see is what you get!
• Count number of galaxies in a region of space, assume they consist of stars much like the sun, so assume
  \color{red}{ \frac{M}{L} = \frac{{M_o }}{{L_o }}}

• Obviously must average over large enough volume such that universe is smooth R > 100 Mpc, and the universe is a very lumpy place!

• (Note all these numbers are uncertain to ∼ 20%!)
• We live forever!!!
• But wait a moment... How much matter is there we that we can't see?

Masses of Spiral galaxies

• direct observation i.e. measurement of velocities of individual stars in nearby => rotation curves or measurement of hydrogen via 21cm line or estimates of no. of stars

• Typical Spiral (NGC3198) R ≈ 20 kpc but outer parts are just seen as H gas

Luminosity of galaxy should reflect mass

• Most of the light is fairly concentrated, so this should be good approx to the mass. but the outside part of the galaxy is rotating far too fast: i.e. velocity curve doesn't drop as expected. Means a lot of mass in outside part of galaxy: the "halo"

• Implication: Mass of observed galaxy ≈ 10¹⁰ M₀, R ≈ 2 kpc (for core) Mass of halo ≈ 10¹³M₀, R ≈ 100kpc (except that we can't measure out there!)
  \color{red}{ \Omega \approx .05}
• What do we mean by mass of galaxy? In fact the visible part of the galaxy may just reflect the dark matter.

Large clusters of galaxies:

Can measure speeds of individual galaxies in a cluster: faster moving galaxies imply more mass in cluster This gives much higher masses than individual spirals \color{red}{ \frac{M}{L} \approx 300\frac{{M_o }}{{L_o }}}

A check: The Coma cluster

• Large clusters contain a lot of hot gas, which is strong X-ray source. Picture is negative optical + contours of X-rays X-ray pictures measure density and temp:

• but the X-rays don't come from where the matter is .....

Also large masses bend light, so large clusters show "gravitational lensing" of very distant objects.

• Allows us to estimate the mass. For Abell 2218 we seem to have at least 300 times as much dark matter as luminous matter

The Bullet Cluster

• a) What the hell? i.e. what is the dark matter?

• b) Why the hell? i.e. why is Ω~1 (after all it could be anything?)

• Actually, there is a limit

  Ω < 3 
  

  otherwise the universe would be younger than the earth (wouldn't that make the creationists happy!!)

What the hell:

1. Brown dwarfs
2. Hydrogen gas
3. Jupiters
4. Hydrogen rain
5. Low surface brightness galaxies
6. Maxi Black holes
7. Mini Black holes
8. Neutrinos
9. He H ⁺
10. Modified 1/r² law
11. Axions
12. Weakly Interacting Massive Particles (WIMPS)
13. Magnetic Monopoles
14. Majorons
15. Photinos
16. E₈ shadow matter
17. Cosmic Strings

1. Baryonic (BDM): (we use this as shorthand for "ordinary matter") maybe in some odd form e.g. rocks
2. Hot (HDM) light particles e.g. neutrinos ν's
3. Cold (CDM): heavy (usually) particles e.g. WIMPs

What the hell:

• Brown dwarfs Not enough
• Hydrogen gas Would be seen unless it was very diffuse, in which case, not enough
• Jupiters Not enough
• Hydrogen rain Too hot
• Low surface brightness galaxies Doesn't fix the problems in spirals
• Maxi Black holes Only exist at the centre of galaxies: we need halos
• Mini Black holes Not enough
• Neutrinos Part of the solution, but too light
• He H ⁺ Unstable
• Modified 1/r² law Hard to reconcile with Bullet cluster
• Axions Negative searches so far
• Weakly Interacting Massive Particles (WIMPS)
  • Magnetic Monopoles Screw up magnetic fields in galaxy
  • Photinos Will see them in 2008 (maybe)
  • E₈ shadow matter and there is a tooth fairy...
• Cosmic StringsWrong properties

WIMPS

• Heavy particles (say 100 m_proton) with interactions like a neutrino
• A lot can be ruled out by "in vitro" experiments (e.g. OPAL: Richard Hemingway and others at Carleton + Alberta +UBC + Victoria + Montreal + 300 others) at CERN

• ATLAS (2008) will be able to rule out a lot more options

• e.g. Picasso (Queens-Montreal) Nucleus will recoil and transfer energy to super-heated freon liquid and cause transition to gas.

• DEAP (Queens-Carleton ++ ): will use liquid argon and look at recoil

Where did the galaxies come from?

• COBE and WMAP comparison

• But note that the actual variations are tiny: 10^-5K

Normally density fluctuations die away (e.g sound waves) but in massive fluid they get amplified by gravity

• CDM decouples
• CDM dominates and clumps
• Atoms (baryons) decouple
• Baryons clump onto CDM
• Galaxies form

Dark Energy

• Dark Matter is bad enough, but now dark energy ...

Luminosity distance "standard candle"

SuperNova Legacy Survey

Canada-France Hawaii Telescope (CFHT)

(U of T and others) now provides best data from CFHT: The implication is that the expansion of the universe is accelerating.

May imply cosmological constant Λ (Einstein's "fudge factor"): in other words vacuum has an energy.

What can dark energy be?

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Combining all the data gives "concordance model ΩMatter = 0.27 ± .02 ΩΛ = 1 - ΩM

• Dark energy implies that the vacuum has an energy density: $$ \color{red}{ \rho _\Lambda \approx 100\rho _B \approx 10^{-13} JM^{ - 3} } $$
• We could understand Ω_Λ ≡ 0. : but....

• The only working theory for particles (the standard model) gives \color{red}{ \Omega _\Lambda = 10^{110} - V_0 } where V₀ is a (unknown) correction. You will notice a discrepancy!

• 1000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000.0000000000000
• -99999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999.9999999999999
• = .00000000000001
• get real!

• Statutory Warnings

• All of this depends on the assumption that type 1a SN are always the same at 4x10⁹ L_o, even at z = .5. Effect disappears if some (unknown) effect reduces L by 30%
• e.g. Hubble original estimate for H₀ was wrong by factor 7 because 2 different kinds of Cepheids.
• Ω_Λ and Ω_Matter are almost equal at present. In the past they would have differed by 10⁴⁰

Summary/Take Home Message

• We need dark matter
• We need Ω_DM ∼ .26
• We know Ω_baryons ∼ .03
• We have quite reasonable models for DM
• We will (likely) see it by 2010
• If we don't we'll have eliminated a lot of models
• We seem to require dark energy
• We need Ω_Λ ∼ .74
• We have no convincing models
• The good models we do have predict nothing like the values we see
• We may not know anything more for 20 years.
• Talk, references and other material at http://www.physics.carleton.ca/~watson/
• Most of the pictures from Astronomy Picture of the Day at http://antwrp.gsfc.nasa.gov/apod/astropix.html