Cosmological Structure Formation A Short Course

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Cosmological Structure FormationA Short Course

• I. Why Dark Matter, and why Cold?
• Chris Power

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Evidence for Missing Matter

• Zwicky (1933) measured the radial velocities for
  eight galaxies in the Coma cluster and found an
  unexpectedly large velocity dispersion of 1000
  km/s.
• He used the Virial Theorem to deduce that the
  mass density of Coma would have to be 400 times
  that of the luminous matter -- although he
  assumed a Hubble parameter of 500 km/s/Mpc. For
  present day value of Hubble parameter mass
  discrepancy of 50.
• What caused this mass discrepancy? What could
  resolve it?

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The Virial Theorem

• Recall the Virial of Clausius -- a useful tool
  from statistical mechanics that can be applied to
  a gravitating system -- related to the moment of
  inertia
• The time derivative of the virial leads to the
  virial theorem
• For a gravitationally bound system, RHS tends to
  zero, so twice the kinetic energy should equal
  the potential energy.

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Evidence for Missing Matter

• Zwicky had found evidence for missing matter.
• If this overdensity is confirmed we would arrive
  at the astonishing conclusion that dark matter is
  present with a much greater density than luminous
  matter.
• From these considerations it follows that the
  large velocity dispersions in Coma (and in other
  clusters of galaxies) represents an unsolved
  problem
• but waited for New Physics to resolve the
  discrepancy

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Fritz Zwicky

• Zwicky was educated at ETH in Zurich but
  emigrated to US to work with Millikan at Caltech
  in 1925, where he was made Professor of Astronomy
  20 years later.
• Widely regarded as a visionary but was infamous
  during his lifetime as a prickly and eccentric
  character.
• Coined the term supernovae with Baade and
  proposed that galaxy clusters could be used as
  gravitational lenses.

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Evidence for Missing Matter

• Smith (1936) confirmed Zwickys earlier result
  using galaxies in the Virgo cluster and
  speculated that a great mass of internebular
  material existed within the cluster.
• Babcock (1939) obtained long slit spectra of M31
  and noted that the outer parts of the disk were
  rotating with unexpectedly high velocities
• The great range in the calculated ratio of mass
  to luminosity in proceeding outward from the
  nucleus suggests that absorption plays a very
  important role in the outer portions of the
  spiral, or, perhaps, that new dynamical
  considerations are required, which will permit of
  a smaller relative mass in the outer parts.

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Cosmologys Early Years

• Hubble published A relation between distance and
  radial velocity among extra-galactic nebulae in
  1929
• Prompted Einstein to regret including a
  cosmological constant in his field equations --
  his greatest blunder is now known as dark
  energy
• In 1940s George Gamow and his collaborators
  argued that galaxies must have been closer
  together at earlier times -- and the Universe
  could have been infinitely hot at some distant
  point in time.
• Essence of idea revived by Dicke and Peebles at
  Princeton in the mid-1960s -- without knowledge
  of Gamows work -- or that of Penzias and Wilson
  at Bell Labs

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Cosmologys Early Years

• In 1965 Penzias and Wilson discovered the Cosmic
  Microwave Background Radiation as a source of
  excess noise in their radio receiver.
• Could it be pigeons?? No, relic radiation left
  over from Big Bang!
• Received Nobel Prize in Physics in 1978
• Cosmology became a respectable science.

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Cosmologys Early Years

• Between 1965 and 1989, a number of efforts were
  made to measure the temperature of the CMB as a
  function of wavelength in its first minutes of
  operation, COBE was able to provide this
  measurement in unprecedented detail and verified
  that the CMBR followed a black body curve.
• Vindication of the hot Big Bang model.
• The CMB was observed to be very smooth -- we now
  know that the rms deviations are smaller than 1
  part in 100,000 -- so how did the Universe get to
  be so clumpy?
• Gravitational instability

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Gravitational Collapse Stability

• Sir James Jeans (1877-1946) -- who also proposed
  a theory for planet formation -- developed a
  framework within which to understand the
  formation of structures from gravitational
  collapse.
• If we consider a cloud of ideal gas with
  temperature T, it should be clear that the
  temperature of the cloud can help prevent
  collapse under its own gravity. As the cloud
  cools however, there will come a point when the
  internal pressure is no longer able to prevent
  collapse. The cloud will contract and a point
  will be reached where the configuration is in
  equilibrium.
• This process is important in the formation of
  stars and in the cooling of gas on to dark matter
  haloes.

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Cosmologys Early Years

• Two schools of thought investigated how structure
  in the Universe formed
• The Russian school led by Yakob Zeldovich, who
  argued for top-down or the adiabatic scenario
• The American school led by Jim Peebles, who
  argued for bottom-up or the isothermal
  scenario
• Both assumed baryons radiation
• Neither could work

• Adiabatic scenario predicted fragmentation of
  structure from pancakes
• But also predicted enormous anisotropies in the
  CMB - inconsistent with observations.
• Isothermal scenario predicted formation of
  GC-mass structures that merged
• But no plausible mechanism for producing
  perturbations of this kind

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Evidence for Missing Matter

• Babcocks study of the rotation curve of M31
  predated the work of Rubin Ford (1970) and
  Roberts Whitehurst (1975).
• These provided the first widely recognised
  observational evidence in favour of dark matter
  in galaxies.
• Roberts Whitehursts study important because it
  mapped HI rotation curve, which extended to
  roughly 10 times optical radius.

Credit M. S. Roberts
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Evidence for Missing Matter

• At around this time there were a number of
  influential theoretical studies that examined the
  impliciations of dark matter in galaxies...
• Ostriker Peebles (1974) suggested that the
  stability of galactic disks required the presence
  of a massive halo around galaxies
• Ostriker, Peebles Yahil (1975) noted that if
  the mass-to-light ratios of galaxies increase
  with increasing radius, then this dark mass could
  be cosmologically significant.
• But what could this dark matter be?

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Evidence for Dark Matter

• One of the earliest proposals for the dark matter
  was that it could be comprised of a large
  population of faint low-mass halo stars such as
  M-dwarfs -- what we might call MACHOs or Massive
  Compact Halo Objects.
• Rees (1977) concluded that the dark matter could
  be of a more exotic character, such as
  neutrinos with a small rest mass -- an example of
  a WIMP or a Weakly Interacting Massive Particle

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Evidence for Dark Matter

• Gunn Tremaine (1979) used phase space
  constraints and the observed core radii of dwarf
  spheroidals and galaxy clusters to place
  stringent limits on the allowed range of neutrino
  masses.
• White Rees (1978) published one of the seminal
  studies in cosmology -- Core condensation in
  heavy halos - A two stage theory for galaxy
  formation and clustering -- dark matter
  aggregates provided the potential wells within
  which gas could cool, condense and form stars.

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Evidence for Dark Matter

• White, David Frenk (1984) argued that the
  properties of the neutrino aggregates expected in
  a neutrino-dominated universe are incompatible
  with observations irrespective of the efficiency
  with which they form galaxies -- one of the
  earliest examples of the power of the
  cosmological simulation!
• Although Bond et al. (1983) is credited with
  first using the term cold dark matter, White
  (1987) is thought to have been the first to
  assert that cold dark matter (in the sense we now
  use it) is Zwickys missing matter.

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Early History of Dark Matter

• Check out
• Lonely Hearts of the Cosmos by Dennis Overbye,
  a biography of 20th century cosmology and the
  characters who played a part in shaping it. Bear
  in mind that it was written in 1993!
• The First Three Minutes by Steven Weinberg
  nicely presents the physics of the Big Bang
  Nucleosynthesis.
• As is The Very First Light by John C. Mather
  -- great insight into the history of our
  understanding of the CMB.
• The Early History of Dark Matter by Sidney van
  den Bergh (1999, PASP, 111, 657)

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The Cold Dark Matter Model

• Standard theoretical framework for cosmological
  structure formation -
• The Universe is spatially flat..
• It underwent a period of rapid exponential
  inflation shortly after the Big Bang
• The matter content is dominated by non-baryonic
  Cold Dark Matter.
• The expansion rate of the Universe at the present
  epoch is accelerating, driven by dark energy.

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Structure Formation Cold Dark Matter

• The growth of structure proceeds in a
  hierarchical manner
• Smaller structures merge to form progressively
  larger structures
• The bottom-up picture of structure formation
• Consequence of the coldness of the dark matter
• Amplitude of initial density perturbations
  increases with decreasing spatial scale.

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Whats so Cold about CDM?

• Non-thermal relic of the Big Bang
• Lightest supersymmetric particle - the
  neutralino?
• Direct detection experiments place upper limits
  on its mass (e.g. DAMA, CDMS)
• May need to wait for construction of ILC c. 2020

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Whats so Cold about CDM?

• Lets think about the Universe as it was a
  fraction of a second after the Big Bang --
  uncomfortably hot, 1000 billion K.
• At these temperatures, particles could condense
  out of the vacuum and annihilate in accordance
  with Heisenbergs uncertainty principle.
• While the collision rate was much shorter than
  the expansion rate of the Universe, these
  particles were in thermal equilibrium.
• As soon as the collision rate dropped below the
  expansion rate, particles decoupled and were
  frozen in.
• Abundance of these thermal relics can be
  computed from well understood statistical
  mechanical principles.

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Whats so Cold about CDM?

• For thermal relics such as neutrinos relatively
  straightforward to compute their present day
  abundance.
• Neutrinos relativistic at decoupling, velocity
  dispersion large.
• Candidates for Hot Dark Matter -- ruled out by
  observation.
• For non-thermal relics such as Cold Dark
  Matter, very difficult to compute their present
  day abundance.
• Velocity dispersion assumed to be vanishingly
  small.
• Velocity dispersion important for the formation
  of structure

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Velocity Dispersion

• Velocity dispersion has the effect of smearing
  out density perturbations that may develop and
  helps stabilise a mass condensation against
  gravitational collapse.
• Hotter forms of dark matter can free stream --
  this erases density perturbations on small
  scales.
• The negligible velocity dispersion of Cold Dark
  Matter means that density perturbations are
  preserved on all scales.
• Interestingly velocity dispersion has been used
  to derive an upper limit on the central densities
  of Cold Dark Matter haloes -- there does not
  appear to be one!

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Does it have to be cold?

• Big Bang Nucleosynthesis predictions are in
  excellent agreement with observations -- and
  imply that most of the dark matter must be
  non-baryonic.
• Observations also tell us how much of this
  non-baryonic dark matter is present.
• Most crucial tests of the nature of dark matter
  to be made on small scales -- this is hard!
• Need not be cold but we can constrain how hot it
  can be -- and it cannot be too hot. Tepid??

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Next Two Lectures

• Cosmological inflation, the Cosmic Microwave
  Background and the seeds of structure
• Gravitational instability --
• Jeans Theory in an expanding Universe, also known
  as Linear (Perturbation) Theory
• The Spherical Collapse Model
• The Structure of Dark Matter Haloes
• The Formation of the First Stars