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Cosmological Structure Formation A Short Course. I. Why Dark Matter, and why Cold? Chris Power. Zwicky (1933) measured the radial velocities for eight galaxies in the Coma cluster and found an unexpectedly large velocity dispersion of ~1000 km/s.

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cosmological structure formation a short course

Cosmological Structure FormationA Short Course

I. Why Dark Matter, and why Cold?

Chris Power

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?

Evidence for Missing Matter
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.

The Virial Theorem
evidence for missing matter4
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…

Evidence for Missing Matter
fritz zwicky
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.
evidence for missing matter6
Evidence for Missing Matter
  • Smith (1936) confirmed Zwicky’s 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”.
cosmology s early years
Cosmology’s 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 Gamow’s work -- or that of Penzias and Wilson at Bell Labs
cosmology s early years8
Cosmology’s 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.
cosmology s early years9
Cosmology’s 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…
gravitational collapse stability
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.
cosmology s early years11
Two schools of thought investigated how structure in the Universe formed

The Russian school led by Yakob Zel’dovich, 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

Cosmology’s Early Years
evidence for missing matter12
Evidence for Missing Matter
  • Babcock’s 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 & Whitehurst’s study important because it mapped HI rotation curve, which extended to roughly 10 times optical radius.

Credit: M. S. Roberts

evidence for missing matter13
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?
evidence for dark matter
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”
evidence for dark matter15
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.
evidence for dark matter16
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 Zwicky’s missing matter.
early history of dark matter
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)
the cold dark matter model
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.
structure formation cold dark matter
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.
what s so cold about cdm
What’s 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…
what s so cold about cdm21
What’s so Cold about CDM?
  • Let’s 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 Heisenberg’s 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.
what s so cold about cdm22
What’s 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…
velocity dispersion
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!
does it have to be cold
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??
next two lectures
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