Cosmologists dedicate a great deal of effort to determine the density of matter in the universe. Type Ia supernovae observations are consistent with

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1 Notes for Cosmology course, fall 2005 Dark Matter Prelude Cosmologists dedicate a great deal of effort to determine the density of matter in the universe Type Ia supernovae observations are consistent with Ω m,0 = 03 and Ω Λ,0 = 07 however, neither Ω m,0 nor Ω Λ,0 is individually well constrained Can we say anything else about matter in the universe? Visible matter The B-band corresponds to m < λ < m The luminosity density of stars is j,b L,B Mpc 3 (corresponding to a 25 W light bulb in a 1 AU radius sphere) For every 4 solar masses of stars in our neighborhood, roughly 1 solar luminosity of starlight is produced or M/L B 4 M / L,B, ρ, M / Mpc 3, Ω, This is very far from 03 but stars are simply objects which are most conspicuous at visible wavelengths In rich clusters of galaxies, there is a huge amount of very hot intergalactic gas, which radiates strongly at x-ray wavelengths Even within galaxies (particularly in spirals and irregulars), there s a significant amount of interstellar gas There are also inconspicuous stellar remnants such as white dwarfs, neutron stars, and black holes as well as brown dwarfs, which are self-gravitating balls of gas too low in mass to sustain nuclear fusion in their centers

2 The best limit on the baryonic density of our universe comes from the predictions of Big Bang Nucleosynthesis (the efficiency of nucleosynthesis in the early universe depends on the density of protons and neutrons present) combined with studies of primordial gas clouds as well as CMB observations: Ω bary,0 = 004 ± 001 The amount of baryonic matter in the universe is significantly greater than the amount of matter in stars most of the protons and neutrons are too hot to be easily visible to human eyes (the x-ray emitting gas in clusters) or too cold to be easily visible (the infrared emitting brown dwarfs and cool stellar remnants) This component is called baryonic dark matter Dark matter in galaxies Not only is most of the baryonic matter invisible to our eyes; most of the matter in the universe is nonbaryonic dark matter, which doesn t absorb, emit, or scatter photons at all For a stars on a circular orbit around the center of a galaxy, Also, a = v2 R a = GM(R) R 2 Thus, the orbital speed of a star is or v = GM(R) R The distribution of light in a spiral galaxy typically decreases exponentially with a scale length R s of a few kiloparsecs Thus, if stars contributed most of the mass of the galaxy, you would expect v 1/ R at large radii ( Keplerian rotation ) In M31, the rotation speed stays at 240 km s 1 as far as 34 kpc ( R s ) from the center of the galaxy Conclusion: there must be a dark halo surrounding the visible stellar disk Most (if not all) spiral galaxies have comparable dark

3 halos If the rotation speed is constant with radius (a good approximation for most spirals), then ( M(R) = v2 R G = M v 220 kms 1 ) ( 2 R ) 85 kpc The values of v and R in the above equation are scaled to our location in our Galaxy The mass-to-light ratio of our Galaxy is ( ) Rhalo (M/L B ) Gal 50 M / L,B 100 kpc A rough estimate of the halo size can be made by looking at the velocities of the globular clusters and satellite galaxies orbiting our Galaxy R halo > 75 kpc If our Galaxy is typical in having a dark halo, then Ω gal,0 (10 40)Ω,0 ( ) Dark matter in clusters In the 1930 s, Fritz Zwicky deduced that the swiftly moving galaxies in the Coma cluster require dark matter to hold them to the cluster The kinetic energy associated with the random motions of the galaxies inside the cluster is K = 3 2 Mσ2, where M is the mass of the cluster and σ the l-o-s velocity dispersion The gravitational potential energy of the cluster can be written W = α GM2 R, where α depends on the density profile of the cluster (α 1) The virial theorem gives (for a system in equilibrium) K = W/2 M = 3σ2 r h αg An analysis of the velocities in the Coma cluster yields M Coma M

4 Combined with the measured luminosity of the Coma cluster, this yields a mass-to-light ratio of (M/L B ) Coma = 250 M / L B The presence of dark matter in Coma is confirmed by the fact that the hot X-ray gas is still in place Add together the mass of dark halos associated with clusters, and you get What s the matter Ω clus,0 02 The total amount of matter in the universe is significantly greater than the amount of baryonic matter Since dark matter is totally invisible it lacks those inconvenient observations which plague the life of theorists everywhere! Particle physics candidates : The axion is an elementary particles with m 10 5 ev (it would take about 50 billion axions to match the mass of one electron) As a dark matter candidate, neutrinos have the undeniable advantage of actually existing There are three types of neutrino, each associated with a particular lepton: the electron neutrino (ν e ), the muon neutrino (ν µ ), and the tau neutrino (ν τ ) Detailed computations predict a total number density of neutrinos n ν = m 3, at any given moment, there are about two million cosmic neutrinos passing through your body If neutrinos are massless, the mean energy per cosmic neutrino is E 0 = ev If the density parameter in nonbaryonic dark matter is currently Ω nonbary,0 025, then the required mean mass per neutrino would be m ν c 2 4 ev, ie non-relativistic Oscillations indicate that neutrinos do have mass However, structure formation indicates that the mass probably is lower than 4 ev (random velocities smooth out irregularities on small scales) (Hannestad et al m ν c 2 < 05 ev)

5 Astrophysics candidates : Astrophysics candidates are macroscopic objects rather than elementary particles; they are more likely to be detected by astronomers at their telescopes than by particle physicists in their laboratories The possibility exists that some, or all, of the dark matter in the halos of galaxies consists of large lumps of matter (MACHOs or MAssive Compact Halo Objects) instead of a smooth distribution of particles, eg primordial black holes with masses up to 10 5 M Gravitational lensing One way in which MACHOs reveal their presence is by gravitational lensing of background light sources A compact object of mass M causes curvature of space-time in its immediate vicinity, and deflects photons that venture near it If a photon passes with an impact parameter b, it will be deflected through an angle α given by the formula α = 4GM c 2 b Since a massive compact object can deflect light, it can act as a lens The famous eclipse expedition of 1919 verified the prediction that light passing close to the rim of the sun (M = 1 M and b 1 R ) would be deflected by an angle of α = 17 arcsec If the observer, lens and background source are perfectly aligned, the observer will see a so called Einstein ring with radius θ E = 4GM d A (z L, z S ) c 2 d A (z L )d A (z S ), we can estimate the mass from θ E For MACHOs, we have θ E < 1 milli-arcsecond, ie difficult to resolve However, a MACHO passing directly between you and, for instance, a star in the Large Magellanic Cloud, will cause the image of that star to become brighter giving the light curve a distinctive shape (which helps you to distinguish it from a variable star, a long with the achromaicity) By monitoring stars in

6 the LMC, and counting the number of gravitational lensing events, one can estimate the density and mass of MACHOs in the Galactic halo Current results indicate that up to 20% can be made up of MACHOs with masses M > 015M Also galaxies and clusters can act as lenses and we can use gravitational lensing to estimate the mass of galaxies and clusters For galaxies, we have θ E 1 arcsecond For clusters, θ E 1 arcminute Summary Observations indicate that Ω m,0 03 One per cent of this is in stars 10% is in baryonic matter Thus, most of the matter is dark matter and the next largest part is dark baryons We think we know how much matter there is, but we don t know what it is!

Visible Matter. References: Ryden, Introduction to Cosmology - Par. 8.1 Liddle, Introduction to Modern Cosmology - Par. 9.1

Visible Matter. References: Ryden, Introduction to Cosmology - Par. 8.1 Liddle, Introduction to Modern Cosmology - Par. 9.1 COSMOLOGY PHYS 30392 DENSITY OF THE UNIVERSE Part I Giampaolo Pisano - Jodrell Bank Centre for Astrophysics The University of Manchester - March 2013 http://www.jb.man.ac.uk/~gp/ giampaolo.pisano@manchester.ac.uk