←  Galaxy Rotation Curves, CDM and MOND  ↑  →

Dark Matter

Stellar theory gives a good estimate of the mass of an individual star. By counting the visible stars over a large enough region of space we can estimate the mass density of visible matter. This has been done by many researchers, giving the result that, as a fraction of critical density for closure in a no-Λ model, the stellar density is
Under the teleconnection critical density is less by a factor of four, so this becomes
Clearly visible matter accounts for only a small proportion of the mass required by a cosmological model. The remainder is dark matter.

Baryonic Dark Matter

Baryons are particles consisting of three quarks. The only stable baryons are the proton and the neutron which are the constituents of the nucleus of an atom. Baryonic matter is matter which consists mainly of baryons by mass. Traditionally cosmologists include electrons as baryonic matter. Although this is not strictly correct according to the terminology of particle physics, weighing in at well under 1/thousandth of the mass of the proton, the gravitational effects of electrons do not merit separate discussion.

Big Bang Nucleosynthesis describes how the light elements formed at the beginning of the universe from well understood processes studied in earth based laboratories. Based on a value of Hubble’s constant, H₀ ≈ 71 km s^-1 Mpc^-1, there is an excellent match between theory and the observed proportions of light elements for values of the baryonic mass density in the range.
For a teleconnection cosmology with Hubble’s constant, H₀ ≈ 80 km s^-1 Mpc^-1, this corresponds to
Clearly in both models, the bulk of baryonic matter is dark. We may expect that much of it is contained in intergalactic gas and in low luminosity stars such as brown dwarfs. Intergalactic gas is not easy to measure, but its presence is shown in X-rays when it is gravitationally heated in galaxy clusters, where it contains five to ten times the mass of stars.

Neutrinos (Hot Dark matter)

We can also estimate the number density of neutrinos emanating from the Big Bang. The experimental upper mass limit of the electron neutrino is too small to account for the missing mass in either model, but there remains a possibility that muon and tau neutrinos provide sufficient mass to account for the value of Ω. Because in the early universe they would have been relativisitic, the neutrino is described as hot dark matter. Hot dark matter was not gravitationally bound during structure formation in the early universe, and did not contribute to the rate at which galaxies formed.

Bulk Flows and Structure Formation

By analysing the motion of galaxies relative to each other, on the assumption that bulk flows are caused gravitationally, it is possible to obtain a mass estimate Ω ≥ 0.2, considerably greater than the quantity of baryonic matter.

Using supercomputers, we are able to model the formation of galaxies in the early universe. In standard cosmology, a mass density Ω ≥ 0.2 is required to enable galaxies to form at a rate to match the observations of galactic surveys like the 2dFGRS, the Sloan Digital Sky Survey, and observations of the Lyman-alpha forest. However, recent observations of high redshift galaxies have put structure formation models under stress (Glazebrook et al, Cimmatti et al), and we observe fewer small dwarf galaxies than predicted by CDM models by a factor of about 100. This is the missing satellites problem.

These methods are involved, and no corresponding analysis has been carried out under the teleconnection, but the age of high redshift galaxies is so much greater under the teleconnection that there is a prospect of reconciling the analytic models with observation using conventional matter. The observation of more mature galaxies at very high redshifts with the James Webb Space Telescope, scheduled for launch in 2013, and with the Extremely Large Telescopes, currently under design and development and due to come into service around 2018, could give clear evidence of the teleconnection age-redshift relation.

Galaxy Rotation Curves

A galaxy rotation curve shows the velocity of matter rotating in a spiral disk as a function of radius from the centre. If the bulk of galactic mass is towards the center, as indicated by visible matter, then Newton’s inverse square law of gravity will lead to lower velocities further from the center of the galaxy. In fact we observe that galaxies have approximately flat rotation curves. A corresponding result is found from the velocity dispersion of elliptical galaxies. This is taken to be evidence of a spherical dark matter halo. The calculated mass of dark matter haloes is too great to be easily accounted for by baryonic matter.

The rotation curves shown are for the Milky way and for Andromeda fitted to a three part mass model based on visible matter (disk + bulge) and and a dark halo by Klypin, Zhao and Somerville. The rotational velocity due to the halo dominates for large radii.

Cold Dark Matter

Because there is simply not enough baryonic dark matter and hot dark matter to account for these observations, astronomers believe there must be some other sort of dark matter, cold dark matter (CDM) to make up the deficit. It is thought that a CDM halo surrounds galaxies, providing an invisible mass distribution responsible for the shape of the rotation curves. There is no theory of CDM in particle physics. CDM has never been observed in terrestrial experiments, and needs to obey unknown laws to produce observed results, and raises a number of other issues and contradictions, but has become an established tenet of modern cosmology.

MOND

In 1981 Motte Milgrom observed that there is no direct empirical test of Newton’s law of gravity for small accelerations, and that galactic rotation curves can be accounted for by replacing the inverse square law with an inverse law, as an alternative to CDM. Milgrom called his idea MOND.


MOND has been applied to hundreds of galaxies, of many different types, and gives a good match with data for a_M = 1 × 10⁻¹⁰ m s⁻² (see Sanders & McGaugh for a review). The CDM model is further distressed by studies of globular clusters by Scarpa et al., who find that a MONDian curve is obeyed although the amount of CDM in clusters is negligible, and by the dynamical studies of three elliptical galaxies based on the measurement of radial velocities of a large number of planetary nebulae by Romanowsky et al., who find evidence for “little if any dark matter in these galaxies”. In contrast a study of twenty three satellite galaxies to the Milky way by Strigari et al. has found them unaccountably dense in CDM.

MOND receives support because cold dark matter does not give any explanation as to why precisely same acceleration law should be found in galaxies of many sizes and types, and because there is no satisfactory theory of CDM in particle physics. However, while MOND has been successful in a wide range of contexts, it has a problem in galaxy clusters where central accelerations higher than those predicted have been found from studying temperature gradients and in modeling Ly α absorbers. Two relativistic theories, Beckenstein’s Tensor-Vector-Scalar gravity (TeVeS) and Moffat’s Scalar-Tensor-Vector gravity (STVG) attempt to explain MOND by postulating new gravitational fields. The mathematics of these models is somewhat sophisticated, its physical basis obscure, the division between the MONDian and Newtonian regime’s remains artificial, and MONDian theories of gravity meets further problems in accounting for observed gravitational lensing.

Illusory Velocity

Analysis under the teleconnection found that the apparent orbital velocity of matter in circular orbit about a galaxy, calculated from Doppler shift, is given by
For accelerations greater than H₀c ⁄ 8 the inverse square term dominates. For accelerations less than H₀c ⁄ 8 the inverse term dominates and is equal to the MONDian term with a_M = H₀c ⁄ 8. The preferred value of Hubble’s constant, H₀ = 80 km s^-1 Mpc^-1, used in teleconnection cosmology gives a_M = H₀c ⁄ 8 = 0.97 × 10⁻¹⁰ m s⁻² in excellent agreement with the empirical value of a_M = 1 × 10⁻¹⁰ m s⁻². Apparent acceleration is larger than that given by MOND for accelerations in the region of a_M. This prediction agrees with studies on globular clusters by Scarpa et al. in which flattening was observed at accelerations up to 2.1 ±0.5  × 10⁻¹⁰ m s⁻², and qualitatively agrees with de Blok & McGaugh, who adjusted inclination so as to increase accelerations in this region in order to obtain fits with MOND for a number of low surface brightness galaxies.

Lensing

Zhao et al. tested lensing in Beckenstein’s relativistic MOND (TeVeS), and found that lensing may be a good test for CDM theories. The problem for standard no-CDM theories is that, because of the lower galactic masses it is difficult to account for the amount of lensing in all cases. Zhao et al. found that “TeVeS succeeds in providing an alternative to general relativity in some lensing contexts; however, it faces significant challenges when confronted with particular galaxy lens systems”. Under the teleconnection lensing is four times greater for given mass than in standard general relativity.

Halo Profiles

A clearer test is given by the analysis of the profile of the halo. Halo profiles can be determined both from rotation curves, and from lensing. According to evolutionary models dark matter halos should have steep central density cusps but, in many studies, they appear not to. This is the cuspy halo problem. Power et al comment that “there is no well defined value for the central density of the dark matter, which can, in principle, climb to arbitrarily large values near the centre”. Of this result they say “there have been a number of reports in the literature arguing that the shape of the rotation curves of many disk galaxies rules out steeply divergent dark matter density profiles” and conclude that it “may signal a genuine crisis for the CDM paradigm on small scales”. In a one study for which a particularly good analysis is possible, Wayth et al. found lensing consistent with a halo of the same mass distribution as the galaxy itself. This result is not consistent with either the halo distribution required to produce galactic rotation curves, or with evolutionary halo models, though it would be expected in a no-CDM model.

Galaxy Rotation Curves, CDM and MOND ↑ The Slope of the Rotation Curve →