Professor James Binney FRS

Abstract:

A naive extension to modified Newtonian dynamics (MOND) of the standard computation of the two-body relaxation time t2b implies that 2b is comparable to the crossing time regardless of the number W of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of t2b is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case, we find that in the deep-MOND regime t2b scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Near the centre of a spherical system that is in the deep-MOND regime, we show that the fluctuating component of the gravitational force is never small compared to the mean-field force; this conclusion surprisingly even applies to systems with a density cusp that keeps the mean-field force constant to arbitrarily small radius, and suggests that a cuspy centre can never be in the deep-MOND regime. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two-body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ∼10 M⊙ should have spiralled to the centres of dwarf galaxies.

Abstract:

A naive extension to MOND of the standard computation of the two-body relaxation time Tb implies that Tb is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of Tb is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case we find that in the deep-MOND regime Tbb scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ~10M_sun should have spiralled to the centres of dwarf galaxies.(Abridged)

Abstract:

Evidence is summarized which suggests that when a protogalaxy collapses, a fraction f of its gas fails to heat to the virial temperature, where f is large for haloes less massive than the value M* associated with L* galaxies. Stars and galaxies form only from the cool gas fraction. Hot gas is ejected from low-mass systems as in conventional semi-analytic models of galaxy formation. In high-mass systems it is retained but does not cool and form stars. Instead it builds up as a largely inert atmosphere, in which cooling is inhibited by an episodically active galactic nucleus. Cold gas frequently falls into galactic haloes. In the absence of a dense atmosphere of virial-temperature gas it builds up on nearly circular orbits and can be observed in the 21-cm line of H I. When there is a sufficiently dense hot atmosphere, cold infalling gas tends to be ablated and absorbed by the hot atmosphere before it can form stars. The picture nicely explains away the surfeit of high-luminosity galaxies that has recently plagued semi-analytic models of galaxy formation, replacing them by systems of moderate luminosity from old stars and large X-ray luminosities from hot gas.

Abstract:

We determine the critical size l_crit of a filament of cold (T~10^4 K) gas that is in radiative equilibrium with X-ray emitting gas at temperatures T_out~10^6 - 10^8 K. Filaments smaller than l_crit will be rapidly evaporated, while longer ones will induce the condensation of the ambient medium. At fixed pressure P, l_crit increases as T_out^(11/4), while at fixed T_out it scales as 1/P. It scales as f^(1/2), where f is the factor by which the magnetic field depresses the thermal conductivity below Spitzer's benchmark value. For plausible values of f, l_crit is similar to the lengths of observed filaments. In a cluster such as Perseus, the value of l_crit increases by over an order of magnitude between the centre and a radius of 100 kpc. If the spectrum of seed filament lengths l is strongly falling with l, as is natural, then these results explain why filaments are only seen within a few kiloparsecs of the centres of clusters, and are not seen in clusters that have no cooling flow. We calculate the differential emission measure as a function of temperature for the interface between filaments and ambient gas of various temperatures. We discuss the implications of our results for the origin of the galaxy luminosity function.