ON THE THEORY OF THE ORIGIN OF GLOBAL CLUSTER SYSTEMS AROUND THE GALAXIES

The origin of poor and moderate globular cluster systems around galaxies against the background of a nonlinear non-stationary model of collapsing galaxies is studied. The stability of the model with respect to four perturbation modes is studied, and the degree of the mode determines on average the number of clusters in the system. A critical dependence of the initial virial relation on the degree of rotation is constructed for each mode. The dependences of the instability increments on the physical parameters of the model are found.

The stellar mass Fundamental Plane: the virial relation and a very thin plane for slow rotators

ABSTRACT Early-type galaxies – slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars – define a Fundamental Plane (FP) in the space of half-light radius Re, enclosed surface brightness Ie, and velocity dispersion σe. Since Ie and σe are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which Ie and σe can be used to estimate sizes Re. We show that: (1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in Re is $\sim 16{{\ \rm per\ cent}}$, of which only $\sim 9{{\ \rm per\ cent}}$ is intrinsic. Removing galaxies with M* < 1011 M⊙ further reduces the observed scatter to $\sim 13{{\ \rm per\ cent}}$ ($\sim 4{{\ \rm per\ cent}}$ intrinsic). The observed scatter increases to $\sim 25{{\ \rm per\ cent}}$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only 5 per cent orthogonal to the plane. (2) The structure within the FP is most easily understood as arising from the fact that Ie and σe are nearly independent, whereas the Re−Ie and Re−σe correlations are nearly equal and opposite. (3) If the coefficients of the FP differ from those associated with the virial theorem the plane is said to be ‘tilted’. If we multiply Ie by the global stellar mass-to-light ratio M*/L and we account for non-homology across the population by using Sérsic photometry, then the resulting stellar mass FP is less tilted. Accounting self-consistently for M*/L gradients will change the tilt. The tilt we currently see suggests that the efficiency of turning baryons into stars increases and/or the dark matter fraction decreases as stellar surface brightness increases.

Broken baby Skyrmions

The baby Skyrme model is a (2+1)-dimensional analogue of the Skyrme model, in which baryons are described by topological solitons. We introduce a version of the baby Skyrme model in which the global O (3) symmetry is broken to the dihedral group D N . It is found that the single soliton in this theory is composed of N partons that are topologically confined. The case N =3 is studied in some detail and multi-soliton solutions are computed and related to polyiamonds, which are plane figures composed of equilateral triangles joined by common edges. It is shown that the solitons may be viewed as pieces of a doubly periodic soliton lattice. It is proved, for a general baby Skyrme model on a general torus, that the condition that the energy of a soliton lattice is critical with respect to variations of the torus is equivalent to the field satisfying a virial relation and being, in a precise sense, conformal on average. An alternative model with D 3 symmetry is also introduced, which has an exact explicit soliton lattice solution. Soliton solutions are computed and compared in the two D 3 theories. Some comments are made regarding the extension of these ideas to the Skyrme model.

Out of one, many — Using moment expansions of the virial relation to deduce universal density functionals from a single system

Moment expansions for density functionals are revisited. This allows for a simple proof of the equivalence between the integrodifferential virial relation and the coordinate-scaling equation. The virial relation is then used to show how, starting from an exact and explicit form of a functional for one system, one may deduce the exact functional for other systems with the same number of electrons.