N=8 Supergravity on the Light Cone

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.Comment: 38

The dynamical distance and intrinsic structure of the globular cluster omega Centauri

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster omega Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on D tan i. Application of our axisymmetric implementation of Schwarzschild's orbit superposition method to omega Cen reveals no dynamical evidence for a significant radial dependence of M/L. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3 kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6 M_sun. The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.Comment: 37 pages (23 figures), accepted for publication in A&A, abstract abridged, for PS and PDF file with full resolution figures, see http://www.strw.leidenuniv.nl/~vdven/oc

Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies

A general basis set algorithm for galactic haloes and discs

We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a first-order differential operator that is self-adjoint with respect to this inner product, and prove a general theorem that gives the conditions under which a (bi-)orthogonal basis set arises by repeated application of this differential operator. We then show that these conditions are fulfilled by all the families of analytical basis sets with infinite extent that have been discovered to date. The new theoretical framework turns out to be closely connected to Fourier-Mellin transforms, and it is a powerful tool for constructing general basis sets. We demonstrate this by deriving a basis set for the isochrone model and demonstrating its numerical reliability by reproducing a known result concerning unstable radial modes.Comment: to be published in Astronomy & Astrophysic

Formation and evolution of dwarf early-type galaxies in the Virgo cluster II. Kinematic Scaling Relations

We place our sample of 18 Virgo dwarf early-type galaxies (dEs) on the V-K - velocity dispersion, Faber-Jackson, and Fundamental Plane (FP) scaling relations for massive early-type galaxies (Es). We use a generalized velocity dispersion, which includes rotation, to be able to compare the location of both rotationally and pressure supported dEs with those of early and late-type galaxies. We find that dEs seem to bend the Faber-Jackson relation of Es to lower velocity dispersions, being the link between Es and dwarf spheroidal galaxies (dSphs). Regarding the FP relation, we find that dEs are significantly offset with respect to massive hot stellar systems, and re-casting the FP into the so-called kappa-space suggests that this offset is related to dEs having a total mass-to-light ratio higher than Es but still significantly lower than dSph galaxies. Given a stellar mass-to-light ratio based on the measured line indices of dEs, the FP offset allows us to infer that the dark matter fraction within the half light radii of dEs is on average >~ 42% (uncertainties of 17% in the K band and 20% in the V band), fully consistent with an independent estimate in an earlier paper in this series. We also find that dEs in the size-luminosity relation in the near-infrared, like in the optical, are offset from early-type galaxies, but seem to be consistent with late-type galaxies. We thus conclude that the scaling relations show that dEs are different from Es, and that they further strengthen our previous findings that dEs are closer to and likely formed from late-type galaxies.Comment: 14 pages, 9 figures, 2 appendixes. Accepted for publication in A&