On Borel Probability Measures and Noncooperative Game Theory

In this paper the well-known minimax theorems of Wald, Ville and VonNeumann are generalized under weaker topological conditions onthepayoff function Æ’ and/or extended to the larger set of the Borelprobabilitymeasures instead of the set of mixed strategies.minimax theory;infinite dimensional separation;Borel measures;noncooperative game theory;weak compactness

The Role of Starbursts in the Formation of Galaxies & Active Galactic Nuclei

Starbursts are episodes of intense star-formation in the central regions of galaxies, and are the sites of roughly 25% of the high-mass star-formation in the local universe. In this contribution I review the role starbursts play in the formation and evolution of galaxies, the intergalactic medium, and active galactic nuclei. Four major conclusions are drawn. 1) Starburst galaxies are good analogues (in fact, the only plausible local analogues) to the known population of star-forming galaxies at high-redshift. 2) Integrated over cosmic time, supernova-driven galactic-winds (`superwinds') play an essential role in the evolution of galaxies and the inter-galactic medium. 3) Circumnuclear starbursts are an energetically-significant component of the Seyfert phenomenon. 4) The evolution of the population of the host galaxies of radio-quiet quasars is significantly different than that of powerful radio galaxies, and is at least qualitatively consistent with the standard picture of the hierarchical assembly of massive galaxies at relatively late times.Comment: 16 pages, 4 figures, Royal Society discussion meeting `The formation of galaxies

On Borel Probability Measures and Noncooperative Game Theory

In this paper the well-known minimax theorems of Wald, Ville and Von Neumann are generalized under weaker topological conditions onthe payoff function ƒ and/or extended to the larger set of the Borel probabilitymeasures instead of the set of mixed strategies

A halo expansion technique for approximating simulated dark matter haloes

We apply a basis function expansion method to create a time-evolving density/potential approximation of the late growth of simulated N-body dark matter haloes. We demonstrate how the potential of a halo from the Aquarius Project can be accurately represented by a small number of basis functions, and show that the halo expansion (HEX) method provides a way to replay simulations. We explore the level of accuracy of the technique as well as some of its limitations. We find that the number of terms included in the expansion must be large enough to resolve the large-scale distribution and shape of the halo but, beyond this, additional terms result in little further improvement. Particle and subhalo orbits can be integrated in this realistic, time-varying halo potential approximation, at much lower cost than the original simulation, with high fidelity for many individual orbits, and a good match to the distributions of orbital energy and angular momentum. Statistically, the evolution of structural subhalo properties, such as mass, half-mass radius and characteristic circular velocity, are very well reproduced in the HEX approximation over several Gyr. We demonstrate an application of the technique by following the evolution of an orbiting subhalo at much higher resolution than can be achieved in the original simulation. Our method represents a significant improvement over commonly used techniques based on static analytical descriptions of the halo potential

A G1-like globular cluster in NGC 1023

The structure of a very bright (MV = -10.9) globular cluster in NGC 1023 is analyzed on two sets of images taken with the Hubble Space Telescope. From careful modeling of King profile fits to the cluster image, a core radius of 0.55+/-0.1 pc, effective radius 3.7+/-0.3 pc and a central V-band surface brightness of 12.9+/-0.5 mag / square arcsec are derived. This makes the cluster much more compact than Omega Cen, but very similar to the brightest globular cluster in M31, G1 = Mayall II. The cluster in NGC 1023 appears to be very highly flattened with an ellipticity of about 0.37, even higher than for Omega Cen and G1, and similar to the most flattened clusters in the Large Magellanic Cloud.Comment: 14 pages, 3 figures, 1 table. Accepted for AJ, Oct 200

Physical Bias of Galaxies From Large-Scale Hydrodynamic Simulations

We analyze a new large-scale ($100h^{-1}$Mpc) numerical hydrodynamic simulation of the popular $\Lambda$CDM cosmological model, including in our treatment dark matter, gas and star-formation, on the basis of standard physical processes. The method, applied with a numerical resolution of $<200h^{-1}$kpc (which is still quite coarse for following individual galaxies, especially in dense regions), attempts to estimate where and when galaxies form. We then compare the smoothed galaxy distribution with the smoothed mass distribution to determine the "bias" defined as $b\equiv (\delta M/M)_{gal}/(\delta M/M)_{total}$ on scales large compared with the code numerical resolution (on the basis of resolution tests given in the appendix of this paper). We find that (holding all variables constant except the quoted one) bias increases with decreasing scale, with increasing galactic age or metallicity and with increasing redshift of observations. At the $8h^{-1}$Mpc fiducial comoving scale bias (for bright regions) is 1.35 at $z=0$ reaching to 3.6 at $z=3$, both numbers being consistent with extant observations. We also find that $(10-20)h^{-1}$Mpc voids in the distribution of luminous objects are as observed (i.e., observed voids are not an argument against CDM-like models) and finally that the younger systems should show a colder Hubble flow than do the early type galaxies (a testable proposition). Surprisingly, little evolution is found in the amplitude of the smoothed galaxy-galaxy correlation function (as a function of {\it comoving} separation). Testing this prediction vs observations will allow a comparison between this work and that of Kauffmann et al which is based on a different physical modelingmethod.Comment: in press, ApJ, 26 latex pages plus 7 fig

Early structure in Lambda CDM

We use a novel technique to simulate the growth of one of the most massive progenitors of a supercluster region from redshift z 80, when its mass was about 10 M, until the present day. Our nested sequence of N-body resimulations allows us to study in detail the structure both of the dark matter object itself and of its environment. Our effective resolution is optimal at redshifts of 49, 29, 12, 5 and 0 when the dominant object has mass 1.2 × 105, 5 × 107, 2 × 1010, 3 × 1012 and 8 × 1014 h1 M, respectively, and contains 106 simulation particles within its virial radius. Extended Press–Schechter (EPS) theory correctly predicts both this rapid growth and the substantial overabundance of massive haloes we find at early times in regions surrounding the dominant object. Although the large-scale structure in these regions differs dramatically from a scaled version of its present-day counterpart, the internal structure of the dominant object is remarkably similar. Molecular hydrogen cooling could start as early as z 49 in this object, while cooling by atomic hydrogen becomes effective at z 39. If the first stars formed in haloes with virial temperature 2000 K, their comoving abundance at z= 49 should be similar to that of dwarf galaxies today, while their comoving correlation length should be 2.5 h1 Mpc

Simulations of AGN feedback in galaxy clusters and groups: impact on gas fractions and the Lx-T scaling relation

Recently, rapid observational and theoretical progress has established that black holes (BHs) play a decisive role in the formation and evolution of individual galaxies as well as galaxy groups and clusters. In particular, there is compelling evidence that BHs vigorously interact with their surroundings in the central regions of galaxy clusters, indicating that any realistic model of cluster formation needs to account for these processes. This is also suggested by the failure of previous generations of hydrodynamical simulations without BH physics to simultaneously account for the paucity of strong cooling flows in clusters, the slope and amplitude of the observed cluster scaling relations, and the high-luminosity cut-off of central cluster galaxies. Here we use high-resolution cosmological simulations of a large cluster and group sample to study how BHs affect their host systems. We focus on two specific properties, the halo gas fraction and the X-ray luminosity-temperature scaling relation, both of which are notoriously difficult to reproduce in self-consistent hydrodynamical simulations. We show that BH feedback can solve both of these issues, bringing them in excellent agreement with observations, without alluding to the `cooling only' solution that produces unphysically bright central galaxies. By comparing a large sample of simulated AGN-heated clusters with observations, our new simulation technique should make it possible to reliably calibrate observational biases in cluster surveys, thereby enabling various high-precision cosmological studies of the dark matter and dark energy content of the universe.Comment: 4 pages, 2 figures, minor revisions, ApJL in pres