Effect of the W-term for a t-U-W Hubbard ladder

Antiferromagnetic and d_{x2-y2}-pairing correlations appear delicately balanced in the 2D Hubbard model. Whether doping can tip the balance to pairing is unclear and models with additional interaction terms have been studied. In one of these, the square of a local hopping kinetic energy H_W was found to favor pairing. However, such a term can be separated into a number of simpler processes and one would like to know which of these terms are responsible for enhancing the pairing. Here we analyze these processes for a 2-leg Hubbard ladder

The COBE Normalization for Standard CDM

The COBE detection of CMB anisotropies provides the best way of fixing the amplitude of fluctuations on the largest scales. This normalization is usually given for an n=1 spectrum, including only the anisotropy caused by the Sachs- Wolfe effect. This is certainly not a good approximation for a model containing any reasonable amount of baryonic matter. In fact, even tilted S-W spectra are not a good fit to models like CDM. Here we normalize standard CDM (sCDM) to the 2-year COBE data, and quote the best amplitude in terms of the conventionally used measures of power. We also give normalizations for some specific variants of this standard model, and we indicate how the normalization depends on the assumed values of n, Omega_B and H_0. For sCDM we find =19.9\pm1.5uK, corresponding to sigma_8=1.34\pm0.10, with the normalization at large scales being B=(8.16\pm1.04)\times10^5 (Mpc/h)^4, and other numbers given in the Table. The measured rms temperature fluctuation smoothed on 10deg is a little low relative to this normalization. This is mainly due to the low quadrupole in the data: when the quadrupole is removed, the measured value of sigma(10) is quite consistent with the best-fitting . The use of should be preferred over sigma(10), when its value can be determined for a particular theory, since it makes full use of the data.Comment: 4 pages compressed uuencoded postscript. We have corrected an error in our analysi

Resolving the virial discrepancy in clusters of galaxies with modified Newtonian dynamics

A sample of 197 X-ray emitting clusters of galaxies is considered in the context of Milgrom's modified Newtonian dynamics (MOND). It is shown that the gas mass, extrapolated via an assumed $\beta$ model to a fixed radius of 3 Mpc, is correlated with the gas temperature as predicted by MOND ($M_g \propto T^2$). The observed temperatures are generally consistent with the inferred mass of hot gas; no substantial quantity of additional unseen matter is required in the context of MOND. However, modified dynamics cannot resolve the strong lensing discrepancy in those clusters where this phenomenon occurs. The prediction is that additional baryonic matter may be detected in the central regions of rich clusters.Comment: Submitted to A&A, 4 pages, 3 figures, A&A macro

Is Cosmology Solved?

We have fossil evidence from the thermal background radiation that our universe expanded from a considerably hotter denser state. We have a well defined and testable description of the expansion, the relativistic Friedmann-Lemaitre model. Its observational successes are impressive but I think hardly enough for a convincing scientific case. The lists of observational constraints and free hypotheses within the model have similar lengths. The scorecard on the search for concordant measures of the mass density parameter and the cosmological constant shows that the high density Einstein-de Sitter model is challenged, but that we cannot choose between low density models with and without a cosmological constant. That is, the relativistic model is not strongly overconstrained, the usual test of a mature theory. Work in progress will greatly improve the situation and may at last yield a compelling test. If so, and the relativistic model survives, it will close one line of research in cosmology: we will know the outlines of what happened as our universe expanded and cooled from high density. It will not end research: some of us will occupy ourselves with the details of how galaxies and other large-scale structures came to be the way they are, others with the issue of what our universe was doing before it was expanding. The former is being driven by rapid observational advances. The latter is being driven mainly by theory, but there are hints of observational guidance.Comment: 13 pages, 3 figures. To be published in PASP as part of the proceedings of the Smithsonian debate, Is Cosmology Solved

Satellite Galaxies and Fossil Groups in the Millennium Simulation

We use a semianalytic galaxy catalogue constructed from the Millennium Simulation to study the satellites of isolated galaxies in the LCDM cosmogony. This sample (~80,000$ bright primaries, surrounded by ~178,000 satellites) allows the characterization, with minimal statistical uncertainty, of the dynamical properties of satellite/primary galaxy systems in a LCDM universe. We find that, overall, the satellite population traces the dark matter rather well: its spatial distribution and kinematics may be approximated by an NFW profile with a mildly anisotropic velocity distribution. Their spatial distribution is also mildly anisotropic, with a well-defined ``anti-Holmberg'' effect that reflects the misalignment between the major axis and angular momentum of the host halo. The isolation criteria for our primaries picks not only galaxies in sparse environments, but also a number of primaries at the centre of ''fossil'' groups. We find that the abundance and luminosity function of these unusual systems are in reasonable agreement with the few available observational constraints. We recover the expected L_{host} \sigma_{sat}^3 relation for LCDM models for truly-isolated primaries. Less strict primary selection, however, leads to substantial modification of the scaling relation. Our analysis also highlights a number of difficulties afflicting studies that rely on blind stacking of satellite systems to constrain the mean halo mass of the primary galaxies.Comment: 18 pages, 14 figures, MNRAS in press. Accepted version with minor changes. Version with high resolution figures available at: http://www.astro.uvic.ca/~lsales/SatPapers/SatPapers.htm

Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation

The abundance of clusters at the present epoch and weak gravitational lensing shear both constrain roughly the same combination of the power spectrum normalization sigma_8 and matter energy density Omega_M. The cluster constraint further depends on the normalization of the mass-temperature relation. Therefore, combining the weak lensing and cluster abundance data can be used to accurately calibrate the mass-temperature relation. We discuss this approach and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in the analysis move the cluster contours in Fig1 slightly upwards. No changes in the conclusion

The formation of ion acoustic shocks

Recent experiments performed in the double plasma (DP) device have verified the existence of electrostatic ion acoustic laminar shocks. The influence of the piston on the shock structure is investigated by modeling the DP device and by numerically solving the temporal and spatial evolution of the shock. In order to isolate piston effects, as opposed to kinetic theory effects such as reflected ions and trapped electrons, the DP plasma is modeled as a cold ion fluid with isothermal Boltzmann electrons. It is shown that laminar shock transitions with structure agreeing with DP shock experiments can be excited

The Growth in Size and Mass of Cluster Galaxies since z=2

We study the formation and evolution of Brightest Cluster Galaxies starting from a $z=2$ population of quiescent ellipticals and following them to $z=0$. To this end, we use a suite of nine high-resolution dark matter-only simulations of galaxy clusters in a $\Lambda$CDM universe. We develop a scheme in which simulation particles are weighted to generate realistic and dynamically stable stellar density profiles at $z=2$. Our initial conditions assign a stellar mass to every identified dark halo as expected from abundance matching; assuming there exists a one-to-one relation between the visible properties of galaxies and their host haloes. We set the sizes of the luminous components according to the observed relations for $z\sim2$ massive quiescent galaxies. We study the evolution of the mass-size relation, the fate of satellite galaxies and the mass aggregation of the cluster central. From $z=2$, these galaxies grow on average in size by a factor 5 to 10 of and in mass by 2 to 3. The stellar mass growth rate of the simulated BCGs in our sample is of 1.9 in the range $0.3<z<1.0$ consistent with observations, and of 1.5 in the range $0.0<z<0.3$. Furthermore the satellite galaxies evolve to the present day mass-size relation by $z=0$. Assuming passively evolving stellar populations, we present surface brightness profiles for our cluster centrals which resemble those observed for the cDs in similar mass clusters both at $z=0$ and at $z=1$. This demonstrates that the $\Lambda$CDM cosmology does indeed predict minor and major mergers to occur in galaxy clusters with the frequency and mass ratio distribution required to explain the observed growth in size of passive galaxies since $z=2$. Our experiment shows that Brightest Cluster Galaxies can form through dissipationless mergers of quiescent massive $z=2$ galaxies, without substantial additional star formation.Comment: submitted to MNRAS, 10 pages, 8 figures, 2 table