Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables $\rho$, the number density, and $B$, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.Comment: 48 pages, 3 figure

Field Theoretic Formulation of Kinetic theory: I. Basic Development

We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables \rho the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables \rho and B.Comment: 45 page

Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays

Supermassive black hole -- host galaxy relations are key to the computation of the expected gravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. It has been recently pointed out that standard relations adopted in GWB computations are in fact biased-high. We show that when this selection bias is taken into account, the expected GWB in the PTA band is a factor of about three smaller than previously estimated. Compared to other scaling relations recently published in the literature, the median amplitude of the signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to $4\times10^{-16}$. Although this solves any potential tension between theoretical predictions and recent PTA limits without invoking other dynamical effects (such as stalling, eccentricity or strong coupling with the galactic environment), it also makes the GWB detection more challenging.Comment: 6 pages 4 figures, submitted to MNRAS letter

A Statistical Semi-Empirical Model: Satellite galaxies in Groups and Clusters

We present STEEL a STatistical sEmi-Empirical modeL designed to probe the distribution of satellite galaxies in groups and clusters. Our fast statistical methodology relies on tracing the abundances of central and satellite haloes via their mass functions at all cosmic epochs with virtually no limitation on cosmic volume and mass resolution. From mean halo accretion histories and subhalo mass functions the satellite mass function is progressively built in time via abundance matching techniques constrained by number densities of centrals in the local Universe. By enforcing dynamical merging timescales as predicted by high-resolution N-body simulations, we obtain satellite distributions as a function of stellar mass and halo mass consistent with current data. We show that stellar stripping, star formation, and quenching play all a secondary role in setting the number densities of massive satellites above $M_*\gtrsim 3\times 10^{10}\, M_{\odot}$. We further show that observed star formation rates used in our empirical model over predict low-mass satellites below $M_*\lesssim 3\times 10^{10}\, M_{\odot}$, whereas, star formation rates derived from a continuity equation approach yield the correct abundances similar to previous results for centrals.Comment: 21 pages, 17 Figures. MNRAS, in pres

Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation

I show that the hamiltonian theory of Composite Fermions (CF) is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure

Galaxy size trends as a consequence of cosmology

We show that recently documented trends in galaxy sizes with mass and redshift can be understood in terms of the influence of underlying cosmic evolution; a holistic view which is complimentary to interpretations involving the accumulation of discreet evolutionary processes acting on individual objects. Using standard cosmology theory, supported with results from the Millennium simulations, we derive expected size trends for collapsed cosmic structures, emphasising the important distinction between these trends and the assembly paths of individual regions. We then argue that the observed variation in the stellar mass content of these structures can be understood to first order in terms of natural limitations of cooling and feedback. But whilst these relative masses vary by orders of magnitude, galaxy and host radii have been found to correlate linearly. We explain how these two aspects will lead to galaxy sizes that closely follow observed trends and their evolution, comparing directly with the COSMOS and SDSS surveys. Thus we conclude that the observed minimum radius for galaxies, the evolving trend in size as a function of mass for intermediate systems, and the observed increase in the sizes of massive galaxies, may all be considered an emergent consequence of the cosmic expansion.Comment: 14 pages, 13 figures. Accepted by MNRA

Super-massive Black Hole Demography: the Match between the Local and Accreted Mass Functions

We have performed a detailed analysis of the local super-massive black-hole (SMBH) mass function based on both kinematic and photometric data and derived an accurate analytical fit in the range 10^6 <= (M_BH/M_sun) <= 5*10^9. We find a total SMBH mass density of (4.2+/-1.1)*10^5 M_sun/Mpc^3, about 25% of which is contributed by SMBHs residing in bulges of late type galaxies. Exploiting up-to-date luminosity functions of hard X-ray and optically selected AGNs, we have studied the accretion history of the SMBH population. If most of the accretion happens at constant \dot{M_BH}/M_BH the local SMBH mass function is fully accounted for by mass accreted by X-ray selected AGNs, with bolometric corrections indicated by current observations and a standard mass-to-light conversion efficiency \epsilon ~10%. The analysis of the accretion history highlights that the most massive BHs accreted their mass faster and at higher redshifts (z>1.5), while the lower mass BHs responsible for most of the hard X-ray background have mostly grown at z<1.5. The accreted mass function matches the local SMBH mass function if \epsilon ~0.09(+0.04,-0.03) and the Eddington ratio \lambda=L/L_Edd \~0.3(+0.3,-0.1) (68% confidence errors). The visibility time, during which AGNs are luminous enough to be detected by the currently available X-ray surveys, ranges from ~0.1 Gyr for present day BH masses M_BH(z=0) ~10^6 M_sun to ~0.3 Gyr for M_BH(z=0) >= 10^9 M_sun. The mass accreted during luminous phases is >= 25-30% even if we assume extreme values of \epsilon (\epsilon \~0.3-0.4). An unlikely fine tuning of the parameters would be required to account for the local SMBH mass function accomodating a dominant contribution from 'dark' BH growth (due, e.g., to BH coalescence).Comment: 12 pages, 14 figures, accepted for publication in MNRAS, minor changes following referee's comment