Nuclear Black Hole Formation in Clumpy Galaxies at High Redshift

Massive stellar clumps in high redshift galaxies interact and migrate to the center to form a bulge and exponential disk in <1 Gyr. Here we consider the fate of intermediate mass black holes (BHs) that might form by massive-star coalescence in the dense young clusters of these disk clumps. We find that the BHs move inward with the clumps and reach the inner few hundred parsecs in only a few orbit times. There they could merge into a supermassive BH by dynamical friction. The ratio of BH mass to stellar mass in the disk clumps is approximately preserved in the final ratio of BH to bulge mass. Because this ratio for individual clusters has been estimated to be ~10^{-3}, the observed BH-to-bulge mass ratio results. We also obtain a relation between BH mass and bulge velocity dispersion that is compatible with observations of present-day galaxies.Comment: 10 pages, 3 figures, accepted by Ap

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Physical Processes in Star-Gas Systems

First we present a recently developed 3D chemodynamical code for galaxy evolution from the K**2 collaboration. It follows the evolution of all components of a galaxy such as dark matter, stars, molecular clouds and diffuse interstellar matter (ISM). Dark matter and stars are treated as collisionless N-body systems. The ISM is numerically described by a smoothed particle hydrodynamics (SPH) approach for the diffuse (hot) gas and a sticky particle scheme for the (cool) molecular clouds. Physical processs such as star formation, stellar death or condensation and evaporation processes of clouds interacting with the ISM are described locally. An example application of the model to a star forming dwarf galaxy will be shown for comparison with other codes. Secondly we will discuss new kinds of exotic chemodynamical processes, as they occur in dense gas-star systems in galactic nuclei, such as non-standard ``drag''-force interactions, destructive and gas producing stellar collisions. Their implementation in 1D dynamical models of galactic nuclei is presented. Future prospects to generalize these to 3D are work in progress and will be discussed.Comment: 4 pages, 4 figures, "The 5th Workshop on Galactic Chemodynamics" - Swinburne University (9-11 July 2003). To be published in the Publications of the Astronomical Society of Australia in 2004 (B.K. Gibson and D. Kawata, eds.). Accepted version, minor changes relative to origina

Recurrent neural networks and proper orthogonal decomposition with interval data for real-time predictions of mechanised tunnelling processes

A surrogate modelling strategy for predictions of interval settlement fields in real time during machine driven construction of tunnels, accounting for uncertain geotechnical parameters in terms of intervals, is presented in the paper. Artificial Neural Network and Proper Orthogonal Decomposition approaches are combined to approximate and predict tunnelling induced time variant surface settlement fields computed by a process-oriented finite element simulation model. The surrogate models are generated, trained and tested in the design (offline) stage of a tunnel project based on finite element analyses to compute the surface settlements for selected scenarios of the tunnelling process steering parameters taking uncertain geotechnical parameters by means of possible ranges (intervals) into account. The resulting mappings of time constant geotechnical interval parameters and time variant deterministic steering parameters onto the time variant interval settlement field are solved offline by optimisation and online by interval analyses approaches using the midpoint-radius representation of interval data. During the tunnel construction, the surrogate model is designed to be used in real-time to predict interval fields of the surface settlements in each stage of the advancement of the tunnel boring machine for selected realisations of the steering parameters to support the steering decisions of the machine driver

Rapid formation of exponential disks and bulges at high redshift from the dynamical evolution of clump cluster and chain galaxies

Many galaxies at high redshift have peculiar morphologies dominated by 10^8-10^9 Mo kpc-sized clumps. Using numerical simulations, we show that these "clump clusters" can result from fragmentation in gravitationally unstable primordial disks. They appear as "chain galaxies" when observed edge-on. In less than 1 Gyr, clump formation, migration, disruption, and interaction with the disk cause these systems to evolve from initially uniform disks into regular spiral galaxies with an exponential or double-exponential disk profile and a central bulge. The inner exponential is the initial disk size and the outer exponential is from material flung out by spiral arms and clump torques. A nuclear black hole may form at the same time as the bulge from smaller black holes that grow inside the dense cores of each clump. The properties and lifetimes of the clumps in our models are consistent with observations of the clumps in high redshift galaxies, and the stellar motions in our models are consistent with the observed velocity dispersions and lack of organized rotation in chain galaxies. We suggest that violently unstable disks are the first step in spiral galaxy formation. The associated starburst activity gives a short timescale for the initial stellar disk to form.Comment: ApJ Accepted, 13 pages, 9 figure

Merger of Black Holes in the Galactic Center

We present the results of three body simulations focused on understanding the fates of intermediate mass black holes (IBH) that drift within the central 0.5 pc of the Galaxy. In particular, we modeled the interactions between pairs of $4000 {\rm M}_{\odot}$ black holes as they orbit a central blac k hole of mass $4 \times 10^6 {\rm M}_{\odot}$. The simulations performed assume a Schwarzschild geometry and account for Chandrasekhar dynamical friction as well as acceleration resulting from energy lost due to gravitational radiation. We found the branching ratio for one of the orbiting IBHs to merge with the CBH was 0.95 and is independent of the inner IBH's initial eccentricity as well as the rate of sinking. This, coupled with an infall rate of $\sim 10^7$ yrs for an IBH to drift into the Galactic center, results in an IBH-CBH merger every $\lesssim 11$ Myrs. Lastly we found that the IBH-IBH-CBH triple body system ``resets'' itself, in the sense that a system with an inner I BH with an initially circular orbit generally left behind an IBH with a large eccentricity, whereas a system in which the inner IBH had a high eccentricity ($e_0 \sim 0.9$) usually left a remnant with low eccentricity. Branching ratios for different outcomes are also similar in the two cases.Comment: Official paper to appear in November 2008 issue of Ap