Introduction to Library Trends 23 (3) Winter 1975: Music and Fine Arts in the General Library

published or submitted for publicatio

The influence of initial mass segregation on the runaway merging of stars

We have investigated the effect of initial mass segregation on the runaway merging of stars. The evolution of multi-mass, dense star clusters was followed by means of direct N-body simulations of up to 131.072 stars. All clusters started from King models with dimensionless central potentials of 3.0 <= W_0 <= 9.0. Initial mass segregation was realized by varying the minimum mass of a certain fraction of stars whose either (1) distances were closest to the cluster center or (2) total energies were lowest. The second case is more favorable to promote the runaway merging of stars by creating a high-mass core of massive, low-energy stars. Initial mass segregation could decrease the central relaxation time and thus help the formation of a high-mass core. However, we found that initial mass segregation does not help the runaway stellar merger to happen if the overall mass density profile is kept constant. This is due to the fact that the collision rate of stars is not increased due to initial mass segregation. Our simulations show that initial mass segregation is not sufficient to allow runaway merging of stars to occur in clusters with central densities typical for star clusters in the Milky Way.Comment: 25 pages, 9 figures, 3 tables, accepted for publication in Ap

Runaway collisions in young star clusters. II. Numerical results

We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, MBH > 100 Msun) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (Mstar =~ 30-120 Msun) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence (MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, ``sticky-sphere'' mergers or using realistic prescriptions derived from 3-D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (~3 Myr), we obtain the growth of a single very massive star (VMS, Mstar =~ 400-4000 Msun) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma1D ~ 1000 km/s, does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma1D > 300 km/s, collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to > 1000 Msun in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. [abridged]Comment: 23 pages, 24 figures. For publication in MNRAS. Paper revised to follow requests and suggestions of referee. Companion paper to Freitag, Rasio & Baumgardt 200

Initial Populations of Black Holes in Star Clusters

Using an updated population synthesis code we study the formation and evolution of black holes (BHs) in young star clusters following a massive starburst. This study continues and improves on the initial work described by Belczynski, Sadowski & Rasio (2004). In our new calculations we account for the possible ejections of BHs and their progenitors from clusters because of natal kicks imparted by supernovae and recoil following binary disruptions. The results indicate that the properties of both retained BHs in clusters and ejected BHs (forming a field population) depend sensitively on the depth of the cluster potential. In particular, most BHs ejected from binaries are also ejected from clusters with central escape speeds Vesc < 100 km/s. Conversely, most BHs remaining in binaries are retained by clusters with Vesc > 50 km/s. BHs from single star evolution are also affected significantly: about half of the BHs originating from primordial single stars are ejected from clusters with Vesc < 50 km/s. Our results lay a foundation for theoretical studies of the formation of BH X-ray binaries in and around star clusters, including possible ultra-luminous sources, as well as merging BH--BH binaries detectable with future gravitational-wave observatories.Comment: 35 pages, 8 tables, 17 figures; resubmitted to ApJ (revised version

Role of Single Defects in Electronic Transport through Carbon Nanotube Field-Effect Transistors

The influence of defects on electron transport in single-wall carbon nanotube field effect transistors (CNFETs) is probed by combined scanning gate microscopy (SGM) and scanning impedance microscopy (SIM). SGM reveals a localized field effect at discrete defects along the CNFET length. The depletion surface potential of individual defects is quantified from the SGM-imaged radius of the defect as a function of tip bias voltage. This provides a measure of the Fermi level at the defect with zero tip voltage, which is as small as 20 meV for the strongest defects. The effect of defects on transport is probed by SIM as a function of backgate and tip-gate voltage. When the backgate voltage is set so the CNFET is "on" (conducting), SIM reveals a uniform potential drop along its length, consistent with diffusive transport. In contrast, when the CNFET is "off", potential steps develop at the position of depleted defects. Finally, high-resolution imaging of a second set of weak defects is achieved in a new "tip-gated" SIM mode.Comment: to appear in Physical Review Letter

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