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

Post-Glitch RXTE-PCA Observations of the Vela Pulsar

We report the results of analysis of observations of the Vela Pulsar by PCA on RXTE. Our data consists of two parts. The first part contains observations at 1, 4, and 9 days after the glitch in 1996 and has 27000 sec. total exposure time. The second part of observations were performed three months after this glitch and have a total exposure time of 93000 sec. We found pulsations in both sets. The observed spectrum is a power-law with no apparent change in flux or count rate. The theoretical expectations of increase in flux due to internal heating after a glitch are smaller than the uncertainty of the observations.Comment: 6 pages, 5 figures in 9 ps/eps files. Accepted for publication in A&A Main Journa

The present day mass function in the central region of the Arches cluster

We study the evolution of the mass function in young and dense star clusters by means of direct N-body simulations. Our main aim is to explain the recent observations of the relatively flat mass function observed near the centre of the Arches star cluster. In this region, the power law index of the mass function for stars more massive than about 5-6 solar mass, is larger than the Salpeter value by about unity; whereas further out, and for the lower mass stars, the mass function resembles the Salpeter distribution. We show that the peculiarities in the Arches mass function can be explained satisfactorily without primordial mass segregation. We draw two conclusions from our simulations: 1) The Arches initial mass function is consistent with a Salpeter slope down to ~1 solar mass, 2) The cluster is about half way towards core collapse. The cores of other star clusters with characteristics similar to those of the Arches are expected to show similar flattening in the mass functions for the high mass (>5 solar mass) stars.Comment: 6 pages with 6 figures and 1 table. Submitted to the letters section of MNRAS. Incorporates changes following suggestions by the refere

An approach to represent time series forecasting via fuzzy numbers

This paper introduces a new approach for estimating the uncertainty in the forecast through the construction of Triangular Fuzzy Numbers (TFNs). The interval of the proposed TFN presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE). Here, instead of the representing the forecast with a crisp value with a Prediction Interval (PI), the level of uncertainty associated with the point forecasts will be quantified by defining TFNs (linguistic terms) within the uncertainty interval provided by the FLUBE. This will give the opportunity to handle the forecast as linguistic terms which will increase the interpretability. Moreover, the proposed approach will provide valuable information about the accuracy of the forecast by providing a relative membership degree. The demonstrated results indicate that the proposed FLUBE based TFN representation is an efficient and useful approach to represent the uncertainty and the quality of the forecast

An enhanced fuzzy linguistic term generation and representation for time series forecasting

This paper introduces an enhancement to linguistic forecast representation using Triangular Fuzzy Numbers (TFNs) called Enhanced Linguistic Generation and Representation Approach (ElinGRA). Since there is always an error margin in the predictions, there is a need to define error bounds in the forecast. The interval of the proposed presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE) by getting the models of forecast errors. Thus, instead of a classical statistical approaches, the level of uncertainty associated with the point forecasts will be defined within the FLUBE bounds and these bound can be used for defining fuzzy linguistic terms for the forecasts. Here, ElinGRA is proposed to generate triangular fuzzy numbers (TFNs) for the predictions. In addition to opportunity to handle the forecast as linguistic terms which will increase the interpretability, ElinGRA improved forecast accuracy of constructed TFNs by adding an extra correction term. The results of the experiments, which are conducted on two data sets, show the benefit of using ElinGRA to represent the uncertainty and the quality of the forecast

Progressive Arm Cycling Ergometry With 3- And 5-Minute Stage Durations Yields Similar Estimates of Substrate Oxidation in Healthy Adults

International Journal of Exercise Science 17(2): 468-479, 2024. Arm cycling ergometry (ACE) leads to a lower maximal oxygen uptake (VO2max) than cycling which is related to a smaller active muscle mass. This study compared estimates of fat and carbohydrate oxidation (FOx and CHOOx) between progressive exercise protocols varying in stage duration in an attempt to create a standard exercise protocol for determining substrate metabolism using ACE. Four men and seven women (age = 24 ± 9 yr) unfamiliar with ACE completed incremental exercise to determine peak power output and VO2peak. During two subsequent sessions completed after an overnight fast, they completed progressive ACE using 3- or 5-min stages during which FOx, CHOOx, and blood lactate concentration (BLa) were measured. Results showed no difference (p \u3e 0.05) in FOx, CHOOx, or BLa across stage duration, and there was no difference in maximal fat oxidation (0.16 ± 0.08 vs. 0.13 ± 0.07 g/min, p = 0.07). However, respiratory exchange ratio in response to the 3 min stage duration was significantly lower than the 5 min duration (0.83 ± 0.05 vs. 0.86 ± 0.03, p = 0.04, Cohen’s d = 0.76). Results suggest that a 3 min stage duration is preferred to assess substrate metabolism during upper-body exercise in healthy adults