Extreme mass ratio inspiral rates: dependence on the massive black hole mass

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.Comment: Accepted to CQG, special LISA issu

Different charging strategies for electric vehicle fleets in urban freight transport.

The transition from diesel-driven urban freight transport towards more electric urban freight transport turns out to be challenging in practice. A major concern for transport operators is how to find a reliable charging strategy for a larger electric vehicle fleet that provides flexibility based on different daily mission profiles within that fleet, while also minimizing costs. This contribution assesses the trade-off between a large battery pack and opportunity charging with regard to costs and operational constraints. Based on a case study with 39 electric freight vehicles that have been used by a parcel delivery company and a courier company in daily operations for over a year, various scenarios have been analyzed by means of a TCO analysis. Although a large battery allows for more flexibility in planning, opportunity charging can provide a feasible alternative, especially in the case of varying mission profiles. Additional personnel costs during opportunity charging can be avoided as much as possible by a well-integrated charging strategy, which can be realized by a reservation system that minimizes the risk of occupied charging stations and a dense network of charging stations

The influence of preparation methodology on high voltage behaviour of alumina insulators in vacuum

The flashover characteristics of an insulator bridged high voltage vacuum gap can play an important role in the overall performance of a high voltage device, for example in the extreme environments of high energy particle accelerators. The detailed preparation of the insulators is, at present, governed by the commercial production methods and by standard bulk cleaning processes, which for a particular application may be far from optimum. The influence of particular cleaning technique have been investigated for commercially available alumina samples, with measurement of surface characteristics by scanning electron microscopy and laser diffraction and fields up to 200 kV/cm. The results of the different measurements are discussed in the overall context of the problems encountered in the full sized high voltage devices, and suggestions are made as to how the performance of alumina insulators could be improved by modification of the production and preparation specification

Dynamical evolution of the young stars in the Galactic center: N-body simulations of the S-stars

We use N-body simulations to study the evolution of the orbital eccentricities of stars deposited near (<0.05 pc) the Milky Way massive black hole (MBH), starting from initial conditions motivated by two competing models for their origin: formation in a disk followed by inward migration; and exchange interactions involving a binary star. The first model predicts modest eccentricities, lower than those observed in the S-star cluster, while the second model predicts higher eccentricities than observed. The N-body simulations include a dense cluster of 10 M_sun stellar black holes (SBHs), expected to accumulate near the MBH by mass segregation. Perturbations from the SBHs tend to randomize the stellar orbits, partially erasing the dynamical signatures of their origin. The eccentricities of the initially highly eccentric stars evolve, in 20 Myr (the S-star lifespan), to a distribution that is consistent at the ~95 % level with the observed eccentricity distribution. In contrast, the eccentricities of the initially more circular orbits fail to evolve to the observed values in 20 Myr, arguing against the disk migration scenario. We find that 20 % - 30 % of the S-stars are tidally disrupted by the MBH over their lifetimes, and that the S-stars are not likely to be ejected as hypervelocity stars outside the central 0.05 pc by close encounters with stellar black holes.Comment: 6 pages, 2 figures. Minor corrections, Sumitted to Ap

Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica

The environment near super massive black holes (SMBHs) in galactic nuclei contain a large number of stars and compact objects. A fraction of these are likely to be members of binaries. Here we discuss the binary population of stellar black holes and neutron stars near SMBHs and focus on the secular evolution of such binaries, due to the perturbation by the SMBH. Binaries with highly inclined orbits in respect to their orbit around the SMBH are strongly affected by secular Kozai processes, which periodically change their eccentricities and inclinations (Kozai-cycles). During periapsis approach, at the highest eccentricities during the Kozai-cycles, gravitational wave emission becomes highly efficient. Some binaries in this environment can inspiral and coalesce at timescales much shorter than a Hubble time and much shorter than similar binaries which do not reside near a SMBH. The close environment of SMBHs could therefore serve as catalyst for the inspiral and coalescence of binaries, and strongly affect their orbital properties. Such compact binaries would be detectable as gravitational wave (GW) sources by the next generation of GW detectors (e.g. advanced- LIGO). About 0.5% of such nuclear merging binaries will enter the LIGO observational window while on orbit that are still very eccentric (e>~0.5). The efficient gravitational wave analysis for such systems would therefore require the use of eccentric templates. We also find that binaries very close to the MBH could evolve through a complex dynamical (non-secular) evolution leading to emission of several GW pulses during only a few yrs (though these are likely to be rare). Finally, we note that the formation of close stellar binaries, X-ray binaries and their merger products could be induced by similar secular processes, combined with tidal friction rather than GW emission as in the case of compact object binaries.Comment: 15 pages, 7 Figures. ApJ accepte

Dynamical constraints on the origin of the young B-stars in the Galactic center

Regular star formation is thought to be inhibited close to the massive black hole (MBH) in the Galactic center. Nevertheless, tens of young main sequence B stars have been observed in an isotropic distribution close to it. Various models have been suggested for the formation of the B-stars closest to the MBH (<0.05 pc; the S-stars), typically involving the migration of these stars from their original birthplace to their currently observed position. Here we explore the orbital phase space distribution of the B-stars throughout the central pc expected from the various suggested models for the origin of the B-stars. We find that most of these models have difficulties in explaining, by themselves, both the population of the S-stars (<0.05 pc), and the population of the young B-stars further away (up to 0.5 pc). Most models grossly over-predict the number of B-stars up to 0.5 pc, given the observed number of S-stars. Such models include the intermediate-mass black hole assisted cluster inspiral scenario, Kozai-like perturbations by two disks, spiral density waves migration in a gaseous disk, and some of the eccentric disk instability models. We focus on one of the other models, the massive perturber induced binary disruption, which is consistent with both the S-stars and the extended population of B-stars further away. For this model we use analytical arguments and N-body simulations to provide further observational predictions. These could be compared with future observations to further support this model, constrain it or refute it. These predictions include the radial distribution of the young B-stars, their eccentricity distribution and its dependence on distance from the MBH (higher eccentricities at larger distances from the MBH), as well as less specific expectations regarding their mass function.Comment: Comments are welcome

Additional Support for Simple Imputation of Missing Quality of Life Data in Nursing Research

Background. Missing data are a significant problem in health-related quality of life (HRQOL) research. We evaluated two imputation approaches: missing data estimation (MDE) and assignment of mean score (AMS). Methods. HRQOL data were collected using the Medical Outcomes Trust SF-12. Missing data were estimated using both approaches, summary statistics were produced for both, and results were compared using intraclass correlations (ICC). Results. Missing data were imputed for 21 participants. Mean values were similar, with ICC >.99 within both the Physical Component Summary and the Mental Component Summary when comparing the two methodologies. When imputed data were added into the full study sample, mean scores were identical regardless of methodology. Conclusion. Results support the use of a practical and simple imputation strategy of replacing missing values with the mean of the sample in cross-sectional studies when less than half of the required items of the SF-12 components are missing

The S-Star Cluster at the Center of the Milky Way: On the nature of diffuse NIR emission in the inner tenth of a parsec

Sagittarius A*, the super-massive black hole at the center of the Milky Way, is surrounded by a small cluster of high velocity stars, known as the S-stars. We aim to constrain the amount and nature of stellar and dark mass associated with the cluster in the immediate vicinity of Sagittarius A*. We use near-infrared imaging to determine the $K_\mathrm{s}$-band luminosity function of the S-star cluster members, and the distribution of the diffuse background emission and the stellar number density counts around the central black hole. This allows us to determine the stellar light and mass contribution expected from the faint members of the cluster. We then use post-Newtonian N-body techniques to investigate the effect of stellar perturbations on the motion of S2, as a means of detecting the number and masses of the perturbers. We find that the stellar mass derived from the $K_\mathrm{s}$-band luminosity extrapolation is much smaller than the amount of mass that might be present considering the uncertainties in the orbital motion of the star S2. Also the amount of light from the fainter S-cluster members is below the amount of residual light at the position of the S-star cluster after removing the bright cluster members. If the distribution of stars and stellar remnants is strongly enough peaked near Sagittarius A*, observed changes in the orbital elements of S2 can be used to constrain both their masses and numbers. Based on simulations of the cluster of high velocity stars we find that at a wavelength of 2.2 $\mu$m close to the confusion level for 8 m class telescopes blend stars will occur (preferentially near the position of Sagittarius A*) that last for typically 3 years before they dissolve due to proper motions.Comment: 14 pages, 11 figures, minor changes to match the published version in Astronomy & Astrophysic