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

Elevation in blood flow and shear rate prevents hyperglycemia-induced endothelial dysfunction in healthy subjects and those with type 2 diabetes

Hyperglycemia, commonly present after a meal, causes transient impairment in endothelial function. We examined whether increases in blood flow (BF) protect against the hyperglycemia- mediated decrease in endothelial function in healthy subjects and patients with type 2 diabetes mellitus (T2DM). Ten healthy subjects and 10 age- and sex-matched T2DM patients underwent simultaneous bilateral assessment of brachial artery endothelial function by means of flow- mediated dilation (FMD), using high-resolution echo-Doppler. FMD was examined before and 60, 120 and 150 minutes after a 75-gr oral glucose challenge. We unilaterally manipulated BF by heating one arm between minute 30 and 60. Oral glucose administration caused a statistically significant, transient increase in blood glucose in both groups (P<0.001). Forearm skin temperature, brachial artery BF and shear rate significantly increased in the heated arm (P<0.001), and to a greater extent compared to the non-heated arm in both groups (interaction- effect, P<0.001). The glucose load caused a transient decrease in FMD% (P<0.05), whilst heating significantly prevented the decline (interaction-effect: P<0.01). Also when correcting for changes in diameter and shear rate, we found that the hyperglycemia-induced decrease in FMD can be prevented by local heating (P<0.05). These effects on FMD were observed in both groups. Our data indicate that non-metabolically driven elevation in BF and shear rate can similarly prevent the hyperglycemia-induced decline in conduit artery endothelial function in healthy volunteers and in patients with type 2 diabetes. Additional research is warranted to confirm that other interventions increasing BF and shear rate equally protect the endothelium when challenged by hyperglycemia

PHYSICAL ACTIVITY AND COGNITIVE FUNCTION OF LONG DISTANCE WALKERS: STUDYING FOUR DAYS MARCHES PARTICIPANTS.

OBJECTIVE: Studies show physical activity to be beneficial for cognitive function. However, studies usually included individuals who were not particularly inclined to exercise. Following research among master athletes, we examined associations between physical activity and cognitive function in participants of the International Nijmegen Four Days Marches. These individuals are also inclined to exercise. On 4 consecutive days > 40,000 participants walk a daily distance of 30-50 km (120-200 km or 75-125 miles in total). METHOD: Four Days Marches participants and less active or inactive control participants from the Nijmegen Exercise Study were examined. Self-reported current and lifelong physical activities were quantified in Metabolic Equivalent of Task minutes/day and training walking speed was estimated in km/h. Cognitive functioning in the domains of working memory, executive function, and visuospatial short-term memory was assessed using the validated Brain Aging Monitor. RESULTS: Data from 521 participants (mean age 54.7, standard deviation 12.9) showed neither positive associations between lifelong physical activity and working memory, executive function, and visuospatial short-term memory nor positive associations between current physical activity and cognitive functioning in these domains (P-values > 0.05). However, a positive association between training walking speed and working memory was revealed (age adjusted Beta = 0.18, P-value < 0.01). CONCLUSION: Walking speed, as a surrogate marker of fitness, but not lifelong and current physical activity levels were associated with cognitive function. Therefore, walking speed deserves more attention in research aimed at unravelling associations between physical activity and cognitive function

High angular resolution integral-field spectroscopy of the Galaxy's nuclear cluster: a missing stellar cusp?

We report on the structure of the nuclear star cluster in the innermost 0.16 pc of the Galaxy as measured by the number density profile of late-type giants. Using laser guide star adaptive optics in conjunction with the integral field spectrograph, OSIRIS, at the Keck II telescope, we are able to differentiate between the older, late-type ($\sim$ 1 Gyr) stars, which are presumed to be dynamically relaxed, and the unrelaxed young ($\sim$ 6 Myr) population. This distinction is crucial for testing models of stellar cusp formation in the vicinity of a black hole, as the models assume that the cusp stars are in dynamical equilibrium in the black hole potential. Based on the late-type stars alone, the surface stellar number density profile, $\Sigma(R) \propto R^{-\Gamma}$, is flat, with $\Gamma = -0.27\pm0.19$. Monte Carlo simulations of the possible de-projected volume density profile, n(r) $\propto r^{-\gamma}$, show that $\gamma$ is less than 1.0 at the 99.73 % confidence level. These results are consistent with the nuclear star cluster having no cusp, with a core profile that is significantly flatter than predicted by most cusp formation theories, and even allows for the presence of a central hole in the stellar distribution. Of the possible dynamical interactions that can lead to the depletion of the red giants observable in this survey -- stellar collisions, mass segregation from stellar remnants, or a recent merger event -- mass segregation is the only one that can be ruled out as the dominant depletion mechanism. The lack of a stellar cusp around a supermassive black hole would have important implications for black hole growth models and inferences on the presence of a black hole based upon stellar distributions.Comment: 35 pages, 5 tables, 12 figures, accepted by Ap

A symmetry-preserving second-order time-accurate PISO-based method

A new conservative symmetry-preserving second-order time-accurate PISO-based pressure-velocity coupling for solving the incompressible Navier-Stokes equations on unstructured collocated grids is presented in this paper. This new method for implicit time stepping is an extension of the conservative symmetry-preserving incremental-pressure projection method for explicit time stepping and unstructured collocated meshes of Trias et al. [35]. In order to assess and compare both methods, we have implemented them within one unified solver in the open source code OpenFOAM where we use a Butcher array to prescribe the Runge-Kutta method. Thus, by changing the entries of the Butcher array, explicit and diagonally implicit Runge-Kutta schemes can be combined into one solver. We assess the energy conservation properties of the implemented discretisation methods and the temporal consistency of the selected Runge-Kutta schemes using Taylor-Green vortex and lid-driven cavity flow test cases. Finally, we use a more complex turbulent channel flow test case in order to further assess the performance of the presented new conservative symmetry-preserving incremental-pressure PISO-based method. Although both implemented methods are based on a symmetry-preserving discretisation, we show they still produce a small amount of numerical dissipation when the total pressure is directly solved from a Poisson equation. When an incremental-pressure approach is used, where a pressure correction is solved from a Poisson equation, both methods are effectively fully-conservative. For high-fidelity simulations of incompressible turbulent flows, it is highly desirable to use fully-conservative methods. For such simulations, the presented numerical methods are therefore expected to have large added value, since they pave the way for the execution of truly energy-conservative high-fidelity simulations in complex geometries. Furthermore, both methods are implemented in OpenFOAM, which is widely used within the CFD community, so that a large part of this community can benefit from the developed and implemented numerical methods

Rates and Characteristics of Intermediate Mass Ratio Inspirals Detectable by Advanced LIGO

Gravitational waves (GWs) from the inspiral of a neutron star (NS) or stellar-mass black hole (BH) into an intermediate-mass black hole (IMBH) with mass between ~50 and ~350 solar masses may be detectable by the planned advanced generation of ground-based GW interferometers. Such intermediate mass ratio inspirals (IMRIs) are most likely to be found in globular clusters. We analyze four possible IMRI formation mechanisms: (1) hardening of an NS-IMBH or BH-IMBH binary via three-body interactions, (2) hardening via Kozai resonance in a hierarchical triple system, (3) direct capture, and (4) inspiral of a compact object from a tidally captured main-sequence star; we also discuss tidal effects when the inspiraling object is an NS. For each mechanism we predict the typical eccentricities of the resulting IMRIs. We find that IMRIs will have largely circularized by the time they enter the sensitivity band of ground-based detectors. Hardening of a binary via three-body interactions, which is likely to be the dominant mechanism for IMRI formation, yields eccentricities under 10^-4 when the GW frequency reaches 10 Hz. Even among IMRIs formed via direct captures, which can have the highest eccentricities, around 90% will circularize to eccentricities under 0.1 before the GW frequency reaches 10 Hz. We estimate the rate of IMRI coalescences in globular clusters and the sensitivity of a network of three Advanced LIGO detectors to the resulting GWs. We show that this detector network may see up to tens of IMRIs per year, although rates of one to a few per year may be more plausible. We also estimate the loss in signal-to-noise ratio that will result from using circular IMRI templates for data analysis and find that, for the eccentricities we expect, this loss is negligible.Comment: Accepted for publication in ApJ; revised version reflects changes made to the article during the acceptance proces

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

Extreme Mass Ratio Inspirals: LISA's unique probe of black hole gravity

In this review article I attempt to summarise past and present-ongoing-work on the problem of the inspiral of a small body in the gravitational field of a much more massive Kerr black hole. Such extreme mass ratio systems, expected to occur in galactic nuclei, will constitute prime sources of gravitational radiation for the future LISA gravitational radiation detector. The article's main goal is to provide a survey of basic celestial mechanics in Kerr spacetime and calculations of gravitational waveforms and backreaction on the small body's orbital motion, based on the traditional `flux-balance' method and the Teukolsky black hole perturbation formalism.Comment: Invited review article, 45 pages, 23 figure

Compact Binary Coalescences in the Band of Ground-based Gravitational-Wave Detectors

As the ground-based gravitational-wave telescopes LIGO, Virgo, and GEO 600 approach the era of first detections, we review the current knowledge of the coalescence rates and the mass and spin distributions of merging neutron-star and black-hole binaries. We emphasize the bi-directional connection between gravitational-wave astronomy and conventional astrophysics. Astrophysical input will make possible informed decisions about optimal detector configurations and search techniques. Meanwhile, rate upper limits, detected merger rates, and the distribution of masses and spins measured by gravitational-wave searches will constrain astrophysical parameters through comparisons with astrophysical models. Future developments necessary to the success of gravitational-wave astronomy are discussed.Comment: Replaced with version accepted by CQG