Hydrostatic Gas Constraints On Supermassive Black Hole Masses: Implications For Hydrostatic Equilibrium And Dynamical Modeling In A Sample Of Early-Type Galaxies

We present new mass measurements for the supermassive black holes (SMBHs) in the centers of three early-type galaxies. The gas pressure in the surrounding, hot interstellar medium (ISM) is measured through spatially resolved spectroscopy with the Chandra X-ray Observatory, allowing the SMBH mass (M(BH)) to be inferred directly under the hydrostatic approximation. This technique does not require calibration against other SMBH measurement methods and its accuracy depends only on the ISM being close to hydrostatic, which is supported by the smooth X-ray isophotes of the galaxies. Combined with results from our recent study of the elliptical galaxy NGC4649, this brings the number of galaxies with SMBHs measured in this way to four. Of these, three already have mass determinations from the kinematics of either the stars or a central gas disk, and hence join only a handful of galaxies with MBH measured by more than one technique. We find good agreement between the different methods, providing support for the assumptions implicit in both the hydrostatic and the dynamical models. The stellar mass-to-light ratios for each galaxy inferred by our technique are in agreement with the predictions of stellar population synthesis models assuming a Kroupa initial mass function (IMF). This concurrence implies that no more than similar to 10%-20% of the ISM pressure is nonthermal, unless there is a conspiracy between the shape of the IMF and nonthermal pressure. Finally, we compute Bondi accretion rates (M(bondi)), finding that the two galaxies with the highest M(bondi) exhibit little evidence of X-ray cavities, suggesting that the correlation with the active galactic nuclei jet power takes time to be established.NASA NAS5-26555, NNG04GE76G, G07-8083XAstronom

The correlation between black hole mass and bulge velocity dispersion in hierarchical galaxy formation models

Recent work has demonstrated that there is a tight correlation between the mass of a black hole and the velocity dispersion of the bulge of its host galaxy. We show that the model of Kauffmann & Haehnelt, in which bulges and supermassive black holes both form during major mergers, produces a correlation between M_bh and sigma with slope and scatter comparable to the observed relation. In the model, the M_bh - sigma relation is significantly tighter than the correlation between black hole mass and bulge luminosity or the correlation between bulge luminosity and velocity dispersion. There are two reasons for this: i) the gas masses of bulge progenitors depend on the velocity dispersion but not on the formation epoch of the bulge, whereas the stellar masses of the progenitors depend on both; ii) mergers between galaxies move black holes along the observed M_bh - sigma relation, even at late times when the galaxies are gas-poor and black holes grow mainly by merging of pre-existing black holes. We conclude that the small scatter in the observed M_bh - sigma relation is consistent with a picture in which bulges and black holes form over a wide range in redshift.Comment: 5 pages, LaTeX, 3 postscript figures included; submitted to MNRA

The kernel Kalman rule: efficient nonparametric inference with recursive least squares

Nonparametric inference techniques provide promising tools for probabilistic reasoning in high-dimensional nonlinear systems. Most of these techniques embed distributions into reproducing kernel Hilbert spaces (RKHS) and rely on the kernel Bayes’ rule (KBR) to manipulate the embeddings. However, the computational demands of the KBR scale poorly with the number of samples and the KBR often suffers from numerical instabilities. In this paper, we present the kernel Kalman rule (KKR) as an alternative to the KBR. The derivation of the KKR is based on recursive least squares, inspired by the derivation of the Kalman innovation update. We apply the KKR to filtering tasks where we use RKHS embeddings to represent the belief state, resulting in the kernel Kalman filter (KKF). We show on a nonlinear state estimation task with high dimensional observations that our approach provides a significantly improved estimation accuracy while the computational demands are significantly decreased

Learning robust policies for object manipulation with robot swarms

Swarm robotics investigates how a large population of robots with simple actuation and limited sensors can collectively solve complex tasks. One particular interesting application with robot swarms is autonomous object assembly. Such tasks have been solved successfully with robot swarms that are controlled by a human operator using a light source. In this paper, we present a method to solve such assembly tasks autonomously based on policy search methods. We split the assembly process in two subtasks: generating a high-level assembly plan and learning a low-level object movement policy. The assembly policy plans the trajectories for each object and the object movement policy controls the trajectory execution. Learning the object movement policy is challenging as it depends on the complex state of the swarm which consists of an individual state for each agent. To approach this problem, we introduce a representation of the swarm which is based on Hilbert space embeddings of distributions. This representation is invariant to the number of agents in the swarm as well as to the allocation of an agent to its position in the swarm. These invariances make the learned policy robust to changes in the swarm and also reduce the search space for the policy search method significantly. We show that the resulting system is able to solve assembly tasks with varying object shapes in multiple simulation scenarios and evaluate the robustness of our representation to changes in the swarm size. Furthermore, we demonstrate that the policies learned in simulation are robust enough to be transferred to real robots

Assessment of a standard ULS design procedure for offshore wind turbine sub-structures

Sub-structures of offshore wind turbines are designed according to several design load cases (DLCs) that cover various fatigue (FLS) and ultimate limit states (ULS). The required DLCs are given in the current standards, and are supposed, on the one hand, to cover accurately all significant load conditions to guarantee reliability. On the other hand, they should include only necessary conditions to keep computing times manageable. For ULS conditions, the current work addresses the question whether the current design practice is, firstly, sufficient, and secondly, sensible concerning the computing time by only including necessary DLCs. To address this topic, data of five years of normal operation, simulated using a probabilistic approach, is used to extrapolate 20-year ULS loads (comparable to a probabilistic version of DLC 1.1 for substructures). These ULS values are compared to several deterministic DLCs required by current standards. Results show that probabilistic, extrapolated ULS values are fairly high and exceed standard DLC loads. Hence, the current design practice might not always be conservative. Especially, the benefit of an additional DLC for wave peak periods close to the eigenfrequency of the sub-structure is indicated

Robust learning of object assembly tasks with an invariant representation of robot swarms

— Swarm robotics investigates how a large population of robots with simple actuation and limited sensors can collectively solve complex tasks. One particular interesting application with robot swarms is autonomous object assembly. Such tasks have been solved successfully with robot swarms that are controlled by a human operator using a light source. In this paper, we present a method to solve such assembly tasks autonomously based on policy search methods. We split the assembly process in two subtasks: generating a high-level assembly plan and learning a low-level object movement policy. The assembly policy plans the trajectories for each object and the object movement policy controls the trajectory execution. Learning the object movement policy is challenging as it depends on the complex state of the swarm which consists of an individual state for each agent. To approach this problem, we introduce a representation of the swarm which is based on Hilbert space embeddings of distributions. This representation is invariant to the number of agents in the swarm as well as to the allocation of an agent to its position in the swarm. These invariances make the learned policy robust to changes in the swarm and also reduce the search space for the policy search method significantly. We show that the resulting system is able to solve assembly tasks with varying object shapes in multiple simulation scenarios and evaluate the robustness of our representation to changes in the swarm size. Furthermore, we demonstrate that the policies learned in simulation are robust enough to be transferred to real robots

A possible bias on the estimate of Lbol/Ledd in AGN as a function of luminosity and redshift

The BH mass (and the related Eddington ratio) in broad line AGN is usually evaluated by combining estimates (often indirect) of the BLR radius and of the FWHM of the broad lines, under the assumption that the BLR clouds are in Keplerian motion around the BH. Such an evaluation depends on the geometry of the BLR. There are two major options for the BLR configuration: spherically symmetric or ``flattened''. In the latter case the inclination to the line of sight becomes a relevant parameter. This paper is devoted to evaluate the bias on the estimate of the Eddington ratio when a spherical geometry is assumed (more generally when inclination effects are ignored), while the actual configuration is ``flattened'', as some evidence suggests. This is done as a function of luminosity and redshift, on the basis of recent results which show the existence of a correlation between the fraction of obscured AGN and these two parameters up to at least z=2.5. The assumed BLR velocity field is akin to the ``generalized thick disk'' proposed by Collin et al. (2006). Assuming an isotropic orientation in the sky, the mean value of the bias is calculated as a function of luminosity and redshift. It is demonstrated that, on average, the Eddington ratio obtained assuming a spherical geometry is underestimated for high luminosities, and overestimated for low luminosities. This bias converges for all luminosities at z about 2.7, while nothing can be said on this bias at larger redshifts due to the lack of data. The effects of the bias, averaged over the luminosity function of broad line AGN, have been calculated. The results imply that the bias associated with the a-sphericity of the BLR make even worse the discrepancy between the observations and the predictions of evolutionary models.Comment: 6 pages, 3 figures, accepted for publication in A&