Assisted Inspirals of Stellar Mass Black Holes Embedded in AGN Disks: Solving the "Final AU Problem"

We explore the evolution of stellar mass black hole binaries (BHBs) which are formed in the self-gravitating disks of active galactic nuclei (AGN). Hardening due to three-body scattering and gaseous drag are effective mechanisms that reduce the semi-major axis of a BHB to radii where gravitational waves take over, on timescales shorter than the typical lifetime of the AGN disk. Taking observationally-motivated assumptions for the rate of star formation in AGN disks, we find a rate of disk-induced BHB mergers ($\mathcal{R} \sim 3~{\rm yr}^{-1}~{\rm Gpc}^{-3}$, but with large uncertainties) that is comparable with existing estimates of the field rate of BHB mergers, and the approximate BHB merger rate implied by the recent Advanced LIGO detection of GW150914. BHBs formed thorough this channel will frequently be associated with luminous AGN, which are relatively rare within the sky error regions of future gravitational wave detector arrays. This channel could also possess a (potentially transient) electromagnetic counterpart due to super-Eddington accretion onto the stellar mass black hole following the merger.Comment: 10 pages, 3 figures, changes made to match MNRAS published versio

A Latent Parameter Node-Centric Model for Spatial Networks

Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological interactions between users, but spatial interactions as well. The defining property of spatial networks is that edge distances are associated with a cost, which may subtly influence the topology of the network. However, the cost function over distance is rarely known, thus developing a model of connections in spatial networks is a difficult task. In this paper, we introduce a novel model for capturing the interaction between spatial effects and network structure. Our approach represents a unique combination of ideas from latent variable statistical models and spatial network modeling. In contrast to previous work, we view the ability to form long/short-distance connections to be dependent on the individual nodes involved. For example, a node's specific surroundings (e.g. network structure and node density) may make it more likely to form a long distance link than other nodes with the same degree. To capture this information, we attach a latent variable to each node which represents a node's spatial reach. These variables are inferred from the network structure using a Markov Chain Monte Carlo algorithm. We experimentally evaluate our proposed model on 4 different types of real-world spatial networks (e.g. transportation, biological, infrastructure, and social). We apply our model to the task of link prediction and achieve up to a 35% improvement over previous approaches in terms of the area under the ROC curve. Additionally, we show that our model is particularly helpful for predicting links between nodes with low degrees. In these cases, we see much larger improvements over previous models

Circumnuclear Media of Quiescent Supermassive Black Holes

We calculate steady-state, one-dimensional hydrodynamic profiles of hot gas in slowly accreting ("quiescent") galactic nuclei for a range of central black hole masses $M_{\bullet}$, parametrized gas heating rates, and observationally-motivated stellar density profiles. Mass is supplied to the circumnuclear medium by stellar winds, while energy is injected primarily by stellar winds, supernovae, and black hole feedback. Analytic estimates are derived for the stagnation radius (where the radial velocity of the gas passes through zero) and the large scale gas inflow rate, $\dot{M}$, as a function of $M_{\bullet}$ and the gas heating efficiency, the latter being related to the star-formation history. We assess the conditions under which radiative instabilities develop in the hydrostatic region near the stagnation radius, both in the case of a single burst of star formation and for the average star formation history predicted by cosmological simulations. By combining a sample of measured nuclear X-ray luminosities, $L_x$, of nearby quiescent galactic nuclei with our results for $\dot{M}(M_{\bullet})$ we address whether the nuclei are consistent with accreting in a steady-state, thermally-stable manner for radiative efficiencies predicted for radiatively inefficiency accretion flows. We find thermally-stable accretion cannot explain the short average growth times of low mass black holes in the local Universe, which must instead result from gas being fed in from large radii, due either to gas inflows or thermal instabilities acting on larger, galactic scales. Our results have implications for attempts to constrain the occupation fraction of SMBHs in low mass galaxies using the mean $L_x-M_{\bullet}$ correlation, as well as the predicted diversity of the circumnuclear densities encountered by relativistic outflows from tidal disruption events.Comment: 24 pages, 11 figures, 2 tables. Published in MNRA

Maximal information component analysis: a novel non-linear network analysis method.

BackgroundNetwork construction and analysis algorithms provide scientists with the ability to sift through high-throughput biological outputs, such as transcription microarrays, for small groups of genes (modules) that are relevant for further research. Most of these algorithms ignore the important role of non-linear interactions in the data, and the ability for genes to operate in multiple functional groups at once, despite clear evidence for both of these phenomena in observed biological systems.ResultsWe have created a novel co-expression network analysis algorithm that incorporates both of these principles by combining the information-theoretic association measure of the maximal information coefficient (MIC) with an Interaction Component Model. We evaluate the performance of this approach on two datasets collected from a large panel of mice, one from macrophages and the other from liver by comparing the two measures based on a measure of module entropy, Gene Ontology (GO) enrichment, and scale-free topology (SFT) fit. Our algorithm outperforms a widely used co-expression analysis method, weighted gene co-expression network analysis (WGCNA), in the macrophage data, while returning comparable results in the liver dataset when using these criteria. We demonstrate that the macrophage data has more non-linear interactions than the liver dataset, which may explain the increased performance of our method, termed Maximal Information Component Analysis (MICA) in that case.ConclusionsIn making our network algorithm more accurately reflect known biological principles, we are able to generate modules with improved relevance, particularly in networks with confounding factors such as gene by environment interactions

On the beta function and the neutrix product of distributions

The Beta function B(x,n) and the related Beta functions B(x ±, n) and B±(x,n) are defined as distributions and a number of neutrix products of distributions are evaluated

The Violent Youth of Bright and Massive Cluster Galaxies and their Maturation over 7 Billion Years

In this study we investigate the formation and evolution mechanisms of the brightest cluster galaxies (BCGs) over cosmic time. At high redshift ($z\sim0.9$), we selected BCGs and most massive cluster galaxies (MMCGs) from the Cl1604 supercluster and compared them to low-redshift ($z\sim0.1$) counterparts drawn from the MCXC meta-catalog, supplemented by SDSS imaging and spectroscopy. We observed striking differences in the morphological, color, spectral, and stellar mass properties of the BCGs/MMCGs in the two samples. High-redshift BCGs/MMCGs were, in many cases, star-forming, late-type galaxies, with blue broadband colors, properties largely absent amongst the low-redshift BCGs/MMCGs. The stellar mass of BCGs was found to increase by an average factor of $2.51\pm0.71$ from $z\sim0.9$ to $z\sim0.1$. Through this and other comparisons we conclude that a combination of major merging (mainly wet or mixed) and \emph{in situ} star formation are the main mechanisms which build stellar mass in BCGs/MMCGs. The stellar mass growth of the BCGs/MMCGs also appears to grow in lockstep with both the stellar baryonic and total mass of the cluster. Additionally, BCGs/MMCGs were found to grow in size, on average, a factor of $\sim3$, while their average S\'ersic index increased by $\sim$0.45 from $z\sim0.9$ to $z\sim0.1$, also supporting a scenario involving major merging, though some adiabatic expansion is required. These observational results are compared to both models and simulations to further explore the implications on processes which shape and evolve BCGs/MMCGs over the past $\sim$7 Gyr.Comment: Accepted for publication in MNRA