Counting Black Holes: The Cosmic Stellar Remnant Population and Implications for LIGO

We present an empirical approach for interpreting gravitational wave signals of binary black hole mergers under the assumption that the underlying black hole population is sourced by remnants of stellar evolution. Using the observed relationship between galaxy mass and stellar metallicity, we predict the black hole count as a function of galaxy stellar mass. We show, for example, that a galaxy like the Milky Way should host millions of $\sim 30~M_\odot$ black holes and dwarf satellite galaxies like Draco should host $\sim 100$ such remnants, with weak dependence on the assumed IMF and stellar evolution model. Most low-mass black holes ($\sim10 M_\odot$) typically reside within massive galaxies ($M_\star \simeq 10^{11} M_\odot$) while massive black holes ($\sim 50~M_\odot$) typically reside within dwarf galaxies ($M_\odot \simeq 10^9 M_\odot$) today. If roughly $1\%$ of black holes are involved in a binary black hole merger, then the reported merger rate densities from Advanced LIGO can be accommodated for a range of merger timescales, and the detection of mergers with $> 50~M_\odot$ black holes should be expected within the next decade. Identifying the host galaxy population of the mergers provides a way to constrain both the binary neutron star or black hole formation efficiencies and the merger timescale distributions; these events would be primarily localized in dwarf galaxies if the merger timescale is short compared to the age of the universe and in massive galaxies otherwise. As more mergers are detected, the prospect of identifying the host galaxy population, either directly through the detection of electromagnetic counterparts of binary neutron star mergers or indirectly through the anisotropy of the events, will become a realistic possibility.Comment: 10 pages, 8 figures. Accepted by MNRA

Visualizing Interstellar's Wormhole

Christopher Nolan's science fiction movie Interstellar offers a variety of opportunities for students in elementary courses on general relativity theory. This paper describes such opportunities, including: (i) At the motivational level, the manner in which elementary relativity concepts underlie the wormhole visualizations seen in the movie. (ii) At the briefest computational level, instructive calculations with simple but intriguing wormhole metrics, including, e.g., constructing embedding diagrams for the three-parameter wormhole that was used by our visual effects team and Christopher Nolan in scoping out possible wormhole geometries for the movie. (iii) Combining the proper reference frame of a camera with solutions of the geodesic equation, to construct a light-ray-tracing map backward in time from a camera's local sky to a wormhole's two celestial spheres. (iv) Implementing this map, for example in Mathematica, Maple or Matlab, and using that implementation to construct images of what a camera sees when near or inside a wormhole. (v) With the student's implementation, exploring how the wormhole's three parameters influence what the camera sees---which is precisely how Christopher Nolan, using our implementation, chose the parameters for \emph{Interstellar}'s wormhole. (vi) Using the student's implementation, exploring the wormhole's Einstein ring, and particularly the peculiar motions of star images near the ring; and exploring what it looks like to travel through a wormhole.Comment: 14 pages and 13 figures. In press at American Journal of Physics. Minor revisions; primarily insertion of a new, long reference 15 at the end of Section II.

Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this we developed a code called DNGR (Double Negative Gravitational Renderer) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering. This paper has four purposes: (i) To describe DNGR for physicists and CGI practitioners . (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie \emph{Interstellar}, were generated with DNGR. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.Comment: 46 pages, 17 figure

A strategic look at how to extend your digital footprint

Purpose: To provide an overview of the key strategic questions that need to be considered when evaluating whether or not to extend a company’s reach across multiple digital platforms. Design/methodology/approach: The viewpoint presented in this paper reflects both the practical experience of conceiving, launching and implementing a multi-platform digital strategy, combined with an academic insight into branding and strategic resource allocation and management. Findings: Before extending your digital footprint, executives need to consider several key questions that will impact on the relative success of their digital strategy. Practical implications: A digital strategy that extends a company’s reach across multiple platforms needs to be considered in terms of delivering against corporate and business level strategy in order to be effective. Originality/value: A unique combination of practical experience fused with academic knowledge on the key questions that should be considered in order to successfully design and implement a multi-platform digital strategy. Keywords: Digital Media, Online Marketing, Digital Distribution, Multi-platform, Brand Building, Customer Relationship Managemen

Deep proteogenomics; high throughput gene validation by multidimensional liquid chromatography and mass spectrometry of proteins from the fungal wheat pathogen Stagonospora nodorum

BACKGROUND: Stagonospora nodorum, a fungal ascomycete in the class dothideomycetes, is a damaging pathogen of wheat. It is a model for necrotrophic fungi that cause necrotic symptoms via the interaction of multiple effector proteins with cultivar-specific receptors. A draft genome sequence and annotation was published in 2007. A second-pass gene prediction using a training set of 795 fully EST-supported genes predicted a total of 10762 version 2 nuclear-encoded genes, with an additional 5354 less reliable version 1 genes also retained. RESULTS: In this study, we subjected soluble mycelial proteins to proteolysis followed by 2D LC MALDI-MS/MS. Comparison of the detected peptides with the gene models validated 2134 genes. 62% of these genes (1324) were not supported by prior EST evidence. Of the 2134 validated genes, all but 188 were version 2 annotations. Statistical analysis of the validated gene models revealed a preponderance of cytoplasmic and nuclear localised proteins, and proteins with intracellularassociated GO terms. These statistical associations are consistent with the source of the peptides used in the study. Comparison with a 6-frame translation of the S. nodorum genome assembly confirmed 905 existing gene annotations (including 119 not previously confirmed) and provided evidence supporting 144 genes with coding exon frameshift modifications, 604 genes with extensions of coding exons into annotated introns or untranslated regions (UTRs), 3 new gene annotations which were supported by tblastn to NR, and 44 potential new genes residing within un-assembled regions of the genome. CONCLUSION: We conclude that 2D LC MALDI-MS/MS is a powerful, rapid and economical tool to aid in the annotation of fungal genomic assemblies

Sweating the small stuff: simulating dwarf galaxies, ultra-faint dwarf galaxies, and their own tiny satellites

We present FIRE/Gizmo hydrodynamic zoom-in simulations of isolated dark matter halos, two each at the mass of classical dwarf galaxies ($M_{\rm vir} \simeq 10^{10} M_{\odot}$) and ultra-faint galaxies ($M_{\rm vir} \simeq 10^9 M_{\odot}$), and with two feedback implementations. The resultant central galaxies lie on an extrapolated abundance matching relation from $M_{\star} \simeq 10^6$ to $10^4 M_{\odot}$ without a break. Every host is filled with subhalos, many of which form stars. Our dwarfs with $M_{\star} \simeq 10^6 M_{\odot}$ each have 1-2 well-resolved satellites with $M_{\star} = 3-200 \times 10^3 M_{\odot}$. Even our isolated ultra-faint galaxies have star-forming subhalos. If this is representative, dwarf galaxies throughout the universe should commonly host tiny satellite galaxies of their own. We combine our results with the ELVIS simulations to show that targeting $\sim 50~ \rm kpc$ regions around nearby isolated dwarfs could increase the chances of discovering ultra-faint galaxies by $\sim 35\%$ compared to random halo pointings, and specifically identify the region around the Phoenix dwarf galaxy as a good potential target. The well-resolved ultra-faint galaxies in our simulations ($M_{\star} \simeq 3 - 30 \times 10^3 M_{\odot}$) form within $M_{\rm peak} \simeq 0.5 - 3 \times 10^9 M_{\odot}$ halos. Each has a uniformly ancient stellar population ($> 10~ \rm Gyr$) owing to reionization-related quenching. More massive systems, in contrast, all have late-time star formation. Our results suggest that $M_{\rm halo} \simeq 5 \times 10^9 M_{\odot}$ is a probable dividing line between halos hosting reionization "fossils" and those hosting dwarfs that can continue to form stars in isolation after reionization.Comment: 12 pages, 6 figures, 1 table, submitted to MNRA