General Relativistic Ray-Tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ($\nu + {\bar \nu} \rightarrow e^{-} + e^{+}$) in the vicinity of accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. For the neutrino opacity, the charged-current $\beta$-processes are taken into account, which are dominant in the vicinity of the accretion tori. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytic solutions. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the general relativistic effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percents. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.Comment: 33 pages, 15 figures, accepted to the Ap

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

Relativistic Effects for Time-Resolved Light Transport

We present a real-time framework which allows interactive visualization of relativistic effects for time-resolved light transport. We leverage data from two different sources: real-world data acquired with an effective exposure time of less than 2 picoseconds, using an ultra-fast imaging technique termed femto-photography, and a transient renderer based on ray-tracing. We explore the effects of time dilation, light aberration, frequency shift and radiance accumulation by modifying existing models of these relativistic effects to take into account the time-resolved nature of light propagation. Unlike previous works, we do not impose limiting constraints in the visualization, allowing the virtual camera to explore freely a reconstructed 3D scene depicting dynamic illumination. Moreover, we consider not only linear motion, but also acceleration and rotation of the camera. We further introduce, for the first time, a pinhole camera model into our relativistic rendering framework, and account for subsequent changes in focal length and field of view as the camera moves through the scene

VisIVO - Integrated Tools and Services for Large-Scale Astrophysical Visualization

VisIVO is an integrated suite of tools and services specifically designed for the Virtual Observatory. This suite constitutes a software framework for effective visual discovery in currently available (and next-generation) very large-scale astrophysical datasets. VisIVO consists of VisiVO Desktop - a stand alone application for interactive visualization on standard PCs, VisIVO Server - a grid-enabled platform for high performance visualization and VisIVO Web - a custom designed web portal supporting services based on the VisIVO Server functionality. The main characteristic of VisIVO is support for high-performance, multidimensional visualization of very large-scale astrophysical datasets. Users can obtain meaningful visualizations rapidly while preserving full and intuitive control of the relevant visualization parameters. This paper focuses on newly developed integrated tools in VisIVO Server allowing intuitive visual discovery with 3D views being created from data tables. VisIVO Server can be installed easily on any web server with a database repository. We discuss briefly aspects of our implementation of VisiVO Server on a computational grid and also outline the functionality of the services offered by VisIVO Web. Finally we conclude with a summary of our work and pointers to future developments

Seeing relativity -- I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars

We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification, Doppler) and general (deflection of light, lensing, gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particular, we study the aspect of the second asymptotic region of the metric as seen by an observer crossing the horizon. We also address several aspects related to the white hole region (i.e., past singularity) seen both from outside the black hole, inside the future horizon and inside the past horizon, which gives rise to the most counter-intuitive effects

Relativistic photography with a wide aperture

We discuss new effects related to relativistic aberration, which is the apparent distortion of objects moving at relativistic speeds relative to an idealized camera. Our analysis assumes that the camera lens is capable of stigmatic imaging of objects at rest with respect to the camera, and that each point on the shutter surface is transparent for one instant, but different points are not necessarily transparent synchronously. We pay special attention to the placement of the shutter. First, we find that a wide aperture requires the shutter to be placed in the detector plane to enable stigmatic images. Second, a Lorentz-transformation window [Proc. SPIE 9193, 91931K (2014) [CrossRef] ] can correct for relativistic distortion. We illustrate our results, which are significant for future spaceships, with raytracing simulations

Simulated Radio and Neutrino Imaging of a Microquasar

Microquasar stellar systems emit electromagnetic radiation and high-energy particles. Thanks to their location within our own galaxy, they can be observed in high detail. Still, many of their inner workings remain elusive; hence, simulations, as the link between observations and theory, are highly useful. In this paper, both high-energy particle and synchrotron radio emissions from simulated microquasar jets are calculated using special relativistic imaging. A finite ray speed imaging algorithm is employed on hydrodynamic simulation data, producing synthetic images seen from a stationary observer. A hydrodynamical model is integrated in the above emission models. Synthetic spectra and maps are then produced that can be compared to observations from detector arrays. As an application, the model synthetically observes microquasars during an episodic ejection at two different spatio-temporal scales: one on the neutrino emission region scale and the other on the synchrotron radio emission scale. The results are compared to the sensitivity of existing detectors