General Relativistic Ray Tracing Research Articles

Imaging fermionic dark matter cores at the centre of galaxies

ABSTRACT Current images of the supermassive black hole (SMBH) candidates at the centre of our Galaxy and M87 have opened an unprecedented era for studying strong gravity and the nature of relativistic sources. Very-long-baseline interferometry data show images consistent with a central SMBH within General Relativity (GR). However, it is essential to consider whether other well-motivated dark compact objects within GR could produce similar images. Recent studies have shown that dark matter (DM) haloes modelled as self-gravitating systems of neutral fermions can harbour very dense fermionic cores at their centres, which can mimic the space–time features of a black hole (BH). Such dense, horizonless DM cores can satisfy the observational constraints: they can be supermassive and compact and lack a hard surface. We investigate whether such cores can produce similar observational signatures to those of BHs when illuminated by an accretion disc. We compute images and spectra of the fermion cores with a general-relativistic ray tracing technique, assuming the radiation originates from standard $\alpha$ discs, which are self-consistently solved within the current DM framework. Our simulated images possess a central brightness depression surrounded by a ring-like feature, resembling what is expected in the BH scenario. For Milky Way-like haloes, the central brightness depressions have diameters down to ${\sim} 35\, \mu \text{as}$ as measured from a distance of approximately $8\,$ kpc. Finally, we show that the DM cores do not possess photon rings, a key difference from the BH paradigm, which could help discriminate between the models.

Images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori

We adopt general relativistic ray-tracing (GRRT) schemes to study images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori, which belong to steady-state solutions of thick accretion disks within the framework of general relativistic magnetohydrodynamics (GRMHD). The black hole possesses an extra dimensionless MOG parameter described its deviation from usual Kerr one. Our results show that the presence of the MOG parameter leads to smaller disks in size, but enhances the total flux density and peak brightness in their images. Combining with observation data of black hole M87* from the Event Horizon Telescope (EHT), we make a constraint on parameters of the Kerr-MOG black hole and find that the presence of the MOG parameter broadens the allowable range of black hole spin.

Self-lensing flares from black hole binaries: General-relativistic ray tracing of circumbinary accretion simulations

Self-lensing flares from black hole binaries: General-relativistic ray tracing of circumbinary accretion simulations

The 230 GHz Variability of Numerical Models of Sagittarius A*. I. Parameter Surveys on Varying the Ion-to-electron Temperature Ratio Under Strongly Magnetized Conditions

The 230 GHz lightcurves of Sagittarius A* (Sgr A*) predicted by general relativistic magnetohydrodynamics and general relativistic ray-tracing (GRRT) models by the Event Horizon Telescope Collaboration have higher variability M ΔT compared to observations. In this series of papers, we explore the origin of such large brightness variability. In this first paper, we performed large GRRT parameter surveys that span from the optically thin to the optically thick regimes, covering the ion-to-electron temperature ratio under strongly magnetized conditions, R Low, from 1 to 60. We find that increasing R Low can lead to either an increase or a reduction in M ΔT depending on the other model parameters, making it consistent with the observed variability of Sgr A* in some cases. Our analysis of GRRT image snapshots finds that the major contribution to the large M ΔT for the R Low = 1 models comes from the photon ring. However, secondary contributions from the accretion flow are also visible depending on the spin parameter. Our work demonstrates the importance of the electron temperature used for modeling radiatively inefficient accretion flows and places new constraints on the ion-to-electron temperature ratio. A more in-depth analysis for understanding the dependencies of M ΔT on R Low will be performed in subsequent papers.

Not all spacetime coordinates for general-relativistic ray tracing are created equal

Not all spacetime coordinates for general-relativistic ray tracing are created equal

Estimating black hole spin from AGN SED fitting: the impact of general-relativistic ray tracing

ABSTRACT Accretion disc model fitting to optical/UV quasar spectra requires that the highest mass black holes have the highest spin, with implications on the hierarchical growth of supermassive black holes and their host galaxies over cosmic time. However, these accretion disc models did not include the effects of relativistic ray tracing. Here, we show that gravitational redshift cancels out most of the increase in temperature and luminosity from the smaller radii characteristic of high spin. Disc models which include the self-consistent general relativistic ray tracing do not fit the UV spectra of the most massive quasars (log M/M⊙ ≥ 9.5), most likely showing that the disc structure is very different to that assumed. We extend the relativistic ray tracing on more complex disc models, where the emission is not limited to (colour-temperature-corrected) blackbody radiation but can instead be emitted as warm and hot Comptonization. We demonstrate this on the broad-band (UV/X-ray) spectrum of Fairall 9, a local intensively monitored ‘bare’ active galactic nucleus (no significant intrinsic cold or warm absorption). We show that including relativistic corrections does make a difference even to these more complex models, but caution that the inferred black hole spin depends on the assumed nature and geometry of the accretion flow. Additionally, we make our model code publicly available, and name it relagn.

Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions

In this work we present the first results from a new ray-tracing tool to calculate cosmological distances in the context of fully nonlinear general relativity. We use this tool to study the ability of the general cosmographic representation of luminosity distance, as truncated at third order in redshift, to accurately capture anisotropies in the “true” luminosity distance. We use numerical relativity simulations of cosmological large-scale structure formation which are free from common simplifying assumptions in cosmology. We find the general, third-order cosmography is accurate to within 1% for redshifts to z ≈ 0.034 when sampling scales strictly above 100 h -1 Mpc, which is in agreement with an earlier prediction. We find the inclusion of small-scale structure generally spoils the ability of the third-order cosmography to accurately reproduce the full luminosity distance for wide redshift intervals, as might be expected. For a simulation sampling small-scale structures, we find a ∼ ±5% variance in the monopole of the ray-traced luminosity distance at z ≈ 0.02. Further, all 25 observers we study here see a 9–20% variance in the luminosity distance across their sky at z ≈ 0.03, which reduces to 2–5% by z ≈ 0.1. These calculations are based on simulations and ray tracing which adopt fully nonlinear general relativity, and highlight the potential importance of fair sky-sampling in low-redshift isotropic cosmological analysis.

Blacklight: A General-relativistic Ray-tracing and Analysis Tool

We describe the Blacklight code, intended for postprocessing general-relativistic magnetohydrodynamic simulation data. Beyond polarized ray tracing of synchrotron radiation, it can produce a number of outputs that aid in analyzing data sets, such as maps of auxiliary quantities and false-color renderings. Additional features include support for adaptive mesh refinement input, slow-light calculations, and adaptive ray tracing. The code is written with ease of use, readability, and transparency as primary objectives, while it still achieves high performance. Blacklight is publicly available and released into the public domain.

Self-lensing flares from black hole binaries: General-relativistic ray tracing of black hole binaries

Self-lensing flares from black hole binaries: General-relativistic ray tracing of black hole binaries

Positron Effects on Polarized Images and Spectra from Jet and Accretion Flow Models of M87* and Sgr A*

Abstract We study the effects of including a nonzero positron-to-electron fraction in emitting plasma on the polarized spectral energy distributions and submillimeter images of jet and accretion flow models for near-horizon emission from M87* and Sgr A*. For M87*, we consider a semi-analytic fit to the force-free plasma regions of a general relativistic magnetohydrodynamic jet simulation, which we populate with power-law leptons with a constant electron-to-magnetic pressure ratio. For Sgr A*, we consider a standard self-similar radiatively inefficient accretion flow where the emission is predominantly from thermal leptons with a small fraction in a power-law tail. In both models, we fix the positron-to-electron ratio throughout the emission region. We generate polarized images and spectra from our models using the general relativistic ray tracing and radiative transfer from GRTRANS. We find that a substantial positron fraction reduces the circular polarization fraction at IR and higher frequencies. However, in submillimeter images, higher positron fractions increase polarization fractions due to strong effects of Faraday conversion. We find an M87* jet model that best matches the available broadband total intensity, and 230 GHz polarization data is a sub-equipartition, with positron fraction of ≃10%. We show that jet models with significant positron fractions do not satisfy the polarimetric constraints at 230 GHz from the Event Horizon Telescope (EHT). Sgr A* models show similar trends in their polarization fractions with increasing pair fraction. Both models suggest that resolved, polarized EHT images are useful to constrain the presence of pairs at 230 GHz emitting regions of M87* and Sgr A*.

Adaptive polygon rendering for interactive visualization in the Schwarzschild spacetime

Interactive visualization is a valuable tool for introductory or advanced courses in general relativity as well as for public outreach to provide a deeper understanding of the visual implications due to curved spacetime. In particular, the extreme case of a black hole where the curvature becomes so strong that even light cannot escape, benefits from an interactive visualization where students can investigate the distortion effects by moving objects around. However, the most commonly used technique of four-dimensional general-relativistic ray tracing is still too slow for interactive frame rates. Therefore, we propose an efficient and adaptive polygon rendering method that takes light deflection and light travel time into account. An additional advantage of this method is that it provides a natural demonstration of how multiple images occur and how light travel time affects them. Finally, we present our method using three example scenes: a triangle passing behind a black hole, a sphere orbiting a black hole and an accretion disk with different inclination angles.

The Role of Adaptive Ray Tracing in Analyzing Black Hole Structure

Abstract The recent advent of the Event Horizon Telescope (EHT) has made direct imaging of supermassive black holes a reality. Simulated images of black holes produced via general relativistic ray tracing and radiative transfer provide a key counterpart to these observational efforts. Black hole images have a wide range of physically interesting image structures, ranging from extremely fine scales in their lensed “photon rings” to the very large scales in their relativistic jets. The multiscale nature of the black hole system is therefore suitable for a multiscale approach to generate simulated images that capture all key elements of the system. Here, we present a prescription for adaptive ray tracing, which enables efficient computation of extremely high-resolution images of black holes. Using the polarized ray-tracing code ipole, we image a combination of semianalytic and general relativistic magnetohydrodynamic (GRMHD) models, and we show that images can be reproduced with a mean squared error of less than 0.1% even after tracing 12× fewer rays. We then use adaptive ray tracing to explore the properties of the photon ring. We illustrate the behavior of individual subrings in GRMHD simulations, and we explore their signatures in interferometric visibilities.

Returning radiation in strong gravity around black holes: reverberation from the accretion disc

ABSTRACT We study reflected X-ray emission that returns to the accretion disc in the strong gravitational fields around black holes using General Relativistic ray-tracing and radiative transfer calculations. Reflected X-rays that are produced when the inner regions of the disc are illuminated by the corona are subject to strong gravitational light bending, causing up to 47 per cent of the reflected emission to be returned to the disc around a rapidly spinning black hole, depending upon the scale height of the corona. The iron Kα line is enhanced relative to the continuum by 25 per cent, and the Compton hump by up to a factor of 3. Additional light traveltime between primary and secondary reflections increases the reverberation time lag measured in the iron K band by 49 per cent, while the soft X-ray lag is increased by 25 per cent and the Compton hump response time is increased by 60 per cent. Measured samples of X-ray reverberation lags are shown to be consistent with X-rays returning to the accretion disc in strong gravity. Understanding the effects of returning radiation is important in interpreting reverberation observations to probe black holes. Reflected X-rays returning to the disc can be uniquely identified by blueshifted returning iron K line photons that are Compton scattered from the inner disc, producing excess, delayed emission in the 3.5–4.5 keV energy range that will be detectable with forthcoming X-ray observatories, representing a unique test of General Relativity in the strong field limit.

Venturing beyond the ISCO: detecting X-ray emission from the plunging regions around black holes

ABSTRACT We explore how X-ray reverberation around black holes may reveal the presence of the innermost stable circular orbit (ISCO), predicted by general relativity, and probe the dynamics of the plunging region between the ISCO and the event horizon. Being able to directly detect the presence of the ISCO and probe the dynamics of material plunging through the event horizon represents a unique test of general relativity in the strong field regime. X-ray reverberation off of the accretion disc and material in the plunging region is modelled using general relativistic ray tracing simulations. X-ray reverberation from the plunging region has a minimal effect on the time-averaged X-ray spectrum and the overall lag-energy spectrum, but is manifested in the lag in the highest frequency Fourier components, above $0.01\, c^{3}\, (GM)^{-1}$ (scaled for the mass of the black hole) in the 2–4 keV energy band for a non-spinning black hole or the 1–2 keV energy band for a maximally spinning black hole. The plunging region is distinguished from disc emission not just by the energy shifts characteristic of plunging orbits, but by the rapid increase in ionization of material through the plunging region. Detection requires measurement of time lags to an accuracy of 20 per cent at these frequencies. Improving accuracy to 12 per cent will enable constraints to be placed on the dynamics of material in the plunging region and distinguish plunging orbits from material remaining on stable circular orbits, confirming the existence of the ISCO, a prime discovery space for future X-ray missions.

First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring

Abstract The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. Here we consider the physical implications of the asymmetric ring seen in the 2017 EHT data. To this end, we construct a large library of models based on general relativistic magnetohydrodynamic (GRMHD) simulations and synthetic images produced by general relativistic ray tracing. We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. The ring radius and ring asymmetry depend on black hole mass and spin, respectively, and both are therefore expected to be stable when observed in future EHT campaigns. Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity. If the black hole spin and M87’s large scale jet are aligned, then the black hole spin vector is pointed away from Earth. Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets. At the same time, in those models that produce a sufficiently powerful jet, the latter is powered by extraction of black hole spin energy through mechanisms akin to the Blandford-Znajek process. We briefly consider alternatives to a black hole for the central compact object. Analysis of existing EHT polarization data and data taken simultaneously at other wavelengths will soon enable new tests of the GRMHD models, as will future EHT campaigns at 230 and 345 GHz.

Elastic scattering in general relativistic ray tracing for neutrinos

We present a covariant ray tracing algorithm for computing high-resolution neutrino distributions in general relativistic numerical spacetimes with hydrodynamical sources. Our formulation treats the very important effect of elastic scattering of neutrinos off of nuclei and nucleons (changing the neutrino's direction but not energy) by incorporating estimates of the background neutrino fields. Background fields provide information about the spectra and intensities of the neutrinos scattered into each ray. These background fields may be taken from a low-order moment simulation or be ignored, in which case the method reduces to a standard state-of-the-art ray tracing formulation. The method handles radiation in regimes spanning optically thick to optically thin. We test the new code, highlight its strengths and weaknesses, and apply it to a simulation of a neutron star merger to compute neutrino fluxes and spectra, and to demonstrate a neutrino flavor oscillation calculation. In that environment, we find qualitatively different fluxes, spectra, and oscillation behaviors when elastic scattering is included.

On the illumination of neutron star accretion discs

The illumination of the accretion disc in a neutron star X-ray binary by X-rays emitted from (or close to) the neutron star surface is explored through general relativistic ray tracing simulations. The applicability of the canonical suite of relativistically broadened emission line models (developed for black holes) to discs around neutron stars is evaluated. These models were found to describe well emission lines from neutron star accretion discs unless the neutron star radius is larger than the innermost stable orbit of the accretion disc at 6rg or the disc is viewed at high inclination, above 60deg where shadowing of the back side of the disc becomes important. Theoretical emissivity profiles were computed for accretion discs illuminated by hotspots on the neutron star surfaces, bands of emission and emission by the entirety of the hot, spherical star surface and in all cases, the emissivity profile of the accretion disc was found to be well represented by a single power law falling off slightly steeper than r^-3. Steepening of the emissivity index was found where the emission is close to the disc plane and the disc can appear truncated when illuminated by a hotspot at high latitude. The emissivity profile of the accretion disc in Serpens X-1 was measured and found to be consistent with a single unbroken power law with index q=3.5 (-0.4,+0.3), suggestive of illumination by the boundary layer between the disc and neutron star surface.

Probing the geometry and motion of AGN coronae through accretion disc emissivity profiles

To gain a better understanding of the inner disc region that comprises active galactic nuclei it is necessary to understand the pattern in which the disc is illuminated (the emissivity profile) by X-rays emitted from the continuum source above the black hole (corona). The differences in the emissivity profiles produced by various corona geometries are explored via general relativistic ray tracing simulations. Through the analysis of various parameters of the geometries simulated it is found that emissivity profiles produced by point source and extended geometries such as cylindrical slabs and spheroidal coronae placed on the accretion disc are distinguishable. Profiles produced by point source and conical geometries are not significantly different, requiring an analysis of reflection fraction to differentiate the two geometries. Beamed point and beamed conical sources are also simulated in an effort to model jet-like coronae, though the differences here are most evident in the reflection fraction. For a point source we determine an approximation for the measured reflection fraction with the source height and velocity. Simulating spectra from the emissivity profiles produced by the various geometries produce distinguishable differences. Overall spectral differences between the geometries do not exceed 15 per cent in the most extreme cases. It is found that emissivity profiles can be useful in distinguishing point source and extended geometries given high quality spectral data of extreme, bright sources over long exposure times. In combination with reflection fraction, timing, and spectral analysis we may use emissivity profiles to discern the geometry of the X-ray source.

Impact of the gravity of a Schwarzschild black hole upon the Rossby wave instability

In an early work the Rossby Wave Instability (RWI) has been proposed to explain variability thought to originate in the close vicinity of black-holes but this was done in the pseudo-Newtonian approach. Here we present the first general relativistic hydrodynamics simulations of this instability not only proving its theorized existence in a full general relativistic (GR) environment but also studying the effect of the strong gravity on the instability. To that end we performed a set of simulations increasingly closer to the black hole with our new GR version of the MPI-AMRVAC code.This allows us to study the minute changes in the behaviour of the instability.We found that the pseudo-Newtonian approach gives adequate results provided that time shifting induced by the black hole gravity is taken into account. Hence, to view the disc as a distant observer would a full GR ray-tracing post treatment of the simulations is a must.

ARE THE kHz QPO LAGS IN NEUTRON STAR 4U 1608–52 DUE TO REVERBERATION?

X-ray reverberation lags have recently been discovered in both active galactic nuclei (AGN) and black hole X-ray binaries. A recent study of the neutron star low-mass X-ray binary 4U 1608-52 has also shown significant lags, whose properties hint at a reverberation origin. Here, we adapt general relativistic ray tracing impulse response functions used to model X-ray reverberation in AGN for neutron star low-mass X-ray binaries. Assuming relativistic reflection forms the broad iron line and associated reflection continuum, we use reflection fits to the energy spectrum along with the impulse response functions to calculate the expected lags as a function of energy over the range of observed kHz QPO frequencies in 4U 1608-52. We find that the lag energy spectrum is expected to increase with increasing energy above 8 keV, while the observed lags in 4U 1608-52 show the opposite behavior. This demonstrates that the lags in the lower kHz QPO of 4U 1608-52 are not solely due to reverberation. We do note, however, that the models appear to be more consistent with the much flatter lag energy spectrum observed in the upper kHz QPO of several neutron star low-mass X-ray binaries, suggesting that lower and upper kHz QPOs may have different origins.