- Research
- Open Access
Observing supermassive black holes in virtual reality
- Jordy Davelaar^{1}Email authorView ORCID ID profile,
- Thomas Bronzwaer^{1},
- Daniel Kok^{1},
- Ziri Younsi^{2, 3},
- Monika Mościbrodzka^{1} and
- Heino Falcke^{1}
https://doi.org/10.1186/s40668-018-0023-7
© The Author(s) 2018
- Received: 29 June 2018
- Accepted: 21 October 2018
- Published: 19 November 2018
Abstract
We present a 360^{∘} (i.e., 4π steradian) general-relativistic ray-tracing and radiative transfer calculations of accreting supermassive black holes. We perform state-of-the-art three-dimensional general-relativistic magnetohydrodynamical simulations using the BHAC code, subsequently post-processing this data with the radiative transfer code RAPTOR. All relativistic and general-relativistic effects, such as Doppler boosting and gravitational redshift, as well as geometrical effects due to the local gravitational field and the observer’s changing position and state of motion, are therefore calculated self-consistently. Synthetic images at four astronomically-relevant observing frequencies are generated from the perspective of an observer with a full 360^{∘} view inside the accretion flow, who is advected with the flow as it evolves. As an example we calculated images based on recent best-fit models of observations of Sagittarius A*. These images are combined to generate a complete 360^{∘} Virtual Reality movie of the surrounding environment of the black hole and its event horizon. Our approach also enables the calculation of the local luminosity received at a given fluid element in the accretion flow, providing important applications in, e.g., radiation feedback calculations onto black hole accretion flows. In addition to scientific applications, the 360^{∘} Virtual Reality movies we present also represent a new medium through which to interactively communicate black hole physics to a wider audience, serving as a powerful educational tool.
Keywords
- Accreting black holes
- Plasma physics
- Radiative transfer
- General relativity
- Virtual reality
1 Introduction
Active Galactic Nuclei (AGN) are strong sources of electromagnetic radiation from the radio up to γ-rays. Their source properties can be explained in terms of a galaxy hosting an accreting supermassive black hole (SMBH) in its core. The Milky Way also harbours a candidate SMBH, Sagittarius A* (Sgr A*), which is subject to intensive Very-Long-Baseline Interferometric (VLBI) studies (Krichbaum et al. 1998; Bower et al. 2004, 2014; Shen et al. 2005; Doeleman et al. 2008; Brinkerink et al. 2016). Sgr A* is one of the primary targets of the Event Horizon Telescope Collaboration (EHTC), which aims to image for the very first time the “shadow” of a black hole (Goddi et al. 2017). Theoretical calculations predict this shadow to manifest as a darkening of the inner accretion flow image anticipated to be observed due to the presence of a black hole event horizon, representing the region within which no radiation can escape (Grenzebach 2016; Goddi et al. 2017; Younsi et al. 2016). The apparent size on the sky of this shadow is constrained by Einstein’s General Theory of Relativity (GR) (Bardeen 1973; Cunningham and Bardeen 1973; Luminet 1979; Viergutz 1993; Falcke et al. 2000; Johannsen and Psaltis 2010; Johannsen 2013; Younsi et al. 2016), and observational measurements of the black hole shadow size and shape can in principle provide a strong test of the validity of GR in the strong-field regime (Johannsen and Psaltis 2010; Abdujabbarov et al. 2015; Younsi et al. 2016; Goddi et al. 2017).
The theoretical aspects of the observational study of Sgr A* require the generation of general-relativistic magnetohydrodynamical (GRMHD) simulation data of the accretion flow onto a black hole, which is subsequently used to calculate synthetic observational data for physically-motivated plasma models which can be compared to actual observational data. In the past, synthetic observational data was generated by ray-tracing radiative transfer codes which calculate the emission originating from the accreting black hole and measured by a far away observer by solving the equations of radiative transfer along geodesics, i.e., the paths of photons (or particles) as they propagate around the black hole in either static spacetimes (e.g. Broderick 2006; Noble et al. 2007; Dexter and Agol 2009; Shcherbakov and Huang 2011; Vincent et al. 2011; Younsi et al. 2012; Chan et al. 2013, 2017; Younsi and Wu 2015; Dexter 2016; Schnittman et al. 2016; Moscibrodzka and Gammie 2017; Bronzwaer et al. 2018) or dynamical spacetimes (Kelly et al. 2017; Schnittman et al. 2018).
These models vary only in the dynamics of the black hole accretion flow, with the observer remaining stationary through the calculations. In this work, we consider the most general case of an observer who can vary arbitrarily in both their position (with respect to the black hole) and their state of motion. In particular, the observer is chosen to follow the flow of the accreting plasma in a physically-meaningful manner through advection, and therefore all dynamical effects introduced by the motion of the observer around the black hole are also correctly included in the imaging calculation.
With recent developments in Graphical Processor Units (GPUs) and Virtual Reality (VR) rendering, it has become possible to visualise these astrophysical objects at high resolutions in a 360^{∘} (i.e., 4π steradian) format that covers the entire celestial sphere of an observer, enabling the study of the surroundings of an accreting black hole from within the accretion flow itself. Virtual Reality is a broad concept that encompasses different techniques, such as immersive visualisation, stereographic rendering, and interactive visualisations. In this work, we explore the first of these three, by rendering the full celestial sphere of the observer along a trajectory. The viewer can then look in any direction during the animation; this is also known as 360^{∘} VR. Another important feature of VR, stereographic rendering, presents different images to each eye, so that the viewer experiences stereoscopic depth. For our application, however, this technique is not relevant, since the physical distance between the eyes of the observer is much smaller than the typical length scale of a supermassive black hole (which is \(6.645\times10^{11}\) cm for Sagittarius A*), and therefore we would not see any depth in the image (just as we do not see stereoscopic depth when looking at the Moon). Interactive visualisations, where the viewer also has the freedom to change his or her position, would require real-time rendering of the environment, which is beyond the reach of current computational resources.
- (1)
falling through the event horizon as illustrated through the gravitational lensing distortions of different regions (e.g., the ergo-region and event horizon), represented as chequerboard patterns projected onto an observer’s image plane (Madore 2011),
- (2)
a flight through a simulation of a non-rotating black hole (Hamilton 1998),
- (3)
a flight through an accretion disk of a black hole using an observer with a narrow field of view camera (Luminet 2011),
- (4)
a 360^{∘} VR movie of an observer falling into a black hole surrounded by vacuum with illumination provided exclusively by background starlight, i.e., without an accretion flow (Younsi 2016),
- (5)
a 360^{∘} VR movie of a hotspot orbiting a SMBH (Moscibrodzka 2018), and
- (6)
a 360^{∘} VR movie of an N-body/hydrodynamical simulation of the central parsec of the Galactic center (Russell 2017).
In this study, we consider a self-consistent three-dimensional GRMHD simulation of the accretion flow onto a spinning (Kerr) black hole, determining its time evolution and what an observer would see in full 360^{∘} VR as they move through the dynamically evolving flow. To image accreting black holes in VR, we use the general-relativistic radiative-transfer (GRRT) code RAPTOR (Bronzwaer et al. 2018). The code incorporates all important general-relativistic effects, such as Doppler boosting and gravitational lensing in curved spacetimes, and can be compiled and run on both Central Processing units (CPU’s) and GPU’s by using NVIDIA’s OpenACC framework.
In this work, we investigate the environment of accreting black holes from within the accretion flow itself with a virtual camera. As an example astrophysical case we model the supermassive black hole Sgr A*, although the methods presented in this work are generally applicable to any black hole as long as the radiation field’s feedback onto the accreting plasma has a negligible effect on the plasma’s magnetohydrodynamical properties, which is the case for Low Luminosity AGNs or low/hard state X-ray binaries.
The trajectory of this camera consists of two phases: a hovering trajectory, where the observer moves with a pre-defined velocity, and a particle trajectory, where the observer’s instantaneous velocity is given by a trajectory of a tracer particle computed with a seperate axisymetric GRMHD simulation. The tracer particle follows the local plasma velocity (specifically, it is obtained by interpolating the plasma velocity of the GRMHD simulation cells to the camera’s location).
We present 360^{∘} VR simulation of Sgr A*, demonstrating the applications of VR for studying not just accreting black holes but also for education, public outreach and data visualisation and interpretation amongst the wider scientific community. In Sect. 2 we describe the camera setup, present several black hole shadow lensing tests, describe the camera trajectories and outline the radiative transfer calculation. In Sect. 3 we present our 360^{∘} VR movie of an accreting black hole. In Sect. 4 we discuss our results and outlook.
2 Methods
In this section, we introduce the virtual camera setup, present black hole shadow vacuum lensing tests using both stationary and free-falling observers at different radial positions, discuss the different camera trajectories used in the VR movie shown later in this article and introduce the GRMHD plasma model that is used as an input for the geometry of the accretion flow onto the black hole.
2.1 VR camera
The original RAPTOR code (Bronzwaer et al. 2018) initialises rays (i.e., photon geodesics) using impact parameters determined form coordinate locations on the observer’s image plane (Bardeen et al. 1972). This method is not suitable for VR since it only applies to distant observers where geometrical distortions in the image which arise from the strong gravitational field (i.e., spacetime curvature) of the black hole are negligible. To generate full 360^{∘} images as seen by an observer close to the black hole, we have extended the procedure of Noble et al. (2007) to use an orthonormal tetrad basis for the construction of initial photon wave vectors, distributing them uniformly as a function of \(\theta\in [0,\pi]\) and \(\phi\in[0,2\pi]\) over a unit sphere.
The advantage of this approach is that all geometrical, relativistic, and general-relativistic effects on the observed emission are naturally and self-consistently folded into the imaging calculation, providing a complete and physically-accurate depiction of what would really be seen from an observer’s perspective.
2.2 Black holes and gravitational lensing
In this work, we adopt geometrical units, \(G=M=c=1\), such that length and time scales are dimensionless. Hereafter M denotes the black hole mass, and setting \(M=1\) is equivalent to rescaling the length scale to units of the gravitational radius, \(r_{\mathrm {g}}:= GM/c^{2}\), and the time scale to units of \(r_{\mathrm {g}}/c = GM/c^{3}\). To rescale lengths and times to physical units, one simply scales \(r_{\mathrm {g}}\) and \(r_{\mathrm {g}}/c\) using the appropriate black hole mass. For Sgr A* these scalings are given by \(r_{\mathrm {g}} = 5.906 \times 10^{11}\) cm and \(r_{\mathrm {g}}/c = 19.7\) seconds, respectively.
To visualise the effect of the observer’s motion on the observed field of view, we place a sphere around both the observer and the black hole, which is centred on the black hole. This is what we subsequently refer to as the “celestial sphere”. The black hole spin is taken to be \(a=0.9375\), the exact value of the spin parameter for Sgr A* is unknown, the chosen value was the best fit of a parameter survey (Mościbrodzka et al. 2009). The observer is positioned in the equatorial plane of the black hole (i.e., \(\theta=90^{\circ}\)), where the effects of gravitational lensing are most significant and asymmetry in the shadow shape due to the rotational frame dragging arising from the spin of the black hole is most pronounced.
Figure 2 presents black hole shadow images and background lensing patterns for the Kerr black hole as seen by both a stationary observer (top panel) and a radially infalling observer (middle panel) located at a distance of \(10~r_{\mathrm { g}}\). The angular size of the shadow is larger for the stationary observer. This observer, being in an inertial frame, is essentially accelerating such that the local gravitational acceleration of the black hole is precisely counteracted by the acceleration of their reference frame. This gives rise to a force on the observer directed away from the black hole itself, reducing the angular momentum of photons oriented towards the black hole (seen as the innermost four rays being bent around the horizon), effectively increasing the black hole’s capture cross-section and producing a larger shadow. Strong gravitational lensing of the image due to the presence of the compact mass of the black hole is evident in the warping of the grid lines.
In Fig. 3 the observers are now placed at \(3~r_{\mathrm { g}}\), i.e., very close to the black hole. For the stationary observer, all photons within a field of view centred on the black hole of >180^{∘} in the horizontal direction and over the entire vertical direction, are captured by the black hole. Such an observer looking at the black hole would see nothing but the darkness of the black hole shadow in all directions. This is clear in the corresponding bottom-left plot of photon trajectories. As the observer approaches the event horizon the entire celestial sphere begins to focus into an ever shrinking point adjacent to the observer. For the infalling observer, the lensed image is far less extreme. Whilst the shadow presents a larger size in the observer’s field of view, this is mostly geometrical, i.e., due to the observer’s proximity to the black hole. There is also visible magnification of regions of the celestial sphere behind the observer. These results clearly follow from the photon trajectories in the bottom-right panel.
In all images of the shadow, repeated patches of decreasingly small area and identical colours are visible. In particular, multiple blue and yellow patches whose photons begin from behind the observer are visible near the shadow. These are a consequence of rays which perform one or more orbits of the black hole before reaching the observer, thereby appearing to originate from in front of the observer.
2.3 Camera trajectories
As described in Sect. 1, we consider two distinct phases for the camera trajectory. The first phase assumes a hovering observer positioned either at a fixed point or on a hovering trajectory around the black hole (i.e., the camera’s motion is unaffected by the plasma motion and is effectively in an inertial frame). For the second phase of the trajectory, the observer’s four-velocity is determined from an axisymmetric GRMHD simulation which includes tracer particles that follow the local plasma velocity. The choice to perform a separate tracer-particle simulation that is axisymmetric, in contrast to the 3D plasma simulation, was made to omit turbulent features in the ϕ direction which can be nauseating to watch in VR environments. This makes the movie scientifically less accurate, but is necessary to prevent viewers from experiencing motion sickness. Since the methods presented in this paper are not dependent on the dimensionality of the tracer particle simulation, they can be used for full 3D tracer particle simulations as well. In the following subsections, these two camera trajectories are described in detail.
2.3.1 Hovering trajectory
In the first phase of the trajectory, the observer starts in a vacuum, with only the light from the distant background stars being considered in the calculation. The observer is initially at a radius of \(400~r_{\mathrm { g}}\) and moves inward to \(40~r_{\mathrm { g}}\). After this, the observer rotates around the black hole, which we term the “initialisation scene”, and comprises 1600 frames. Each frame is separated by a time interval of \(1~r_{\mathrm { g}}/c\). The first phase of the movie, which includes the time-evolving accretion flow, consists of 2000 frames from the perspective of an observer at a radius of \(40~r_{\mathrm { g}}\) and an inclination of 60^{∘} with respect to the spin axis of the black hole. We refer to this first phase as “Scene 1”. We then subsequently rotate around the black hole whilst simultaneously moving inward to a radius of \(20~r_{\mathrm { g}}\) over a span of 1000 frames, which we refer to as “Scene 2”. Within Scene 2, after the first 500 frames the observer then starts to decelerate until stationary once more.
2.3.2 Particle trajectory
- (1)
accreted particles which leave the simulation at the inner radius (i.e., plunge into the event horizon) and remain gravitationally bound,
- (2)
wind particles which become gravitationally unbound, travel through weakly magnetised regions and then exit the simulation at the outer boundary,
- (3)
accelerated jet particles which are similar to wind particles but additionally undergo rapid acceleration within the highly-magnetised jet sheath.
2.4 Radiative-transfer calculations and background images
To create images of an accreting black hole, it is necessary to compute the trajectories of light rays from the radiating plasma to the observer. For imaging applications, such as the present case, it is most computationally efficient to start the light rays at the observer instead—one for each pixel in the image the observer sees—and then trace them backward in time. Given a ray’s trajectory, the radiative-transfer equation is solved along that trajectory, in order to compute the intensity seen by the observer. The radiative-transfer code RAPTOR uses a fourth-order Runge–Kutta method to integrate the equations of motion for the light rays (i.e., the geodesic equation). It simultaneously solves the radiative-transfer equation using a semi-analytic scheme (for a more detailed description of RAPTOR, see Bronzwaer et al. (2018)). The same methodology is applied here in order to create images of the black hole accretion disk, with one small addition. When accretion disks, which tend to be roughly toroidal in shape, are filmed against a perfectly black background, the resulting animations fail to convey a natural sense of motion and scale for the observer as they orbit the black hole. In order to increase the immersiveness of the observer and provide a physically-realistic sense of scale and motion, the present work expands on the aforementioned radiative-transfer calculations by including an additional source of radiation in the form of a background star field that is projected onto the celestial sphere surrounding the black hole and observer.
Using the scheme described above, it is possible to fold the background radiation field directly into the radiative transfer calculations of the accretion disk plasma. A second approach is to render separate movies for both the background and for the plasma, create a composite image for all corresponding time frames between the two movies in post-processing, and then create the new composite movie from the composite images. We adopt the second approach in all results shown in this paper.
We have chosen a background that is obtained from real astronomical star data from the Tycho 2 catalogue which are not in the Galactic Plane. The original equirectangular RGB 3K image was generated by Scott (2008) and converted to a greyscale 2K image.
2.5 Plasma and radiation models
In this work, we seek to model the SMBH Sgr A*. To this end we use a black hole mass of \(M_{\mathrm{ BH}} = 4.0\times10^{6}~\mathrm{M}_{\odot}\) (Gillessen et al. 2009), and a dimensionless spin parameter of \(a=0.9375\), consistent with the particle simulation. The plasma flow was simulated with the GRMHD code BHAC (Porth et al. 2017). The simulation domain had an outer radius of \(r_{\mathrm{outer}} = 1000~r_{\mathrm { g}}\). The simulation is initialised with a Fishbone–Moncrief torus (Fishbone and Moncrief 1976) with an inner radius of \(r_{\mathrm{inner}}=6~r_{\mathrm { g}}\), and with a pressure maximum at \(r_{\mathrm{ max}} = 12~r_{\mathrm { g}}\). Magnetic fields were inserted as poloidal loops that follow iso-contours of density, and the initial magnetisation was low, i.e., \(\beta= P_{\mathrm{ gas}}/B^{2} = 100\), where \(P_{\mathrm{ gas}}\) is the gas pressure of the plasma. The simulation was performed in three dimensions, with a resolution of 256, 128, 128 cells in the r, θ and ϕ directions, respectively. We simulated the flow up to \(t=7000~r_{\mathrm { g}}/c\).
The GRMHD simulation only simulates the dynamically-important ions (protons). We, therefore, require a prescription for the radiatively-important electrons in order to compute the observed emission. Most radiative models for Sgr A* or M87 either assume that the coupling between the temperatures of the electrons and protons is constant or parameterised based on plasma variabels, see e.g. Goldston et al. (2005); Noble et al. (2007); Mościbrodzka et al. (2009); Dexter et al. (2010); Shcherbakov et al. (2012); Mościbrodzka and Falcke (2013); Mościbrodzka et al. (2014); Chan et al. (2015a, 2015b); Gold et al. (2017). In this work we use, an electron model by Mościbrodzka et al. (2014) where the electrons are cold inside the accretion disk and hot inside the highly magnetized outflows. For the electron distribution function, we adopt a thermal distribution, where Davelaar et al. (2018b) showed that this model accurately describes the quiescent state of Sgr A*. The used model (Mościbrodzka et al. 2014) is capable of recovering the observational parameters of Sgr A*, such as radio fluxes and intrinsic source sizes (Falcke et al. 2000; Bower et al. 2004, 2014; Doeleman et al. 2008).
3 VR movie
The resulting VR movie contains 8600 frames at a resolution of \(2000\times1000\) pixels. As a proof of concept, this resolution was chosen to balance image quality and computational resources. Current VR headsets also upscale the provided resolution with interpolation routines. We tested the resolution with the Oculus VR headset, which turned out to be sufficient. Since the provided methods are not limited by the resolution, a larger resolution can in principle be achieved. The movie is available on Youtube VR (Davelaar et al. 2018a). In this section, we discuss several snapshots from this movie.
4 Discussion and conclusion
In this work, we have detailed our methods for visualising the surroundings of accreting black holes in virtual reality. We presented a visualisation of a three-dimensional fully-general-relativistic accreting black hole simulation in a full 360^{∘} VR movie with radiative models based on physically-realistic GRMHD plasma simulations. In order to produce representative images, the radiative-transfer capabilities of our code RAPTOR were extended to include background starlight and an observer in an arbitrary state of motion. To model the emission emerging from the vicinity of a black hole we coupled the GRMHD simulation with our radiative-transfer code to produce a VR movie based on our recent models for Sgr A* (Mościbrodzka et al. 2014; Davelaar et al. 2018b). These methods can be applied to accreting black holes of any size, so long as radiation feedback onto the accretion flow has a negligible impact on the flow’s magnetohydrodynamical properties.
The trajectory of the camera consisted of two phases: a hovering observer and an advected observer. For this second phase, we used an axisymmetric GRMHD simulation, in contrast to the plasma simulation used to calculate the radiation, which was fully-three-dimensional. This choice, whilst scientifically less accurate, was intentional and somewhat necessary. Turbulent features in the ϕ direction were omitted since they can be nauseating to watch in VR environments and commonly lead to motion sickness. A composition of starfield and accretion flow images at four frequencies was then used to create a movie, consisting of 8600 frames, which is freely available on YouTube.
This movie couples GRMHD simulations with GRRT post-processing in VR. Since we do not make any strong a-priori assumptions regarding the field-of-view of the observer, we can calculate the full radiation field measured at a specific point in the accretion disk, where we include all GR effects. This enabled us to calculate light curves of the total measured luminosity at multiple frequency bands at the position of a particle being advected in the flow. This way of calculating the full self-irradiation of the disk is of potential interest in, e.g., studies of X-ray reflection models in AGN, or coupling to GRMHD simulation to calculate the proper radiative feedback onto an emitting, absorbing (and even scattering) plasma in GR in a self-consistent way.
Finally, beyond the aforementioned scientific applications, VR represents a new medium for scientific visualisation which can be used, as demonstrated in this work, to investigate the emission that an observer would measure from inside the accretion flow. It is natural, and of contemporary interest even in the film industry (see e.g. James et al. 2015a, 2015b) to ask the question as to what an observer would see if they were in the immediate vicinity of a black hole. In this work, we have sought to address this question directly, by using state-of-the-art numerical techniques and astrophysical models in a physically-self-consistent manner. Given the EHTC is anticipated to obtain images of the black hole shadows in Sgr A* and M87 in the near future, the calculations we have presented are timely. The VR movies presented in this work also provide an intuitive and interactive way to communicate black hole physics to wider audiences, serving as a useful educational tool.
Declarations
Acknowledgements
The authors thank Oliver Porth, Sera Markoff, Dimitrios Psaltis, Chi-kwam Chan, Christiaan Brinkerink, Yosuke Mizuno, Luciano Rezzolla, and Robin Sip, for useful comments and discussions during this project. The GRMHD simulation was performed on the LOEWE computing facility at the CSC-Frankfurt, the advection simulation and radiative-transfer calculations were performed on the COMA computing facility at Radboud University Nijmegen. This research has made use of NASA’s Astrophysics Data System.
Availability of data and materials
Please contact author for data requests.
Funding
The authors acknowledge support from the ERC Synergy Grant “BlackHoleCam: Imaging the Event Horizon of Black Holes” (Grant 610058). ZY acknowledges support from a Leverhulme Trust Early Career Fellowship.
Authors’ contributions
JD performed GRMHD and GRRT simulations, created the movie, and wrote the initial manuscript. TB provided the RAPTOR code. JD and TB extended RAPTOR to generate 360^{∘} images. DK performed the particle-tracer simulation. TB and ZY helped write the manuscript. ZY provided code to calculate background lensing structures. JD, MM, TB, and HF provided the physically motivated model for Sgr A*. MM provided initial guidance on how to make 360^{∘} movies. ZY, MM and HF provided ideas to initialise the project and provided feedback throughout. All authors discussed and commented on the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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