General relativistic magnetohydrodynamical κ\kappa-jet models for Sgr A*

The observed spectral energy distribution of an accreting supermassive black hole typically forms a power-law spectrum in the Near Infrared (NIR) and optical wavelengths, that may be interpreted as a signature of accelerated electrons along the jet. However, the details of acceleration remain uncertain. In this paper, we study the radiative properties of jets produced in axisymmetric GRMHD simulations of hot accretion flows onto underluminous supermassive black holes both numerically and semi-analytically, with the aim of investigating the differences between models with and without accelerated electrons inside the jet. We assume that electrons are accelerated in the jet regions of our GRMHD simulation. To model them, we modify the electrons' distribution function in the jet regions from a purely relativistic thermal distribution to a combination of a relativistic thermal distribution and the $\kappa$-distribution function. Inside the disk, we assume a thermal distribution for the electrons. We calculate jet spectra and synchrotron maps by using the ray tracing code {\tt RAPTOR}, and compare the synthetic observations to observations of Sgr~A*. Finally, we compare numerical models of jets to semi-analytical ones. We find that in the $\kappa$-jet models, the radio-emitting region size, radio flux, and spectral index in NIR/optical bands increase for decreasing values of the $\kappa$ parameter, which corresponds to a larger amount of accelerated electrons. The model with $\kappa = 3.5$, $\eta_{\rm acc}=5-10\%$ (the percentage of electrons that are accelerated), and observing angle $i = 30^{\rm o}$ fits the observed Sgr~A* emission in the flaring state from the radio to the NIR/optical regimes, while $\kappa = 3.5$, $\eta_{\rm acc}< 1\%$, and observing angle $i = 30^{\rm o}$ fit the upper limits in quiescence.Comment: 17 pages, 16 figures, 1 tabl

RAPTOR II: Polarized radiative transfer in curved spacetime

Accreting supermassive black holes are sources of polarized radiation that propagates through highly curved spacetime before reaching the observer. In order to help interpret observations of such polarized emission, accurate and efficient numerical schemes for polarized radiative transfer in curved spacetime are needed. In this manuscript we extend our publicly available radiative transfer code RAPTOR to include polarization. We provide a brief review of different codes and methods for covariant polarized radiative transfer available in the literature and existing codes, and present an efficient new scheme. For the spacetime-propagation aspect of the computation, we develop a compact, Lorentz-invariant representation of a polarized ray. For the plasma-propagation aspect of the computation, we perform a formal analysis of the stiffness of the polarized radiative-transfer equation with respect to our explicit integrator, and develop a hybrid integration scheme that switches to an implicit integrator in case of stiffness, in order to solve the equation with optimal speed and accuracy for all possible values of the local optical/Faraday thickness of the plasma. We perform a comprehensive code verification by solving a number of well-known test problems using RAPTOR and comparing its output to exact solutions. We also demonstrate convergence with existing polarized radiative-transfer codes in the context of complex astrophysical problems. RAPTOR is capable of performing polarized radiative transfer in arbitrary, highly curved spacetimes. This capability is crucial for interpreting polarized observations of accreting black holes, which can yield information about the magnetic-field configuration in such accretion flows. The efficient formalism implemented in RAPTOR is computationally light and conceptually simple. The code is publicly available

Flares in the Galactic Centre II: polarisation signatures of flares at mm-wavelengths

Recent polarimetric mm-observations of the galactic centre by Wielgus et al. (2022a) showed sinusoidal loops in the Q-U plane with a duration of one hour. The loops coincide with a quasi-simultaneous X-ray flare. A promising mechanism to explain the flaring events are magnetic flux eruptions in magnetically arrested accretion flows (MAD). In our previous work (Porth et al. 2021), we studied the accretion flow dynamics during flux eruptions. Here, we extend our previous study by investigating whether polarization loops can be a signature produced by magnetic flux eruptions. We find that loops in the Q-U plane are robustly produced in MAD models as they lead to enhanced emissivity of compressed disk material due to orbiting flux bundles. A timing analysis of the synthetic polarized lightcurves demonstrate a polarized excess variability at timescales of ~ 1 hr. The polarization loops are also clearly imprinted on the cross-correlation of the Stokes parameters which allows to extract a typical periodicity of 30 min to 1 hr with some evidence for a spin dependence. These results are intrinsic to the MAD state and should thus hold for a wide range of astrophysical objects. A subset of GRMHD simulations without saturated magnetic flux (single temperature SANE models) also produces Q-U loops. However, in disagreement with the findings of Wielgus et al. (2022a), loops in these simulations are quasi-continuous with a low polarization excessComment: submitted to MNRA

Magnetic flux eruptions at the root of time-lags in low-luminosity AGN

Sagittarius A$^\ast$ is a compact radio source at the center of the Milky Way that has not conclusively shown evidence for the presence of a relativistic jet. Nevertheless, indirect methods at radio frequencies do indicate consistent outflow signatures. Brinkerink et al. (2015) found temporal shifts between frequency bands, called time-lags, which are associated with flares and/or outflows of the accretion system. It is possible to gain information on the emission and potential outflow mechanics by interpreting these time-lags. By means of combined general-relativistic magnetrohydrodynamical and radiative transfer modeling, we study the origin of the time-lags for magnetically arrested disc models at three black hole spins ($a_\ast$ = 0.9375, 0, -0.9375). The study also includes a targeted `slow light' study for one of the best-fitting `fast light' windows. We were able to recover the time-lags found by Brinkerink et al. (2015) in various windows of our simulated lightcurves. The theoretical interpretation of these most-promising time-lag windows is threefold; i) a magnetic flux eruption perturbs the jet-disc boundary and creates a flux tube, ii) the flux tube orbits and creates a clear emission feature, and iii) the flux tube interacts with the jet-disc boundary. The best-fitting windows have an intermediate (i=30$^\circ$/50$^\circ$) inclination and zero-BH-spin. The targeted `slow light' study did not yield better-fitting time-lag results, which indicates that the fast vs. slow light paradign is often not intuitively understood and is likely influential in timing-sensitive studies.Comment: 17 pages, 11 figure

Kink instability: evolution and energy dissipation in Relativistic Force-Free Non-Rotating Jets

We study the evolution of kink instability in a force-free, non-rotating plasma column of high magnetization. The main dissipation mechanism is identified as reconnection of magnetic field-lines with various intersection angles, driven by the compression of the growing kink lobes. We measure dissipation rates ${\rm d} U_{B\phi}/{{\rm d}t} \approx -0.1 U_{B\phi}/\tau$, where $\tau$ is the linear growth time of the kink instability. This value is consistent with the expansion velocity of the kink mode, which drives the reconnection. The relaxed state is close to a force-free Taylor state. We constraint the energy of that state using considerations from linear stability analysis. Our results are important for understanding magnetic field dissipation in various extreme astrophysical objects, most notably in relativistic jets. We outline the evolution of the kink instability in such jets and derive constrains on the conditions that allow for the kink instability to grow in these systems.Comment: 18 pages, 13 figure

Observing supermassive black holes in virtual reality

We present a full 360 degree (i.e., 4$\pi$ 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-degree 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-degree 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-degree Virtual Reality movies we present also represent a new medium through which to communicate black hole physics to a wider audience, serving as a powerful educational tool.Comment: 25 pages, 11 figures, 1 movie; https://www.youtube.com/watch?v=SXN4hpv977s&t=57

Linear analysis of the Kelvin-Helmholtz instability in relativistic magnetized symmetric flows

We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed $c_{\rm s}$, Alfv\'en speed $v_{\rm A}$, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity onto the fluid-frame wavevector is larger than the projection of the Alfv\'en speed onto the same direction, i.e., shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed $v$, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $M_{re} \equiv v/v_{\rm f\perp} \sqrt{(1-v_{\rm f\perp}^2)/(1-v^2)} \cos\theta=\sqrt{2}$, where $v_{rm f\perp}=[v_A^2+c_{\rm s}^2(1-v_A^2)]^{1/2}$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and $\theta$ is the laboratory-frame angle between the flow velocity and the wavevector projection onto the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes -- both for single objects and for merging binaries -- where the Alfv\'en speed may approach the speed of light.Comment: 11 pages, 7 figures, 1 table, Accepted for publication in Monthly Notices of the Royal Astronomical Societ

RAPTOR I: Time-dependent radiative transfer in arbitrary spacetimes

Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent.Comment: 18 pages, 14 figures, 5 table

Disappearing thermal X-ray emission as a tell-tale signature of merging massive black hole binaries

The upcoming Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GWs) from massive black hole binaries (MBHB). Finding the electromagnetic (EM) counterparts for these GW events will be crucial for understanding how and where MBHBs merge, measuring their redshifts, constraining the Hubble constant and the graviton mass, and for other novel science applications. However, due to poor GW sky localisation, multi-wavelength, time-dependent electromagnetic (EM) models are needed to identify the right host galaxy among many candidates. We studied merging MBHBs embedded in a circumbinary disc using high-resolution two-dimensional simulations, with a $\Gamma$-law equation of state, incorporating viscous heating, shock heating, and radiative cooling. We simulate the binary from large separation until after merger, allowing us to model the decoupling of the binary from the circumbinary disc (CBD). We compute the EM signatures and identify distinct features before, during, and after the merger. Our main result is a multi-band EM signature: we find that the MBHB produces strong thermal X-ray emission until 1-2 days prior to the merger. However, as the binary decouples from the CBD, the X-ray-bright minidiscs rapidly shrink in size, become disrupted, and the accretion rate drops precipitously. As a result, the thermal X-ray luminosity drops by orders of magnitude, and the source remains X-ray dark for several days after the merger, regardless of any post-merger effects such as GW recoil or mass loss. Looking for the abrupt spectral change where the thermal X-ray disappears is a tell-tale EM signature of LISA mergers that does not require extensive pre-merger monitoring.Comment: 14 pages, 16 figures, 1 table, submitted to journa

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

Self-lensing flares (SLFs) are expected to be produced once or twice per orbit by an accreting massive black hole binary (MBHB), if the eclipsing MBHBs are observed close to edge-on. SLFs can provide valuable electromagnetic (EM) signatures to accompany the gravitational waves (GWs) detectable by the upcoming Laser Interferometer Space Antenna (LISA). EM follow-ups are crucial for, e.g., sky-localization, and constraining the Hubble constant and the graviton mass. We use high-resolution two-dimensional viscous hydrodynamical simulations of a circumbinary disk (CBD) embedding a MBHB. We then use very high-cadence output of these hydrodynamical simulation inputs for a general-relativistic ray-tracing code to produce synthetic spectra and phase-folded light curves. Our main results show a significant periodic amplification of the flux with the characteristic shape of a sharp flare with a central dip, as the foreground black hole (BH) transits across the minidisk and shadow of the background BH, respectively. These corroborate previous conclusions based on the microlensing approximation and analytical toy models of the emission geometry. We also find that at lower inclinations, without some occlusion of the minidisk emission by the CBD, shocks from quasi-periodic mass-trading between the minidisks can produce bright flares which can mimic SLFs and could hinder their identification.Comment: 14 pages, 11 figures, submitted to journal, split Fig. 1 by frequency, fixed some typo