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We present the novel algorithmically regularised integration method MSTAR for high accuracy ($|\Delta E/E| \gtrsim 10^{-14}$) integrations of N-body systems using minimum spanning tree coordinates. The two-fold parallelisation of the $\mathcal{O}(N_\mathrm{part}^2)$ force loops and the substep divisions of the extrapolation method allows for a parallel scaling up to $N_\mathrm{CPU} = 0.2 \times N_\mathrm{part}$. The efficient parallel scaling of MSTAR makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularisation chain (AR-CHAIN) methods, e.g. $N_\mathrm{part} = 5000$ particles on $400$ CPUs for $1$ Gyr in a few weeks of wall-clock time. We present applications of MSTAR on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to $N_\mathrm{part} =10^4$ particles. Combined with a tree or a fast multipole based integrator the high performance of MSTAR removes a major computational bottleneck in simulations with regularised subsystems. It will enable the next generation galactic-scale simulations with up to $10^9$ stellar particles (e.g. $m_\star = 100 M_\odot$ for a $M_\star = 10^{11} M_\odot$ galaxy) including accurate collisional dynamics in the vicinity of nuclear supermassive black holes., Comment: 20 pages, 16 figures, accepted for publication in MNRAS

© 2020. The American Astronomical Society. All rights reserved., Binary black hole (BH) central engine description for the unique blazar OJ 287 predicted that the next secondary BH impact-induced bremsstrahlung flare should peak on 2019 July 31. This prediction was based on detailed general relativistic modeling of the secondary BH trajectory around the primary BH and its accretion disk. The expected flare was termed the Eddington flare to commemorate the centennial celebrations of now-famous solar eclipse observations to test general relativity by Sir Arthur Eddington. We analyze the multi-epoch Spitzer observations of the expected flare between 2019 July 31 and 2019 September 6, as well as baseline observations during 2019 February-March. Observed Spitzer flux density variations during the predicted outburst time display a strong similarity with the observed optical pericenter flare from OJ 287 during 2007 September. The predicted flare appears comparable to the 2007 flare after subtracting the expected higher base-level Spitzer flux densities at 3.55 and 4.49 mu m compared to the optical R-band. Comparing the 2019 and 2007 outburst lightcurves and the previously calculated predictions, we find that the Eddington flare arrived within 4 hr of the predicted time. Our Spitzer observations are well consistent with the presence of a nano-Hertz gravitational-wave emitting spinning massive binary BH that inspirals along a general relativistic eccentric orbit in OJ 287. These multi-epoch Spitzer observations provide a parametric constraint on the celebrated BH no-hair theorem., We thank Sean Carey for useful discussions on Spitzer data. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. L.D. and A.G. acknowledge support of the Department of Atomic Energy, Government of India, under project No. 12-R&D-TFR-5.02-0200. S.Z. acknowledges grant No. NCN 2018/29/B/ST9/01793.

In the binary black hole model of OJ 287 the secondary black hole orbits a much more massive primary, and impacts on the primary accretion disk at predictable times. We update the parameters of the disk, the viscosity $\alpha$ and the mass accretion rate $\dot m$. We find $\alpha=0.26 \pm 0.1$ and $\dot m = 0.08 \pm 0.04$ in Eddington units. The former value is consistent with Coroniti (1981) and the latter with Marscher and Jorstad (2011). Predictions are made for the 2019 July 30 superflare in OJ 287. We expect that it will take place simultaneously at the Spitzer infrared channels as well as in the optical and that therefore the timing of the flare in optical can be accurately determined from Spitzer observations. We also discuss in detail the light curve of the 2015 flare and find that the radiating volume has regions where bremsstrahlung dominates as well as regions that radiate primarily in synchrotron radiation. The former region produces the unpolarised first flare while the latter region gives rise to a highly polarized second flare., Comment: 12 pages, 4 figures, to appear in ApJ

We study the orbital evolution and gravitational wave (GW) emission of supermassive black hole (SMBH) binaries formed in gas-free mergers of massive early-type galaxies using the hybrid tree-regularized N-body code KETJU. The evolution of the SMBHs and the surrounding galaxies is followed self-consistently from the large-scale merger down to the final few orbits before the black holes coalesce. Post-Newtonian corrections are included up to PN3.5-level for the binary dynamics, and the GW calculations include the corresponding corrections up to PN1.0-level. We analyze the significance of the stellar environment on the evolution of the binary and the emitted GW signal during the final GW emission dominated phase of the binary hardening and inspiral. Our simulations are compared to semi-analytic models that have often been used for making predictions for the stochastic GW background emitted by SMBHs. We find that the commonly used semi-analytic parameter values produce large differences in merger timescales and eccentricity evolution, but result in only $\sim 10\%$ differences in the GW spectrum emitted by a single binary at frequencies $f\gtrsim 10^{-1} \, \rm yr^{-1}$, which are accessible by current pulsar timing arrays. These differences are in part caused by the strong effects of the SMBH binaries on the surrounding stellar population, which are not included in the semi-analytic models., 22 pages, 10 figures, published in ApJ

We present an analytic model for computing the luminosity and spectral evolution of flares caused by a supermassive black hole impacting the accretion disc of another supermassive black hole. Our model includes photon diffusion, emission from optically thin regions and relativistic corrections to the observed spectrum and time-scales. We test the observability of the impact scenario with a simulated population of quasars hosting supermassive black hole binaries. The results indicate that for a moderate binary mass ratio of 0.3, and impact distances of 100 primary Schwarzschild radii, the accretion disc impacts can be expected to equal or exceed the host quasar in brightness at observed wavelength {\lambda} = 510 nm up to z = 0.6. We conclude that accretion disc impacts may function as an independent probe for supermassive black hole binaries. We release the code used for computing the model light curves to the community., Comment: 17 pages, 5 figures, 4 tables. Accepted to Monthly Notices of the Royal Astronomical Society

Ray-tracing is a central tool for constructing mock observations of compact object emission and for comparing physical emission models with observations. We present Arcmancer, a publicly available general ray-tracing and tensor algebra library, written in C++ and providing a Python interface. Arcmancer supports Riemannian and semi-Riemannian spaces of any dimension and metric, and has novel features such as support for multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems and automatic parallel propagation. The Arcmancer interface is extensively documented and user-friendly. While these capabilities make the library well suited for a large variety of problems in numerical geometry, the main focus of this paper is in general relativistic polarized radiative transfer. The accuracy of the code is demonstrated in several code tests and in a comparison with GRTRANS, an existing ray-tracing code. We then use the library in several scenarios as a way to showcase the wide applicability of the code. We study a thin variable-geometry accretion disk model, and find that polarization carries information of the inner disk opening angle. Next, we study rotating neutron stars and determine that to obtain polarized light curves at better than $\sim1\%$ level of accuracy, the rotation needs to be taken into account both in the space-time metric as well as in the shape of the star. Finally, we investigate the observational signatures of an accreting black hole lensed by an orbiting black hole. We find that these systems exhibit a characteristic asymmetric twin-peak profile both in flux and polarization properties., 39 pages, 17 figures, refereed version, published in ApJ. The Arcmancer library is available at https://bitbucket.org/popiha/arcmancer

We propose a new mathematical model for $n-k$-dimensional non-linear correlations with intrinsic scatter in $n$-dimensional data. The model is based on Riemannian geometry, and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated datasets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in $n$-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions, and compare our results to existing methods. Finally, we apply our methodology to the well-known $M_\text{BH}$-$\sigma$ correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is $\sim 6$ for the datasets used, rather than the values in the range $\sim 4$-$5$ typically quoted in the literature for these data., Comment: 19 pages, 5 figures. Revision accepted to MNRAS

A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. By using a Hamilton-Jacobi formalism, we show how the special relativistic rotational effects such as aberration of angles, Doppler boosting, and time dilatation naturally emerge from the general relativistic treatment of rotating compact objects. We use the Butterworth-Ipser metric expanded up to the second order in rotation and hence include effects of light bending, frame-dragging, and quadrupole deviations to our geodesic calculations. We also give detailed descriptions of the numerical algorithms used and provide an open source implementation of the numerical framework called bender. As an application, we study spectral line profiles (i.e., smearing kernels) from rapidly rotating oblate neutron stars. We find that in this metric description the second order quadrupole effects are not strong enough to produce narrow observable features in the spectral energy distribution for almost any physically realistic parameter combination, and hence, actually detecting them is unlikely. The full width at tenth-maximum and full width at half-maximum of the rotation smearing kernels are also reported for all viewing angles. These can be then used to quantitatively estimate the effects of rotational smearing on the observed spectra. We also calculate accurate pulse profiles and observer skymaps of emission from hot spots on rapidly rotating accreting millisecond pulsars. These allow us to quantify the strength of the pulse fractions one expects to observe from typical fast spinning millisecond pulsars., 19 pages, 12 figures. published version

We discuss the problem of polarized radiative transfer in general relativity. We present a set of equations suitable for solving the problem numerically for the case of an arbitrary space-time metric, and show numerical solutions to example problems. The solutions are computed with a new ray-tracing code, Arcmancer, developed by the authors., 4 pages, 2 figures. To appear in the Proceedings of the IAU Symposium No. 324, New Frontiers in Black Hole Astrophysics

We analyse the light curve in the R band of the blazar OJ287, gathered during the 2015/2016 observing season. We did a search for quasi-periodic oscillations (QPOs) using several methods over a wide range of timescales. No statistically significant periods were found in the high-frequency domain both in the ground-based data and in Kepler observations. In the longer-period domain, the Lomb–Scargle periodogram revealed several peaks above the 99% significance level. The longest one—about 95 days—corresponds to the innermost stable circular orbit (ISCO) period of the more massive black hole. The 43-day period could be an alias, or it can be attributed to accretion in the form of a two-armed spiral wave.

Poincaré maps are a basic dynamical systems tool yielding information about the geometric structure of the phase space of the system. Poincaré maps are however time consuming to compute. In this paper we have analysed and compared two different schemes to compute Poincaré maps in the context of accuracy versus computation time: a Runge-Kutta method of 7th and 8th order and a time transformed geometric method of 6th order. The dynamical system used is the Restricted Full Three Body Problem, with the primaries, an elongated body and a sphere, in a short axis relative equilibrium configuration. Using these Poincar´e maps we have studied the dynamics near the collinear Lagrange point L3, located on the outer side of the elongated body. We present evidence that the L3 point in this system can have saddle-center, stable or complex unstable behaviour depending on system parameters. We further show that when a low accuracy regime that still captures the correct structure of the Poincaré map is considered, the geometric method clearly outperforms the Runge-Kutta method being up to 4 times faster to compute and free from accumulating local errors that smear the structure of the Poincaré maps.