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The bright blazar OJ 287 is the best-known candidate for hosting a supermassive black hole binary system. It inspirals due to the emission of nanohertz gravitational waves (GWs). Observations of historical and predicted quasi-periodic high-brightness flares in its century-long optical lightcurve, allow us to determine the orbital parameters associated with the binary black hole (BBH) central engine. In contrast, the radio jet of OJ 287 has been covered with Very Long Baseline Interferometry (VLBI) observations for only about $30$ years and these observations reveal that the position angle (PA) of the jet exhibits temporal variations at both millimetre and centimetre wavelengths. Here we associate the observed PA variations in OJ 287 with the precession of its radio jet. In our model, the evolution of the jet direction can be associated either with the primary black hole (BH) spin evolution or with the precession of the angular momentum direction of the inner region of the accretion disc. Our Bayesian analysis shows that the BBH central engine model, primarily developed from optical observations, can also broadly explain the observed temporal variations in the radio jet of OJ 287 at frequencies of 86, 43, and 15 GHz. Ongoing Global mm-VLBI Array (GMVA) observations of OJ 287 have the potential to verify our predictions for the evolution of its $86$ GHz PA values. Additionally, thanks to the extremely high angular resolution that the Event Horizon Telescope (EHT) can provide, we explore the possibility to test our BBH model through the detection of the jet in the secondary black hole., Comment: 12 pages, 7 figures, 1 table. Accepted for publication in MNRAS

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 hours 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., Comment: 8 pages, 4 figures, 1 table, to appear in ApJL

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

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., Comment: 22 pages, 10 figures, published in ApJ

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

Interpolation of data represented in curvilinear coordinates and possibly having some non-trivial, typically Riemannian or semi-Riemannian geometry is an ubiquitous task in all of physics. In this work we present a covariant generalization of the barycentric coordinates and the barycentric interpolation method for Riemannian and semi-Riemannian spaces of arbitrary dimension. We show that our new method preserves the linear accuracy property of barycentric interpolation in a coordinate-invariant sense. In addition, we show how the method can be used to interpolate constrained quantities so that the given constraint is automatically respected. We showcase the method with two astrophysics related examples situated in the curved Kerr spacetime. The first problem is interpolating a locally constant vector field, in which case curvature effects are expected to be maximally important. The second example is a General Relativistic Magnetohydrodynamics simulation of a turbulent accretion flow around a black hole, wherein high intrinsic variability is expected to be at least as important as curvature effects., Comment: 10 pages, 3 figures. Revised version with small additions, accepted to MNRAS

The bright blazar OJ 287 is the best-known candidate for hosting a nanohertz gravitational wave (GW) emitting supermassive binary black hole (SMBBH) in the present observable universe. The binary black hole (BBH) central engine model, proposed by Lehto and Valtonen in 1996, was influenced by the two distinct periodicities inferred from the optical light curve of OJ 287. The current improved model employs an accurate general relativistic description to track the trajectory of the secondary black hole (BH) which is crucial to predict the inherent impact flares of OJ 287. The successful observations of three predicted impact flares open up the possibility of using this BBH system to test general relativity in a hitherto unexplored strong field regime. Additionally, we briefly describe an on-going effort to interpret observations of OJ 287 in a Bayesian framework., Comment: Invited review article; 16 pages, 4 figures, 2 tables, to appear in Universe

Results from regular monitoring of relativistic compact binaries like PSR 1913+16 are consistent with the dominant (quadrupole) order emission of gravitational waves (GWs). We show that observations associated with the binary black hole central engine of blazar OJ 287 demand the inclusion of gravitational radiation reaction effects beyond the quadrupolar order. It turns out that even the effects of certain hereditary contributions to GW emission are required to predict impact flare timings of OJ 287. We develop an approach that incorporates this effect into the binary black hole model for OJ~287. This allows us to demonstrate an excellent agreement between the observed impact flare timings and those predicted from ten orbital cycles of the binary black hole central engine model. The deduced rate of orbital period decay is nine orders of magnitude higher than the observed rate in PSR 1913+16, demonstrating again the relativistic nature of OJ 287's central engine. Finally, we argue that precise timing of the predicted 2019 impact flare should allow a test of the celebrated black hole "no-hair theorem" at the 10% level., Comment: 24 pages, 11 figures, 3 tables, accepted for publication in ApJ

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., Comment: 39 pages, 17 figures, refereed version, published in ApJ. The Arcmancer library is available at https://bitbucket.org/popiha/arcmancer

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., Comment: 19 pages, 12 figures. published version

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

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., Comment: 4 pages, 2 figures. To appear in the Proceedings of the IAU Symposium No. 324, New Frontiers in Black Hole Astrophysics

We present KETJU, a new extension of the widely-used smoothed particle hydrodynamics simulation code GADGET-3. The key feature of the code is the inclusion of algorithmically regularized regions around every supermassive black hole (SMBH). This allows for simultaneously following global galactic-scale dynamical and astrophysical processes, while solving the dynamics of SMBHs, SMBH binaries and surrounding stellar systems at sub-parsec scales. The KETJU code includes Post-Newtonian terms in the equations of motions of the SMBHs which enables a new SMBH merger criterion based on the gravitational wave coalescence timescale pushing the merger separation of SMBHs down to $\sim 0.005$ pc. We test the performance of our code by comparison to NBODY7 and rVINE. We set up dynamically stable multi-component merger progenitor galaxies to study the SMBH binary evolution during galaxy mergers. In our simulation sample the SMBH binaries do not suffer from the final-parsec problem, which we attribute to the non-spherical shape of the merger remnants. For bulge-only models, the hardening rate decreases with increasing resolution, whereas for models which in addition include massive dark matter halos the SMBH binary hardening rate becomes practically independent of the mass resolution of the stellar bulge. The SMBHs coalesce on average 200 Myr after the formation of the SMBH binary. However, small differences in the initial SMBH binary eccentricities can result in large differences in the SMBH coalescence times. Finally, we discuss the future prospects of KETJU, which allows for a straightforward inclusion of gas physics in the simulations., Comment: 28 pages, 18 figures. Accepted for publication in ApJ

The predicted abundance and properties of the low-mass substructures embedded inside larger dark matter haloes differ sharply among alternative dark matter models. Too small to host galaxies themselves, these subhaloes may still be detected via gravitational lensing, or via perturbations of the Milky Way's globular cluster streams and its stellar disk. Here we use the Apostle cosmological simulations to predict the abundance and the spatial and velocity distributions of subhaloes in the range 10^6.5-10^8.5 solar masses inside haloes of mass ~ 10^12 solar masses in LCDM. Although these subhaloes are themselves devoid of baryons, we find that baryonic effects are important. Compared to corresponding dark matter only simulations, the loss of baryons from subhaloes and stronger tidal disruption due to the presence of baryons near the centre of the main halo, reduce the number of subhaloes by ~ 1/4 to 1/2, independently of subhalo mass, but increasingly towards the host halo centre. We also find that subhaloes have non-Maxwellian orbital velocity distributions, with centrally rising velocity anisotropy and positive velocity bias which reduces the number of low-velocity subhaloes, particularly near the halo centre. We parameterise the predicted population of subhaloes in terms of mass, galactocentric distance, and velocities. We discuss implications of our results for the prospects of detecting dark matter substructures and for possible inferences about the nature of dark matter., Comment: 19 pages, submitted to MNRAS, comments welcome

OJ287 is a quasi-periodic quasar with roughly 12 year optical cycles. It displays prominent outbursts which are predictable in a binary black hole model. The model predicted a major optical outburst in December 2015. We found that the outburst did occur within the expected time range, peaking on 2015 December 5 at magnitude 12.9 in the optical R-band. Based on Swift/XRT satellite measurements and optical polarization data, we find that it included a major thermal component. Its timing provides an accurate estimate for the spin of the primary black hole, chi = 0.313 +- 0.01. The present outburst also confirms the established general relativistic properties of the system such as the loss of orbital energy to gravitational radiation at the 2 % accuracy level and it opens up the possibility of testing the black hole no-hair theorem with a 10 % accuracy during the present decade.

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

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator., Comment: Accepted to Celestial Mechanics and Dynamical Astronomy. 22 pages, 4 figures, 3 tables

Context. OJ287 is a quasar with a quasi-periodic optical light curve, with the periodicity observed for over 120 years. This has lead to a binary black hole model as a common explanation of the quasar. The radio jet of OJ287 has been observed for a shorter time of about 30 years. It has a complicated structure that varies dramatically in a few years time scale. Aims. Here we propose that this structure arises from a helical jet being observed from a small and varying viewing angle. The viewing angle variation is taken to be in tune with the binary orbital motion. Methods. We calculate the effect of the secondary black hole on the inner edge of the accretion disk of the primary using particle simulations. We presume that the axis of the helix is perpendicular to the disk. We then follow the jet motion on its helical path and project the jet to the sky plane. This projection is compared with observations both at mm waves and cm waves. Results. We find that this model reproduces the observations well if the changes in the axis of the conical helix propagate outwards with a relativistic speed of about 0.85c. In particular, this model explains at the same time the long-term optical brightness variations as varying Doppler beaming in a component close to the core, i.e. at parsec scale in real linear distance, while the mm and cm radio jet observations are explained as being due to jet wobble at much larger (100 parsec scale) distances from the core., Comment: 5 pages, 7 figures, to be published in Astronomy & Astrophysics

We have studied short-term variations of the blazar OJ 287, suspected to host a supermassive black hole binary. In this study, we use a two-season optical R-band dataset from 2004--2006 which consists of 3991 data points from the OJ 287 observation campaign. It has sections of dense time coverage, and is largely independent from previously published data. We find that this data confirms the existence of a ~50 day periodic component, presumably related to the half-period of the innermost stable circular orbit (ISCO) of the primary black hole. In addition we find several pseudo-periodic components in the 1 to 7 day range, most prominently at 3.5 days, which are likely Lorentz contracted jet re-emission of the 50 day component. The typical 50 day cycle exhibits a slow rise of brightness and a rapid dimming before the start of the new cycle. We explain this as being due to a spiral wave in the accretion disc which feeds the central black hole in this manner., Comment: 8 pages, 12 figures, to be published in Monthly Notices of the Royal Astronomical Society

We have studied three most recent precursor flares in the light curve of the blazar OJ 287 while invoking the presence of a precessing binary black hole in the system to explain the nature of these flares. Precursor flare timings from the historical light curves are compared with theoretical predictions from our model that incorporate effects of an accretion disk and post-Newtonian description for the binary black hole orbit. We find that the precursor flares coincide with the secondary black hole descending towards the accretion disk of the primary black hole from the observed side, with a mean z-component of approximately z_c = 4000 AU. We use this model of precursor flares to predict that precursor flare of similar nature should happen around 2020.96 before the next major outburst in 2022., Comment: to appear in the Astrophysical Journal

We present the results of the study of the substructure and galaxy content of ten rich clusters of galaxies in three different superclusters of the Sloan Great Wall. We determine the substructure in clusters using the 'Mclust' package from the 'R' statistical environment and analyse their galaxy content. We analyse the distribution of the peculiar velocities of galaxies in clusters and calculate the peculiar velocity of the first ranked galaxy. We show that clusters in our sample have more than one component; in some clusters different components also have different galaxy content. We find that in some clusters with substructure the peculiar velocities of the first ranked galaxies are large. All clusters in our sample host luminous red galaxies. They can be found both in the central areas of clusters as well as in the outskirts, some of them have large peculiar velocities. About 1/3 of red galaxies in clusters are spirals. The scatter of colours of red ellipticals is in most clusters larger than that of red spirals. The presence of substructure in rich clusters, signs of possible mergers and infall, as well as the large peculiar velocities of the first ranked galaxies suggest that the clusters in our sample are not yet virialized. We present merger trees of dark matter haloes in an N-body simulation to demonstrate the formation of present-day dark matter haloes via multiple mergers during their evolution. In simulated dark matter haloes we find a substructure similar to that in observed clusters., Comment: 19 pages, 44 figures, accepted for publication in Astronomy and Astrophysics