How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's ...conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.
ABSTRACT
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 yr 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 BH.
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, , and the mass accretion rate, . We find = 0.26 0.1 and in Eddington units. The former value is consistent with Coroniti, and the latter with Marscher & Jorstad. 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 unpolarized first flare, while the latter region gives rise to a highly polarized second flare.
ABSTRACT
The bright blazar OJ 287 routinely parades high brightness bremsstrahlung flares, which are explained as being a result of a secondary supermassive black hole (SMBH) impacting the accretion ...disc of a more massive primary SMBH in a binary system. The accretion disc is not rigid but rather bends in a calculable way due to the tidal influence of the secondary. Next, we refer to this phenomenon as a variable disc level. We begin by showing that these flares occur at times predicted by a simple analytical formula, based on general relativity inspired modified Kepler equation, which explains impact flares since 1888. The 2022 impact flare, namely flare number 26, is rather peculiar as it breaks the typical pattern of two impact flares per 12-yr cycle. This is the third bremsstrahlung flare of the current cycle that follows the already observed 2015 and 2019 impact flares from OJ 287. It turns out that the arrival epoch of flare number 26 is sensitive to the level of primary SMBH’s accretion disc relative to its mean level in our model. We incorporate these tidally induced changes in the level of the accretion disc to infer that the thermal flare should have occurred during 2022 July–August, when it was not possible to observe it from the Earth. Thereafter, we explore possible observational evidence for certain pre-flare activity by employing spectral and polarimetric data from our campaigns in 2004/05 and 2021/22. We point out theoretical and observational implications of two observed mini-flares during 2022 January–February.
Abstract
We present the first polarimetric space very long baseline interferometry (VLBI) observations of OJ 287, observed with RadioAstron at 22 GHz during a perigee session on 2014 April 4 and five ...near-in-time snapshots, together with contemporaneous ground VLBI observations at 15, 43, and 86 GHz. Ground-space fringes were obtained up to a projected baseline of 3.9 Earth diameters during the perigee session, and at a record 15.1 Earth diameters during the snapshot sessions, allowing us to image the innermost jet at an angular resolution of ∼50
μ
as, the highest ever achieved at 22 GHz for OJ 287. Comparison with ground-based VLBI observations reveals a progressive jet bending with increasing angular resolution that agrees with predictions from a supermassive binary black hole model, although other models cannot be ruled out. Spectral analyses suggest that the VLBI core is dominated by the internal energy of the emitting particles during the onset of a multiwavelength flare, while the parsec-scale jet is consistent with being in equipartition between the particles and magnetic field. Estimated minimum brightness temperatures from the visibility amplitudes show a continued rising trend with projected baseline length up to 10
13
K, reconciled with the inverse-Compton limit through Doppler boosting for a jet closely oriented to the line of sight. The observed electric vector position angle suggests that the innermost jet has a predominantly toroidal magnetic field, which, together with marginal evidence of a gradient in rotation measure across the jet width, indicates that the VLBI core is threaded by a helical magnetic field, in agreement with jet formation models.
Abstract
We study the optical flux and polarization variability of the binary black hole blazar OJ 287 using quasi-simultaneous observations from 2015 to 2023 carried out using telescopes in the USA, ...Japan, Russia, Crimea, and Bulgaria. This is one of the most extensive quasi-simultaneous optical flux and polarization variability studies of OJ 287. OJ 287 showed large amplitude, ∼3.0 mag flux variability, large changes of ∼37% in degree of polarization, and a large swing of ∼215° in the angle of the electric vector of polarization. During the period of observation, several flares in flux were detected. Those flares are correlated with a rapid increase in the degree of polarization and swings in electric vector of polarization angle. A peculiar behavior of anticorrelation between flux and polarization degree, accompanied by a nearly constant polarization angle, was detected from JD 2,458,156 to JD 2,458,292. We briefly discuss some explanations for the flux and polarization variations observed in OJ 287.
Successful observations of the seven predicted bremsstrahlung flares from the unique bright blazar OJ 287 firmly point to the presence of a nanohertz gravitational wave (GW) emitting supermassive ...black hole (SMBH) binary central engine. We present arguments for the continued monitoring of the source in several electromagnetic windows to firmly establish various details of the SMBH binary central engine description for OJ 287. In this article, we explore what more can be known about this system, particularly with regard to accretion and outflows from its two accretion disks. We mainly concentrate on the expected impact of the secondary black hole on the disk of the primary on 3 December 2021 and the resulting electromagnetic signals in the following years. We also predict the times of exceptional fades, and outline their usefulness in the study of the host galaxy. A spectral survey has been carried out, and spectral lines from the secondary were searched for but were not found. The jet of the secondary has been studied and proposals to discover it in future VLBI observations are mentioned. In conclusion, the binary black hole model explains a large number of observations of different kinds in OJ 287. Carefully timed future observations will be able to provide further details of its central engine. Such multi-wavelength and multidisciplinary efforts will be required to pursue multi-messenger nanohertz GW astronomy with OJ 287 in the coming decades.
We derive new solutions for the binary black hole model of OJ 287, using the 2005 November outburst as one of the fixed points. Previous models have used the 1994 September outburst, which is in many ...ways ill defined and leads to considerable uncertainty in the orbit. In addition, the inherent asymmetry in the double outburst structure, due to the vantage point of the observer lying to one side of the accretion disk, has been included in the models for the first time. The disk bending is calculated using a million-particle disk as a model for the accretion disk. In addition, allowance is made for the possibility of different values of disk thickness. The parameters of the system to be determined are the orbital period, fixed by the separation of the 1947.30 and 1983.00 outbursts; the orientation of the major axis of the orbit at a given time, fixed by the 1972.99 outburst; the time delay factor, which is a function of the disk thickness, fixed by the 2005.82 outburst; and the precession rate of the binary, fixed by the 1913.02 outburst. A unique solution is found for both the case of gravitational radiation and that of no gravitational radiation. The 2007 September outburst begins 2007 September 9-16 in the former models and 2007 October 8 in the latter model. The 3 week difference will be easily resolved in future observations, and thus the emission of gravitational radiation can be indirectly measured.
ABSTRACT
The highly variable blazar OJ 287 is commonly discussed as an example of a binary black hole system. The 130 yr long optical light curve is well explained by a model where the central body ...is a massive black hole of 18.35 $\times$ 109 solar mass that supports a thin accretion disc. The secondary black hole of 0.15 $\times$ 109 solar mass impacts the disc twice during its 12 yr orbit, and causes observable flares. Recently, it has been argued that an accretion disc with a typical Active Galactic Nuclei (AGN) accretion rate and above mentioned central body mass should be at least six magnitudes brighter than OJ 287’s host galaxy and would therefore be observationally excluded. Based on the observations of OJ 287’s radio jet, detailed in Marscher and Jorstad (2011), and up-to-date accretion disc models of Azadi et al. (2022), we show that the V-band magnitude of the accretion disc is unlikely to exceed the host galaxy brightness by more than one magnitude, and could well be fainter than the host. This is because accretion power is necessary to launch the jet as well as to create electromagnetic radiation, distributed across many wavelengths, and not concentrated especially on the optical V-band. Further, we note that the claimed V-band concentration of accretion power leads to serious problems while interpreting observations of other AGN. Therefore, we infer that the mass of the primary black hole and its accretion rate do not need to be smaller than what is determined in the standard model for OJ 287.
Abstract We report the study of a huge optical intraday flare on 2021 November 12 at 2 a.m. UT in the blazar OJ 287. In the binary black hole model, it is associated with an impact of the secondary ...black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact based on a prediction made 8 yr earlier. The first I -band results of the flare have already been reported by Kishore et al. (2024). Here we combine these data with our monitoring in the R -band. There is a big change in the R – I spectral index by 1.0 ± 0.1 between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary BH. We then ask why we have not seen this phenomenon before. We show that OJ 287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability using the Krakow data set of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In machine-readable Tables 1 and 2, we give the full orbit-linked historical light curve of OJ 287 as well as the dense monitoring sample of Krakow.
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