Electromagnetic and gravitational radiation of blazar OJ 287

Summary

Based on long-term monitoring data of the blazar, a new model for determining the parameters of this close binary supermassive black hole (SMBH) is proposed. The model uses the laws of celestial mechanics and results of harmonic analysis of observational data obtained mainly in the radio and optical wavelength ranges. Within the framework of the proposed model, the masses of SMBH companions, the values of their orbital elements, the parameters of the accretion disk, and its dimensions and thickness were determined. The structure and dynamics of SMBHs and their interaction with the accretion disk are considered. It is shown that OJ 287 may be the most massive close binary SMBH with comparable masses. The obtained characteristics of the SMBH are used to estimate the level of gravitational wave radiation, the lifetime of the system before the merger, as well as the magnitude of changes in the orbits of the companions.

Graphical abstract

Highlights

• •A new model for determining the parameters of close binary supermassive black hole
• •OJ 287 may be the most massive close binary SMBH with comparable masses
• •This system is one of the most powerful emitters of GWs in the universe
• •The lifetime before the merges of components shows that it is a short-lived object

Physics; Space sciences; Astrophysics

Introduction

The blazar OJ 287 is one of brightest and the most researched active galactic nuclei (AGNs) discovered to date. Its activity is possibly related to particular nature. AGNs may consist of binary supermassive black hole (SMBH) in a near-merging evolutionary stage.^1,2 Already at the end of the last century, it was noted that OJ 287 could be a binary SMBH with certain parameters of this system.^3,4 They include masses of components, sizes of their orbits, orbital periods of the central SMBH and companion, the precession of central SMBH, and eccentricity of companion’s orbit. From the monitoring data, we can only have the times, amplitudes, and sequences of the occurrence of flares in the source, which does not allow us to obtain all the named parameters of the close binary SMBH only directly from observations. Thus, to construct the SMBH and determine its parameters, it is necessary to apply a model method using certain assumptions. Observational and theoretical approaches with a minimum of additional assumptions will be preferred.

In addition to the electromagnetic spectrum, binary SMBHs are important sources of gravitational wave (GW). Various detectors can register GWs in different frequency ranges. We will be interested in GW ultra-low-frequency detectors operating in the ultra-low frequency range (10⁻⁹—10⁻⁸ Hz), for example, the International Pulsar Timing Array.⁵ In this frequency range, the power emitted by SMBHs can be very significant. The blazar OJ 287 is considered the most famous AGN in the universe, capable of emitting powerful nano-Hertz GWs.⁶ Even without flares, the GWs power from the object can be as high as dE/dT ≈ 10⁴⁵–10⁴⁶ erg s⁻¹.⁷ But to determine the level of GW radiation from SMBHs, you need to know their exact parameters.

In the previous works^2,8,9,10 we began developing a model of binary SMBH using data, obtained only in radio range. In our opinion, in the case of a bright AGN, we receive radiation in ranges from radio to optics from a narrow angle between the directions of radiation and toward the observer. All relativistic effects are present here: Doppler boosting and transformation of time intervals (periods) from the observer to source systems.^11,12

This article analyzes OJ 287 multi-frequency data to determine the parameters of this SMBH using a new approach based mainly on radio and optical data. Estimates were made of the GW power emitted by OJ 287 and the possible variations in companion orbits.

Results

The proposed method for finding the parameters of binary SMBHs, in the case under consideration for OJ 287, uses celestial mechanics formulas based on Kepler’s laws for observational data. In this case, minimal additional assumptions are used.

In our proposed SMBH model, it is assumed that the axis of rotation of the central SMBH is generally not perpendicular to the plane of the companion’s orbit. Due to incomplete ionization of the substance in the accretion disk (AD), its peripheral regions can rotate and precess somewhat differently from the central SMBH. However, the central parts of the AD can rotate and precess with the SMBH, assuming they are outside the last stationary orbit. The drift of ionized matter due to magnetic, electric fields and rotation of SMBH occurs in the direction of its polar regions, from which emission outflows.

Using the generalized Kepler’s third law, we have

$$T_{orb}^2=\frac{4{\pi }^2·r^3}{G·\left(M+m\right)}\text{,}$$ (Equation 1)

where m, M, r, and G are the mass of the companion, the mass of the central black hole, the radius of the companion’s orbit, and the gravitational constant, respectively.

The precession of the central black hole and ionized regions of the AD occurs due to gravitational disturbances from the companion. The precession T_pr and rotation T_rot periods are determined from the ratio¹³

$${\mathrm{\Omega }}_{\mathit{pr}}=\frac{3G·m·\mathit{Cos}\theta }{4\pi ·r^3·\omega }\text{,}$$ (Equation 2)

or,

$$T_{\mathit{pr}}·T_{orb}=\frac{16{\pi }^2·r^3}{3G·m·Cosi}\text{,}$$ (Equation 3)

Here i is the half-angle of the precession cone. In binary SMBH, there is a strong tidal interaction between the central SMBH and the supermassive companion, so T_rot = T_orb, and we can write taking into account (Equation 1)

$$\frac{M+m}{m}=0.75·\frac{T_{\mathit{pr}}}{T_{orb}}$$ (Equation 4)

Thus, the mass ratio of the central SMBH and the companion depends only on the ratio of the precessional and orbital periods; therefore, the values and periods cannot be set arbitrarily. From the expression (Equation 3) it follows

$$m=\frac{16{\pi }^2·r^3}{3G·T_{orb}·T_{\mathit{pr}}}$$ (Equation 5)

For the mass of the central SMBH (see Equations 4 and 5), we obtain the expression

$$M=\frac{16{\pi }^2·r^3·\left(0.75·T_{\mathit{pr}}-T_{orb}\right)}{3G·T_{obr}^2·T_{\mathit{pr}}}$$ (Equation 6)

Since we receive radiation from an object from a narrow cone with an angle between the directions of ejections ("jets") and toward the observer θ, the time intervals in the observer’s frame of reference must be recalculated into the source system through the Lorentz factor γ in accordance with the expression given by Rieger¹⁴ (Table 2, row 2):

$$T_{source}\approx \frac{T_{obs}·{\gamma }^2}{1+z}$$ (Equation 7)

Table 2.

OJ 287 companion masses for three companion orbit sizes

Radius of the companion’s orbit, cm	Mass of the companion, M·	Mass of central SMBH, M·	Lifetime, years
7.0·1017	1.7·1010	5.3·1010	3·104
4.5·1017	4.4·109	1.4·1010	2.4·105
2.5·1017	6.9·108	2.2·109	8.3·106

The obtained relations (Equations 1, 2, 3, 4, 5, 6, and 7) make it possible to estimate the parameters of the orbit of the double SMBH (r) and their masses (m, M), using the data of long-term multi-frequency monitoring of flux densities and the values of the orbital and precession periods, found from them by harmonic analysis. The data of long-term monitoring of the blazar OJ 287 in the radio and optical ranges are shown in Figure 1.

Figure 1.

Data of OJ 287 multi-frequency monitoring

Only two types of harmonic analysis were used. The first is a harmonic analysis performed using the standard Schuster method.¹⁵ It uses real observational data that do not have a constant time step. This method was able to minimize the influence of the unevenness of the time grid on the calculated periodogram—the estimate of the power spectrum. The advantage of the applied method is also the presence of an analytical relationship between the assessment of the power spectrum and its true value. The Schuster periodogram establishes the relationship between the true power spectrum $g\left(\omega \right)$ and the spectral window $W\left(\omega \right)$ using the relation

$$D\left(\omega \right)=\underset{-\infty }{\overset{\infty }{\int }}g\left({\omega }^{\prime }\right)W\left(\omega -{\omega }^{\prime }\right)d{\omega }^{\prime }$$ (Equation 8)

The presence of such a connection makes it possible to “clean” the spectrum, for example, by the widely known CLEAN method, which was originally developed for processing obtained by aperture synthesis two-dimensional maps. Later, it began to be used in spectral analysis of one-dimensional time series.¹⁶ It was possible to remove extraneous peaks associated with the finiteness and unevenness of the time grid, as well as false maxima, the presence of which is due to noises.

The essence of this algorithm is sequential subtraction of all maxima exceeding a given level from the “dirty” spectrum. Each subtracted spectral peak is determined by its complex amplitude, frequency, and spectral window, which depends on the distribution of time samples. All subtracted peaks form a "clean" spectrum free from false maxima and noise components. The spectrum “cleaning” procedure lasts until there is not a single peak left in the “dirty” spectrum, the value of which exceeds a certain threshold level, depending on the probability of detecting a signal in noise. This level can be determined by knowing the type of distribution of samples of the noise periodogram.^17,18 However, in the case of an uneven time grid, it is impossible to obtain a strict expression for this distribution. The empirical formulas for certain non-uniform series are obtained,¹⁹ but they cannot be considered universal, since for each specific series the distribution under consideration will be specific. Therefore, in order to obtain the threshold for detecting a signal in noise, in this work, for each processed data series, the nature of the distribution of samples of the white noise periodogram was calculated.¹⁸ Such an algorithm was applied for spectral analysis of monitoring data of the spectral density of OJ 287 at different frequencies of the radio range.

The use of radio data to analyze the presence of harmonic components in observational data has an undeniable advantage over the use of optical data.²⁰ Radio data are free from the presence of so-called "red noise" in them. In the optical and radio bands, various methods of receiving and amplifying signals from sources are used. In the optical band, individual quanta are counted, and in the radio range power is received in a certain frequency range. This allows you to get rid of the "red noise" when receiving data in the radio band using the modulation method of reception, which was mentioned in section STAR Methods. “Red noise” has a steep spectrum with a drop in spectral density g toward high frequencies $f\left(g\sim 1/f^2\right)$. Therefore, in the radio range, using diagrammatic modulation, the signal spectrum is transferred to the modulation frequency (1–5 kHz), where the spectral density of the “red noise” drops by tens of decibels. The signal is amplified by the receiving equipment that has these "red noises," and at the output it is converted back to low frequencies. In the optical and other high-frequency bands, it is not yet possible to use this method of reception.

The use of the radio range to determine the parameters of a binary SMBH has another important advantage. Most AGNs are located at cosmological distances. If, at the same time, the central region of the AGN is closed from us by the gas-dust disk surrounding it, then the optical counterpart of the AGN will be very weak or not visible at all. A situation close to this is realized in the radio-bright blazar S 0528 + 134. Its optical magnitude is close to 22. The absorption in the object is more than 5 magnitudes, and it is located at a great distance from the Earth, about 1,500 Mpc.

Our task now is to show that using only optical data and only radio data we obtain similar results from the analysis used. To begin with, we use only long-term monitoring data obtained in the optical wavelength range. The data of the optical range show the presence of a harmonic component for about one year (Figure 1, the bottom panel). Our application of harmonic analysis confirms this assumption. The fragment of the monitoring of OJ 287 in the optical range (R-band) is shown in Figure 2. Here the presence of periods of 1 and 2 years is clearly visible.

Figure 2.

Optical monitoring data (R-band) since 2008 to 2021

Figure 3 shows examples of harmonic analysis results for 4.8 GHz. The spectral power is plotted along the ordinate. Due to limited sample length of observational data, long periods were not considered. On the periodogram we see the pronounced spectral features in the range of periods of 1 and 2 years. The errors in determining the periods were taken equal to the half-width of the harmonic components. Horizontal red line represent confidence probability (confidence level) (p = 0.99). It can be seen that, even without averaging over the radio frequency range, the probability real existence of the considered harmonics is very high. So, for example, the confidence probability of a peak with a period near 1 year at 4.8 GHz exceeds the level p ≈ 0.99. The existence of such period cannot cause any doubt. When analyzing at all frequencies, periods of 1 and 2 years are the most reliable. The use of standard data-processing packages makes it possible to have a mean square measurement error and estimate the probability of a false alarm. The horizontal red line on the spectrum and the given probability values confirm this.

Figure 3.

The dependence the spectral density on the frequency (period T) at frequency 4.8 GHz

The horizontal line represents confidence probability (confidence level) p = 0.99.

To find possible shifts in the values of periodic components throughout the entire monitoring period of the object at 8 GHz, the wavelet data analysis method was used. Practically it consisted of the following. A 25-year data series (half the source’s monitoring time) from the very beginning of observations of the object was examined using harmonic analysis. The duration of 25 years was chosen so that the twice-estimated precession period of 12 years could fall into this interval. Next, a sliding shift of the 25-year dataset was made with an interval of 1 year toward increasing the observation date. As a result of each shift, one year of data were removed from the array, and data of another one year were added to the 25-year data array. Each time, a harmonic analysis of a 25-year data array was performed. As a result, a graph of the harmonic components versus time was constructed (Figure 4).

Figure 4.

Results of wavelet analysis of OJ 287 monitoring data at 8 GHz

A 12-year period is confidently distinguished, which appears in the time interval 1995–2008. Its changes are in the range of values from 11.7 years to 12.3 years. Thus, the changes in the period over 25 years amounted to 0.6 years, which is significantly less than the error of experimental data (Table 1). The probability of the existence of a harmonic component of a 12-year period for spectral density more than 0.2 is greater than p ≥ 0.99999. Therefore, it can be concluded that the 12-year period component is reliable.

Table 1.

The results of harmonic analysis of data from multi-frequency monitoring of the spectral flux density of OJ 287

Т1971–2020 years	12.0 ± 1.3	6.5 ± 0.7	2.1 ± 0.2	1.05 ± 0.1
Т(z=0.86).γ2years	230 ± 22	124.0 ± 12.0	40.2 ± 4.0	20.1.0 ± 2.0

Notes: The first line contains the values of the precession period, its half-period, the orbital period, and the half-period in the observer’s reference frame. In the second row of the table it is the same, but only in the reference frame associated with the source.

Table 1 shows the results of harmonic analysis of data from multi-frequency monitoring of the spectral flux density of OJ 287, averaged over the radio range (4.8, 8, 14 + 15, 22.2 GHz).

The most significant periods that we distinguish from the optical periodogram are T = 1.05, 2.1, 6.5 years. According to optical data, a period of 12 years has long been identified.^3,21 The half-period 6.5 years was detected by analysis of radio and optical data. It has more spectral power than the 12 year period due to the doubled value in the data sample. At all frequencies the periods that are shorter than 2.1 and 1.05 years have a smaller amplitude.

The period of 12 years can be associated with the precession movements of the central SMBH and the AD. According to radio and optical data, the periods 2.1 and 1.05 are present at all frequencies in the error limits. These can be the period of the companion’s orbital motion and its half-period, connected with double crossing of AD by companions in one orbital period. The second row of Table 1 gives the periods in the coordinate system associated with the source (z = 0.306, γ = 5), calculated by Equation 7. In general, γ is a parameter that is not obtained directly from monitoring observations. Its value can be estimated from a comparison of the durations of flares in different AGNs, assuming that there is a relationship between the duration of flares and value of γ-factors.²² Besides, there are estimates of γ-factors made by other authors. So, in the work of Terasranta et al.²³ the value γ = 4 can be obtained for OJ 287. Our data do not contradict this value. We found a reference to the Doppler factor δ ≈ 3.4 of the emitting component.²⁴ Both factors are interrelated with each other, and at small values of the ejection (jet) angles they have comparable values.²⁵

The changes in the gamma factor were insignificant, since there were no changes in the amplitudes of the flares more than several times. The gamma factor and the Doppler factor are related values.^23,26 A 2-fold change in the Doppler factor leads to a change in the flare amplitude by almost an order of magnitude. For example, even a 1.5-fold change in the gamma factor can lead to a 20% change in the period. However, the wavelet analysis did not detect such changes in the fifty-year monitoring data of OJ 287. About 5% of changes in the period were noticed, but one cannot say for sure. Therefore, we suppose that the random error prevailed in the experimental data.

Our choice of precessional and orbital periods does not contradict the data of other authors. So, for 3C120, the values T_pr = 12.3 years and T_orb = 1.4 years are given.²⁷ In the source OJ 287 identified two periods (one 11.65 years, the second 1.1 or 1.6 years) based on optical data.^1,3,28,29,30 The precession and orbital periods 12.4 and 3.0 years were identified in the 3C 273.¹⁵

In addition to the orbital and precessional periods determined from observations and by spectral analysis, Equations 5 and 6 include the value of the radius of the companion’s orbit (r). The value of r is not determined directly from the observations. Therefore, its estimation can only be performed using physical constraints on m and M from above and below. Table 2 shows three data variants for the orbit sizes and companion masses calculated for the periods presented in line 2 (Table 1) and by Equations 5 and 6.

Equations 5 and 6 show that there is a cubic dependence between the masses of the companions and the size of the orbit. This means that we cannot choose an arbitrary size for the companion’s orbit without colliding with unrealistic values for the companion masses. The Eddington’s limit of luminosity L_Edd ≈ 1.38·10³⁸M/M_· erg s⁻¹ is setting the limit on value of masses of SMBHs. The total luminosity of OJ 287 from radio to UV has been estimated as 2·10⁴⁶ erg s⁻¹.³¹ When inverse Compton contributions are added, the total luminosity may be as high as 3·10⁴⁷ erg s⁻¹.³¹ If we equate this value to the Eddington luminosity L ≈ 1.4·10³⁸M/M_· erg s⁻¹, we get a minimum estimate for the mass of the central SMBH M ≈ 2.2·10⁹ M_· (line 3, Table 2).

On the other hand, it is known that astronomers Kianush Merhgan and her colleagues from the Max Planck Institute for Extraterrestrial Physics using the Very Large Telescope have discovered a huge black hole believed to be 4·10¹⁰ M_· at the center of the massive elliptical galaxy Holmberg 15A.³² It is the most massive black hole found in the local universe. Given the accuracy of determining the mass of this SMBH, its mass may turn out to be 3·10¹⁰ M_·. That way the resulting masses of companions in the first row of Table 2 look to be overestimate.

The companion masses obtained in the second row of Table 2 look more realistic. About the mass of 17 billion solar masses for the central SMBH in OJ 287 was reported by Lehto and Valtonen.^33,34 The mass of the central SMBH of 14 billion solar masses does not contradict the aforementioned estimate. The mass of companion is only three times lower than that of of central one, and this is a direct consequence of the obtained ratio of T_pr/T_orb (Equation 4). Thus it turns out that this is one of the most massive binary SMBH of all the brightest AGNs.

Discussion

Thus, the accepted masses and orbital sizes for OJ 287 (Table 2, row 2) indicate that this binary SMBH is a very massive one among the known SMBHs. The ratio of masses of companions is ${\mu }_{OJ287}$ ≈ M/m ≈ 3.2. For massive stars in the galaxy, this ratio of masses of companions is common. There, μ is frequently found to be close to unity.³⁵ In our scheme, supermassive companions revolve around a common center of gravity in almost circular orbits with radii $r_{comp}$ ≈ 4.5·10¹⁷ cm and $r_{center}\approx r_{comp}·\sqrt{\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$M$}\right.}$ ≈ 2.5·10¹⁷ cm. The distance between the companions during their movement around the common center of gravity is a ≈ r_comp+r_centr = 7.0·10¹⁷ cm. At the same time, the periods of rotation around the axis due to the strong gravitational interaction between supermassive companions are also equal to the orbital period.

It is possible to compare the obtained values of the companion masses and values of their orbits obtained for OJ 287 with other known binary SMBHs. The first on this list will be the famous blazar 3C 454.3.¹² Its companions have masses m ≈ 6.8·10⁹ M_· and M ≈ 2.4·10¹⁰ M_·. The orbital radius is r ≈ 4.5·10¹⁷ cm. Next we can note AGN 3C 273.^36,37 The parameters of its binary system are as follows: m ≈ 1.1·10¹⁰ M_·, M ≈ 2.0·10¹⁰ M_·, and r ≈ 5·10¹⁷ cm. In Paltani and Türler’s work, the mass of 3C 273 turns out to be less than m ≈ 10⁹ M_·. We apply the specifically reverberation method to determine the mass of the black hole in 3C 273 from the Ly_α and C_IV emission lines. And the final one is AGN AO 0235 + 164 with the characteristics of its binary system as follows: m ≈ 7·10⁹ M_·, M ≈ 1.5·10¹⁰ M_·, and r ≈ 2·10¹⁸ cm.³⁸ We see that they are all binary SMBH with system parameters close to each other. The most massive among the known double SMBHs is AGN 3C 454.3. It is also the shortest-lived system. Its lifetime before merging is only t_merge ≈ 5.5·10⁴ years. It also holds the record for the most powerful GW emission: $dE/d{t}_{3C454.3}$ ≈ 0.9·10⁴⁸ erg s⁻¹. Figure 5 shows a graph of the mass of the central SMBH versus the size of the companion’s orbit. It also shows a similar dependence for a massive binary star system that is at a stage of evolution close to merging (blue lines).³⁹ For OJ 287, the dependence of the mass of the central body on the radius of the companion’s orbit is shown in Figure 5.

Figure 5.

The dependence of the mass of the central body on the radius of the companion’s orbit for OJ 287

We currently know little about the characteristics of AD in a system with two SMBHs, especially in a situation where the distance between the companions is already less than the size of an AD. The idea was advanced that in close binary SMBH, at the evolutionary stage close to merging, there can exist only one AD common for both SMBHs. Due to dynamic friction in the environment, the orbital separation between the SMBH will decrease to 0.1–1 pc, and the smaller black hole will lose their AD over time.⁴⁰ In this case, SMBH can have one AD, which will be located near the common center of gravity. For OJ 287, an estimate of the radius of the AD can be made using the formula for the precession of the central body in the binary system. In the framework of the particular model for AD, we could write⁴¹

$$T_{\mathit{pr}}\approx {10}^6{\left(\frac{M+m}{{10}^9·M_o}\right)}^{\frac{1}{2}}·{\left(\frac{a}{{10}^{19}}\right)}^3·{\left(\frac{a_d}{{10}^{18}}\right)}^{-\frac{3}{2}}·\frac{{\left(1+q\right)}^{\frac{1}{2}}}{q·\mathit{cos}i}\text{years,}$$ (Equation 9)

where q=1/μ, a = r_comp+r_centr is the distance between companions, a_d is the radius of AD, and i is the angle between orbital and AD planes. As in Equation 3, the precession is due to the tidal gravitational influence on the central SMBH from the companion. Relativistic effects may be ignored, since the distance between the companions is significantly greater than their gravitational radii. Equation 10 is converted to a form that is convenient for calculating the radius of AD at known values M ≈ 1.4·10¹⁰ М_·, m ≈ 4.4·10⁹ М_· (Table 2 row 2), Т_пр ≈ 230 years (Table 1 row 2), $q=1/{\mu }_{OJ287}$ ≈ 0.3, a≈ 7·10¹⁷cm, and i ≈ 0:

$$a_d\approx {10}^{22}{\left(\frac{M+m}{{10}^9·M_O}\right)}^{\frac{1}{3}}·{\left(\frac{a}{{10}^{19}}\right)}^2·\frac{{\left(1+q\right)}^{\frac{1}{3}}}{{\left(T_{\mathit{pr}}·q·\mathit{cos}i\right)}^{\frac{2}{3}}}\text{cm.}$$ (Equation 10)

As a result, we get the radius $a_{d_{OJ287}}$ ≈ 8·10¹⁸ cm ≈ 2.6 pc. The size of AD is an order of a magnitude larger than the size of the companion’s orbit. If we take the half-thickness of AD equal to the standard α-disk,⁴² then we have $d_{OJ287}$ ≈ 0.07·a_d ≈ 5.6·10¹⁷ cm, which even exceeds the size of the companion’s orbit (r_comp ≈ 4.5·10¹⁷cm) but is less than the distance between companions (a≈7.0·10¹⁷ cm). This is consistent with the fact that at a precession half-cone angle i = 1/γ² ≈ 2.5^о you get the maximum value of the AD half-thickness: $d_{OJ287}\approx 0.04·a_{d_{OJ287}}\approx$ 3.2·10¹⁷ cm.

Based on the data obtained on the orbital radius (middle row of Table 2) and the orbital period (row 2 of Table 1), it is possible to determine the speed of the companion in the orbit: ${\nu }_{OJ287}^{comp}\approx 2\pi r/T_{orb}\approx$ 2.3·10⁴ km s⁻¹. This is even higher than the maximum speed ever recorded in young type I supernova remnants—${\upsilon }_{I_{Type}}\approx$ 2·10⁴ km s⁻¹. At the same time, the speed of the central SMBH is only 1.8 times less than the speed of the companion ${\upsilon }_{OJ287}^{comp}\approx$ 1.3·10⁴ km s⁻¹. Moving in a dense environment, at such speeds, companions experience strong dynamic friction against matter, losing orbital moments of motions and approaching each other. This significantly reduces the lifetime of the system before merging.

Using the data for the OJ 287 (second row of Table 2), we can calculate the rate of energy loss due to the emission GWs, by taking into account the value e=0:⁴³

$$⟨\frac{dE}{dt}⟩=\frac{32·G^4·M^2·m^2·\left(M+m\right)·\left(1+\frac{73·e^2}{24}+\frac{37·e^4}{96}\right)}{5·c^5·r^5·{\left(1-e^2\right)}^{\frac{7}{2}}}\approx 6.2·{10}^{47}\text{erg}/\mathrm{s}\text{.}$$ (Equation 11)

This loss value is only slightly less than that in the case of another powerful AGN 3C 454.3.¹² The value of the lifetime of the system due to the GW radiation only can be calculated using the formula⁴⁴

$$t_{merge}=\frac{5.8·{10}^6·{\left(\frac{r}{0.01pc}\right)}^4·{\left(\frac{{10}^8{M}_O}{M}\right)}^3{M}^2·{\left(1-e^2\right)}^{\frac{7}{2}}}{m\left(M+m\right)}\text{years.}$$ (Equation 12)

In the case of the accepted value of the companion orbit radius r = 4.5·10¹⁷ cm, M ≈ 1.4·10¹⁰ М_·, m ≈ 4.4·10⁹ М_·, and e = 0, the lifetime of OJ 287 before merging is $t_{merge}^{OJ287}\approx$ 2.4·10⁵ years. The presence of orbital eccentricity increases power loss due to GWs radiation and reduces the lifetime of the system as a whole. For example, when e = 0.7, this change will be 10 times.

Due to the high speeds of the companions, the kinetic energy must be calculated using the relativistic formula

$$E_{kin}=m·c^2\left(\frac{1}{1-\frac{{\nu }^2}{c^2}}-1\right)\text{.}$$ (Equation 13)

For the values of the masses of the OJ 287 companions (the middle row of Table 2) and the speeds of movements ${\upsilon }_{OJ287}^M\approx$ 1.3·10⁴ km s⁻¹, ${\upsilon }_{OJ287}^m\approx$ 2.3·10⁴ km s⁻¹, we obtain the kinetic energy of the companions $E_{kin}\approx E_{kin}^M+E_{kin}^m\approx$ 5·10⁶¹ + 4.7·10⁶¹≈ 10⁶² erg. This energy is spent on the gravitational radiation, on the dynamic friction in a dense medium of the AD. Much of the dynamic friction energy is converted into broadband radiation from radio to gamma.

To determine the rate of change in the companion orbit radius due to GW radiation and to assess the possibility of experimentally determining these changes, let us estimate the rate of change in the orbit⁴³

$$\frac{d\alpha }{dt}=\frac{64·G^3·M·m·\left(M+m\right)·\left(1+\frac{73·e^2}{24}+\frac{37·e^4}{96}\right)}{5·c^5·r^3}\approx 1.6·{10}^4\text{cm}/\mathrm{s}\text{,}$$ (Equation 14)

where G is the gravitational constant. In our case, M and m are the masses of companions (row 2 of Table 3), r=4.5·10¹⁷ cm, and e = 0. For one orbital period (row 2 of Table 1), the change in the orbit size is Δr ≈ 5.3·10¹³ cm. The decrease in the orbital period will be ΔТ_per ≈ 0.26 days. Over 50 years of observations (Δt ≈ 23 periods), this change will be ΔТ_obs ≈ 6 days ≈ 0.016 years, which is more than 10 times less than the determination error period (Table 1) and time fixation accuracy of the occurrence of the flare phenomenon, duration which can last for many month. Therefore, determining change in the orbital period of the OJ 287 will be the joint art of experimenters and theorists.

Table 3.

The parameters of the calibration sources at the frequency 22.2 GHz

8 GHz	Sources	DR 21	3C 274	3C 144	3C 353
	F, Jy	21.6	49.1	585.0	15.5
22.2 GHz	Sources	DR 21	3C 274	NGC 7027	3C 286
	F, Jy	19.5	21.5	5.4	2.37

The first term of the relativistic equation for changing the satellite’s orbit due to precession (Δφ) can be found using the expression³⁴

$$\Delta \phi =\frac{6\pi ·G·M}{a·\left(1-e^2\right)·c^2}\text{rad}/\text{period.}$$ (Equation 15)

Here G is the gravitational constant, a is the half-axis of the companion’s orbit, and c is the speed of light. In our case, for the mass of central black hole M ≈ 1.4·10¹⁰ M_·, a = 4.5·10¹⁷ cm, the displacement over the one period will be Δφ ≈ 5^o.

After all this, a natural question arises: how does the accretion of a matter onto a black hole, which moves at such a high speed relative to the accreting matter, behave? The answer can be obtained from the accretion formula, which shows how the speed of SMBH motion relative to accreting matter affects the accretion rate:⁴⁵

$$\left(\frac{dE}{dt}\right)=2·{10}^{33}{\left({10}^{-2}\frac{M}{M_O}\right)}^{\frac{3}{2}}·{\left({10}^{-1}\nu \right)}^{-\frac{9}{4}}{n}^{\frac{1}{2}}\text{erg}/\mathrm{s}\text{,}$$ (Equation 16)

where n is the density of an accreting matter and v is the speed of the black hole relative to the accreting matter. When the velocity of a SMBH relative to the accreting medium is much higher than the speed of sound in gas (in our case, it is several orders of magnitude), the shock front near the SMBH has the shape of a narrow cone, which is practically perpendicular to the gas falling onto the SMBH. In this case, the gas "slides" along the shock front outside the SMBH, and the accretion rate decreases.

In our case, for the values of M ≈ 1.4·10¹⁰M_·, n ≈ 3·10⁹ cm⁻³, and v ≈ 2.3·10⁴ km s⁻¹, the luminosity due to accretion onto a black hole is equal to L ≈ 5·10⁴² erg s⁻¹, which is 5 orders of magnitude less than the luminosity at sound velocities, and the accretion can be neglected. This once again confirms the position according to which in the SMBH the release of primary energy can occur not only due to the accretion of matter onto the black hole. In our concept, this energy release can occur due to the loss of the companions’ orbital moments when they ram the AD, the only way that the close binary SMBHs at the stage not far from merging can be bright AGNs. We have proposed this physical picture in a discussion plan.

Conclusions

• (1)On the basis of the new proposed method for calculating the parameters of binary SMBH using multi-frequency monitoring data in the radio and optical bands, the parameters of the OJ 287 are determined. The obtained parameters are close in magnitude in the optical and radio ranges. The data obtained show that this is one of the most massive systems among the brightest AGNs.
• (2)Estimates of the size and thickness of the AD are obtained, showing that the companions are inside the AD most of the time of movement in the orbits. This situation requires considering the influence of dynamic friction on the parameters of the companion’s orbits and the lifetimes before merging.
• (3)The estimates of the level of GWs coming from OJ 287 are made. It is shown that this system is one of the most powerful emitters of GWs in the universe.
• (4)The calculated lifetime of OJ 287 before the merges of components shows that it is a fairly short-lived object in the universe.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Flux density	4.8, 8, 14.5 GHz	https://doi.org/10.1134/S106377291001004X
Flux density	15 GHz	https://sites.astro.caltech.edu
Flux density	Optical data	http://james.as.arizona.edu
Flux density	Optical data	https://doi.org/10.3847/1538-4357/aadd95
Flux density	Optical data	http://quasar.square7.ch/fqm/fqm-home.html

Resource availability

Lead contact

Further information and requests for resources should be directed to the lead contact, Alexandr Volvach (a.volvach@gmail.com).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •The data produced in this study:

At frequencies of 4.8, 8 and 14 GHz, long-term monitoring in the period up to 2012 was performed using the RT-26 radio telescope of Michigan Observatory, the databases of which were previously used and published in the work.⁹ Since 2012, observations at 8 GHz have been carried out with the RT-22 radio telescope in Simeiz. Data at a frequency of 15 GHz in the period 2013-2019 received with the Owens Valley Radio Observatory 40-meter radio telescope.⁴⁶

Optical data of 1998-2020 were taken from the Steward Observatory Spectropolarimetric Monitoring Project.⁴⁷ Optical data for 2008-2021 were taken from the Frankfurt quasar monitoring project by Stefan Karge (Frankfurt, Germany). These data were obtained of the Bradford Robotic Telescope at the University of Bradford (United Kingdom) and the Tzec Maun Observatory (USA). Optical data since 1973 to 2008 was taken from the work.⁴⁸

• •This paper does not report original code.
• •For any additional information required to reanalyze the data reported in this paper, please contact the lead author.

Experimental model and study participant details

The proposed method for finding the parameters of binary SMBHs uses celestial mechanics formulas based on Kepler’s laws for observational data. In proposed supermassive black hole (SMBH) model, it is assumed that the axis of rotation of the central SMBH is general not perpendicular to the plane of the companion’s orbit. Some of the detail in this and following sections is reproduced from previous work.^12,47

Method details

Observations at a frequency of 22.2 GHz were carried out using the 22-meter RT-22 radio telescope in Katsively. The diagram-modulated receivers were used to collect information. The antenna temperature T_a from the source was determined as the difference between the signals from the radiometer output in two antenna positions, when the radio telescope was installed on the source alternately with one or the other receiving horns (on-on observation method). Observations of each source consisted of 5-20 such measurements to achieve the required signal-to-noise ratio. Then the mean and the root mean square error of the mean were calculated. In parallel with the observations of the objects under study, observations of calibration sources were carried out, the parameters of which are indicated in Table 3.

The antenna temperature from the source was recalculated into the flux density according to the dependence:

$$F=\frac{2k·T_a}{A_{eff}}\text{,}$$ (Equation 17)

where F is the spectral flux density of the radio source, k is the Boltzmann constant, T_a is the antenna temperature from the source, and A_eff is the effective area of the radio telescope.

Quantification and statistical analysis

Linear regressions were implemented with the MATLAB function regress. It uses real observational data that does not have a constant time step. Two types of harmonic analysis were used: the standard Schuster method¹⁵ and CLEAN method. These methods were possible to minimize the influence of the unevenness of the time grid on the calculated periodogram - the estimate of the power spectrum. The advantage of the applied method is also the presence of an analytical relationship between the assessment of the power spectrum and its true value.

Published: March 5, 2024