© The Authors 2023

1. Introduction

Galaxy OJ 287 is a BL Lacertae object (blazar) in the constellation Cancer and is located at a distance of five billion light years from Earth. As is known, blazars are associated with a supermassive black hole (SMBH), which collects the surrounding matter, dust, and gas, forming an accretion disk. However, OJ 287 is interesting not only because of this. At its center is not one, but two SMBHs (Gömez et al. 2022; Dou et al. 2022). These two black holes (BHs) form an orbital pair located in the core of this galaxy. This pair is the only close binary system of two SMBHs known to date (Valtonen et al. 2006; Laine et al. 2020; Gömez et al. 2022). In turn, a large BH (primary) has a mass equal to 18 billion solar masses, which is in fact equal to the mass of a small galaxy. The less massive BH (secondary) weighs as much as 100 million solar masses. The secondary revolves around the primary (see Fig. 1), piercing and drilling through its accretion disk twice every 12 years (Shi et al. 2007; Dey et al. 2019a). SMBH binaries are an amazing by-product of galaxy mergers in a hierarchical universe (Begelman et al. 1980). In the last stage of their orbital evolution, gravitational wave radiation provides the binary inspiral. Periodically varying radiation from active galactic nuclei has been proposed as a powerful tool for studying such binary systems (Chen et al. 2020; Charisi et al. 2016; Liu et al. 2016; Zheng et al. 2016; Graham et al. 2015).

Fig. 1. Schematic view of OJ 287 model used in our analysis.

The goal of our paper is to check a mass value of the secondary BH in OJ 287, applying the scaling method for a BH mass determination (Shaposhnikov & Titarchuk 2009, hereafter ST09) based on observations during source X-ray outbursts. Because OJ 287 exhibited a more or less strict 12-year cycle, several hypotheses have been proposed to explain the optical/X-ray periodic variability of the object (Sillanpaa et al. 1988; Shi et al. 2007). In particular, according to Valtonen et al. (2012, hereafter V12), the periodicity is presumably due to the orbital rotation of the components in a BH binary, in which the secondary periodically perturbs the accretion disk around the primary.

V12 presented results of the two X-ray observations of OJ 287 by XMM-Newton in 2005 April 12 and November 3−4. V12 claimed that the spectral energy distribution, the spectrum from radio to X-rays on 2005 April 12, nicely followed a synchrotron self-Compton (SSC) model (see Ciprini et al. 2007). In contrast, the November 3−4 spectrum was quite different. The flux rose prominently in the optical/UV region; however, in the radio or hard X-rays, the flux remained at the preoutburst level, making the single zone SSC model unlikely. However, the V12 model of the optical/UV outburst in the context of an interaction between the secondary and the primary accretion disk leads to a mass estimate of M_sec ∼ 1.4 × 10⁸ M_⊙. V12 also formulated a question regarding the primary BH mass so that it could guarantee the stability of the primary accretion disk. They found that the minimum value of the primary mass 1.8 × 10¹⁰ M_⊙ is quite close to the BH mass determined from the orbit solution technique, 1.84 × 10¹⁰ M_⊙.

To find evidence for the emission of the secondary, V12 needed to look at short time-scale variability in OJ 287. It has been found to be variable from a 15 min time scale upward on many occasions (see, for example, Gupta et al. 2012) and on one occasion the light curve has shown sinusoidal variations for the period of 228 min (Sagar et al. 2004). If this variation is associated with the last stable orbit of a maximally rotating BH, the mass of the BH would be 1.46 × 10⁸ M_⊙ (Gupta et al. 2012), that is to say identical to the mass obtained from the orbit solution (Valtonen et al. 2010).

Komossa et al. (2021, hereafter KOM21), provide a detailed analysis of XMM-Newton spectra of OJ 287 spanning 15 yr. KOM21 also present their achieved findings from the Swift Ultra-violet Optical Telescope (UVOT) and X-Ray Telescope (XRT) observation of OJ 287, which began in 2015, along with all public Swift information after 2005. During this period, OJ 287 was found to be in an “extreme” low-hard state (LHS) and outburst high-soft states (HSSs). In addition, they have established that the OJ 287 X-ray spectra were highly variable and passed all states seen in blazars from a “flat” LHS through an intermediate state (IS) to an exceptionally soft steep (ST) state. KOM21 found that these spectra are made up of the following: inverse-Compton (IC) radiation, which is prevailing in the LHS, and very soft radiation, which became extremely powerful once OJ 287 was more luminous. KOM21 claim that their 2018 XMM-Newton measurements, close-in time with the EHT examination of OJ 287, were well characterized by a model with a hard IC component with the photon index Γ ∼ 1.5 and a soft component. It is important to emphasize that they conclude that that the LHS spectra limited any long-lived accretion disk-corona contribution in X-rays and related to a very low value of L_X/L_Edd < 5.6 × 10⁻⁴ (for M_BH of the primary ∼1.8 × 10¹⁰ M_⊙).

We are suggesting a revision of this claim by KOM21 and to reanalyze data of X-ray telescope (XRT) on board the Swift observatory for OJ 287 and to apply the ST09 scaling method to these data in order to make a BH mass estimate. Using this method requires accurate knowledge of the distance to the source OJ 287. The method was proposed back in 2007 by Shaposhnikov & Titarchuk (2007, hereafter ST07), and by ST09. It is worth noting that there are two scaling methods: based on the correlation between the photon index, Γ, and the quasi-periodic oscillation (QPO) frequency, ν_L; and one based on the correlation between Γ and the normalization of the spectrum proportional to Ṁ. If, for the first method (Γ − ν_L), the source distance is not required to estimate the black hole mass (ST07), while for the second method, Γ − Ṁ (see ST09), the source distance and the inclination of the accretion disk relative to the Earth observer are needed.

For both methods, it is necessary for the source to show a change in spectral states, accompanied by a characteristic behavior of the index Γ, during the outburst. A monotonic increase of Γ with ν_L or Ṁ in the LHS→IS→HSS transition and reaching a constant level (saturating) at high values of ν_L or Ṁ. Then Γ monotonic decreases during a HSS→IS→LHS transition when the outburst decays. The saturation of Γ (so-called Γ–saturation phase) during an outburst is a specific signature that this particular object contains a BH (Titarchuk & Zannias 1998). Indeed, the Γ–saturation phase can only be caused by an accretion flow converging to the event horizon of a BH (see the Monte-Carlo simulation results in Laurent & Titarchuk 1999, 2011). Then, it makes sense to compare BH sources that have the same Γ–saturation levels. In the second method (Γ − Ṁ), it is assumed that BH luminosity is directly proportional to Ṁ (and, consequently, to the mass of the central BH), and inversely proportional to the squared distance to the source. Thus, we can determine the BH mass by comparing the corresponding tracks Γ − Ṁ for a pair of sources with BHs, in which all parameters are known for one source, and for the other source all parameters are known except for the BH mass (for more details on the scaling method, see Titarchuk et al. 2010; Seifina & Titarchuk 2010 and ST09).

The scaling method has a number of advantages over other methods in determining a BH mass. Calculation of the X-ray spectrum originating in the innermost part of the source based on first-principle (fundamental) physical models, taking into account the Comptonization of the soft disk photons by hot electrons of the internal disk part and in a converging flow to a BH. In fact, in the case of a 10⁸ M_⊙ BH, the disk peak temperature is relatively low, kT_s < 1 keV/(M_BH/10 M_⊙)^1/4, that is to say about 20−100 eV and its thermal peak is in the UV energy range (see details of our observation in Sect. 3 and Shakura & Sunyaev 1973). It is worth noting that using this scaling method for a BH mass estimate Titarchuk & Seifina (2016a, 2017), Seifina et al. (2017, 2018a,b), and Titarchuk et al. (2020) applied it to intermediate mass BHs and SMBHs.

In this paper, based on Swift data analysis, we estimate a BH mass in OJ 287 using the scaling technique. In Sect. 2 we provide details of our data analysis, while in Sect. 3 we present a description of the spectral models used for fitting these data. In Sect. 4 we focus on the interpretation of our observations. In Sect. 5 we focus on the construction of the power density spectra (PDS) and its interpretation. In Sect. 6 we discuss the main results of the paper. In Sect. 7 we present our final conclusions.

2. Data reduction

Using Swift/XRT data in 0.3−10 keV energy range, we studied a total of 385 observations of OJ 287 during its flaring events from 2005 to 2018. The data used in this paper are public and available through the GSFC public archive¹. In Table 1 we report the log of observations for OJ 287 used in our study. We must admit that not all of the flare events may be related to the secondary BH – disk interactions. Thus, it may be challenging to disentangle them from other flaring events going on in OJ 287 all the time, which may be completely unrelated to any binary’s presence.

Data were processed using the HEASOFT v6.14, the tool xrtpipeline v0.12.84, and the calibration files (CALDB version 4.1). The ancillary response files were created using xrtmkarf v0.6.0 and exposure maps were generated by xrtexpomap v0.2.7. Source events were accumulated within a circular region with a radius of 47″ centered at the position of OJ 287 ($\alpha ={08}^{\mathrm{h}}{58}^{\mathrm{m}}47\stackrel{\text{s}}{.}15$ and $\delta =+20°{08}^{\prime }00\stackrel{″}{.}5$, J2000.0). We used XRT data both in the Windowed Timing mode (≥1 count s⁻¹) and in the Photon Counting mode for the remaining observations when the X-ray source became sufficiently faint. The background was estimated in a nearby source-free circular region with a 118″ radius.

Using the xselect v2.4 task, source and background light curves and spectra were generated. Spectra were rebinned with at least ten counts in each energy bin using the grppha task in order to apply χ² statistics. We also used the online XRT data product generator² to obtain the image of the source field of view in order to make a visual inspection and to get rid of possible contamination from nearby sources (Evans et al. 2007, 2009). The Swift/XRT (0.3−10 keV) image of the OJ 287 field of view is presented in Fig. 2 and demonstrates absence of the X-ray jet-like (elongated) structure as well as the minimal contamination by other point sources and diffuse emission within a region with a 120″ radius around OJ 287. We used Swift observation of OJ 287 (2005–2018) extracted from the HEASARC archives and found that these data cover a wide range of X-ray luminosities.

Fig. 2. Swift X-ray image on 2005 May 20–2018 June 13 with a 455 ks exposure. The contours correspond to fourteen logarithmic intervals with respect to the brightest pixel.

Before proceeding and providing the details of the spectral fitting, we study a long-term behavior of OJ 287, in particular, its activity patterns. We present a long-term X-ray light curve of OJ 287 detected by the XRT on board Swift from 2005–2018 (see Fig. 3).

Fig. 3. Evolution of the XRT/Swift count rate during the 2005−2018 observations of OJ 287.

We note that this X-ray light curve makes it rather difficult to judge the 12-yr periodicity found earlier from optical observations. But it can be unequivocally stated that the object OJ 287 has become active over the past 10 years and shows sporadic X-ray activity (e.g., MJD 54500–58200, see Fig. 3).

3. Analysis and results

the outburst. We adhere to the scenario in which OJ 287 is a binary system consisting of two BHs with a larger and smaller mass (Fig. 1). In this case, a heavier BH (primary BH) is surrounded by a powerful accretion disk, and a lighter BH (secondary BH) orbits around the primary BH in a plane different from the equatorial plane of the primary BH accretion disk, crossing it twice during the orbital period (12 years). We also assume that when the secondary BH passes through the disk around the primary BH, “tidal disruption” of nearby parts of the disk occurs, due to which the partial disruption and subsequent matter replenishment of the accretion disk around the secondary BH is possible (see a similar process in Chan et al. 2021). In this case, a powerful transient disk develops around the secondary SBH with subsequent accretion of the material of the transient disk onto the secondary BH. This provides an increase in luminosity in the form of an ouburst in the X-ray/optical/radio bands.

To fit the energy spectra of this source, we used an XSPEC model consisting of the bulk motion Comptonization (BMC) component (see Titarchuk & Zannias 1998; Laurent & Titarchuk 1999). We also used a multiplicative tbabs model (Wilms et al. 2000) which takes absorption by neutral material into account. We assume that accretion onto a BH is described by two main zones (see, for example, Fig. 1 in Titarchuk & Seifina 2021): a geometrically thin accretion disk (e.g., the standard Shakura–Sunyaev disk, see SS73) and a transition layer (TL), which is an intermediate link between the accretion disk, and a converging (bulk) region (see Titarchuk & Fiorito 2004), which is assumed to exist below 3 Schwarzschild radii, 3 R_S = 6GM_BH/c², at least. The spectral model parameters are the equivalent hydrogen absorption column density N_H; the photon index Γ; log(A), which is related to the Comptonized factor f [=A/(1 + A)]; and the color temperature and normalization of the seed photon blackbody component kT_s and N, respectively. The parameter log(A) of the BMC component is fixed at two when the best-fit log(A)≫1. In fact, for a sufficiently high log(A)≫1 (and, therefore, a high value for A A), the illumination factor f = A/(1 + A) becomes a constant value close to one (that is, the same as in the case of log(A) = 2). We note that N_H was fixed at the Galactic absorption level of 2.49 × 10²⁰ cm⁻² (Wilms et al. 2000).

Similarly to the bbody XSPEC model, the normalization is a ratio of the source (disk) luminosity L to the square of the distance d (ST09, see Eq. (1) there):

$$\begin{array}{c}\hfill N=\left(\frac{L}{{10}^{39}\mathrm{erg}{\mathrm{s}}^{-1}}\right){\left(\frac{10\mathrm{kpc}}{d}\right)}^2.\end{array}$$(1)

This encompasses an important property of our model. Namely, using this model, one can correctly evaluate normalization of the original “seed” component, which is presumably a correct Ṁ indicator (Seifina & Titarchuk 2011). In turn,

$$\begin{array}{c}\hfill L=\frac{G{M}_{\mathrm{BH}}\dot{M}}{R_{\ast }}=\eta (r_{\ast })\dot{m}{L}_{\mathrm{Edd}}.\end{array}$$(2)

Here R_* = r_*R_S is an effective radius where the main energy release takes place in the disk, R_S = 2GM/c² is the Schwarzschild radius, η = 1/(2r_*), ṁ = Ṁ/Ṁ_crit is the dimensionless Ṁ in units of the critical mass accretion rate Ṁ_crit = L_Edd/c², and L_Edd is the Eddington luminosity. For the formulation of the Comptonization problem, one can refer to Titarchuk et al. (1997), Titarchuk & Zannias (1998), Laurent & Titarchuk (1999), Borozdin et al. (1999), and Shaposhnikov & Titarchuk (2009).

Spectral analysis of the Swift/XRT data fits of OJ 287, in principle, provides a general picture of the source evolution. We can trace the change in the spectrum shape during the LHS–IS–HSS transition. In Fig. 4, we show three representative E * F_E spectral diagrams for different states of OJ 287.

Fig. 4. Three representative spectra of OJ 287 from Swift data with the best-fit modeling for the LHS (ID = 00035011001), IS (ID = 00088085001), and HSS (ID = 00034934051) states in units of E * F(E) using the tbabs*bmc model. The data are denoted by black crosses, while the spectral model is shown by a red histogram.

We put together spectra of the LHS, IS, and HSS, to demonstrate the source spectral evolution from the low-hard to high-soft states to states based on the Swift observations. The data are presented here as follows: in the left panel for LHS (taken from observation 00088085001), in the central panel for IS (00035011001), and in the right panel for the HSS (taken from observation 00034934051) in units E * F(E) fitted using the tbabs*bmc model. Periods of exposure are 3.7, 1.9, and 1.1 ks, respectively.

The best-fit parameters in the HSS state (right panel) are Γ = 2.77±0.02, kT_s = 50±4 eV, N = 7.2±0.6 $L_{35}/d_{10}^2$, and log(A) = 0.28±0.06 for which ${\chi }_{\text{red}}^2$ = 0.98 for 265 degrees of freedom (d.o.f.), while the best-fit model parameters for the IS state (central panel) are Γ = 2.6±0.2, kT_s = 40±2 eV, N = 4.3±0.9 $L_{35}/d_{10}^2$, and log(A) = −0.72±0.08 (${\chi }_{\text{red}}^2$ = 0.93 for 215 d.o.f.); and, finally, the best-fit model parameters for the LHS state (left panel) are Γ = 1.7±0.3, kT_s = 120±6 eV, N = 0.19±0.05 $L_{35}/d_{10}^2$, and log(A) = −0.24±0.08 (${\chi }_{\text{red}}^2$ = 1.06 for 237 d.o.f.). A systematic uncertainty of 1% is intended to represent the instrumental flux calibration uncertainty and has been applied to all analyzed Swift spectra.

Analysis of the Swift/XRT data fits (see Fig. 5) showed that Γ monotonically increases from 1.5 to 2.8, when the normalization of the spectral component (or Ṁ) increases by a factor of about 5.

Fig. 5. Correlation of the photon index Γ (=α + 1) versus the BMC normalization, N (proportional to the mass accretion rate) in units of $L_{39}/D_{10}^2$.

4. A BH mass estimate of the OJ 287 secondary

We used the scaling method for our estimate of the BH mass, M_OJ 287. Beforehand we did not know what kind of BH mass could be estimated using our data for OJ 287. The BH mass using the scaling method applies the Γ − N correlation (see ST09 for details). This method ultimately (i) identifies a pair of BHs for which the Γ correlates with increasing normalization N (which is proportional to mass accretion rate Ṁ and a BH mass M, see ST09, Eq. (7)) and for which the saturation levels, Γ_sat, are the same and (ii) calculates the scaling coefficient s_N, which allows us to determine a BH mass of the target object. We also should emphasize that one needs a ratio of distances for the target and reference sources in order to estimate a BH mass using the following equation for the scaling coefficient

$$\begin{array}{c}\hfill s_{\mathrm{N}}=\frac{N_{\mathrm{r}}}{N_{\mathrm{t}}}=\frac{m_{\mathrm{r}}}{m_{\mathrm{t}}}\frac{d_{\mathrm{t}}^2}{d_{\mathrm{r}}^2}{f}_{\mathrm{G}},\end{array}$$(3)

where N_r and N_t are normalizations of the spectra, m_t = M_t/M_⊙ and m_r = M_r/M_⊙ are the dimensionless BH masses with respect to solar masses, and d_t and d_r are distances to the target and reference sources, correspondingly. A geometrical factor, f_G = cos i_r/cos i_t, where i_r and i_r are the disk inclinations for the reference and target sources, respectively (see ST09, Eq. (7)).

We found that XTE 1550–564, H 1743–322, 4U 1630–47, GRS 1915+105, ESO 243–49, and M101 ULX–1 can be used as the reference sources because these sources met all aforementioned requirements to estimate a BH mass of the target source OJ 287 (see items (i) and (ii) above).

In Fig. 6 we demonstrate how the photon index Γ evolves with normalization N (proportional to the mass accretion rate Ṁ) in the Galactic source XTE 1550–564 and OJ 287, where N is presented in units of $L_{39}/D_{10}^2$ (L₃₉ is the source luminosity in units of 10³⁹ erg s⁻¹ and d₁₀ is the distance to the source in units of 10 kpc).

Fig. 6. Scaling of the photon index Γ versus the normalization NBMC for OJ 287 (red points – target source) using the correlation for the Galactic reference sources, XTE J1550–564 (blue diamonds), H 1743–322 (pink squares), 4U 1630–47 (greed stars), and GRS 1915+105 (light blue stars).

As we show in Fig. 7, the correlations Γ versus N are self-similar for the target source (OJ 287) and two M101 ULX–1 and ESO 243–49 HLX–1 are ultraluminous X-ray sources. Moreover, these three sources have almost the same index saturation level Γ about 2.8. We estimated a BH mass for OJ 287 using the scaling method (see e.g., ST09). In Fig. 6 we illustrate how the scaling method works shifting one correlation versus another. From these correlations we could estimate N_t, N_r for OJ 287 and for the reference sources (see Table 2). A value of N_t = 2.4 × 10⁻⁴, N_r in units of $L_{39}/D_{10}^2$ is determined in the beginning of the Γ–saturation part (see Figs. 6 and 7, ST07, ST09, Seifina et al. 2014; Titarchuk & Seifina 2016a,b, 2009).

Fig. 7. Scaling of the photon index Γ versus the normalization N for OJ 287 (red line – target source) using Γ − N correlations for extragalactic sources, ESO 243–49 HLX–1 and M101 ULX–1 (blue and green points).

A value of f_G = cos i_r/cos i_t for the target and reference sources can be obtained using inclination for OJ 287 i_t = 50° and for i_r (see Table 2). As a result of the estimated target mass (OJ 287), m_t we find that

$$\begin{array}{c}\hfill m_{\mathrm{t}}=f_{\mathrm{G}}\frac{m_{\mathrm{r}}}{s_{\mathrm{N}}}\frac{d_{\mathrm{t}}^2}{d_{\mathrm{r}}^2}\end{array}$$(4)

where we used values of d_t = 1.073 Gpc.

Applying Eq. (4), we can estimate m_t (see Table 2) and we find that the secondary BH mass in OJ 287 is about 1.25 × (1 ± 0.18) × 10⁸ solar masses. To obtain this estimate with appropriate error bars, we need to consider error bars for m_r and d_r assuming, in the first approximation, errors for m_r and d_r only. We rewrote Eq. (4) as

$$\begin{array}{c}\hfill m_{\mathrm{t}}(1+\mathrm{\Delta }{m}_{\mathrm{t}}/m_{\mathrm{t}})=f_{\mathrm{G}}\frac{m_{\mathrm{r}}}{s_{\mathrm{N}}}\frac{d_{\mathrm{t}}^2}{d_{\mathrm{r}}^2}(1+\mathrm{\Delta }{m}_{\mathrm{r}}/m_{\mathrm{r}})(1+2\mathrm{\Delta }{d}_{\mathrm{r}}/d_{\mathrm{r}}).\end{array}$$(5)

Thus we obtained errors for the m_t determination (see Table 2, second column for the target source), such that

$$\begin{array}{c}\hfill \mathrm{\Delta }{m}_{\mathrm{t}}/m_{\mathrm{t}}\sim \mathrm{\Delta }{m}_{\mathrm{r}}/m_{\mathrm{r}}+2\mathrm{\Delta }{d}_{\mathrm{r}}/d_{\mathrm{r}}.\end{array}$$(6)

In order to calculate the dispersion 𝒟 of the arithmetic mean ${\overline{m}}_{\mathrm{t}}$ for a BH mass estimate using different reference sources 𝒟 (see Table 2), one should keep in mind that

$$\begin{array}{c}\hfill \mathcal{D}({\overline{m}}_{\mathrm{t}})=D/n,\end{array}$$(7)

where D is the dispersion of m_r using each of the reference sources and n = 6 is a number of the reference sources. As a result we determined that the mean deviation of the arithmetic mean

$$\begin{array}{c}\hfill \sigma ({\overline{m}}_{\mathrm{t}})=\sigma /\sqrt{n}\sim 0.18\end{array}$$(8)

and finally we came to the following conclusion (see also Table 2):

$$\begin{array}{c}\hfill {\overline{m}}_{\mathrm{t}}\sim 1.25\times (1\pm 0.18)\times {10}^8\mathrm{solar}\mathrm{masses}.\end{array}$$(9)

It should be noted that in our calculations, we assume the angle between the normal to the secondary disk and the line of sight to be about 50°. However, this angle may be different. In fact, Dey et al. (2019b) and Valtonen et al. (2021) argue that one should see the secondary disk almost face-on, namely, this angle i_t is about zero. Consequently the mass of the secondary should then be slightly lower, ${\overline{m}}_{\mathrm{t}}\sim 0.8\times {10}^8$ solar masses.

5. Power density spectrum

In Fig. 8 we present the evolution of the power density spectrum of OJ 287 with a bintime of 4000 s using RXTE/ASM data from 1997 to 2015 in the 0.3−12 keV energy range. We made PDSs in the range of 10⁻⁷ − 10⁻⁴ Hz frequency and subtracted the contribution because of Poissonian statistics. As it is seen from this figure, the PDS undergoes temporal evolution. If, in the upper plot, we see a wide plateau from 7 × 10⁻⁶ to 10⁻⁵ Hz, it would take place in a much wider frequency range from 10⁻⁶ to 10⁻⁵ Hz in the lower panel. We can evaluate the size of the Compton cloud (CC) emitting the emergent spectra using the presented plateaus. The characteristic frequency of these plateaus ν_plat can be estimated as

$$\begin{array}{c}\hfill {\nu }_{\mathrm{plat}}\sim V_{\mathrm{plas}}/L_{\mathrm{CC}}=1.4\times {10}^8\frac{V_{\mathrm{plas}}/({10}^8\mathrm{cm}{\mathrm{s}}^{-1})}{L_{\mathrm{CC}}(\mathrm{cm})}\mathrm{cm}{\mathrm{s}}^{-1},\end{array}$$(10)

Fig. 8. Evolution of the power density spectrum of OJ 287 with time. The PDS evolution is clearly seen with the characteristic peaks in the range of 10−6 and 10−5 Hz.

where L_CC is the CC size and V_plas = 1.4 × 10⁸ cm s⁻¹ is a typical plasma (proton) velocity in the CC related to the plasma temperature on the order of 10 keV (see e.g., Shaposhnikov & Titarchuk 2009). We used a frequency ν_plat ∼ 10⁻⁵ Hz in order to estimate the CC size:

$$\begin{array}{c}\hfill L_{\mathrm{CC}}\sim 1.4\times {10}^{13}\frac{V_{\mathrm{plas}}/{10}^8\mathrm{cm}{\mathrm{s}}^{-1}}{{\nu }_{\mathrm{plat}}/{10}^{-5}\mathrm{Hz}}\mathrm{cm}.\end{array}$$(11)

Using this CC size L_CC, one can easily estimate the appropriate BH mass

$$\begin{array}{c}\hfill M_{\mathrm{OJ}287}\sim L_{\mathrm{CC}}/R_{\mathrm{S}\odot }\sim {10}^8\mathrm{solar}\mathrm{masses},\end{array}$$(12)

which is, by order of magnitude, close to our BH mass value using the Γ–mass accretion rate correlation (see Eq. (9), Table 2 and Fig. 7).

6. Discussion

In the previous section and using the power spectra (see Fig. 8), we estimated the CC size as L_CC ∼ 1.4 × 10¹³ cm where the X-ray emergent spectrum was formed. Applying this value of L_CC, we confirmed a BH mass value on the order of 10⁸ solar masses which was found using the Γ–mass accretion rate correlation (see Table 2, Figs. 6 and 7, Sect. 4). This type of CC, with L_CC on the order of 10¹³ cm, is definitely not related to a BH mass on the order of 10¹⁰ as KOM21 claim.

KOM21 also note that their inferred X-ray luminosity with respect to the Eddington one, L_X/L_Edd < 6 × 10⁻⁴, was too small for M_BH primary ∼ 1.8 × 10¹⁰ M_⊙. Furthermore, they mention in their Sect. 4.3 the possibility that L_X, iso = 1.3 × 10⁴⁵ erg s⁻¹ can be associated with the secondary of a BH mass M_{BH,  secondary} ∼ 1.5 × 10⁸ M_⊙. In KOM21 the authors present a profound spectral evolution from the low to high states (see their Figs. 4–7). They correctly claim, using their spectral results, that all spectral states observed in OJ 287 in the 0.3−10 keV band evolved from being rather flat to ultra-steep (Γ_X = 1.5 − 2.8). We confirm this kind of spectral behavior in our Figs. 4 and 5 that Γ significantly evolved depending on normalization (proportional to the mass accretion rate) from 1.5 to 2.8 as well.

One can argue that we did not realize that the emission from this BL Lac object comes from a jet. In fact, we do not see any serious arguments for this statement. A particularly important point regards the fitting of Swift X-ray spectra. One could think that our spectral models contain too many components and thus that they could not be fitted to low-resolution Swift data, since there would then be many more free parameters than actual independent data bins. This is not the case because our continuum spectral model is an XSPEC model consisting of the BMC component. The spectral model parameters are the equivalent hydrogen absorption column density N_H; the photon index Γ; log(A), which is related to the Comptonized factor f; and the color temperature and normalization of the seed photon blackbody component kT_s and N, respectively. One can claim that simple power-law models are appropriate for Swift spectral fitting.

However, it is important to emphasize that a power law itself is not a physical model. In fact, in any process of up-scattering (or simply acceleration) of particles in the energetic cloud, which a particle energy is much greater than that of photons, then a power law is formed (see proof of this statement in ST09).

However, it is important to emphasize that the power law itself is still not a physical model. Indeed, in any process of up-scattering (or simply acceleration) of particles in the energetic cloud, the particle energy of which is much greater than the energy of photons, a power law is formed (see the proof of this statement in ST09).

In light of the obtained results, we can take an updated look at the discrepancy between the BH mass in the nucleus of the M 87 galaxy, which was obtained using different methods. Namely, the discrepancy in the estimates of the BH mass in M 87 (3.5 − 6.5) × 10⁹ M_⊙ (from its EHT radio image Akiyama et al. 2019 and based on the gas dynamic analysis Walsh et al. 2013; Akiyama et al. 2019 and stellar dynamics of M 87 Akiyama et al. 2019 using long-term optical observations Gebhardt et al. 2011) and 6.5 × 10⁷ M_⊙ (by the method BH mass scaling from X-ray data Titarchuk et al. 2020). Titarchuk et al. (2020) reduced the BH mass in M 87 by a factor of 100 compared to standard methods (Gebhardt et al. 2011; Walsh et al. 2013; Akiyama et al. 2019), using the timing analysis of the X-ray variability in M 87. This discrepancy is difficult to explain only due to different ranges of radiation energy observations. Assuming that M 87 contains a binary BH at its center (Emami & Loeb 2020; Davelaar & Haiman 2022; Dou et al. 2022), an estimate of the BH mass by analyzing the power spectrum of M 87 using a characteristic variability time of 5 × 10⁻⁷ s yields an estimate with a CC size in M 87 of L_CC ∼ 2 × 10¹³ cm and a BH mass of (6.5 ± 0.5) × 10⁷ M_⊙. At the same time, these two SMBHs can only be distinguished by the scale of variability. In terms of this approach, it is possible that the BH mass measurement in M 87 by Titarchuk et al. (2020) specifically refers to the BH of smaller mass (secondary), in contrast to the approach of the gas and stellar dynamics as well as the EHT image analysis methods for an estimate of the primary BH mass or the total (primary + secondary) BH mass. This can be considered as a possible observational indication of the presence of a BH binary in M 87.

Recently, Ning Jiang and his colleagues (Jiang et al. 2022) have pointed out a similar picture of BH duality in the active galaxy nuclear. Namely, they argue for the probable presence of a BH binary in the Seyfert galaxy SDSS J143016.05+230344.4. Dou et al. (2022) indicate that in this binary system, consisting of two SMBHs of different masses, a decay of the orbital period was observed, which confirms the initial hypothesis of the presence of an eccentric SMBH binary in the center of this galaxy.

7. Conclusions

The multiwavelength outburst activity in OJ 287 with the X-ray telescope on board Swift incited several questions as to whether the source contains one or two BHs. It is very important to reveal the characteristics of this binary. In the present paper, we demonstrate that the OJ 287 X-ray spectra underwent the state transition from the LHS to the IS and then to the HSS (see Fig. 4). We have determined that energy spectra in all spectral states can be modeled using a product of the was and a BMC Comptonization component.

Moreover, we discover in OJ 287 the correlation of the index Γ with normalization, N (proportional to the disk mass accretion rate Ṁ, see Fig. 7), similar to those established in BH Galactic sources by ST09. We find that Γ increases monotonically with Ṁ from the LHS to IS and HSS, and then saturates at Γ ∼ 2.8. This can be considered as observational evidence of the presence of a BH in OJ 287. Based on this correlation, we applied the scaling method of ST09 to estimate a BH mass is about 1.25 × 10⁸ solar masses, using the well-studied Galactic X-ray BHs, XTE 1550–564, H 1743–322, 4U 1630–47, and GRS 1915+105 and extra-galactic BHs ESO 243–49 and M101 ULX–1 as reference sources.

Also using the power spectrum analysis, we inferred the size of the Compton cloud L_CC ∼ 10¹³ cm where X-ray spectra were formed. Using this value of L_CC, we confirmed that a BH mass of the secondary in OJ 287 was on the order of 10⁸ solar masses consistent with the index, Γ–correlation (the scaling method) with respect to the mass accretion rate.

Acknowledgments

We acknowledge support from UK Swift Science Data Centre at the University of Leicester for supplied data. We thank the anonymous referee for the careful reading of the manuscript and for providing valuable comments. This research has made using the data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. The data used in this paper are public and available through the GSFC public archive (https://heasarc.gsfc.nasa.gov). This work was made use of XRT and BAT data supplied by the UK Swift Science Data Centre at the University of Leicester (https://www.swift.ac.uk/swift_portal).

References

All Tables

All Figures

	Fig. 1. Schematic view of OJ 287 model used in our analysis.
In the text

	Fig. 2. Swift X-ray image on 2005 May 20–2018 June 13 with a 455 ks exposure. The contours correspond to fourteen logarithmic intervals with respect to the brightest pixel.
In the text

	Fig. 3. Evolution of the XRT/Swift count rate during the 2005−2018 observations of OJ 287.
In the text

	Fig. 4. Three representative spectra of OJ 287 from Swift data with the best-fit modeling for the LHS (ID = 00035011001), IS (ID = 00088085001), and HSS (ID = 00034934051) states in units of E * F(E) using the tbabs*bmc model. The data are denoted by black crosses, while the spectral model is shown by a red histogram.
In the text

	Fig. 5. Correlation of the photon index Γ (=α + 1) versus the BMC normalization, N (proportional to the mass accretion rate) in units of $L_{39}/D_{10}^2$.
In the text

	Fig. 6. Scaling of the photon index Γ versus the normalization NBMC for OJ 287 (red points – target source) using the correlation for the Galactic reference sources, XTE J1550–564 (blue diamonds), H 1743–322 (pink squares), 4U 1630–47 (greed stars), and GRS 1915+105 (light blue stars).
In the text

	Fig. 7. Scaling of the photon index Γ versus the normalization N for OJ 287 (red line – target source) using Γ − N correlations for extragalactic sources, ESO 243–49 HLX–1 and M101 ULX–1 (blue and green points).
In the text

	Fig. 8. Evolution of the power density spectrum of OJ 287 with time. The PDS evolution is clearly seen with the characteristic peaks in the range of 10−6 and 10−5 Hz.
In the text