The duality of objects is a fairly common phenomenon in astrophysics. Most stars in the universe are binary. Duality is also common among galaxies. Over the past few years, the number of detected binary black holes (BHs) in the centers of galaxies has increased sharply. Although such double objects are no longer uncommon, the manifestation of their binarity remains not fully understood. Analysis of the dual nature of BHs in active galactic nuclei (AGNs) confirms the reality of supermassive BH (SMBH) mergers in galactic nuclei. Scientists have long been concerned about the problem of the origin of ultra-massive BHs, because due to matter accretion onto stellar-mass BHs, they could not form since this would require time longer than the lifetime of the universe. The discovery of binary AGNs, observations of massive BH merger events, and confirmations of the high resulting masses of such BHs obtained in recent years are a real breakthrough in our understanding of the origin of ultra-massive BHs through massive BH mergers in galactic nuclei.

Binary supermassive BHs are a remarkable by-product of galaxy mergers in the hierarchical universe (Begelman et al., 1980). In the very last stage of their orbital evolution, gravitational wave radiation powers the binary inspiral. Periodic X-ray/optical/radio flares from AGNs during their orbital rotation have been proposed as a powerful tool for studying such binary systems (Liu et al., 2016; Chen et al., 2020). It should be noted that the very idea of binary systems with SMBHs was expressed by Komberg (1967). Subsequently, their hypothesis about the possible duality of nuclei in quasars was brilliantly confirmed by observations (Section 3). However, the methods for establishing the duality of SMBHs are tenuous at best and are based on four criteria (Seifina, 2024).

First, the duality of galactic nuclei is, in some cases, demonstrated by analyzing their observed images (for nearby galaxies), which allows us to resolve the double structure of their central regions (for example, NGC 7727; Voggel et al. (2022); NGC 6240; Kollatschny et al. (2020); Mrk 739; Koss et al. (2011); and UGC 4211; Koss et al. (2023)). For distant AGNs, spectroscopic studies make it possible to establish duality by the characteristic behavior of spectral line systems [SDSS J1537 + 044; Boroson and Lauer (2009); SDSS J0927 + 294; Eracleous et al. (2012)]. It is clear that the described methods are no longer applicable for very distant sources. In fact, the collision of galaxies (and, accordingly, their nuclei) in the past led to the formation of a binary system from two SMBHs; however, there is no definitive way to indicate the duality of their new “nucleus,” except perhaps for the presence of “extra” jets in 3C 75 (Molnar et al., 2017) or the strict periodicity of the source flares in OJ 287 (Zhang, 2022; Titarchuk et al., 2023). In such cases, the duality of the nucleus can sometimes be established by individual exotic features, for example, by the same bending of the jets of each of the SMBHs, by the specific shape of the light curve (for example, from periodicity and from the double-humped flare maximum in the light curve), or as a possible way to connect the results on optical, X-ray, and radio data for the same object. As an interesting additional criterion for duality, Titarchuk et al. (2023) pointed to the duality of SMBHs in an AGN, established by peculiarities, i.e., the discrepancy between the BH mass according to X-ray and optical data as a possible consequence of the duality of the central AGN in M87 [Titarchuk et al. (2023; 2020); Seifina (2024)].

Binary BHs in distant quasars are of particular interest and complexity. Because of their remoteness, it is impossible to establish the duality of their nuclei by direct imaging or Doppler shift analysis of spectral lines. Therefore, the main method for establishing their duality is through analysis of the periodicity of radiation from such sources, which may reveal quasi-periodic oscillations (QPOs) of their emission.

Recently, a QPO with a periodicity of 6.4 years was discovered in the SDSS J075217.84 + 193542.2 quasar (herein referred to as SDSS J0752) by Zhang (2022) at a redshift of 0.117 (Paris et al., 2018). The discovery of this QPO made this quasar a reliable candidate for the binary systems containing SMBHs. In fact, the BH duality in the SDSS J0752 center is indicated by the detection of two Gaussian components in the broad H _α line, with an expected spatial distance of approximately 0.02 pc between these two central SMBHs. Their virial masses are approximately 8.8 × 10⁷ M _⊙ and 1.04 × 10⁹ M _⊙ (Table 1).

This periodicity is derived from the analysis of the 13.6-year optical light curve from the Catalina Sky Survey (CSS) (Drake et al., 2009) and from the All Sky Automated Survey for SuperNovae (ASAS-SN) (Shappee et al., 2014; Kochanek et al., 2017). The 6.4-year QPOs are also confirmed using the generalized Lomb–Scargle periodogram with a confidence level of above 99.99%, as well as using the results of autocorrelation analysis and using the weighted wavelet z-transformation technique.

In this paper, we test the binary BH hypothesis in SDSS J0752 (schematically presented in Figure 1) using Swift/XRT data obtained from an X-ray counterpart of this source (Figure 2). The specific goal of our paper is to estimate the mass of the secondary BH in SDSS J0752 applying the scaling method to determine the mass of the BH (Shaposhnikov and Titarchuk (2009), hereafter referred to as ST09) based on Swift observations obtained during X-ray flaring events (Figure 3). Based on the discovered more or less strict 6.4-year cycle, we adhere to the hypothesis of the orbital rotation of components in a binary BH, in which the secondary BH periodically disturbs the accretion disk around the primary BH (Figure 1) to explain the optical (and possibly X-ray) periodic variability of SDSS J0752 (Zhang, 2022). In this case, the secondary BH is surrounded by a smaller disk, a minidisk, consisting of matter captured during such periodic passages of the primary BH disk (Figure 1).

The scaling method was proposed by Shaposhnikov and Titarchuk (2007), hereafter referred to as 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 QPO frequency, ν _L , and based on the correlation between Γ and the normalization of the spectrum proportional to M ̇ . For the first method (Γ − ν _L ), the source distance is not required to estimate the BH mass (ST07), while for the second method, Γ − M ̇ (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 flare. Γ monotonically increases with ν _L or M ̇ during the transition from the low-hard state (LHS) through the intermediate state (IS) to the high–soft state (HSS) and reaching a constant level (saturating) at high values of ν _L or M ̇ . Then, Γ monotonically decreases during an HSS → IS → LHS transition when the flare decays. The saturation of Γ (the so-called Γ-saturation phase whereby Γ reaches a constant value in our parameter space; see Figure 6) during a flare is a specific indication that this particular object contains a BH (Titarchuk and Zannias, 1998). Indeed, the Γ-saturation phase can be only caused by an accretion flow converging to the event horizon of a BH [see numerical simulation results obtained by Laurent and Titarchuk (1999); Laurent and Titarchuk (2011)]. Then, it makes sense to compare BH sources that have the same Γ-saturation levels. In the second method ( Γ − M ̇ ) , it is assumed that BH luminosity is directly proportional to M ̇ (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 − M ̇ for a pair of sources with BHs, in which all parameters are known except for the BH mass (more details on the scaling method are given in the studies by Titarchuk et al. (2010); Seifina and Titarchuk (2010); and ST09).

The scaling approach, in general, has a number of advantages over other methods for the determination of a BH mass. A determination of the X-ray spectrum arising from the innermost part of the source, based on fundamental physical models, takes into account the Comptonization of soft disk photons by hot electrons from the Compton cloud and in the converging flow into a BH. In this case, the latest achievements in modeling the BH states using the Monte Carlo method were used based on the numerical solution of the complete relativistic kinetic equation and the detection of the “saturation” phase of the spectral index at the maximum of the X-ray flare of the BH. We developed and tested the method on various astrophysical objects, and the results showed excellent agreement with classical methods (see, e.g., Seifina and Titarchuk (2010); Titarchuk et al. (2014); Titarchuk and Seifina (2016a), Titarchuk and Seifina (2017); Seifina et al. (2017); Seifina et al. (2018b); Titarchuk et al. (2020); Titarchuk and Seifina (2023). The method is based on the first principles and fundamental assessments of the gravitational effect of a BH on the matter surrounding it, as well as on calculating the effective size and mass of the reaction zone to such an effect.

In this paper, based on a particular Swift/XRT data analysis, we estimate a BH mass in SDSS J0752 using the scaling method. Section 2 provides the details of our data analysis; Section 3 presents a description of the spectral models used for fitting these data and results; Section 4 discusses the main results of the paper. In Section 5 we present the conclusion.

Using Swift/XRT data in the 0.3–10-keV energy range, we studied flaring events of SDSS J0752 from 2008 to 2010 (see the log of observations in Table 2). The data used in this paper are publicly available through the GSFC public archive ¹ . It must be noted that not all flare events can be associated with the disk–secondary BH interactions. Therefore, it is difficult to separate the sporadic flares that often occur in SDSS J0752, which are completely unrelated to the presence of any binary system in the SDSS J0752 center. However, the identified periodicity of the optical source facilitates such identification since it can be associated mainly with orbital variability. Here, we assume that X-ray variability is caused by flares due to the passage of a smaller BH through the disk around a larger BH. Moreover, it will be accompanied by corresponding spectral changes, which will help us separate the X-ray flare activity of the small BH. Section 3 presents the X-ray variability analysis of SDSS J0752 (using Swift/XRT) and shows that SDSS J0752 follows spectral patterns typical of galactic and extragalactic sources with BHs.

Data were processed using HEASoft v6.14, the xrtpipeline tool 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 using xrtexpomap v0.2.7. Source events were accumulated within a circular region with a radius of 50″ centered at the position of SDSS J0752 (α = 07 ^h 52 ^m 17 ^s .63 and δ = +19°35′42″.7, J2000.0). Given the low count rate of SDSS J0752, most of the data were collected using the most sensitive photon counting (PC) mode. The background was estimated in a nearby source-free circular region with a radius of 85″.

Using the xselect v2.4 task, source and background light curves and spectra were generated. Spectra were rebinned with at least 10 counts in each energy bin using the grppha task in order to apply χ ² statistics. We also used the online XRT data product generator ² to obtain the image of the source field of view (FOV) in order to make a visual inspection and remove possible contamination from nearby sources (Evans et al., 2007; Evans et al., 2009). The Swift/XRT (0.3–10 keV) image of the SDSS J0752 FOV is given in the right panel of Figure 2, where panel (a) demonstrates the absence of the X-ray jet-like (elongated) structure and the minimal contamination by other point sources and diffuse emission within a region with a radius of 85″ around SDSS J0752. The next nearest source 2SXPS J075211.6 + 193519 is 86″ away (marked by the orange circle). We used the Swift observation of SDSS J0752 (2008–2010) extracted from the HEASARC and found that these data cover a wide range of X-ray luminosities.

Before proceeding and providing the details of the spectral fitting, we study the long-term behavior of SDSS J0752, in particular, its activity patterns. We present a long-term X-ray light curve of SDSS J0752 detected using the XRT on board Swift from 2008 to 2010 (see Figure 3).

We note that this X-ray light curve makes it rather difficult to judge the 6.4-year periodicity found earlier from optical observations (see also the top panel of Figure 3). However, it can be unequivocally stated that the SDSS J0752 quasar has become active over the past 15 years and shows sporadic X-ray activity (e.g., MJD 54700–55400; Figure 3).

We estimated the minidisk inclination of the secondary BH by combining scaling of the X-ray spectral properties of SDSS J0752 and the virial mass obtained from optical observations (CSS ⁴ and ASAS-SN ⁵ V-band light curve) of this quasar (Zhang, 2022). A high value of the inclination of the minidisk of the secondary BH was obtained ( ≤ 8 0 o ) . However, it is necessary to emphasize that the IR and radio data available for SDSS J0752 are consistent with such a high minidisk inclination. It is known that SDSS J0752, a so-called blue quasar (Zhang, 2022), is a quasar whose IR is weakly absorbed. As a working hypothesis to explain the status of blue quasars, it was argued that they are observed at a low inclination angle (Klindt et al., 2019) to the observer and are, thus, weakly subject to IR absorption. According to this hypothesis, blue quasars are fundamentally different from the so-called red quasars, whose radiation is predominantly red at optical wavelengths due to the presence of dust in the line of sight. However, Klindt et al. (2019) ruled out orientation as the cause of the differences between red and blue quasars based on an analysis of quasar radio properties using FIRST data (1.4 GHz/6 μm).

However, even in the case of the “face-on” orientation of the main disk of the SDSS J0752 quasar, when we observe the galaxy disk almost from the pole, the high inclination of the secondary BH (mini)disk we obtained is consistent with the fact that the orbit of the secondary BH is oriented perpendicular to the plane of the main disk around the primary BH. This is consistent with our orbital flare scenario (Figure 1), in which the orbit of the secondary BH does not coincide with the galactic plane but makes a significant angle, in our case, ∼ 80 ° . Therefore, we clearly observe periodic X-ray and optical flares during the orbital passage of a secondary BH through the disk around the primary BH (i.e., through the disk of the galaxy).

We obtained a fairly low temperature of the seed photons kT _s from the inner part of the disk around the secondary BH (80–115 eV). This is consistent with calculations of the X-ray spectrum arising from the innermost part of the source, based on first-principle physical models, taking into account the Comptonization of soft disk photons by hot electrons of the Compton cloud originating from the innermost part of the disk and from the converging flow of the BH. Indeed, in the case of a 10⁸ M _⊙ BH, the peak temperature of the disk is relatively low, k T s < 1 k e V / ( M B H / 10 M ⊙ ) 1 / 4 , i.e., approximately 20–100 eV, and its thermal peak is in the UV energy range.

We proceed with a scenario of orbital rotation of a binary system in the center of the SDSS J0752 quasar, consisting of two BHs of higher and lower mass (Figure 1), which explains its X-ray variability. In this case, a heavier BH is surrounded by a powerful accretion disk, and a lighter BH, surrounded by the minidisk, rotates around the primary BH in a plane different from the equatorial plane of the accretion disk of the primary BH, crossing it twice during the orbital period (6.4 years). We also assumed that when a secondary BH passes through the disk around the primary BH, “tidal disruption” of nearby parts of the disk occurs. As a result, a partial destruction and subsequent replenishment of matter from the accretion minidisk around the secondary BH takes place [see a similar process given in the study by Chan et al. (2021)]. In this case, a powerful transition minidisk is developed around the secondary BH with the subsequent accretion of material from the transition minidisk onto the secondary BH. This provides an increase in luminosity in the X-ray/optical/radio bands.

To complete our analysis, we list other possible reasons leading to the variability in quasar emission. It should be also taken into account that this variability of quasars may be associated with changes in the emission of their jets. This source is a weak radio emitter and is not classified as “radio loud.” By the conventional definition of radio loudness, it is R = L _radio /L _bolometric ∼ 10. For this object, it is R ∼ 0.3. A recent structural analysis of 447 of the radio sources in the northern sky at 15 GHz (Lister et al., 2021) showed variations in the position angle of the jets with an average amplitude of 10°–50° on a timescale of approximately 10 years. For some sources, variations reach 200°. There are several scenarios that could explain this behavior, for example, orbital motion in a binary BH (Begelman et al., 1980). The Lense–Thirring effect (Lense and Thirring, 1918; Thirring, 1918) in a binary system with a rotating BH is widely discussed. In this case, fluctuations in the internal orientation of the jet are caused by the precession of the accretion disk, the rotation axis of which is shifted relative to the rotation axis of the BH (Caproni et al., 2004). For example, based on observations made over 22 years in 170 epochs, a study of the structure of the jet in the radio Galaxy M87 showed a periodic change in the position angle of the jet with a peak-to-peak amplitude of ∼ 10 ° and a period of T ∼11 years on scales ∼600–2,500 r _g (Cui et al., 2023). The periodicity of the light curve in the optical range and variations in the position angle of the jet in the quasar 3C 120 suggest the existence of a precession of the jet caused by the Lense–Thirring effect with a period of 12.3 years (Caproni and Abraham, 2004). The same is also shown for the jet in M81*, the precession period of which is estimated at ∼7 years (von Fellenberg et al., 2023). A detailed analysis of the orientation oscillations of other jets also indicates their periodicity and possible connection with precession, for example, PKS 2131–021 (O’Neill et al., 2022) (T ∼ 22 years), PG 1553 + 113 (Lico et al., 2020), 4C 38.41 (Algaba et al., 2019) (T = 23 ± 5 years), 3C 279 (Abraham and Carrara, 1998) (T ∼ 22 years), 3C 273 (Abraham and Romero, 1999) (T ∼ 16 years), and OJ 287 (Britzen et al., 2018) (T ∼ 12 years). This list may be supplemented by SDSS J0752, but this requires additional research.

One can argue that the emission from this quasar object comes from a jet. However, 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, 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 components kT _s and N, respectively.

Since the more massive BH is not active in the X-rays, then the active culprit for the X-ray flares, for example, in M87, is precisely the secondary (less massive) BH. It is this activity that underlies the X-ray scaling and timing analysis methods, and their results relate to the smaller BH of this binary system in M87. Now, it is not surprising that a BH mass, according to X-ray estimates by Titarchuk et al. (2020), turned out to be two orders of magnitude less than results of the EHT method (Akiyama et al., 2019) and the classical gas and stellar dynamic approach (Gebhardt et al., 2011; Walsh et al., 2013).

The optical periodic variability of the SDSS J0752 quasar has raised several questions regarding whether the source contains one or two BHs. It was very important to identify the X-ray characteristics indicating the duality of this quasar. In this paper, we demonstrated that an X-ray source coupled to an optical source exhibits flux variability in the 0.3–10 keV energy range by a factor of 15. At the same time, the X-ray spectra of SDSS J0752 undergo transitions from the LHS to the IS and then to the HSS (Figure 5) based on data obtained using the XRT on board the Swift observatory. We fitted the SDSS J0752 energy spectrum to a Comptonization model and described the evolution of the spectrum parameters. The temperature of the seed disk photons turned out to be very low (kT _s = 0.08–0.15 keV), the degree of disk illumination varied in a wide range (illumination factor f = 0.1–1), and the disk luminosity in the soft X-ray range L _0.3−10keV showed a monotonic increase during the state evolution—the LHS → IS → HSS—with a factor of 10 and was correlated with the optical flash of SDSS J0752 ( N bmc = ( 0.1 − 8 ) × L 34 / d 10 2 ) . In addition, we discovered the saturation of the photon index with the mass accretion rate in SDSS J0752, which allowed us to scale the secondary BH in this object using the scaling method. We thus determined a mass of 9 × 10⁷ M_⊙ for the secondary BH. We showed that a scenario in which two supermassive BHs at the center of the SDSS J0752 quasar form an orbital pair, and the less massive secondary BH periodically crosses/pierces the disk around the more massive primary BH, can be applied to SDSS J0752. Thus, we associated an increase in the X-ray flux in SDSS J0752 with intersections of the disk of the primary BH with the secondary BH. In addition, we estimated the orbital inclination of the secondary BH, i = 80°, based on a combination of our scaling approach and virial BH mass estimates obtained by Zhang (2022).