Abstract
Precise measurements of black hole (BH) masses are necessary to understand the coevolution of these sources and their host galaxies. Sometimes in the center of a galaxy, there is not one but two BHs. The BH duality of the quasar nucleus SDSS J075217.84 + 193542.2 (herein referred to as SDSS J0752) was recently proposed based on the observed strict periodicity of optical emission from the source. We tested this assumption using X-ray observations obtained using Swift/XRT (2008–2010). We fitted the SDSS J075217 spectrum using a Comptonization model and discovered soft X-ray variability in the 0.3–10-keV energy range. We pursued a scenario in which two supermassive BHs at the center of SDSS J0752 form a pair, and the less massive (secondary) BH periodically crosses/punctures the disk around the more massive (primary) BH. We associated these periodic crossings with tidal disruptions of the disk and, as a consequence, with an increase in X-rays observed as a flare in SDSS J0752. During such an X-ray flare event (2008–2010), we discovered a change in the source spectral states and the photon index saturation at the Γ ∼ 3 level with mass accretion rate . For BH mass scaling, we used OJ 287, M101 ULX–1, and HLX–1 ESO 243–49 as reference sources and found that MSDSS = 9 × 107 solar masses, assuming that dSDSS = 500 Mpc. Thus, we obtained a lower limit to a BH mass due to the unknown inclination. In addition, we used the virial mass of the secondary BH based on Hα-line measurements, and we estimated the inclination of the binary at SDSS J0752, i = 80°, using a scaling technique.
1 Introduction
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 (). 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 (; ). It should be noted that the very idea of binary systems with SMBHs was expressed by . 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 ().
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; ; NGC 6240; ; Mrk 739; ; and UGC 4211; ). For distant AGNs, spectroscopic studies make it possible to establish duality by the characteristic behavior of spectral line systems [SDSS J1537 + 044; ; SDSS J0927 + 294; ]. 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 () or the strict periodicity of the source flares in OJ 287 (Zhang, 2022; ). 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, 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 [; ; ].
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 (). 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 Hα line, with an expected spatial distance of approximately 0.02 pc between these two central SMBHs. Their virial masses are approximately 8.8 × 107M⊙ and 1.04 × 109M⊙ (Table 1).
TABLE 1
| Parameter | Value | Reference |
|---|---|---|
| Source class | QSO | Zhang (2022) |
| Virial mass of a primary black hole (BH), M⊙ | ∼1.04 × 109 | Zhang (2022) |
| Virial mass of a secondary BH, M⊙ | ∼8.8 × 107 | Zhang (2022) |
| Orbital inclination, i, deg | ∼ 80 | This work |
| Orbital period, P, yr | 6.4 | Zhang (2022) |
| Distance D, Mpc | ∼ 500 | This work |
| Redshift, z | 0.117 |
Basic parameters of SDSS J0752.
This periodicity is derived from the analysis of the 13.6-year optical light curve from the Catalina Sky Survey (CSS) () and from the All Sky Automated Survey for SuperNovae (ASAS-SN) (; ). 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 (, 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).
FIGURE 1
FIGURE 2
FIGURE 3
The scaling method was proposed by , 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, νL, and based on the correlation between Γ and the normalization of the spectrum proportional to . For the first method (Γ − νL), the source distance is not required to estimate the BH mass (ST07), while for the second method, (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 νL or 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 νL or . 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 (). 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 ; ]. Then, it makes sense to compare BH sources that have the same Γ-saturation levels. In the second method , it is assumed that BH luminosity is directly proportional to (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 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 ; 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., ; ; , ; ; ; . 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.
2 Data reduction
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 archive1. 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.
TABLE 2
| Obs. ID | Start time (UT) | Exposure time (ks) | Start time (MJD) |
|---|---|---|---|
| 00038041001 | 2008 October 31, 07:06:59 | 3.6 | 54,770.297 |
| 00038041002 | 2009 February 24, 04:55:17 | 1.3 | 54,886.205 |
| 00038041003 | 2009 September 12, 19:12:59 | 1.5 | 55,086.800 |
| 00038041004 | 2010 May 30, 00:07:16 | 2.7 | 55,346.005 |
| 00039551001 | 2010 May 30, 09:44:39 | 5.0 | 55,346.406 |
List of the Swift observations of SDSS J0752 used in our analysis.
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 = 07h52m17s.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 χ2 statistics. We also used the online XRT data product generator2 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 (; ). 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).
3 Results
3.1 Image of SDSS J0752
We detected an X-ray source (within the error radius 3.6″ with 90% confidence) at the location of SDSS J0752 indicated by optical observations RA = 118.0735° and Dec = 19.5952° (Zhang, 2022; see also https://skyserver.sdss.org/edr/en/sdss/skyserver/). At the same time, some of the coordinates of our X-ray source associated with SDSS J0752 were refined RA = 118.0779° (α = 07h52m18s.70) and Dec = +19.6351° (δ = +19°38′06″, J2000.0) in accordance with the analysis of XTR/Swift data. The visual inspection of the source with the indicated coordinates showed the presence of an almost point-like source at the SDSS J0752 position and the absence of other nearby objects within a radius of 85″.
3.2 X-ray light curve of SDSS J0752
We discovered the variability of SDSS J0752 in X-rays. The Swift/XRT light curves of this source in the 1.5–10-keV energy range (central panel) and in the 0.3–1.5-keV energy range (bottom panel) from 2008 to 2010 are presented in Figure 3. The figure shows light curves obtained with the binning mode by time. To test source variability within one observation, we set the time interval size to ∼100 s. The figure shows that the source is variable within one observation, even taking into account observational errors. Figure 3 also demonstrates the change in the maximum count rate achieved in each observation during the full source observation interval of 2008–2010. Comparing the source light curves in different energy bands showed that the main variability of SDSS J0752 is due to changes in the hard band (1.5–10 keV), although minor variability in the soft band (0.3–1.5 keV) also occurs. We also present CSS V-band light curve data, obtained from http://nesssi.cacr.caltech.edu/DataRelease/, to compare the variability of SDSS J0752 in different energy bands for the time interval MJD 54770 (October 2008) to 55650 (March 2011). The figure shows that the source is variable in both the X-ray and optical bands. Both bands show the tendency of the source to flare at MJD 54900–55100. In this case, the contribution of hard photons is significant for all states, but for MJD 55100, it is significantly smaller, which corresponds to a typical flare state for BHs () and with a softened X-ray spectrum of the source (see the red spectrum in Figure 5). The phases LHS, IS, and HSS are marked with blue, gray, and red vertical strips, respectively, for which the corresponding spectra are presented in Figure 5 in the next section.
3.3 Hardness–intensity diagram of SDSS J0752
By applying the Swift data of SDSS J0752, we defined the hardness ratio (HR) as a ratio of the hard and soft counts in the 1.5–10-keV and 0.3–1.5-keV bands, respectively. Figure 4 presents the hardness–intensity diagram (HID) for SDSS J0752 using the Swift/XRT observations (2008–2009) during the spectral evolution from the high state to the low state. The diagram demonstrates that different count-rate observations are related to different color regimes. The larger HR values correspond to harder spectra. For clarity, we plot only one point with error bars (in the bottom left corner) to demonstrate typical uncertainties for the soft count rate and HR. Figure 4 clearly shows that the HR monotonically decreases with the soft count rate (0.3–1.5 keV). This HID indicates the X-ray variability of SDSS J0752 with changing spectral states. This particular sample is similar to those of most flares of galactic X-ray binary transients (; ; ; ; ; ).
FIGURE 4
Below, we analyzed the SDSS J0752 spectrum in each observation to better understand the nature of this X-ray variability.
3.4 Spectral analysis of SDSS J0752
To fit the energy spectra of SDSS J0752, we used an XSPEC bulk motion Comptonization model (hereafter referred to as BMC model) []. We also used a multiplicative tbabs model (), which takes into account the absorption by the neutral material. We assume that accretion onto a BH is described by two main zones [see Figure 1 in the study by ]: a geometrically thin accretion disk (e.g., the standard Shakura–Sunyaev disk; see SS73) and a transition layer (TL), which is an intermediate zone between the accretion disks, and a converging (bulk) region, which is assumed to exist below 3 Schwarzschild radii, 3RS = 6GMBH/c2 [details given in the study by ]. The spectral model parameters are the equivalent hydrogen absorption column density NH; 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 kTs and Nbmc, 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), the illumination factor f becomes a constant value close to 1 (i.e., the same as in the case of log(A) = 2). We note that NH was fixed at the galactic absorption level of 2.13 × 1022 cm−2 ().
Similar to the bbody XSPEC model, the normalization parameter of the BMC model is a ratio of the source (disk) luminosity L to the square of the distance d (see Eq. 1 in ST09):
This encompasses an important property of our model. That is, using this model, one can accurately evaluate the normalization of the original “seed” component, which is presumably a correct indicator (). In turn,
Here, R* = r*RS is an effective radius, where the main energy release takes place in the disk, RS = 2GM/c2 is the Schwarzschild radius, η = 1/(2r*), is the dimensionless in units of the critical mass accretion rate , and LEdd is the Eddington luminosity. The formulation of the Comptonization problem is given in the studies by ; ; ; ; and .
Spectral analysis of the Swift/XRT data fits for SDSS J0752 provides a general picture of the source evolution. We can trace the change in the spectrum shape during the LHS–IS–HSS transition. Figure 5 shows three representative E*FE spectral diagrams for different states of SDSS J0752. Here, we put together spectra of the LHS, IS, and HSS to demonstrate the source spectral evolution from the low–hard to high–soft states based on the Swift observations. The data are presented as follows: the LHS (taken from observation 00038041001, blue), the IS (00039551001, black), and the HSS (00038041002, red) in units E*F(E) fitted using the tbabs*bmc model. Exposure times are 3.6, 1.3, and 5.0 ks, respectively. It is worth noting that the source spectra were constructed based on the integral flux during the entire observation without taking into account binning to achieve a good signal-to-noise value. These spectra (blue, red, and black) are plotted for the LHS, IS, and HSS phases, marked with blue, gray, and red vertical stripes, respectively, as shown in Figure 3.
FIGURE 5
The best-fit parameters in the HSS (red spectrum in Figure 5) are Γ = 2.9 ± 0.6, kTs = 130 ± 5 eV, N = 8.2 ± 0.6 , and log(A) = −1.47 ± 0.08, for which the reduced chi-square value = 1.04 for 964 degrees of freedom (dof); the best-fit model parameters for the IS (black spectrum) are Γ = 2.2 ± 0.6, kTs = 140 ± 3 eV, N = 2.3 ± 0.8 , and log(A) = −0.32 ± 0.09 ( = 0.95 for 288 dof); and, finally, the best-fit model parameters for the LHS (blue spectrum) are Γ = 1.9 ± 0.4, kTs = 88 ± 9 eV, N = 1.1 ± 0.4 , and log(A) = −3.58 ± 0.07 ( = 1.06 for 249 dof). A systematic uncertainty of 1% represents the instrumental flux calibration uncertainty and has been applied to all analyzed Swift spectra.
Analysis of the Swift/XRT data fits (Figure 6, pink circles) showed that Γ monotonically increases from 1.85 to 2.95 when the normalization of the spectral component (or ) increases by a factor of approximately 15. We determined that the energy spectra of SDSS J0752 in all spectral states can be well modeled using a product of the tbabs and a BMC component.
FIGURE 6
We plotted the dependence of Γ on Nbmc (Figure 6) and discovered a linear section of a monotonic increase in the index with increasing N, which is proportional to the accretion rate . It is interesting that the dependence Γ − Nbmc for high Nbmc clearly shows the area of index saturation at the level Γ ∼ 3. This effect is well known as an index saturation (see ST09) (pink line in Figure 6). It was previously tested on a large number of sources with BHs of different masses [stellar-mass BHs; ; ; ; ], intermediate-mass BHs (; ), and supermassive BHs (; ; ; ; ; ) and has established itself as a reliable indicator of the BH presence in the source (). In addition to diagnosing the presence of a BH, this effect makes it possible to estimate the parameters of a BH object, such as mass and inclination.
3.5 A mass estimate of the SDSS J0752 secondary BH
We used a previously developed technique to estimate the BH mass, MSDSS (). Previously, we did not know for which BH in the SDSS J0752 quasar the mass can be estimated using our X-ray data for SDSS J0752. We used the Γ − Nbmc correlation to estimate a BH mass (see ST09 for details). This method ultimately (i) deals with a pair of BHs, for which Γ correlates with an increasing normalization Nbmc (which is proportional to the mass accretion rate and a BH mass M; ST09, Eq. 7) and for which the saturation levels Γsat are the same, and (ii) calculates the scaling factor sN, which allows us to determine the BH mass of the target object. It should also be emphasized that to estimate a BH mass using the following equation for the scale factor, the ratio of the distances to the target and reference sources is necessary:where Nr and Nt are the BMC normalizations of the spectra, mt = Mt/M⊙ and mr = Mr/M⊙ are the dimensionless BH masses with respect to solar mass, and dt and dr are distances to the target and reference sources, repectively. A geometrical factor, fG = cos ir/cos it, where ir and ir are the disk inclinations for the reference and target sources, respectively (see ST09, Eq. 7).
For appropriate scaling, we have to select X-ray sources (reference sources), which also show the effect of index saturation, and at the same Γ level as SDSS J0752 (target source). For reference sources, a BH mass, inclination, and distance must be well known. We found that OJ 287, M101 ULX–1, and HLX–1 ESO 243 can be used as the reference sources because these sources met all the aforementioned requirements to estimate a BH mass of the target source OJ 287 (see (i) and (ii) above).
Figure 6 shows how the photon index Γ evolves with normalization N (proportional to the mass accretion rate ) in the blazar OJ 287 and in the SDSS J0752 quasar, where N is presented in units of (L39 is the source luminosity in units of 1039 erg/s and d10 is the distance to the source in units of 10 kpc).
In Figure 6, the correlations Γ versusN are self-similar for the target source (SDSS J0752), and two M101 ULX–1 and ESO 243–49 HLX–1 are ultra-luminous X-ray (ULX) sources. Moreover, these three sources have almost the same index saturation level Γ of approximately 2.8. We estimated a BH mass for SDSS J0752 using the scaling approach (see ST09). Figure 6 shows how the scaling method works shifting correlations relative to another. From these correlations, we could estimate Nt and Nr for SDSS J0752 and for the reference sources (Table 3). A value of Nt = 5 × 10−6 and Nr in units of are determined in the beginning of the Γ-saturation part [Figure 6; ST07; ST09; ; , , ].
TABLE 3
| Reference Source | mr, M⊙ | deg | Nr, L39/d210 | Mpc |
|---|---|---|---|---|
| HLX–1 | ||||
| ESO 243–49(1) | (7.2 ± 0.7) × 104 | 75 | 4.2 × 10−6 | 95 ± 10 |
| M101 ULX–1(2) | (3.7 ± 0.6) × 104 | 18 | 3 × 10−4 | 6.9 ± 0.7 |
| OJ 287(3) | (1.25 ± 0.5) × 108 | 50 | 2.4 × 10−4 | 1037 ± 10 |
| Target source | mt, M⊙ | it(a), deg | dt(b), Mpc | |
|---|---|---|---|---|
| SDSS J0752 | ∼9×(1±0.45)×107 | 50 | 500 | That using ESO 243-49 as a reference source |
| SDSS J0752 | ∼9×(1±0.45)×107 | 50 | 500 | That using M101 ULX-1 as a reference source |
| SDSS J0752 | Final estimate | 50 | 500 | As a standard deviation for a mean |
| ∼9×(1±0.45)×107 | 0.45/31/2 = 0.31 |
Black hole (BH) masses and distances.
(a) System inclination in the literature and (b) source distance found in the literature. (1) Titarchuk and Seifina (2016b); (2) Titarchuk and Seifina (2016a); and (3) Titarchuk et al. (2023).
To determine the distance to SDSS J0752, we used the formula (for z < 1)where the redshift zSDSS = 0.117 for SDSS J0752, H0 = 70.8 ± 1.6 km−1Mpc−1 is the Hubble constant, and c = 3 × 105 km/s is the speed of light. This distance dSDSS agrees with the luminosity distance estimate using Ned Wright’s Javascript Cosmology Calculator3 Mpc (Wright, 2006).
A value of fG = cos ir/cos it for the target and reference sources can be obtained using a trial inclination for SDSS J0752 it = 50o and for ir (Table 3). As a result of the estimated target mass (SDSS J0752), mt, we find thatwhere dt = 500 Mpc.
Applying Eq. 5, we can estimate mt (Table 3), and we find that the secondary BH mass in SDSS J0752 is approximately 9 × (1 ± 0.31) × 107 M⊙. To obtain this estimate with appropriate error bars, we need to consider error bars for mr and dr assuming, in the first approximation, errors for mr and dr only. We rewrote Eq. 5 as
Thus, we obtained errors for the mt determination (see Table 3, second column for the target source) such that
As a result, we find that MSDSS∼ 9 × 107 M⊙ (MSDSS= Mt) assuming that dSDSS= 500 Mpc to SDSS J0752. Thus, we obtained a lower limit to the BH mass due to the unknown inclination. These results are given in Table 3.
In order to calculate the dispersion of the arithmetic mean for a BH mass estimate using different reference sources (Table 3), it should be noted thatwhere D is the dispersion of mr using each of the reference sources and n = 3 is the number of the reference sources. As a result, we determined the mean deviation of the arithmetic mean,and finally, we obtained the following conclusion (Table 3):
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 approximately 50°. However, the actual inclination may be different.
3.6 Secondary disk inclination estimate in SDSS J0752
The inclination of SDSS J0752 is still unknown. However, we can attempt to estimate it using the scaling method and the virial BH mass in SDSS J0752 from optical data (Zhang, 2022) under the assumption that the source of the X-ray variability is a secondary BH. Zhang (2022) reported that the virial mass of the secondary BH is approximately 8.8 × 107 M⊙. Then, using the second scaling law (, we find the inclination of the secondary BH disk in SDSS J0752:where we used ESO 243–49 HLX–1 as a reference source and parameters Mr = 7.2 × 104 M⊙, M⊙, dr = 95 ± 10 Mpc, dt = 500 Mpc, Nt = 5 × 10−6, and Nr = 4.2 × 10−6.
As the inclination of the (mini)disk around the secondary BH based on its virial mass is estimated, we can refine our scaling estimate of a BH mass of the secondary BH. If we previously assumed fG = 1, then clarifying the angle it leads to fG = 8. Since the secondary disk should be observed almost edge-on, i.e., this angle it tends to be 90°, then the mass of the secondary BH component should be slightly larger, i.e., M⊙.
4 Discussion
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 (CSS4 and ASAS-SN5 V-band light curve) of this quasar (Zhang, 2022). A high value of the inclination of the minidisk of the secondary BH was obtained . 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 () 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, 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, . 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 kTs 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 108M⊙ BH, the peak temperature of the disk is relatively low, , 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 ]. 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 = Lradio/Lbolometric ∼ 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 () 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 (). The Lense–Thirring effect (; ) 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 (). 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 and a period of T ∼11 years on scales ∼600–2,500 rg (). 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 (). The same is also shown for the jet in M81*, the precession period of which is estimated at ∼7 years (). A detailed analysis of the orientation oscillations of other jets also indicates their periodicity and possible connection with precession, for example, PKS 2131–021 () (T ∼ 22 years), PG 1553 + 113 (), 4C 38.41 () (T = 23 ± 5 years), 3C 279 () (T ∼ 22 years), 3C 273 () (T ∼ 16 years), and OJ 287 () (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 NH; 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 kTs 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 turned out to be two orders of magnitude less than results of the EHT method () and the classical gas and stellar dynamic approach (; ).
5 Conclusion
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 (kTs = 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 L0.3−10keV 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 . 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).
Statements
Data availability statement
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
Author contributions
LT: writing–review and editing and writing–original draft. ES: writing–review and editing, writing–original draft, supervision, methodology, and investigation.
Funding
The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.
Acknowledgments
The authors thank the anonymous reviewer for the careful reading of the manuscript and for providing valuable comments. The authors thank Chris Shrader for the careful reading and editing of the manuscript. We acknowledge the UK Swift Science Data Centre at the University of Leicester for the supplied data. This paper used the data from the CSS projects http://nesssi.cacr.caltech.edu/DataRelease/.
Conflict of interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Footnotes
1.^https://heasarc.gsfc.nasa.gov
2.^http://www.swift.ac.uk/user_objects/
3.^https://www.astro.ucla.edu/wright/CosmoCalc.html
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Summary
Keywords
accretion, accretion disks, black hole physics, galaxies: active galaxies, individual SDSS J075217.84 + 193542.2
Citation
Titarchuk L and Seifina E (2024) SDSS J075217.84 + 193542.2: X-ray weighing of a secondary BH. Front. Astron. Space Sci. 11:1368633. doi: 10.3389/fspas.2024.1368633
Received
10 January 2024
Accepted
13 March 2024
Published
24 April 2024
Volume
11 - 2024
Edited by
Alberto Rodriguez-Ardila, Laboratório Nacional de Astrofísica, Brazil
Reviewed by
Zhiyuan Ma, University of Massachusetts Amherst, United States
Filiberto Hueyotl-Zahuantitla, Cátedra CONACYT-UNACH, Mexico
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© 2024 Titarchuk and Seifina.
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*Correspondence: Lev Titarchuk, titarchuk@fe.infn.it
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