A MILLIPARSEC SUPERMASSIVE BLACK HOLE BINARY CANDIDATE IN THE GALAXY SDSS J120136.02+300305.5

When SDSS J1201+30 becomes invisible to Swift during 2010 July 7 and July 28, the flux in X-rays decreases by more than 47 times within 7 days from the last detection of 2010 June 30. Although the present observations can give only upper limits to the decay timescale with Δt_dc < 7 days and to the duration of being invisible in X-rays with 21 days ⩽ Δt_in ⩽ 116 days due to gaps in the observed light curve, we still have Δt_dc ≪ Δt_in and can give severe constraints on the possible models for the origin of the intermittence of the tidal flare. Here, we explore in detail the SMBHB model as suggested by LLC09, and give a discussion on alternatives in Section 4.1.

In the SMBHB model (LLC09), the orbits of the less-bound and unbound stellar plasma change due to the strong perturbation by a massive object at a distance of several hundreds of Schwarzschild radii. Then, a significant fraction of the stellar plasma cannot fall back to form an accretion disk and to fuel the SMBH, leading to an intermittence of accretion onto the SMBH, and thus of the tidal flare. Because the massive perturber must be compact in order for it to survive the tidal force of the central SMBH, it is most likely a second SMBH. Before we numerically show how well the observations of SDSS J1201+30 can be reproduced by the theoretical light curves predicted by the SMBHB model in the Section 3.2, we first briefly introduce and discuss the merits of the SMBHB model.

After a star is tidally disrupted by a SMBH, the viscous interaction among the stellar plasma is negligible and the plasma fluid elements move ballistically with Keplerian orbits before they fall back to the pericenter and circularize because of strong shocks among the stellar tidal plasma (Evans & Kochanek 1989). For the ultra-bound fluid elements of Keplerian orbits with semi-major axis, much less than that of the SMBHB (hierarchical triple systems), the orbits of the fluid elements evolve secularly under the perturbation of the secondary SMBH on the Kozai-Lidov timescale (Kozai 1962; Lidov 1962), which is much larger than the Keplerian periods of the stellar fluid elements. The orbital angular momentum change, within one Keplerian period of the fluid elements, due to the torque caused by the quadrupole force of the secondary is

$$\begin{equation} \delta {J_{\rm fl}} \sim {3\over 4} {{GM}_2 a_{\rm fl} \over a_{\rm b}^3} a_{\rm fl} 2\pi \left({a_{\rm fl}^3 \over {GM}_1}\right)^{1/2}, \end{equation} \tag{ 13 }$$

where a_fl and a_b are, respectively, the semi-major axis of the fluid elements and the SMBHB. Because the relative change of the orbital angular momentum of the fluid elements

$$\begin{eqnarray} {\delta {J_{\rm fl}} \over J_{\rm fl}} & \sim & { 3\pi \over 2} {q ({GM}_1 a_{\rm fl})^{1/2} \over ({GM}_1 2 r_{\rm p})^{1/2}} \left({a_{\rm fl} \over a_{\rm b}}\right)^{3} \nonumber \\ &\sim & 2.2\times 10^{-3} \beta ^{1/2} q_{-1} \left({10 a_{\rm fl} \over a_{\rm b}}\right)^{7/2} \left({a_{\rm b} \over 10^{-3} \, {\rm pc}}\right)^{1/2}\nonumber\\ &&\times m_6^{-1/6} r_*^{-1/2} m_*^{1/6} \end{eqnarray} \tag{ 14 }$$

is very small, the fluid elements must fall back to the pericenter and accrete onto the SMBH as in a single SMBH system. In Equation (14), q = M₂/M₁ = 0.1q₋₁ is the ratio of masses of the secondary and primary SMBHs.

However, when the fluid elements are less bound with semi-major axes a_fl ≳ a_b/3, the analytical and numerical simulations show that the orbits of the fluid elements become chaotic and change significantly on a Keplerian timescale (Mardling & Aarseth 2001; Liu et al. 2009) due to the nonlinear overlap of the multiple resonances (Mardling 2007). From Equation (14), we obtain the relative change of the orbital angular momentum of the fluid elements with a_fl ∼ a_b on Keplerian time

$$\begin{eqnarray} {\delta {J_{\rm fl}} \over J_{\rm fl}} &\sim & 7.1 \beta ^{1/2} q_{-1} \left({a_{\rm fl} \over a_{\rm b}}\right)^{7/2} \left({a_{\rm b} \over 10^{-3} \, {\rm pc}}\right)^{1/2} m_6^{-1/6} r_*^{-1/2} m_*^{1/6}, \nonumber\\ \end{eqnarray} \tag{ 15 }$$

and the fluid elements would move with chaotic orbits of pericenter r_{p, fl} ∼ 110r_p, which is much larger than the pericenter r_p at disruption. Therefore, the fluid elements move with chaotic orbits significantly different from one another. They neither fall back to the pericenter at disruption, nor cross each other to form shocks and accretion. The transition radius, or corresponding Keplerian time T_tr of the fluid elements from secular to chaotic orbits, critically depends on the orbital parameters of the stars and also of the SMBHB system, but T_tr can relate to the SMBHB orbit period, with T_tr = ηT_b (LLC09). The parameter η is a strong function of the orbital parameters of the star, but is insensitive to the SMBH masses (LLC09). Statistically, η is in the range 0.15 ≲ η ≲ 0.5 with a mean value η ∼ 0.25 for a SMBHB system with eccentricity e_b = 0. Therefore, if η is known, one can determine the orbital parameters of the star and SMBHB system. Taking into account that the first detection of the tidal flare in SDSS J1201+30 is about 11.8 days after the tidal disruption of the star and that the X-ray flux becomes invisible at a time between 20 and 27 days after discovery, we determine that the observed truncation time is 31.8 days ⩽ T_{tr, obs} ⩽ 38.8 days in the observer frame, or 27.7 days ⩽ T_tr ⩽ 33.9 days in the object rest frame.

When the stellar plasma stops falling back and fueling the accretion disk of the outer radius r_d ≈ r_c, the accretion disk evolves dynamically on the viscous timescale at r ≈ r_d

$$\begin{eqnarray} t_{\rm \nu, d} & = & {2\over 3} {r_{\rm d}^2 \over \nu (r_{\rm d})} \simeq {2\over 3} \alpha ^{-1} \left(\frac{r_{\rm d}^3}{{GM}_{\rm BH}}\right)^{1/2} \left(\frac{H}{r}\right)_{\rm r=r_d}^{-2} \nonumber \\ &\simeq & 0.12\; {\rm days} \times \alpha _{-1}^{-1} \left({\beta \over 2}\right)^{-3/2} \left(\frac{H}{r}\right)_{\rm r=r_d}^{-2} r_*^{3/2} m_*^{-1/2}, \end{eqnarray} \tag{ 16 }$$

where α = 0.1α₋₁ is the disk viscosity coefficient and H is the scale height of the disk with H ≃ r for the accretion rate $\dot{m} \gtrsim 0.3 \dot{M}_{\rm Edd}$ (Shakura & Sunyaev 1973; Abramowicz et al. 1988; Strubbe & Quataert 2009). Equation (16) suggests that t_{ν, d} is independent of the mass of the central SMBH. For SDSS J1201+30, Equations (5) and (6) suggest that the accretion rate $\dot{M}$ is much larger than $\dot{M}_{\rm Edd}$ when the source was absent from the Swift observation on 2010 July 7, or 33.9 days after tidal disruption. Therefore, the accretion disk in SDSS J1201+30 dynamically evolves on the viscous timescale t_{ν, d} ∼ 0.12 days for a typical viscous parameter α = 0.1. This is about 60 times less than the time interval between the last detection on 2010 June 30 and the first absence from the Swift observation on 2010 July 7 (S2012).

For the dynamic evolution of the accretion disk without the fueling of stellar plasma, here we construct a simple model to describe it by assuming that ν is only a function of radius with ν∝rⁿ. For the physical model of an accretion disk in tidal disruption as proposed by Strubbe & Quataert (2009), a kinematical viscosity ν = αc_sH∝rⁿ with n = 1/2 is a good approximation and adopted in the model. For an accretion disk with ν∝rⁿ, the dynamic evolution can be solved analytically and the surface density Σ can be given by making use of a Green's function G(r, t)

$$\begin{eqnarray} \Sigma (r,t) & = & \int _{r_{\rm in}}^{r_{\rm d}} G(r,R,t) \Sigma (R,t=t_{\rm tr}) dR, \end{eqnarray} \tag{ 17 }$$

(Lynden-Bell & Pringle 1974; Tanaka 2011), where Σ(R, t = t_tr) is the initial disk surface density when the stellar plasma stops fueling the accretion disk at t = t_tr, r_in (r_in ≃ 3r_g for a Schwarzschild black hole) is the inner radius of the accretion disk, and the Green's function G(r, R, t) is

$$\begin{eqnarray} G(r,R,t) & \approx & {2-n \over \Gamma (l+1)} \left({r\over r_{\rm d}}\right)^{-n} r_{\rm d}^{-5/2} R^{3/2} \tau ^{-1-j}\nonumber\\ &&\times \exp \left[-{\left(r/r_{\rm d}\right)^{2-n} +\left(R/r_{\rm d}\right)^{2-n} \over \tau }\right] \end{eqnarray} \tag{ 18 }$$

for t − t_tr ≳ t_ν(r_d). Here, j = (4 − 2n)⁻¹, τ = 2(2 − n)²(t − t_tr)/t_{ν, d}, and Γ(j) is the Gamma function. At the moment, when the stellar plasma stops fueling the accretion disk, the surface density is approximately

$$\begin{equation} \Sigma (R,t=t_{\rm tr}) \approx \Sigma _{\rm d} \left(R/r_{\rm d}\right)^{-n}, {\quad {\rm for} \quad r_{{\rm in}} \le R \le r_{\rm d}} \end{equation} \tag{ 19 }$$

where $\Sigma _{\rm d} \approx \dot{M}_0 / (3\pi \nu (r_{\rm d}))$ and $\dot{M}_0$ is the accretion rate at time t = t_tr. From Equations (17), (18), and (19), we have

$$\begin{eqnarray} \Sigma (r,t) & \approx & {2(2-n) \over (5-2n) \Gamma (l+1)} \Sigma _{\rm d} \left({r \over r_{\rm d}}\right)^{-n} \left[2(2-n)^2 {(t-t_{\rm tr}) \over t_{\rm \nu,d}}\right]^{-1-j}\nonumber\\ &&\times \left[1-\left({r_{\rm in} \over r_{\rm d}}\right)^{{5\over 2}-n}\right], \end{eqnarray} \tag{ 20 }$$

which gives an inward radial mass flow

$$\begin{eqnarray} \dot{M} &=& 6\pi r^{1/2} \frac{\partial }{\partial r}(\nu \Sigma r^{1/2}) \approx {2(2-n) \over (5-2n) \Gamma (l+1)}\nonumber\\ &&\times \dot{M}_0 \left[1-\left({r_{\rm in} \over r_{\rm d}}\right)^{{5\over 2}-n}\right] \left[2(2-n)^2 {(t-t_{\rm tr}) \over t_{\rm \nu,d}}\right]^{-1-j} \end{eqnarray} \tag{ 21 }$$

for (t − t_tr) ≳ t_{ν, d}. For a typical value n = 1/2, we have

$$\begin{eqnarray} &&\dot{M}(t-t_{\rm tr} \gtrsim t_{\rm \nu,d}) \approx 0.113 \, \dot{M}_0 \left[1-\left({r_{\rm in} \over r_{\rm d}}\right)^2\right] \left[{t-t_{\rm tr} \over t_{\rm \nu,d}}\right]^{-4/3}. \nonumber \\ \end{eqnarray} \tag{ 22 }$$

Equation (22) shows that the accretion rate in SDSS J1201+30 decreases 50 times within about 3.7t_{ν, d} ∼ 0.4 − 1 days after the stellar plasma stops fueling the accretion disk. One has to note that the accretion disk changes the accretion mode to advection-dominated accretion flows (ADAFs) for $\dot{M} \lesssim 10^{-2} \dot{M}_{\rm Edd}$ (Narayan & Yi 1995) and our simple model cannot be applied to the transition. Because an ADAF is radiatively inefficient, it is expected that the object becomes even dimmer.

The numerical simulations by LLC09 suggested that after a time interval, the stellar plasma starts refueling the accretion disk and the tidal disruption flare recurs. The exact time when the tidal flare recurs depends on both the parameters of the star and the SMBHB system, but it is about at time T_r = ξT_b with ξ of the order of unity. Given the gaps in the light curve of SDSS J1201+30, the recurrence of the tidal flare can happen between 2010 July 28 and 2010 October 24, suggesting a recurrent time T_{r, obs} between 60 days and 148 days in the observer frame or T_r between 52 days and 129 days in the object rest frame. Therefore, the orbital period, T_b (∼T_r), of the SMBHB in SDSS J1201+30 is on order of, or less than, a few hundred days. The suggested orbital period of the SMBHB, together with 28 days < T_tr < 34 days, suggests 0.2 ≲ η ≲ 0.6, which is consistent with the prediction of the SMBHB model. Whether and when the recurrent flare is interrupted again depends not only on the orbital parameters of the star and SMBH system, but also on the mass ratio and the total masses of the SMBHs, which have to be determined numerically (LLC09).

In Section 3.1, we showed that the observations of the tidal flare in SDSS J1201+30 are consistent over all with the predictions of the SMBHB model of LLC09. In this section, we numerically calculate the model light curves for the different parameters and quantitatively compare them one by one with the light curve of SDSS J1201+30 in X-rays. Given the sampling of the light curve of the tidal flare, we do not use the least-square method to get the best fit of the model predictions to the observations, but instead numerically explore the model parameter space to obtain the range of the parameters with which the SMBHB model can give theoretical light curves reasonably reproducing the observations of SDSS J1201+30.

In the simulations, for simplicity, we assume that the disrupted star is a solar-type main-sequence star of parameter k = 2.5, and that the SMBHs is a Schwarzschild black hole, which is consistent with the suggestions given by the correlation of black hole spin and jet power (Narayan & McClintock 2012). In this section, we consider SMBHB systems of circular orbit with e_b = 0, while the effects of the orbital eccentricity of the SMBHB are investigated in Section 3.3. The other parameters, both of the disrupted star and the SMBHB system, are explored and tested in a large range of values.

The method of the numerical simulations used in this work was described in detail in LLC09. Here we give only a summary and interested readers are referred to that paper. Because the interaction between the fluid elements is negligible before they return to the pericenter of the disrupted star and experience strong shocks because of the intersection and collision of the fluid elements with one another near pericenter, we can simulate the orbital evolution of the fluid elements with scattering experiments and calculate the fallback and accretion rate of the stellar plasma onto the central SMBH by assuming that all the stellar plasma falling back to a radius of around 2r_p or less is accreted. In each scattering experiment, the mass of the star is divided into fluid elements with specific energy E_fl and constant pericenter r_p by assuming a constant distribution of mass in the specific energy in a range of −ΔE and ΔE, which is given by Equation (12) with k = 2.5. When the fluid elements moving in the pseudo-Newtonian potential return and pass by the central SMBH within a distance 2r_p, the calculation stops and the fluid element and the time are recorded, respectively, as accreted matter and accretion time. Otherwise, the calculation continues until time 4T_b (the largest timescale in which we are interested) or the fluid element escapes from the system. The accretion rate of the stellar plasma is computed using the recorded fluid element masses and accretion time. We then compare the model accretion rate and the observations by adjusting the free parameter f_x in Equation (9). To reproduce the observations, we require a model light curve (1) to have an interruption between 2010 June 30 and July 6, one day before the first observation of absence on 2010 July 7; (2) that a recurrent flare begins between 2010 July 28 and October 24, and ends between 2010 December 13 and 2011 March 5; and (3) to have a second interruption during the period around 2011 April 1.

Because the SMBH masses cannot be determined uniquely in the SMBHB model by fitting the observations of the tidal flare, they have to be estimated separately and taken as input values in the simulations. Based on the relationship of black hole mass and bulge luminosity of the host galaxy, S2012 estimated a black hole mass in the range 3 × 10⁵ M_☉ < M_BH < 2 × 10⁷ M_☉ with a higher value of M_BH ∼ 10⁷ M_☉ preferred. We have only done scattering experiments for three typical values of the mass of the primary SMBH, M_BH = 10⁶ M_☉, 5 × 10⁶ M_☉, and 10⁷ M_☉. For a given mass of the primary black hole, the mass of the secondary is calculated with the mass ratio q, which is determined by reproducing the observed light curve. The results of the numerical simulations show that the interruption time T_tr, the recurrent time T_r, and the duration of the recurrent flare strongly not only depend on the orbital parameters of the disrupted star at disruption, including (1) the penetration factor β, (2) the inclination angle θ between the orbital planes of the star and the SMBHB, and (3) the longitude of ascending node Ω and the argument of pericenter ω of the stellar orbits relative to the orbit plane of the SMBHBs. They also depend on the orbital period of the SMBHB, the SMBH masses, and the black hole mass ratio q. To obtain the possible model light curves consistent with the observations, in principle we must perform many high-precision simulations to cover all the space of the seven model parameters, which would consume a large amount of computation resources and is prohibitive for present computing power. However, the discussions in Section 3.1 suggested that the orbital period of the SMBHB is of the order of hundreds of days, which could be taken as a good initial value of the orbital period T_b and used to reduce the computations. LLC09 suggested that, with a given orbital period of the SMBHB, the interruption time T_tr and the characters of recurrent flares depend sensitively on the stellar orbital parameters θ, Ω, and ω, but less on the parameters of the SMBHB system. Therefore, we started the simulations from taking T_b ∼ 135 days and q ∼ 0.1 as initial values and carried out the simulations for different values of θ ∈ [0, π], Ω ∈ [0, 2π), and ω ∈ [0, 2π) with a resolution of 0.1π in all the parameter space to obtain the typical sets of parameter values giving model light curves closest to (but not necessary fully reproducing) the observations. After many simulations, we found that the model light curves obtained with both θ ∼ 0.3π and θ ∼ 0.5π can give a reasonable fit to the observations, and the present observations of SDSS J1201+30 cannot tell which one is preferred. Those simulations with θ < 0.3π tend to give a longer duration for the first part of the light curve, which is inconsistent with the observed truncated light curve around 2010 July 7. For the simulations with θ > 0.5π, most of the results cannot give a proper recurrence as observed in SDSS J1201+30. Therefore, our results prefer a disrupted star with a prograde orbit relative to the SMBHB for SDSS J1201+30. However, our model cannot entirely exclude a disrupted star with a retrograde orbit because there are a few results with θ ≳ 0.5π still marginally consistent with the observation. Further observations with higher time resolution may help to solve the ambiguity. The simulation results suggest that the required values of the parameters of the SMBHB are nearly independent of the values of either θ ∼ 0.3π or θ ∼ 0.5π, although the solutions for θ = 0.5π are fine tuning, in the sense that the solutions become significantly different from the observations for a small deviation of θ from θ = 0.5π. Because we are mostly interested in the values of the parameters of the SMBHB system and the large gaps in the light curve do not warrant any fine tuning solution, we adopt the solutions of θ ∼ 0.3π. After θ ∼ 0.3π is chosen, we obtain the corresponding values of the other orbital parameters of the star: Ω = 0.2π and ω = 1.5π. Again, our test simulation results show that the values of the model parameters of the SMBHB system required to reproduce the observed light curve are nearly independent of the values of Ω and ω. Therefore, we will give the numerical simulation results for θ = 0.3π, Ω = 0.2π, and ω = 1.5π. With the given values of θ, Ω, and ω, we have carried out the numerical simulations iteratively, starting from the initial values T_b = 135 days, q = 0.1, and β = 2, for the penetration factor β between 1 ⩽ β ⩽ 6, 1 ⩽ β ⩽ 3, and 1 ⩽ β ⩽ 2.5 and for the orbital period T_b between 130 days ⩽ T_b ⩽ 160 days, 135 days ⩽ T_b ⩽ 170 days, and 120 days ⩽ T_b ⩽ 200 days, respectively, for M_BH = 10⁶ M_☉, M_BH = 5 × 10⁶ M_☉, and M_BH = 10⁷ M_☉, and the mass ratio q between 0.03 < q < 0.9, in order to obtain all the model light curves fully consistent with the observations, including the positive detections and upper limits in X-ray flux.

We first carry out the numerical simulations for SMBHB systems with a primary black hole of mass M_BH = 10⁶ M_☉. The top panel in Figure 1 gives two examples of the model light curve for a penetration factor β = 3.0 (solid red line) and β = 3.5 (dashed blue line), with l = 2, which can fully reproduce the X-ray observations of the tidal flare in SDSS J1201+30. To obtain the model light curve in Figure 1, we have adopted a SMBHB with an orbital eccentricity e_b = 0 and a period T_b  ≃  140 days, and a black hole mass ratio q ≃ 0.1. To compare the theoretical light curve and the observations in the X-rays, we overplot the observational X-ray data and shift the theoretical light curve up and down in order to obtain a good fit by eye, which gives a scaling factor in Equation (9), f_x = 0.004. For a typical transfer efficiency of matter to radiation = 0.1, this gives a total mass accreted ΔM_acc ∼ 0.02 M_☉, very small but consistent with the reported values for TDEs in the literature (e.g., Komossa 2002; Li et al. 2002; Komossa et al. 2004; Esquej et al. 2008; Gezari et al. 2009; Cappelluti et al. 2009; Maksym et al. 2010; Donato et al. 2014). We recall that a number of unknowns determines the precise amount of X-ray emission in the early evolution of TDEs and the unobserved EUV component may dominate the bolometric luminosity, as discussed in Section 2. Therefore the value we report here just serves as an order-of-magnitude estimate and lower limit. We note that the orbital period of the SMBHB, T_b ≃ 140 days, obtained by detailed numerical simulations, is consistent with the simple estimation given in Section 3.1. The period T_b ≃ 140 days together with the black hole mass ratio q = 0.1, suggests that the SMBHB in SDSS J1201+30 has an orbital radius $a_{\rm b} \simeq 0.26 M_6^{1/3} \, {\rm mpc} \simeq 2.8 \times 10^3 M_6^{-2/3} r_{\rm g}$. Figure 1 shows that the recurrent flares in the SMBHB model light curve fit the observations of SDSS J1201+30 in the X-rays better than a simple t^−5/3-power law decay, except for the observation on 2010 November 23, which was strongly affected by radiation (S2012).

For comparison, we re-do the simulations in Figure 1 with the same parameters, except l = 0. The results have been plotted in the middle panel of Figure 1. Compared to the top panel, there are only small differences at the beginning of the light curve. Based on Equation (3), the energy dispersion for l = 0 is smaller than l = 2 when β > 1, which results in a larger t_min. However, those changed t_min in Figure 1 are still consistent with the observation. Besides, as implied by Equations (5) and (9), since $\dot{M}(t) \propto t_{\rm min}^{2/3}$, a larger t_min will lead to a smaller f_x. As a result, f_x = 0.0004 for the middle panel of Figure 1, which is an order of magnitude lower than for the model of the top panel. As shown in the middle panel, however, ΔE is independent of β when l = 0, and the overall light curve is still impacted by β because the truncation and recurrence of the light curve in the SMBHB system are sensitively depending on the size of the circularized accretion disk, which should be changed for a different β value.

From Figure 1, the first interruption in the model light curve for β = 3.0 happens at about time T_{tr, obs} = 34 days after the tidal disruption of the star, or on 2010 July 2, which is about two days after the last detections on June 30 or five days before the first upper limit of the Swift observation on 2010 July 7. Equation (22) suggests a decay of the accretion rate by about a factor 600 within five days. This is consistent with the observation of a factor >48 within 7 days. We note that for such a large decrease of the accretion rate, the simple dynamic model of the accretion disk may not be applicable anymore. The theoretical light curve for β = 3.0 suggests that the stellar plasma stops returning and fueling the accretion disk for a period ΔT_{tr, obs} ≈ 98 days, intermingling with a flicker of accretion for about four days around 2010 August 7. The stellar plasma restarts fueling the accretion disk at about 131 days after the tidal disruption or about 16 days before the detection with Swift on 2010 October 24. After about 92 days, the recurrent tidal flare is interrupted again, at about 16 days after the last detection with XMM-Newton on 2010 December 23. This model predicts that the interrupted tidal flare will recur again later.

The results given in Figure 1 show that the observed X-ray light curve of SDSS J1201+30 can be fully reproduced by the theoretical light curve obtained with the typical model parameters θ = 0.3π, Ω = 0.2π, ω = 1.5π, β = 3.0, M_BH = 10⁶ M_☉, q = 0.1, e_b = 0, and T_b = 140 days. While our simulation results also show that the observed light curve can be well reproduced by the theoretical light curves obtained with model parameters in a broader range of values, namely, 1.2 ≲ β ≲ 5.0, 132 days ≲ T_b ≲ 145 days and 0.05 ≲ q ≲ 0.18. The upper panel of Figure 1 also gives the theoretical light curve obtained with penetration factor β = 3.5 (dashed blue line). Values of the other model parameters are the same as for β = 3.0. Figure 1 shows that a small change of the penetration factor β from β = 3.0 to β = 3.5 would result in significant changes not only of the time and duration of interruption, but also of the variability of the recurrent flares. The simulation results show that the variations of the penetration factor β can significantly change the timescale t_min, interruption and recurrent time, the duration of the recurrent flare, and the secondary recurrent time. In fact, all the key signatures in the light curves for SMBHBs strongly depend on complex combinations of the parameters β, T_b, and q. This implies that the orbital parameters of the star and the SMBHB system, together with black hole mass ratio (except for the mass of the primary SMBH), can be determined observationally, when one can obtain very densely sampled TDE light curves in the future. A deeper exploration of the allowed values in parameter space is given in Section 4.2.

Because the mass of the primary BH in SDSS J1201+30 is loosely constrained by observations (approximately within the range 3 × 10⁵ M_☉ and 2 × 10⁷ M_☉), we have also carried out the numerical simulations for SMBHB systems with black hole mass M_BH = 5 × 10⁶ M_☉ and M_BH = 10⁷ M_☉, and compare the model light curves with the X-ray observations of SDSS J1201+30. Again, here we only consider SMBHB systems with circular orbit. The simulations are carried out for model parameters in the ranges 0.03 ⩽ q ⩽ 0.9, 1 ⩽ β ⩽ 3 and 1 ⩽ β ⩽ 2.5, respectively, for M_BH = 5 × 10⁶ M_☉ and M_BH = 10⁷ M_☉. The simulation results show that for a SMBHB system with M_BH = 5 × 10⁶ M_☉ and e_b = 0 a set of fine-tuned values of model parameters can give theoretical light curves consistent with the observations. However, for a SMBHB system with M_BH = 10⁷ M_☉ and e_b = 0, no theoretical light curve is found to be fully consistent with the observations, in the sense that either the predicted first interruption date is later than the first upper limit on July 7 or the predicted recurrent flares do not cover all the observations from 2010 October 24 to December 23. As a result, if the orbit of the SMBHB in SDSS J1201+30 is circular, the primary SMBH most probably has a mass M_BH ≲ 5 × 10⁶ M_☉. Otherwise, if the SMBH has a mass M_BH ∼ 10⁷ M_☉ as preferred by the observations (S2012), the SMBHB is hardly circular, however, because of the limited coverage of the parameter space the present simulations cannot completely rule out the possibility that fine-tuning the model parameters might give solutions to the observational light curve. We will explore the effects of orbital eccentricity on the results in the next section.

The orbits of SMBHBs in galactic nuclei could be elliptical as suggested by some models for the formation and evolution of SMBHBs in galaxies (Armitage & Natarajan 2005; Berczik et al. 2006; Preto et al. 2011; Iwasawa et al. 2011; Sesana et al. 2011; Chen et al. 2011). Because the eccentricity of SMBHBs is of great importance in modeling the templates of gravitational waveforms, we now investigate if the observations of SDSS J1201+30 can give any constraint on the orbital eccentricity. For an elliptical orbit, in addition to the model parameters described in Section 3.2, we now have two more parameters, the eccentricity e_b and the initial phase ϕ_b of the SMBHB orbit at the disruption of the star. In the simulations, ϕ_b is set to be zero when the two SMBHs are at closest distance. We have carried out the scattering experiments by using the methods given in Section 3.2 and varying the eccentricity and initial orbital phase in the ranges of 0 ⩽ e_b ⩽ 0.9 and 0 ⩽ ϕ_b < 2π, respectively. The simulation results show that both the time of interruption and recurrence, and the durations of the recurrent flares of the model light curves significantly change with e_b and ϕ_b. If the mass of the primary SMBH is M_BH = 10⁶ M_☉, the observations of SDSS J1201+30 can be well reproduced with the model light curves obtained with the eccentricity 0 ⩽ e_b ≲ 0.5 and initial orbital phase 1.3π ≲ ϕ_b ≲ 2π. The bottom panel of Figure 1 gives two examples of model light curves for SDSS J1201+30 computed with e_b = 0.1, e_b = 0.2 and l = 2. The first interruption in the light curve for e_b = 0.2 occurs on 2010 July 4, about four days after the last detection and three days before the first upper limit on 2010 July 7. The recurrent fluxes in the model light curves fit the observations of SDSS J1201+30 better than a simple power-law decay. To obtain the light curves in the bottom panel of Figure 1, we have used the parameters T_b ≃ 150 days (or a_b ≃ 0.28 mpc), ϕ_b = 1.7π and q = 0.1 for the SMBHB system, and β = 2.0, θ = 0.3π, Ω = 0.2π, and ω = 1.5π for the star. For e_b = 0.2, the model light curves obtained with 0.05 ≲ q ≲ 0.15, 1.2 ≲ β ≲ 4.7 and 140 days ≲ T_b ≲ 155 days, can fully reproduce the observations of SDSS J1201+30. We note that the values of θ, Ω, and ω used in the simulations are the same as for circular SMBHB systems. In fact, to reproduce the observed light curve of SDSS J1201+30, we take θ = 0.3π, Ω = 0.2π, and ω = 1.5π in all the simulations for different eccentricities. However, we have to adopt different mass ratios and values of the SMBHB orbital parameters, because the interruption and recurrence in the model light curves depend on a complex combination of the parameters of the SMBHBs. In conclusion, the present observations of SDSS J1201+30 can constrain the eccentricity of the SMBHB only in the range 0 ⩽ e_b ≲ 0.5, if the primary SMBH has a mass 10⁶ M_☉.

For M_BH = 5 × 10⁶ M_☉, the simulation results show that the X-ray observations of SDSS J1201+30 can also be reproduced with model light curves obtained with binary eccentricity 0 ⩽ e_b ≲ 0.5. For a SMBHB system with orbital eccentricities e_b ≳ 0.5, no model light curve is able to reproduce the X-ray light curve of SDSS J1201+30. For SMBHB systems with an even higher SMBH mass of the primary, of M_BH ∼ 10⁷ M_☉, our results show that we can obtain model light curves to reproduce the X-ray observations of SDSS J1201+30 if the orbit of the SMBHB is elliptical with eccentricity 0.1 ≲ e_b ≲ 0.5. If so, the SMBHB system in SDSS J1201+30 would have an orbital period 140 days ≲ T_b ≲ 160 days and a black hole mass ratio 0.04 ≲ q ≲ 0.09. The disrupted star would have a penetration factor 1.3 ≲ β ≲ 1.6 at disruption. The orbital parameters then adopt the typical values: θ ≃ 0.3π, Ω ≃ 0.2π, ω ≃ 1.5π, and ϕ_b ≃ 1.5π. Figure 2 gives the simulated light curves for SDSS J1201+30 by a SMBHB model with M_BH = 10⁷ M_☉ and e_b = 0.3. To obtain the light curve, we have used the scaling factor f_x = 0.0004, penetration factor β = 1.3, black hole mass ratio q = 0.08, and SMBHB orbital period T_b = 150 days or semi-major axis a_b ≃ 0.59 mpc ≃ 620r_g. Our results suggest that if the mass of the SMBH in SDSS J1201+30 is indeed about 10⁷ M_☉, as preferred by the observations (S2012), the orbit of the SMBHB system should be elliptical with moderate eccentricity e_b ∼ 0.3.

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Several candidate small-separation SMBHBs have emerged in recent years. They are not spatially resolved, but the SMBHBs' presence has been indirectly inferred from semi-periodicities in light curves or structures in radio jets (see Section 1 for the observational evidence for SMBHBs; see also Komossa 2006 for a complete review).

We have shown that the presence of a SMBHB can naturally explain the characteristics of the light curve of the TDE in SDSS J1201+30, based on models of LLC09. In fact, other possible explanations that might at first glance come to mind, do not well reproduce the features of the light curve, or the overall multi-wavelength properties of SDSSJ1201+30. We comment on each of them in turn.

4.1.1. Jetted TDEs and a Comparison with Swift J1644+57

4.1.2. Temporary Absorption due to Blobs in the Accretion Disk, Stellar Streams, or an Expanding Disk Wind

4.1.3. Transient Eclipses due to Stars or an Optically-thick Dense Molecular Cloud Infalling toward the Central SMBHs

4.1.4. Blobby Accretion Near Last Stable Orbit or Other AGN-like Variability

4.1.5. Lense–Thirring Precession of an Accretion Disk Misaligned with a Spinning SMBH

If the central SMBH is spinning and the accretion disk is misaligned with the spin axis, the disk may precess about the total angular momentum of the black hole accretion disk system as a solid body due to the Lense–Thirring torque (Fragile et al. 2007). The precession of the accretion disk would lead to quasi periodic oscillations in TDE light curves (Dexter & Fragile 2011; Stone & Loeb 2012a; Shen & Matzner 2014) and to a reduction of the observed flux up to about 50 times if the disk precesses from a face-on into edge-on phases (Ulmer 1999). For an accretion disk with surface density given by the Equation (19), the precession period is

$$\begin{eqnarray} T_{\rm prec} &\simeq& {8\pi {GM}_{\rm BH} (1+2n) \over a c^3 (5-2n)}\nonumber\\ &&\times {(r_{\rm d} /r_{\rm g})^{5/2-n} (r_{\rm in} /r_{\rm g})^{1/2+n} (1-(r_{\rm in} /r_{\rm d})^{5/2-n}) \over 1-(r_{\rm in} /r_{\rm d})^{1/2+n}} \end{eqnarray} \tag{ 23 }$$

(Fragile et al. 2007; Stone & Loeb 2012a; Shen & Matzner 2014), where a is the dimensionless black hole spin parameter with 0 ⩽ a < 1. For a black hole mass M_BH = 10⁷ M_☉ and typical disk parameters n = 1/2, r_in ≃ 3r_g, and r_d ≃ 2r_t ≃ 10r_g, the typical disk precession period is T_prec ≈ 2.84 days a⁻¹M₇, or in the observer frame, T_{prec, obs} = (1 + z)T_prec ≈ 3.25 days a⁻¹M₇ ≳ 3.25 days M₇. While for a black hole mass M_BH = 10⁶ M_☉ and typical disk parameters n = 1/2, r_in ≃ 3r_g, and r_d ≃ 2r_t ≃ 47r_g, the typical precession period is T_prec ≈ 5.2 days a⁻¹M₆, or in the observer frame, T_{prec, obs} = (1 + z)T_prec ≈ 5.9 days a⁻¹M₆. If the large drop in the light curve of SDSS J1201+30 is due to the disk Lense–Thirring precession with period T_{prec, obs} ≳ 3.25 days M₇, the observations with regular time intervals of 10 days between 2010 June 10 and June 30, and 7 days between 2010 July 7 and July 28 of S2012 suggest that the face- and edge-on phases should be, respectively, longer than 20 days and 21 days. Therefore, the observations obtained between 2010 June 10 and July 28 imply that the precession period should have T_{prec, obs} ⩾ 48 days. However, the observations of the TDE between 2010 October 24 and December 23 suggest a face-on phase longer than 60 days and thus a precession period T_{prec, obs} ≳ 81 days. The observation of 2010 December 23 suggests T_{prec, obs} ⩾ 84.5 days, while the observation of 2010 October 24 indicates T_{prec, obs} < 88 days. In conclusion, if the large drop in the flux was due to the disk Lense-Thirring precession, the precession period would be 84.5 days < T_{prec, obs} < 88 days. The drop in flux by a factor 50 within 7 days, or ≲ 8% of the precession period, is too steep to be consistent with the predictions of Lense–Thirring precession (Dexter & Fragile 2011; Stone & Loeb 2012a; Shen & Matzner 2014).

All of our results were obtained with ΔE given by Equation (12) with l = 2. However, some numerical simulations (e.g., Stone et al. 2013; Guillochon & Ramirez-Ruiz 2013) suggest a weaker dependence of ΔE on β. To investigate the dependence of our results on the different relationships of ΔE and β, we have carried out test numerical scattering experiments with l = 0.

The test numerical simulations are only carried out for M_BH = 10⁶ M_☉, because the present results obtained with ΔE∝β² show a large variation of β with 1.2 ≲ β ≲ 5 for M_BH = 10⁶ M_☉ but nearly a constant β with 1.3 ≲ β ≲ 1.6 for M_BH = 10⁷ M_☉. Similar to Figure 1, our results show that the simulated light curves for SDSS J1201+30 and the obtained model parameters of the star and SMBHB systems are nearly the same as those obtained with l = 2, which can be understood as follows. Different relationships of ΔE and β significantly change only t_min, which is degenerate with the scaling free parameter f_x as discussed in Section 2. Meanwhile, although ΔE is independent of β for l = 0, the truncation and recurrence of the light curve sensitively depends on β. Therefore, we will not discuss the results obtained with l = 0 any further.

We have shown that the peculiar characteristics of the light curves of the TDE in SDSS J1201+30 can be naturally explained by the SMBHB model given by LLC09. In the SMBHB model, the orbital parameters of the disrupted star approaching with negligible initial total energy can be determined to be θ ∼ 0.3π, Ω ∼ 0.2π, and ω ∼ 1.5π independent of the detailed choices of the model parameters. By fully reproducing the X-ray light curve of the TDE with the model light curves of a SMBHB system, we have found that the orbit of the SMBHB in SDSS J1201+30 should be elliptical with moderate eccentricity $e_{\rm _b} \simeq 0.3$ (with 0.1 ≲ e_b ≲ 0.5) and typical orbital period T_b ≃ 150 days (with 140 days ≲ T_b ≲ 160 days) for a primary SMBH of mass M_BH = 10⁷ M_☉. A SMBH with that value is preferred by observations (S2012). The orbital period of the SMBHB suggests a semi-major axis of a_b ≃ 0.59 mpc ≃ 620r_g. The black hole mass ratio, the penetration factor of that star, and the initial orbital phase at disruption have typical values of q ≃ 0.08, β ≃ 1.3, and ϕ_b ≃ 1.5π, respectively. Because the parameters q, e_b, and β are three important model quantities and the simulation results sensitively depend on their values, we have carried out many simulations in three-dimensional space. The results are given in panels (a)–(l) of Figure 3. In the simulations, we have adopted ϕ_b = 1.5π for simplicity. The simulation results show that the model solutions to the X-ray light curve of the TDE consist only of a small domain in the four-dimensional space (β, q, e_b, and T_b) with T_b ∼ 150 days. In panels (a)–(b) of Figure 3, we show the results obtained with T_b = 140 days only for e_b = 0.1 and 0.2 and 0.03 ⩽ q ⩽ 0.2, although we have done simulations for 0.1 ⩽ e_b ⩽ 0.9 and 0.03 ⩽ q ⩽ 0.9 because no model light curve obtained with parameters outside the ranges can reproduce the X-ray light curve of the TDE. In panels (c)–(l), we show the simulation results in the three-dimensional space (β, q, and e_b) for T_b = 145, 150, 155, 160 days. Because the model solutions are insensitive to the small change of the orbital period, we have only done the simulations for 0.1 ⩽ e_b ⩽ 0.6, 1.2 ⩽ β ⩽ 1.6, and 0.03 ⩽ q ⩽ 0.09.

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However, the mass of the central black hole can be smaller. If the SMBH has a mass M_BH = 10⁶ M_☉, we have shown that the X-ray light curve of the TDE can also be reproduced with the model light curves obtained with SMBHB systems of orbits either circular e_b = 0 or elliptical e_b ≲ 0.5. The fitted orbital period of the SMBHB weakly depends on the orbital eccentricities and has a typical value of T_b ≃ 140 days (or a_b ≃ 0.26 mpc) with 132 days ≲ T_b ≲ 145 days if e_b = 0 or T_b ≃ 150 days (or a_b ≃ 0.28 mpc) with 142 days ≲ T_b ≲ 156 days if e_b = 0.2. The fitted mass ratio of the SMBHB system in SDSS J1201+30 has a typical value q ∼ 0.1 for any possible orbit with e_b ≲ 0.5, but distributes in a range depending sensitively on the values of eccentricity and penetration factor. The panels from (m)–(r) of Figure 3 show the complex dependence among q, e_b, and β in the parameter space, which are adopted from our simulation results for 0 ⩽ e_b ⩽ 0.9 and 0.03 ⩽ q ⩽ 0.9. In the simulations, we have taken T_b = 140 days for e_b = 0 and T_b = 150 days and ϕ_b = 1.7π for e_b > 0 for simplicity. Different orbital periods are adopted here for different types of orbits in order to give the largest domain of model solutions in the parameter space. Again, the results depend only weakly on the orbital periods, in the sense that the variation of the orbital period in a certain range only changes the boundaries, but not the shape of the domain of the model solutions in the parameter space.

The model solutions of the observed X-ray light curve are obtained with the assumption that the disrupted star is a solar-type main-sequence star. The disrupted star may be a different type of star, with different internal structures, masses, and/or radii. The tidal disruption of stars with different internal structures would lead to different light curves with different peak luminosities, peak time t_peak, and power-law indices other than −5/3 (Lodato et al. 2009; Guillochon & Ramirez-Ruiz 2013). Because the key features of the interruptions and recurrences in the model light curves do not change with the structure of the star, our conclusions regarding the model solutions and the parameters are robust. For a certain orbital pericenter, Equation (12) suggests the maximum specific energy ΔE changes with the radius of the star. The differences in ΔE do not change our conclusions as discussed before. However, our results do sensitively depend on the orbital pericenter r_p or β for a certain tidal radius r_t. If we have the knowledge of the star, with the condition r_p ⩽ r_t or from Equation (10) we may give some more strict constraints on r_p (or β) and thus the mass ratio q (and probably e_b), based on Figure 3. Note that in Figure 3 β = β_☉ ≡ r_{t, ☉}/r_p with r_{t, ☉} the tidal radius of a solar-type star.

We have carried out numerical simulations to scan a significant fraction of the large model parameter space, but it is still prohibitive for the present computing powers to cover the whole space of the parameters (θ, Ω, ω, β, T_b, q, e_b, and M_BH). From the first principles, the potential sphere of the restricted three-body systems consisting of the SMBHB and the stellar plasma elements is split into inner and outer regions by the SMBHB orbit. As argued for Newtonian potential analytically by Mardling (2007) and numerically by LLC09, the shell of the potential sphere centered on the SMBHB orbit is chaotic because of the nonlinear overlap of the multiple resonances due to the strong perturbations by the secondary SMBH. The fluid elements with orbits inside the chaotic shell regions are resonantly scattered off, and thus the inner and outer boundaries of the chaotic shell regions determine, respectively, the interruption and recurrence time of the TDE light curve. For a circular SMBHB orbit, the orbit of the SMBHB binary roughly determines the centers of the chaotic regions, suggesting that the Keplerian orbital period of the SMBHB is roughly between the time of the interruption and recurrence. The BH mass ratio determines the strength of the resonant perturbation, the extent of the nonlinear overlap of multiple resonances, and how effectively the fluid elements with orbits inside or crossing the chaotic shell regions are scattered off on the timescale when they move inside the chaotic shell, deciding the duration and shapes (e.g., smooth or flickering) of the interruptions and the recurrent light curves. The orbital parameters of the star could modify the characteristics of the key features of the SMBHB system only moderately. The high-quality X-ray light curve obtained by S2012 did not only catch the time of the interruption, the recurrence, and the re-interruption of the TDE, but also constrains the long durations of the phases of low and high flux. The long duration of the recurrence suggests that the resonant perturbation by the secondary BH should not be too strong and the merger should not be a major merger with q ≳ 0.3, while the long duration of the interruption implies that the perturbation cannot be too weak and the merger should not have an extreme mass ratio q ≲ 0.01 irrespective to the detailed modeling of the light curve. Therefore, the solutions with q ∼ 0.08 are certain. With a moderate small mass ratio q ∼ 0.08, the duration of the recurrent flare should not be much longer than the observed one, suggesting that the time of recurrence should not be much earlier than the first detection of the recurrent flare and the SMBHB orbital period is about the time of recurrence. Therefore, the model solutions with T_b ∼ 150 days are also robust. However, we have to note that the orbital period of the SMBHB is the Keplerian period, but the return time of the bound stellar plasma elements is determined by the radial epicyclic frequency. The Keplerian and epicyclic frequencies are equal in Newtonian gravity, but the latter is smaller than the former in GR. The differences between the two frequencies become significant for tidal disruptions by the SMBH with M_BH ≳ 10⁷ M_☉ because the tidal radius for a solar-type star is $r_{\rm t} \lesssim 5 r_{\rm g} M_7^{-2/3}$. Therefore, for the certain orbital period T_b, the time of the interruption in the model light curves is delayed so much that it is significantly later than the date of the first upper limit, which, for a SMBHB system with circular orbit, is hardly compensated by adjusting the other parameters. To significantly shift the time of interruption to an earlier date, we need an elliptical orbit for the SMBHB system. For the SMBHB system with the given orbital period, the moderate eccentricity decreases significantly the pericenter and thus the inner boundary of the chaotic shell region, resulting in the appearance of the interruption before the first upper limit on 2010 July 7 and after the last detection on 2010 June 30. Therefore, we expect that the solution for M_BH = 10⁷ M_☉ with e_b ∼ 0.3 is robust.

Upon final coalescence, SMBHB systems like the one in SDSS J1201+30 are prime sources for future space-based GW missions like eLISA. However, in its current state of evolution, it would be challenging to detect the GWs from this system. It would radiate GW emission at a frequency of f_obs = 2/T_b(1 + z) ≃ 0.13 nHz(T_b/150 days)⁻¹ in the observer frame and with a characteristic strain in an observation of duration τ_obs

$$\begin{equation} h_{\rm c} = h_{\rm r} \sqrt{f_{\rm obs} \tau _{\rm obs}}, \end{equation} \tag{ 24 }$$

where h_r is the strain amplitude at the object rest frequency, f_b = 2/T_b, and

$$\begin{equation} h_{\rm r} = {8\pi ^{2/3} \over 10^{1/2}} {G^{5/3} M^{5/3} \over c^4 r(z)} f_{\rm b}^{2/3}, \end{equation} \tag{ 25 }$$

where M = (M₁M₂)^3/5/(M₁ + M₂)^1/5 = M_BHq^3/5/(1 + q)^1/5 is the "chirp mass" of the SMBHB and r(z) is the comoving distance. The frequency f_obs ≃ 0.13 nHz is in the range observable with PTAs, but much smaller than that of eLISA. For a five-year PTA observation, the expected characteristic strain of the binary is

$$\begin{eqnarray} &&h_{\rm c} \approx 1.7\times 10^{-20} \left({T_{\rm b} \over 140 \, {\rm days}}\right)^{-7/6} \left({\tau _{\rm obs} \over 5\, {\rm yr}}\right)^{1/2} M_6^{5/3} {q_{-1} \over (1+q)^{1/3}} \nonumber \\ &&\approx 6.0 \times 10^{-19} \left({T_{\rm b} \over 150 \, {\rm days}}\right)^{-7/6} \left({\tau _{\rm obs} \over 5\, {\rm yr}}\right)^{1/2} M_7^{5/3} {(q/0.08) \over (1+q)^{1/3}}, \nonumber\\ \end{eqnarray} \tag{ 26 }$$

which is about four orders of magnitude smaller than the detection limit of PTA at the frequency f_obs (e.g., Ellis et al. 2012). If GW radiation was the only contribution to the orbital shrinkage, the lifetime of the system is

$$\begin{equation} \tau _{\rm gw} \simeq 1.0\times 10^8 \, {\rm yr}\, \left({T_{\rm b} \over 140\, {\rm days}}\right)^{8/3} M_6^{-5/3} q_{-1}^{-1} f^{-1} (1+q)^{1/3} \end{equation} \tag{ 27 }$$

(Peters & Mathews 1963), where f is a function of the eccentricity e_b

$$\begin{equation} f = \left(1 + {73 \over 24}e_{\rm b}^2 + {37 \over 96} e_{\rm b}^4\right) \left(1-e_{\rm b}^2\right)^{-7/2}. \end{equation} \tag{ 28 }$$

For a SMBHB system with M_BH = 10⁷ M_☉ and typical parameter values T_b = 150 days, q = 0.08, and e_b = 0.3, the lifetime is τ_gw ≃ 1.9 × 10⁶ yr, while for a SMBHB system with M_BH = 10⁶ M_☉ and the parameter values T_b = 140 days, q = 0.1 and e_b = 0, the lifetime is longer, with τ_gw ≃ 1.0 × 10⁸ yr. However, a longer lifetime τ_gw does not necessarily imply that the 10⁶ M_☉ fit is favored, nor that TDE light curve searches for SMBHBs are biased toward systems with larger separations and smaller SMBH masses for a given observed binary period. This is because of the biases in event detection in any (X-ray, transient) survey, which preferentially selects for the most luminous, most frequent events. In particular, X-ray surveys are biased toward SMBHs of higher mass M_BH ≈ 10⁷ M_☉ because of their higher peak luminosities. Furthermore, the TDE rate N_TDE is a function of a_b. A preliminary estimation suggests that N_TDE is a complicated function of a_b and does not change significantly for 10⁻³ pc ≲ a_b ≲ 1 pc (Chen et al. 2011; Liu & Chen 2013). Thus, for a given observed T_b in an X-ray transient survey, a SMBHB system with higher SMBH mass M_BH ∼ 10⁷ M_☉ and smaller separation within the range of 10⁻³ pc ≲ a_b ≲ 1 pc would likely be favored.

Approximately 20 to 25 TDEs and candidates have been identified from the observations (see Komossa 2012 for a recent review), including the X-rays (e.g., Komossa & Bade 1999), UV (Gezari et al. 2008), optical and emission lines (Komossa et al. 2008b; van Velzen et al. 2011), and gamma-rays (e.g., Burrows et al. 2011; Bloom et al. 2011; Cenko et al. 2012). We have inspected these light curves, with the exception of the two jetted TDEs, in order to search for similar features as seen in SDSSJ1201+30. None are clearly present. This might have several reasons. It could be due to the gaps in the light curves of the TDEs (and so escaped detection). Alternatively, the orbital timescales of the SMBHBs can be longer or shorter, so their effects would be undetectable on the timescales observed so far. Currently, this then makes SDSS J1201+30 the only good SMBHB candidate among the known TDEs.

We conclude that the SMBHB model for SDSS J1201+30 is a viable model that naturally explains the abrupt dips and recoveries of the X-ray light curve of the event. Future sky surveys are expected to detect TDEs in the thousands. Analysis of their light curves will then provide a powerful new tool for searching for SMBHBs in otherwise non-active galaxies.