The Peculiar X-Ray Transient Swift J0840.7−3516: An Unusual Low-mass X-Ray Binary or a Tidal Disruption Event?

Figure 6 presents representative soft X-ray spectra obtained with the Swift/XRT, MAXI/GSC, and NICER/XTI at different epochs. The spectrum was hardest at the initial, brightest phase (T ≲ 10⁴ s), then rapidly softened, and finally became almost flat in the EF_E form, where E and F_E are the photon energy and the energy flux per unit energy, respectively. A hint of an absorption feature is seen at 3–4 keV in the Swift and NICER spectra taken between T = 2 × 10⁴ and 5 × 10⁴ s (blue and magenta spectra in the left panel of Figure 6), which we look into in Section 3.3.2.

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To quantify the overall spectral behavior, we applied an absorbed power-law model to each spectrum. Throughout the spectral analysis, we used the 0.5–10 keV, 2–20 keV, and 1.0–10 keV ranges of the Swift, MAXI and NICER data, respectively. The C-statistic (Cash 1979) was employed because many of the spectra have relatively low statistics. The TBabs model was adopted for the absorption component, with the solar abundance table given by Wilms et al. (2000). The equivalent hydrogen column density N_H was allowed to vary in Swift and NICER data, while it was fixed in the MAXI data at 3 × 10²¹ cm⁻², which is the Galactic column in the direction of Swift J0840.7−3516 estimated with the tool nh in HEAsoft. This is because MAXI is not sensitive to the soft X-rays below 2 keV and it is difficult to constrain N_H. We note that the free parameters obtained from the MAXI spectra remained consistent within their 90% confidence ranges when N_H = 0 and 1.0 × 10²² cm⁻² were adopted. When N_H is allowed to vary, it is not constrained at all and only the lower limits of Γ and unabsorbed fluxes were obtained.

The model successfully reproduced all the spectra. Figure 7 plots the individual fit parameters in chronological order. The spectrum until T ∼ 10⁴ s had a small photon index of Γ = 1.0–1.2. The value increased in the following rapid decline, and became Γ ∼ 2.0 after the decay. During the decay, the column density was comparable with the total Galactic column, except for the plateau phase at T ∼ (3 × 10⁴)–10⁵ s, where N_H increased up to ∼1 × 10²² cm⁻². At this phase, Γ was estimated to be slightly larger, Γ ∼ 2–3. These behaviors may suggest variations of the intrinsic absorption, although it could be affected by the degeneracy with Γ. At late times of and after the decay, the N_H values are consistent with or slightly smaller than the Galactic column, but have large uncertainties due to the low statistics.

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In Figure 6, a possible absorption feature was found at 3–4 keV in the Swift and NICER spectra obtained between T = 2 × 10⁴ and 5 × 10⁴ s. To describe the profile, we tested (1) a Gaussian line model (gauss, with a negative normalization) and (2) a simplified edge model (edge). The same absorbed power-law model as in Section 3.3.1 was used as the continuum model, where all the parameters were allowed to vary. We also adopted the same energy ranges of the spectra as those in that section.

The best-fit values of the gauss and edge components are listed in Table 1, and the Swift/XRT and NICER data and their best-fit models with edge are shown in Figure 8. The quality of fit for the Swift/XRT spectrum was significantly improved from the case of the continuum model, whereas the improvement was not significant in the NICER data. Using the script simftest on XSPEC, we estimated the chance probability of improvement by the additional edge component as 0.001 and 0.2 (corresponding ∼4σ and ∼1σ) for the Swift and NICER data, respectively. The two spectra gave consistent edge/line energies. The Fe K line and/or edge around 6–7 keV are most prominently seen in many X-ray sources including accreting black holes and neutron stars. Assuming the observed feature originated in the neutral Fe K-shell edge, the redshift estimated from the edge model is z ∼ 1.1 (see Section 4.2 for discussion).

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Table 1. Best-fit Parameters of Absorption Components

Parameter	Unit	Swift	NICER
(1) TBabs∗edge∗powerlaw
Eedge	keV	3.3 ± 0.1	${3.4}_{-0.2}^{+0.6}$
τ		1.43 ± 0.7	${0.52}_{-0.51}^{+0.78}$
C-stat/d.o.f		204/263	316/326
(2) TBabs∗(gauss+powerlaw)
Ecen	keV	${3.7}_{-0.1}^{+0.2}$	${3.9}_{-0.2}^{+0.1}$
σ	keV	${0.2}_{-0.1}^{+0.2}$	<0.36
Ngau a		${5}_{-3}^{+2}\times {10}^{-4}$	${1.4}_{-1.1}^{+1.7}\times {10}^{-5}$
EW	keV	${0.5}_{-0.2}^{+0.3}$	${0.24}_{-0.18}^{+0.29}$
C-stat/d.o.f		206/262	314/325
TBabs∗powerlaw (continuum)
C-stat/d.o.f		276/265	319/328

Note.

^a Absolute value of the normalization of gauss, defined as the total photon flux in the absorption line, in units of photons cm⁻² s⁻¹.

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If the feature is the neutral Fe K absorption edge of cold gas, Fe K emission or absorption lines would also be produced, depending on its geometry and temperature. We tested adding a negative/positive Gaussian component at z = 1.1 with a line center energy of 6.4 keV to the absorbed power-law continuum model, to consider the neutral Fe Kα absorption/emission line. The 90% upper limits of the line strengths for the Swift data were estimated to be 4.0 × 10⁻⁴ and 3.3 × 10⁻⁴ photons cm⁻² s⁻¹ (∼1.2 × 10² eV and ∼97 eV in the equivalent width), for the positive and negative Gaussian cases, respectively.

We also applied, to the Swift spectrum, the neutral Compton reflection model pexmon (Nandra et al. 2007), which accounts for both the Fe K emission lines and edge self-consistently, to test the possibility of a reflection component like those seen in X-ray binaries and AGNs. We replaced the power-law component in the original continuum model by pexmon and allowed the reflection scale factor (rel_refl) to vary; the latter is the solid angle Ω of the reflector visible from the illuminating source, in units of 2π. The abundance of Fe and other elements was assumed to be the same as the solar abundance, and the redshift and the cutoff energy were fixed at 1.1 and 0 keV (i.e., the high-energy cutoff was not included). We tested two cases of inclination angles: i = 0° and 60°. In both cases, the model gave somewhat better fits than the absorbed power-law model, yielding C-stat/d.o.f. = 217/263. We obtained only a weak upper limit of the reflection factor, Ω/2π < 2.0 and 2.6, for i = 0° and 60°, respectively.

Hard X-ray spectra with good statistics were obtained from the Swift/BAT observation at an early phase (T ∼ 10² s) and the NuSTAR observation in the last part of decay (T ∼ 2 × 10⁵ s). Combining them with the Swift/XRT and NICER data taken (quasi-)simultaneously, we obtained wideband spectra at T ∼ 2 × 10² s (hereafter SP1) and at T ∼ 2 × 10⁵ s (SP2), as shown in Figures 9(a) and (f), respectively. The SP1 spectrum was produced from the Swift/XRT and BAT data of OBSID = 00954304000, and the SP2 spectrum was from the Swift/XRT, NICER, and NuSTAR data of OBSID = 00954304004, 2201010105, and 90601304002, respectively. The former spectrum has a clear high-energy cutoff at ∼30 keV, while the latter shows a flat profile extending to at least ∼20 keV. Here, we adopted χ² statistics for the Swift/BAT spectrum, because it was already grouped by channels to have a Gaussian distribution and hence C-statistics should not be used. ²⁰ For consistency, the χ² statistics are applied to the Swift/XRT, NICER, and NuSTAR spectra as well. To ensure that the distribution underlying the data can be approximated by the Gaussian distribution, the Swift/XRT data of SP1 were binned so that at least 40 counts are included in each spectral bin. The Swift/XRT, NICER, and NuSTAR spectra in SP2 were binned to have at least 20, 20, and 40 counts per bin, respectively.

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We first fit the two spectra with an absorbed cutoff power-law model: TBabs∗cutoffpl in the XSPEC terminology. The ratios of data to model are shown in Figures 9(b) and (g) and the best-fit parameters are listed in Table 2. Although the model fit both spectra fairly well, small residual structures remained. In Figure 9(b) the discrepancy between the data and model can be seen at the lowest energies, and in Figure 9(g), a small hump at 0.8–2 keV and an excess above ∼10 keV are present.

Table 2. Best-fit Parameters for the Wideband Spectra

ID	NH	Γ	Ecut	Na	kTin, kTbb	Rin, Rbb b	${N}_{{\rm{H}}}^{\mathrm{pcf}}$	Cv c	FX	χ2/dof
	(1021 cm−2)		(keV)		(keV)	(km)	(1021 cm−2)		(erg s−1 cm−2)
TBabs∗cutoffpl
SP1	2.4 ± 0.1	0.8 ± 0.1	${24}_{-5}^{+7}$	0.13 ± 0.02	⋯	⋯	⋯	⋯	9 × 10−9	119/99
SP2	2.5 ± 0.3	1.98 ± 0.09	>196	(7 ± 1) × 10−4	⋯	⋯	⋯	⋯	5 × 10−12	204/172
TBabs∗pcfabs∗cutoffpl
SP1	<1.8	${1.2}_{-0.1}^{+0.3}$	${36}_{-9}^{+30}$	${0.24}_{-0.04}^{+0.12}$	⋯	⋯	${17}_{-5}^{+13}$	${0.7}_{-0.15}^{+0.04}$	8 × 10−9	96/97
SP2	2.6 ± 0.2	2.0 ± 0.1	>193	(7 ± 1) × 10−4	⋯	⋯	<0.25	⋯ e	5 × 10−12	203/170
TBabs∗(bbodyrad+cutoffpl)
SP1	6.8 ± 0.2	1.0 ± 0.2	${30}_{-8}^{+14}$	${0.19}_{-0.03}^{+0.04}$	${0.07}_{-0.01}^{+0.02}$	${6}_{-4}^{+12}\times {10}^{3}$	⋯	⋯	8 × 10−9	97/97
SP2	2.1 ± 0.5	${1.7}_{-0.2}^{+0.1}$	>49	(4 ± 1) × 10−4	0.33 ± 0.05	${2.0}_{-0.5}^{+0.8}$	⋯	⋯	6 × 10−12	150/170
TBabs∗(diskbb+cutoffpl)
SP1	6.7 ± 0.2	1.0 ± 0.2	${31}_{-8}^{14}$	${0.19}_{-0.03}^{+0.04}$	0.08 ± 0.02	${8}_{-6}^{+19}\times {10}^{3}$	⋯	⋯	8 × 10−9	97/97
SP2	${2.6}_{-0.4}^{+0.5}$	${1.7}_{-0.3}^{+0.1}$	>33	(3 ± 1) × 10−4	0.5 ± 0.1	${1.4}_{-0.4}^{+0.7}$	⋯	⋯	6 × 10−12	150/170

Notes.

^a Normalization of cutoffpl, defined as the photon flux in units of photons keV⁻¹ cm⁻² s⁻¹ at 1 keV. ^b D = 8 kpc and i = 60° (for diskbb) were assumed. ^c Covering fraction of pcfabs. ^d Unabsorbed 1–100 keV flux. ^e Not constrained.

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Next we investigated whether an additional, optically thick thermal component or partial covering absorption can better reproduce the soft X-ray profiles. We adopted pcfabs as the partial covering absorption model at z = 0. For the thermal component, we tested a blackbody component (bbodyrad) and a disk blackbody component (diskbb; Mitsuda et al. 1984). In SP1, these models significantly improved the quality of fit (Figures 9(c), (d), and (e)), and in any of the models the χ² values decreased by ∼20 with the degrees of freedom reduced by 2 (Table 2) from the simple absorbed cutoff power-law model. The fit quality of SP2 was not improved by adding the pcfabs model (Figure 9(h)), but an additional thermal component (Figures 9(i) and (j)) reduced the χ² value by ∼50. We obtained a low temperature and a large radius of (disk) blackbody in SP1, and a slightly higher temperature and a much smaller radius in SP2.

Let us first investigate the possibility of a Galactic transient. Given that the source is located near the Galactic plane, it would be reasonable to take this possibility into account. Because the absorption column density is comparable to the total Galactic column for a large fraction of the outburst period, the source would not be very near. Assuming isotropic emission, the maximum and minimum luminosities at 0.5–10 keV are estimated as 2 × 10³⁷(D/8 kpc)² erg s⁻¹ and 7 × 10³²(D/8 kpc)² erg s⁻¹, respectively. The large luminosity range and the short timescale of the decay, and the relatively faint optical counterpart (with an apparent $r^{\prime}$ band magnitude of ∼20 mag; Mazaeva & IKI-FuN follow-up Collaboration 2020), rule out the possibility of a high-mass X-ray binary (e.g., Walter et al. 2015). Also the timescale of the X-ray decay is much shorter than magnetar outbursts (∼100 days; Coti Zelati et al. 2018), although a couple of them showed two-step decays reminiscent of that seen in our target. The observed hard, nonthermal spectrum without any prominent emission lines also makes unlikely the possibilities of a stellar flare (Güdel & Nazé 2009) and a cataclysmic variable (Mukai 2017).

We have confirmed the 8.96 s peak reported by Kennea et al. (2020) in the periodogram made with the first Swift/XRT observation. Given the fact that it did not appear in any other observations, the variation was either a transient phenomenon of the source or an artifact (such as red noise). If the former is the case, it is difficult, due to the limited exposure, to determine whether it is a pulsation or a quasi-periodic oscillation (QPO). Hence, the possibilities of an X-ray binary pulsar and a magnetar are neither proved nor ruled out.

Typical black hole (BH) and neutron star (NS) low-mass X-ray binaries (LMXBs) also make it difficult to explain some of the observed properties of Swift J0840.7−3516. The luminosity range of the decay is consistent with LMXBs, and the upper limit of the radio flux, 18 μJy at 7.5 Hz, obtained five days after the discovery (Borghese et al. 2020), also agrees with the radio/X-ray flux correlations of both BH and NS LMXBs (e.g., Corbel et al. 2013). However, the observed decay period of ∼5 days is much shorter than those of typical LMXBs: a few tens of days to more than a year. This means that Swift J0840.7−3516 accreted a much smaller mass than normal LMXBs in an unusually short period. Moreover, the spectrum in the rise of the outburst had a somewhat small photon index, Γ ∼ 1.0, compared with typical LMXBs in the hard state, Γ ∼ 1.5–1.9 (e.g., Done et al. 2007).

Yet these unusual properties cannot completely rule out an LMXB nature. There are actually some LMXBs that show similar properties. An LMXB candidate showing such a short outburst with a similar luminosity range has recently been found (MAXI J1957+032; Beri et al. 2019). There are also several known LMXBs with short outbursts but smaller peak luminosities of 10³⁴–10³⁶ erg s⁻¹, which are called "very faint X-ray transient" (Wijnands et al. 2006; Degenaar & Wijnands 2010; Bahramian et al. 2021). In addition, very hard spectra in a bright hard state have been observed in a couple of NS LMXBs (Parikh et al. 2017) and BH LMXBs including V 404 Cyg (e.g., Kimura et al. 2016), V4641 Sgr (e.g., Maitra & Bailyn 2006), and Swift J1858.6−0814 (Hare et al. 2020). All these sources have a strong short-term flux variation by a more than order of magnitude (e.g., Kitamoto et al. 1989; Revnivtsev et al. 2002; Wijnands et al. 2017), also in agreement with the present case. In addition, partial covering absorption is sometimes required in these sources, especially in high-flux phases (Kimura et al. 2016), consistent with Swift J0840.7−3516 in a bright phase.

We note that the photon index of Swift J0840.7−3516 after the decay, ≲2, is reminiscent of a BH rather than an NS LMXB, which usually shows a larger value, Γ ∼ 3 (Wijnands et al. 2015), although the NS LMXB EXO 1745−248 showed a similar hard spectrum in quiescence (Rivera Sandoval et al. 2018). On the other hand, an NS LMXB would rather be favored, in that a very small radius of the thermal component, 1–2(D/8 kpc) km, consistent with emission from an NS surface, was obtained from the NuSTAR+Swift/XRT+NICER spectrum in a faint phase. This holds even if the observed power-law component was entirely produced by Comptonized disk photons. Assuming conservation of the number of photons and an isotropic scattered emission (Kubota & Makishima 2004), and using the intrinsic disk photons estimated from the best-fit diskbb+cutoffpl model, we obtain the inner disk radius as ∼3(D/8 kpc) km (where i = 60° is assumed). Similar thermal emission likely emitted by the NS surface can be seen in NS LMXBs at low X-ray luminosities below ∼10³⁵ erg s⁻¹ but not in a more luminous hard state, where the power-law component dominates the X-ray flux (e.g., Sakurai et al. 2014; Shidatsu et al. 2017). The thermal component in Swift J0840.7−3516 was observed at a consistent luminosity; the second rapid decay from 10⁵ s since the discovery, in which this component was found, started at ∼10³⁵(D/8 kpc)² erg s⁻¹.

Even if an LMXB scenario works for all the properties raised above, the observed absorption feature is difficult to explain. Although ionized Si and S lines from disk winds are sometimes seen at similar energies (e.g., Ueda et al. 2009), they are much weaker than the present case and always with strong iron Kα lines at ∼7 keV. Assuming the observed feature to be the redshifted Fe K edge, we obtained z = 1.1. If this is the gravitational redshift caused by a Schwarzschild stellar-mass BH, the feature should be produced at ∼1.3 R_S, where R_S is the Schwarzschild radius. It is unclear that an absorber with such a small size can exist in the vicinity of a BH. Another possibility is that the observed feature is a different blueshifted line produced by an outflow at a relativistic speed, like baryonic jets observed in SS 433. However, it is unclear whether such baryonic jets can exist at a low Eddington ratio and produce a single absorption feature.

Instead, the origin of the source might be explained by a tidal disruption of an asteroid by a neutron star (Newman & Cox 1980; Colgate & Petschek 1981), which was considered for the origin of GRBs 30–40 years ago. In this model, the collision of an asteroid and an NS surface produces strong MeV gamma rays and hot plasma. The plasma could be rapidly cooled by radiation and cause Compton downscattering, resulting in a power-law-shaped X-ray spectrum. The radiation energy of Swift J0840.7−3516 released in 10⁷ s is estimated as 2 × 10³⁹(D/8 kpc)² erg, which is converted to a total accreted mass of ∼10²⁰(η/0.01)(D/8 kpc)² g (where η is the radiative efficiency), consistent with an asteroid. It is unclear, however, whether or not this scenario can explain the observed evolution of the photon index of the X-ray spectrum and the absorption feature.

We next investigate the possibility of an extragalactic origin. If the source is an extragalactic X-ray binary located in a nearby galaxy, the maximum luminosity is far beyond the Eddington luminosity of a BH with a mass of 10 M_⊙. Even if the distance is as small as ∼1 Mpc, the peak luminosity is calculated as ≳ 10⁴¹ erg s⁻¹. Such a bright X-ray binary is categorized as a hyperluminous X-ray source and considered to have an intermediate-mass BH (Farrell et al. 2009). In this case, it is even more difficult than in the case of a normal X-ray binary with a stellar-mass BH to explain the short duration of the outburst, because of the large size of the accretion disk. For the same reason, an AGN origin is unlikely.

Some of the observed properties of Swift J0840.7−3516 agree with those of GRBs. Absorption features have been detected in a few GRBs (Amati et al. 2000; Frontera et al. 2004; Bellm et al. 2014) and interpreted as the redshifted iron K line or edge, although they were detected mainly in the prompt phase, unlike the present case (but see Bellm et al. 2014). The absorption feature in our case was observed just after the first rapid decay, which may be considered to be the beginning of the afterglow, and could be explained by the interaction between the jets and the surrounding gas. If the estimated redshift z = 1.1 is the cosmological redshift, it is converted to a luminosity distance of 7 Gpc, assuming H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_M = 0.3, and Ω_Λ = 0.7. In this case, the maximum and minimum luminosities are calculated to be 1 × 10⁴⁹ erg s⁻¹ and 4 × 10⁴⁴ erg s⁻¹, respectively, where isotropic emission is assumed. The redshift and maximum luminosity are well within the distribution of known GRBs. The source showed a hard spectrum with Γ ∼ 1 and a spectral rollover at ∼30 keV in the early phase, which are compatible with soft GRBs in the prompt phase (e.g., Yonetoku et al. 2010). Using the best-fit cutoff power-law model of the Swift/XRT+BAT spectrum (see Section 3.3.3), we obtain the 2–10 keV luminosity of 5 × 10⁴⁸ erg s⁻¹ in the rest frame of the source. This is consistent with the correlation between the peak energy and X-ray luminosity of Swift-detected GRBs reported by D'Avanzo et al. (2012).

The decay profile for the first 10⁶ s and the spectral evolution of Swift J0840.7−3516 also share similar properties with GRBs. The two-step decay could be attributed to the prompt and afterglow emission. However, the observed plateau phase started later and lasted an order of magnitude longer than the typical shallow decay phase of GRBs (Zhang et al. 2006). Moreover, the constant flux over nine months after the decay is very different from, and difficult to explain by, X-ray afterglows of GRBs.

Instead, the source may be interpreted as a TDE by a supermassive BH. The overall decay profile is approximated to t^−1.7, which is consistent with what is theoretically expected for a TDE (t^−5/3; Rees 1988; Phinney 1989) and the actual X-ray light curves of observed TDEs (e.g., Burrows et al. 2011; Cenko et al. 2012). The strong short-term variability is reminiscent of the jetted TDE Swift J164449.3+573451 (Burrows et al. 2011; Mangano et al. 2016, hereafter Swift J1644). X-ray absorption features have also been detected in a TDE at lower energies than that in the present case (Miller et al. 2015), and were interpreted as an outflow at a velocity of a few hundred km s⁻¹. The total radiation energy at 1–20 keV is calculated from the fluence to be 9 × 10⁵² erg in the rest frame of Swift J0840.7−3516, assuming isotropic emission and a luminosity distance of 7 Gpc. This corresponds to a total accreted mass of ∼0.9 M_⊙, assuming the radiative efficiency of the standard accretion disk of a Schwarzschild BH. The peak luminosity, ∼10⁴⁹ erg s⁻¹, is more than one order of magnitude larger than that of the most luminous TDE, Swift J1644.

Swift J1644 exhibited a steep flux drop ∼500 days after the discovery and an almost constant flux for the following ∼1000 days, which can be explained by the end of accretion and scattering of X-rays by the surrounding gas, respectively (Cheng et al. 2016). Similar flux behaviors were observed in Swift J0840.7−3516, with a rapid decay until T ∼ 5 × 10⁵ s and a subsequent constant-flux phase. If the end of the decay at ∼5 × 10⁵ s actually reflects the end of accretion, the BH mass (M_BH) of Swift J0840.7−3516 can be estimated by comparing the decay times, or the accretion periods, of the two sources, as described below. We note that the scattering echo scenario for the constant-flux phase requires spectral softening, because of the energy dependence of the scattering angle. However, no significant softening was observed and therefore a different explanation would be needed in the present case.

When a star is tidally disrupted by a BH, some of the disrupted matter orbits around it and falls onto the BH (Rees 1988). The kinetic energy of the disrupted matter in a unit mass is described as

$$\begin{eqnarray}&&\epsilon \sim \displaystyle \frac{{{GM}}_{\mathrm{BH}}}{a},\end{eqnarray} \tag{ 2 }$$

where a and G are the semimajor axis and the gravitational constant, respectively. Using Kepler's third law, $T\sim \sqrt{{a}^{3}/{{GM}}_{\mathrm{BH}}}$, we obtain

$$\begin{eqnarray}&&T\propto {M}_{{\rm{BH}}}{\epsilon }^{-3/2}.\end{eqnarray} \tag{ 3 }$$

Thus, the accretion time is proportional to M_BH.

Using this relation, the BH mass of Swift J0840.7−3516 should be ∼10² times smaller than that of Swift J1644, which was previously estimated as 10⁶–10⁷ M_⊙ (Burrows et al. 2011). In this case, we obtain a BH mass of Swift J0840.7−3516 of 10⁴–10⁵ M_⊙, and therefore we may have witnessed a rare case of a TDE in a dwarf galaxy. The smaller BH mass and higher peak luminosity than those of Swift J1644 imply that Swift J0840.7−3516 is a more highly beamed, jetted TDE. This is of course just a rough estimate, and different approaches such as observations of the host galaxy would be required for a more accurate measurement.

A QPO at 5 mHz was detected in Swift J1644 and associated with the Keplerian frequency at the innermost stable circular orbit of the BH (Reis et al. 2012). If the observed 8.96 s variation in Swift J0840.7−3516 is explained by a QPO produced in the same manner, its BH mass is calculated to be 10⁴–10⁵ M_⊙, depending on the BH spin. This is consistent with the mass estimated above from the decay period.