Dissonance in Harmony: The UV/Optical Periodic Outbursts of ASASSN-14ko Exhibit Repeated Bumps and Rebrightenings

We use the X-Ray Telescope (XRT) on board the Neil Gehrels Swift Observatory to perform X-ray photometry of the object, with a sensitivity range of 0.3–10.0 keV (Burrows et al. 2005). To monitor its multiwavelength behavior, we have requested 10 ToO observations with high cadence starting from 2022 December 2. We also retrieve the public data (PI: Payne) from the High Energy Astrophysics Science Archive Research Center (HEASARC) website. The Swift data are processed with HEASoft 6.31.1. To obtain the products (e.g., light curves and spectra), we run the task xrtpipeline, and then xrtproducts. The source region is chosen as a circular region centered on the object with a radius of 471, and the background region is chosen as a nearby circular region with a radius of 120''.

The UV/Optical Telescope (UVOT) is another instrument in the Swift observatory, which is equipped with seven filters (V, B, U, UVW1, UVM2, UVW2, and white; Roming et al. 2005). We run uvotimsum to sum up the images and then execute the task uvotsource to generate the light curves with the source and background regions defined by circles with radii of 10'' and 40'', respectively. Following Schlafly & Finkbeiner (2011), we derive the Galactic extinction value of E(B − V) = 0.043 using an online tool, ⁶ and then we corrected the magnitude for each band using the extinction law of Cardelli et al. (1989). In this work, we adopt the Galactic extinction values of 0.14, 0.18, 0.21, 0.27, 0.42, and 0.41 mag for the V, B, U, UVW1, UVM2, and UVW2 bands, respectively.

The UV/optical light curves of ASASSN-14ko show a "fast rise and slow decay" pattern, which has been reported in previous work (Payne et al. 2021, 2022, 2023). Long-term multiwavelength light curves are shown in Figure 1. For convenience, we have divided the period of MJD 58,927–60,110 into different epochs. As we can see, the UV/optical light curves in epochs 10 and 11 do not follow a trend similar to that in previous epochs. Interestingly, early bumps can be seen in the rising part of the UV/optical light curves in epochs 10 and 11. Additionally, the rebrightening feature is also detected in both epochs 10 and 11. We carefully examined the light curves of previous epochs and read the detailed reports of Payne et al. (2021, 2022, 2023), and discovered that the bump during the rising phase and the rebrightening during the declining phase is an unprecedented occurrence. Moreover, the X-ray light curve in the interval covering epochs 10 and 11 shows signs of quasiperiodicity and we derive a probable period of 2 months using the Lomb–Scargle package (VanderPlas 2018). However, more high-cadence X-ray observations are needed to confirm the periodicity.

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2.3.1. UV/Optical Light Curves in Epoch 10

2.3.2. UV/Optical Light Curves in Epoch 11

We use the Python package lmfit (Newville et al. 2016) to fit the spectral energy distributions (SEDs) of the simultaneous UV/optical bands with a blackbody model, and obtain the evolution of the blackbody temperature (T_bb) and radius (R_bb). SED fittings are shown in Figure 2. During epochs 10 and 11, the blackbody temperature evolves with luminosity (L_bb), but remains high (>10⁴ K) even when the source is quiescent (around $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=43$, within an amplitude of 0.2). The results are shown in Figure 3.

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In the first peak during epoch 10 (MJD 59,962), we derive a peak luminosity of $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=44.24\pm 0.22$, with $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})=4.37\pm 0.05$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.95\pm 0.06$. For the early bump, we derive a maximum luminosity of $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=43.78\pm 0.27$ in MJD 59,943, with $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})=4.32\pm 0.05$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.81\pm 0.08$. During the rebrightening phase, we derive a maximum luminosity of $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=44.04\pm 0.25$ in MJD 59,975, with $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})=4.34\pm 0.05$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.92\pm 0.08$.

During epoch 11, we obtain a peak luminosity of $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=44.33\pm 0.23$ in MJD 60,070, and the temperature and radius are $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})=4.39\pm 0.05$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.97\pm 0.06$, respectively. On the short plateau, we derive $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})=43.81\pm 0.27$, $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})=4.31\pm 0.05$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.85\pm 0.09$ in MJD 60,060. In the rebrightening phase of epoch 11, we derive a maximum luminosity of $\mathrm{log}({L}_{\mathrm{bb}}/\mathrm{erg}\,{{\rm{s}}}^{-1})\,=44.17\pm 0.20$ in MJD 60,081, with $\mathrm{log}({T}_{\mathrm{bb}}/{\rm{K}})\,=4.33\pm 0.04$ and $\mathrm{log}({R}_{\mathrm{bb}}/\mathrm{cm})=14.99\pm 0.06$.

During epochs 10 and 11, Swift observes a relatively low brightness with a mean count rate of 0.01, compared to the previous epochs, which have an average count rate of 0.03. The average hardness ratio (HR) ⁷ in epochs 10–11 is −0.08, while for previous epochs, the value is −0.24.

To analyze the X-ray spectra in epochs 10 and 11, we stack the spectra in the three epochs separately and group them with a minimum of 10 photons. The effective exposure times are 363, 82.5, and 90.58 ks for the spectrum of previous epochs, epoch 10, and epoch 11, respectively. Through xspec v12.13.0c, three spectra including previous epochs, epochs 10 and 11 are fitted by an absorb power-law model (tbabs∗zashift∗powerlw). The XRT spectra exhibit the Fe Kα line; however, Payne et al. (2023) find that the feature originates from the nearby source. Therefore, we only used the 0.3–2.0 keV range in our spectral fitting to exclude the contribution of the nearby source. Fixing a Galactic hydrogen density of 3.49 × 10²⁰ cm⁻² (HI4PI Collaboration et al. 2016), we derive the photon index of 2.17 ± 0.07 (χ²/dof = 1.42), ${2.27}_{-0.21}^{+0.20}$ (χ²/dof = 0.92), and ${2.33}_{-0.16}^{+0.15}$ (χ²/dof = 1.20) for the results of 0.3–2.0 keV in previous epochs, epoch 10 and epoch 11, respectively. The spectra in epochs 10 and 11 are slightly softer than those in the previous epochs, but no significant difference in profile is found in these X-ray spectra. Due to the inability of Swift/XRT to distinguish the source adjacent to ASASSN-14ko in the image, we limit ourselves to a qualitative comparison here. The fitted results are shown in Figure 4.

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It should be noted that the variability of the X-rays is not consistent with the UV/optical bands. The X-ray and UV/optical fluxes show anticorrelated behavior in epochs 10 and 11, as they did in previous epochs. When the UV/optical fluxes increase, the X-ray fluxes decrease, and vice versa. This phenomenon has been observed by Payne et al. (2021, 2022, 2023). Therefore, we suggest that the X-ray flare near the UV/optical bumps and rebrightenings is not a new feature, but a continuation of the previous epoch. To measure the X-ray to UV/optical flux ratio, we use the parameter ${\alpha }_{\mathrm{ox}}=0.3838\,\mathrm{log}\left[\tfrac{{\rm{F}}(2\ \mathrm{keV})}{{\rm{F}}(2500\,\mathring{\rm A} )}\right]$, where F(2 keV) and F(2500 Å) are the flux at 2 keV and 2500 Å, respectively (Tananbaum et al. 1979; Strotjohann et al. 2016). The values of α_ox range from −1.3 to −2. In Figure 5, α_ox in epochs 10 and 11 lie mainly on different sides from previous epochs. For previous epochs, α_ox mostly ranges from −1.8 to −1.4, while for epochs 10 and 11, it is lower. Especially for epoch 11, we find a dominant distribution of α_ox values between −2.0 and −1.6. For $\mathrm{log}({L}_{2500\,\mathring{\rm A} }/\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{Hz}}^{-1})\gt 28.3$, α_ox in epochs 10 and 11 tends to be lower, where L_{2500 Å} is the luminosity in 2500 Å. The result suggests a distinct correlation between the X-ray and UV/optical bands in epochs 10 and 11.

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Since the light curves in the previous epochs showed a smooth "fast rise and slow decay" pattern, we assume that they resulted from the same mechanism and that the folded light curves in the previous epochs can serve as a baseline for the analysis. Therefore, we can derive the extra energy in epochs 10 and 11 by subtracting the energy in the previous epochs.

The total energy released in epoch 10 is 4.74 × 10⁵⁰ erg, and in epoch 11, the value of 4.66 × 10⁵⁰ erg is reached, while the average energy release in the previous epochs is 2.64 × 10⁵⁰ erg. Compared to previous epochs, the extra energy released in the early bumps of epochs 10 and 11 is 1.15 × 10⁵⁰ erg and 9.15 × 10⁴⁹ erg, respectively. For the rebrightening phases, the extra energy released in epochs 10 and 11 is 7.63 × 10⁴⁹ erg and 7.57 × 10⁴⁹ erg, respectively. The energy released in epoch 10 slightly exceeds that in epoch 11, but both are significantly higher than the average values of previous epochs.

The partial TDE model is thus far the primary model adopted to explain the periodic outbursts of ASASSN-14ko (Payne et al. 2021; Liu et al. 2023). According to this model, a star in an eccentric orbit around the black hole undergoes tidal stripping each time at the pericenter R_p. The stripped material then undergoes circularization and subsequent accretion, resulting in the observed flare.

Tidal stripping requires R_p to be on the same order as the tidal radius, i.e., ${R}_{{\rm{p}}}=\chi {R}_{* }{({M}_{h}/{M}_{* })}^{1/3}$, where χ ≥ 1 is a numerical coefficient; this is the distance to the SMBH at which a tiny amount of mass could be removed from the star. At this point, the star just fills its Roche lobe (though instantaneously due to the eccentric nature of the orbit). Thus, χ ≃ 2 according to early work (Paczyński 1971; Eggleton 1983; Sepinsky et al. 2007). Recent numerical simulation and analytical studies of TDE suggest similar values: χ = 1.7 ∼ 2 (Guillochon & Ramirez-Ruiz 2013; Coughlin & Nixon 2022). Note that a complete disruption would actually correspond to χ ≤ 1). Here, we adopt χ_s = 2. Thus, ${R}_{{\rm{p}}}=2.2\,{M}_{8}^{-2/3}{r}_{* }{m}_{* }^{-1/3}{R}_{{\rm{S}}}$, where M₈ is the mass of the SMBH in unit of 10⁸ M_☉, r_* is the stellar radius in unit of solar radius, m_* is the stellar mass in unit of solar mass and R_S is the Schwarzschild radius of the SMBH. Note that Payne et al. (2021) derived the SMBH mass of 10^7.85 M_⊙ for ASSASN-14ko. The semimajor axis of the stellar orbit is related to the orbital period as in $a=110\,{(P/114\,{\rm{d}})}^{2/3}{M}_{8}^{-2/3}\,{R}_{{\rm{S}}}$.

The unexpected profile change of the light curves during the most recent outbursts poses a challenge to the partial TDE explanation. Why were the bump in the rising phase and the rebrightening in the declining phase absent in the past? We propose the hypothesis that an accumulation effect is responsible for the two repeated bumps and rebrightenings. In this hypothesis, not all debris fragments from the partial TDE are immediately accreted, but instead some remain and gradually accumulate over time. As these materials accumulate from multiple partial TDEs, the accretion disk grows larger. Consequently, a collision occurs between the stripped stream and the disk, resulting in the early bumps and rebrightenings both before and after the flare peak. The schematic representation of the model can be seen in Figure 6. We will quantitatively examine and evaluate this model in the subsequent analysis.

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At the collision radius R_p, for a disk thickness H ≫ R_*, the length of the penetration of the stream through the disk would be l ∼ R_p. The stream–disk velocity difference is ${v}_{\mathrm{rel}}\sim \sqrt{2{{GM}}_{h}/{R}_{{\rm{p}}}}$. The disk material to be shocked is in a volume of $\pi {R}_{* }^{2}{R}_{{\rm{p}}}$, whose mass is ${\rm{\Delta }}{M}_{{\rm{s}}}=\pi {R}_{* }^{2}{R}_{{\rm{p}}}\rho$ where ρ is the vertically averaged density of the disk, which is related to the disk accretion rate as ${\dot{M}}_{\mathrm{acc}}=3\pi \nu \rho H$. Adopting the Shakura–Sunyaev viscosity model ν = 2α P/(3Ω_K ρ) and utilizing H = (P/ρ)^1/2/Ω_K, it can be rewritten as

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{acc}}=2\pi {R}^{2}\rho H\alpha {{\rm{\Omega }}}_{{\rm{K}}}{\left(\displaystyle \frac{H}{R}\right)}^{2},\end{eqnarray} \tag{ 1 }$$

where Ω_K(R) is the disk Keplerian angular speed. With the density from Equation (1), we get the mass of the shocked material ΔM_s. An optimistic estimate of the energy dissipated would be ${\rm{\Delta }}{E}_{{\rm{s}}}\approx {\rm{\Delta }}{M}_{{\rm{s}}}{v}_{\mathrm{rel}}^{2}/2$. Then we get

$$\begin{eqnarray}\begin{array}{rcl}{\rm{\Delta }}{E}_{{\rm{s}}} & = & 8\times {10}^{49}\,{r}_{* }^{1/2}\left(\displaystyle \frac{{\dot{m}}_{\mathrm{acc}}}{0.1}\right){\left(\displaystyle \frac{\alpha }{0.1}\right)}^{-1}\\ & & \times \,{\left(\displaystyle \frac{H/R}{0.01}\right)}^{-3}{M}_{8}{m}_{* }^{1/2}\,{\rm{erg}},\end{array}\end{eqnarray} \tag{ 2 }$$

where the accretion rate has been normalized by the Eddington rate as in ${\dot{m}}_{\mathrm{acc}}\equiv 10\,{\dot{M}}_{\mathrm{acc}}{c}^{2}/{L}_{\mathrm{Edd}}$. To match the observed energies for the early bumps (see Section 3.3), we chose a low (but not extreme) value for the disk height-to-radius ratio.

We note that the separation between the bump and the rebrightening in epoch 11 (Δt₁₁) is shorter than that in epoch 10 (Δt₁₀). The orbital precession of the stripped stream may cause the inequality between Δt₁₀ and Δt₁₁. The stream impacts the accretion disk twice in each period but at different positions due to the precession. This leads to unequal intervals between the two impacts in each period. This explains why we observe Δt₁₀ ≠ Δt₁₁. A similar situation occurs in OJ287, except that in that source it is the secondary black hole that collides with the accretion disk (Valtonen et al. 2008, 2016; Dey et al. 2018; Laine et al. 2020).

For partial TDE, the outer radius of the disk is R_out ≃ 2R_p, and in the case of ASASSN-14ko, R_out = 5.5R_S. Such a short distance to the SMBH makes it difficult to accumulate the stream debris for a long time, and the expansion of the disk is improbable. However, for an evolved star whose envelope is extended R_* ∼ 10R_☉, as advocated by Liu et al. (2023) for ASASSN-14ko, the disk size is much larger R_out = 55 R_S. At this distance, the accretion disk has the possibility of expanding. Furthermore, a larger R_* also helps increase the energy release for the collision.

We explore alternative explanations that could account for the distinct periodic transient ASASSN-14ko, as well as the newly observed features. An abnormal behavior for the TDE scenario is the significant temperature evolution during the outburst (see Figure 3), in contrast to the relatively stable temperature observed in normal optical TDEs. This temperature fluctuation bears resemblance to the disk instability scenario. Particularly, we noticed that the disk instability model has been proposed to explain QPEs in previous studies (Pan et al. 2023; Śniegowska et al. 2023) and the X-ray flares observed in ASASSN-14ko are rather similar to QPEs. Another popular model involved in explaining QPE is the star–disk collision model (Xian et al. 2021; Linial & Metzger 2023), which is yet disfavored by a lower energy released by 1 order of magnitude than that observed in individual flares of ASASSN-14ko (∼10⁵⁰ erg). One potential explanation is that the star periodically intersects with the disk, triggering disk instability and giving rise to the prominent flares observed. In this case, the star has just been disrupted; the stripped material, along with the star itself, falls back onto the disk in two streams. These streams then collide with the accretion disk, resulting in the observed bumps before and after the main flare peaks.