Mid-infrared Flare of TDE Candidate PS16dtm: Dust Echo and Implications for the Spectral Evolution

Previous detections of MIR flares in TDEs are all attributed to dust echoes in the view of the basic fact that the MIR flares lag behind the optical flares (Dou et al. 2016, 2017; Jiang et al. 2016; van Velzen et al. 2016). Nevertheless, the WISE detection time of the PS16dtm MIR flare is surprisingly earlier than the optical detection. At the face value, it is hard to explain the MIR flare of PS16dtm as a dust echo as usual. However, the particularities of the event must be taken into consideration to see whether the contradiction is explicable or not.

First, the host of PS16dtm before the outburst is a low-luminosity Seyfert 1 galaxy with ${L}_{{\rm{X}}}=1.2\times {10}^{42}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Pons & Watson 2014) and $\nu {L}_{\nu }$(5100 Å)/${L}_{{\rm{X}}}=0.5$ (Blanchard et al. 2017). The bolometric luminosity (${L}_{\mathrm{bol}}$) can be roughly estimated as ${L}_{\mathrm{bol}}=9\times \nu {L}_{\nu }$(5100 Å) = $5.4\times {10}^{42}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ (Kaspi et al. 2000), which is $\sim 0.04{L}_{\mathrm{edd}}$ assuming a BH mass $\sim {10}^{6}\,{M}_{\odot }$ (Xiao et al. 2011). At this quiescent state, the inner radius of the dusty torus can be estimated from the sublimation radius (e.g., Namekata & Umemura 2016). For a typical AGN spectrum, the dust sublimation radius is given by

$$\begin{eqnarray}{R}_{\mathrm{sub}} & = & 0.121\,{pc}{\left(\displaystyle \frac{{L}_{\mathrm{bol}}}{{10}^{45}\mathrm{erg}{{\rm{s}}}^{-1}}\right)}^{0.5}\\ & & \times {\left(\displaystyle \frac{{T}_{\mathrm{sub}}}{1800{\rm{K}}}\right)}^{-2.804}{\left(\displaystyle \frac{a}{0.1\mu {\rm{m}}}\right)}^{-0.510},\end{eqnarray} \tag{ 1 }$$

where ${L}_{\mathrm{bol}}$ is the bolometric luminosity of the AGN, ${T}_{\mathrm{sub}}$ is the sublimation temperature of the dust grain, and a is the grain radius. On the other hand, the torus inner radius can be estimated from the K-band reverberation mapping result (e.g., Suganuma et al. 2006; Kishimoto et al. 2007). For example, Kishimoto et al. (2007) has given a time-lag radii ${R}_{\tau K}$ as function of V-band luminosity by fitting data points from Suganuma et al. (2006),

$$\begin{eqnarray}&&{R}_{\tau K}=0.47{\left(\displaystyle \frac{6\nu {L}_{\nu }(V)}{{10}^{46}\mathrm{erg}/{\rm{s}}}\right)}^{1/2}.\end{eqnarray} \tag{ 2 }$$

Both methods yield a physical scale of $\sim 9\times {10}^{-3}\,\mathrm{pc}$, or 10 light days, for the BH in J0158. The small distance of the dusty torus to the continuum source may explain the early detection of the MIR flare because the time delay is too short to measure. By naïvely assuming that the increased MIR flux is coming from the dust thermal emission heated by the TDE, we present the derived blackbody temperature in Figure 4. The blue W1-W2 color (0.27 mag) at E1 corresponds to a blackbody temperature of $\sim 2.5\times {10}^{3}$ K, supporting the assumption that the dust responsible for the early MIR flare is located at around sublimation radius. Second, at the early rising phase, the MIR luminosity is $\gtrsim 10 \%$ of the bolometric one (see the right panel of Figure 3), indicating that the covering factor of the dust is fairly high. In this scenario, the surrounding dust may absorb a significant fraction of UV-optical photons and then re-emit them in the IR, attenuating the optical flare but boosting the MIR flare. Third, it is difficult to detect TDEs in active galaxies in the early rising and is prevented by the dilution of the background emission, including the intrinsic BH accretion and instability. In contrast, the MIR emission is dominated by hot dust heated by black hole accretion and is much less diluted by the host galaxy. Moreover, the photometry based on a ground-based optical survey is severely limited by sky conditions, such as the moon phase's impact on PS16dtm before its detection by ASAS-SN.

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Above three points, the puzzling fact that the flare was detected in MIR earlier than optical is unusual, but not unreasonable. The optical flare should have been rising for some time before it became bright enough for ASAS-SN to detect. If that is the case, then the rising timescale of this event is probably longer than other TDE. It is interesting to compare the optical light curves of PS16dtm with two other well-known TDEs that have been monitored since an early rising stage (PTF09ge and PS1-10jh), as shown in Arcavi et al. (2014). Obviously, the rising slope of PS16dtm is much smoother, agreeing with our expectation. Further studies of the physical nature behind different rising behaviors are valuable for exploration when we have more well-sampled TDE light curves in the future.

This problem can be also reconciled in alternative ways under the TDE scenario. According to the calculation of Guillochon & Ramirez-Ruiz (2015), there is a delay between the flare and the disruption of the star of the order of years for a BH mass of ${10}^{7}\,{M}_{\odot }$. With such a delay, the unbound debris can reach a distance of a light month when we see an optical flare. If the unbound debris collides with molecular clouds in the dust torus, then it will produce strong shocks and emit UV-/X-rays, which can heat the surrounding dust. If a substantial fraction of the kinetic energy of the debris is converted to the radiation energy, then it may explain the early emission of the observed MIR flare. The other interpretation has to do with the uncertain origin of optical emission in TDE disks. Naïve models of TDE disks predict that most emission should be in the soft X-ray/EUV, and the optical emission should be orders of magnitude dimmer than what we have observed for optically discovered TDEs (Miller 2015). The most common solution to this puzzle is that TDEs create some kind of "reprocessing layer" at ∼100–1000 times the Schwarzschild radii to absorb and downgrade the hard photons from the central engine. This layer could either be a quasi-static bound envelope of poorly circularized debris (Metzger & Stone 2016) or some sort of outflowing wind (Guillochon et al. 2014). It is possible that this reprocessing layer takes some time to set up, and thus the optical emission lags behind the MIR emission heated by the bare, unreprocessed X-ray/EUV emission from the inner accretion disk. These scenarios are interesting and possible, yet the current data for PS16dtm are insufficient to test and can only be checked by other X-ray discovered TDEs.

As the bolometric luminosity of PS16dtm increases, dust in the inner region evaporates gradually, pushing the inner side of dusty torus outward. The peak luminosity of the flare ($\sim 2.2\times {10}^{44}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$) determines a new torus inner radius of about ∼7 times larger than its quiescent size, or 70 light days (${R}_{\mathrm{sub}}\propto {L}_{\mathrm{bol}}^{1/2}$). During this process, the time-lag effect on the light curve becomes important because the UV continuum rising timescale (of the order of 30 days) is shorter than the light-crossing timescale. Basing on this evolution picture, more evidence for the dust echo appears at the second and third WISE detection epochs (E2 and E3), which is a rest-frame ∼150 and 330 days after the optical detection.

The bolometric luminosity at E2 remains at nearly the same as the peak, while the MIR color becomes much redder (W1-W2 = 0.65) than E1 (see Figure 3), indicating a blackbody dust temperature of $1.3\times {10}^{3}$ K. This fact implies that the average dust temperature (${T}_{\mathrm{dust}}$) may have dropped to well below the sublimation temperature (see Figure 4); the dominated IR emission comes from further away, and the dust around the inner region must be optically thin. It is also notable that the IR luminosity is only a small fraction ($\lt 0.1$) of the bolometric luminosity at E2, implying a smaller covering factor at E2 than E1, as a result of dust sublimation. Since the optical light curve is almost flat and is declining very slowly at E3, the dust emission from the inner region should not change much. However, the dust emission located further out is an add-on, and thus it will lead to a continuously rising light curve and yet a declining dust temperature in the case of extended, optically thin dust. The prediction is exactly consistent with the WISE observation at E3, which has a higher MIR luminosity and yet redder color (W1-W2 = 0.97), namely lower dust temperature (∼900 K).

To obtain a stricter ${T}_{\mathrm{dust}}$ value and a more quantitative calculation, we have collected the UV-optical-IR photometric data observed quasi-simultaneous with E2 (see Figure 5). First, we tried to fit the spectral energy distribution (SED) with the double-blackbody model, yielding a ${T}_{\mathrm{dust}}$ of $1.2\times {10}^{3}$ K. During the fit, we have fixed the blackbody temperature responsible for the UV-optical emission to $1.4\times {10}^{4}$ K, as given in Blanchard et al. (2017). Assuming that the equilibrium temperature ${T}_{\mathrm{dust}}$ is determined by the balance between the radiative heating by the absorption of UV-optical photons and the thermal re-emission in the IR,

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{\mathrm{bol}}}{4\pi {R}^{2}}\pi {a}^{2}=4\pi {a}^{2}\sigma {T}^{4}.\end{eqnarray} \tag{ 3 }$$

The calculated ${L}_{\mathrm{bol}}$ is $5.2\times {10}^{44}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$, which comparable, and yet slightly higher, than the observed peak ${L}_{\mathrm{bol}}$. Here, we have used the dust distance calculated from a light travel time of 120 days, which is the time interval since the peak. Similar to the case of ASASSN-14li (Jiang et al. 2016), the blackbody assumption for the dust emission could be over-simplistic and the dust absorption efficiency (${Q}_{\mathrm{abs}}\propto {\nu }^{\beta }$) should be taken into account. The β value is quite uncertain; it approaches zero for a very large grain (gray case); while for small grains, β strongly depends on the composition (i.e., $\simeq 2$ for graphite, $\simeq 1$ for silicate, and $\simeq -0.5$ for SiC). If we adopt $\beta =2$ (see formula 8.16 in Kruegel 2003),

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{\mathrm{bol}}}{16{\pi }^{2}{R}^{2}}\simeq 1.47\times {10}^{-6}{{aT}}^{6},\end{eqnarray} \tag{ 4 }$$

we get ${T}_{\mathrm{dust}}=700\,K$ and an integrated IR luminosity of $9.0\times {10}^{42}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$, calling for ${L}_{\mathrm{bol}}$ of $3.1\times {10}^{42}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ and $4.1\times {10}^{43}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}$ for dust with an MRN size distribution (Mathis et al. 1977) and an average size of 0.1 μm, respectively. This can be taken as a lower limit for the dust temperature and the required ${L}_{\mathrm{bol}}$.

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Despite the large uncertainties caused by the dust absorption efficiency and grain size, we can conclude that the derived ${L}_{\mathrm{bol}}$ is basically comparable to the observed peak luminosity of PS16dtm, providing a substantial evidence of the dust echo associated with the TDE.

In the introduction, we have mentioned that various intriguing spectral characteristics have been found in PS16dtm after its discovery. Most remarkably, the optical spectra of PS16dtm show complex emission structures with narrow and broad components in the range ∼4500–5400 Å arising primarily from the Fe ii multiplets. Moreover, the Fe ii lines overall become stronger, as revealed by monitored spectrum spanning +25 to +189 rest-frame days since the beginning of the rise (MJD 57600). The rapid emergence of prominent optical Fe ii lines makes PS16dtm resemble a classical NLS1. The physical mechanism that drives the formation of Fe ii lines in NLS1s is still a mystery, although it is well known that Fe ii strength is generally correlated with the Eddington ratio (e.g., Boroson & Green 1992; Dong et al. 2011). PS16dtm may offer us a marvellous opportunity to explore the mechanism taking advantage of the dynamic transition process from a normal type-1 AGN to an NLS1 witnessed by us.

To explain its IR light curve, a simple model for PS16dtm is proposed as follows. After the TDE occurred, the rising bolometric luminosity inevitably evaporated the proximate dust gradually until the peak of the flare. The new inner radius of the torus recedes to ∼70 light days, and the original dust between 10 to 70 light days is replaced with a gas torus. This part of the gas is exposed to the radiation field, so it will be ionized and will emit emission lines. Its velocity is lower than the intermediate-width line gas since it is further out ($v\propto {r}^{-1/2}$), which is consistent with the fact that the observed intermediate-width component of Hα line has become narrower, while its equivalent width increased (Blanchard et al. 2017). On the other hand, the metal released from dust will be ionized and will give pronounced metal lines, particularly Fe ii emission lines. However, previous studies show that Fe ii emission cannot be fully explained in the framework of photoionization models (Collin & Joly 2000; Sigut & Pradhan 2003; Baldwin et al. 2004); additional mechanisms such as collisional excitation might also act (e.g., Joly 1981; Véron-Cetty et al. 2006). The unbound debris ejected from the disrupted star may produce intense shocks by interacting with the gas torus and excite the iron, hence collisional excitation is likely also essential here.

A rough estimate of area of Fe ii emitting region can be made by comparing the constant temperature collisional excitation model of Joly (1987), which gave an estimate of Fe ii flux per unit surface area of the detailed heating mechanism. Using the highest Fe ii $\lambda 4570$ intensity ($3.7\times {10}^{6}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$) in their calculation (${T}_{{\rm{e}}}=8000$ K, ${n}_{{\rm{H}}}={10}^{23}\,{\mathrm{cm}}^{-1}$) and an observed intensity of $\sim {10}^{-14}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ (see Figure 8 of Blanchard et al. 2017), we can reach the conclusion that the Fe ii emission area is equivalent to a spherical surface of radius of ∼5 × 10¹⁶ cm or 1 light month. This is a lower limit, and is yet comparable with the size of photon traveling from the initial outburst, implying that the physical conditions to account for the strong Fe ii in PS16dtm is indeed critical.

While the optical spectra of PS16dtm matches strikingly with NLS1s, its near-UV (NUV) spectra taken by HST/STIS appears to be very similar to BAL quasars, exhibiting a broad absorption trough at around 2700 Å, with a velocity width of $\sim {10}^{4}\,\mathrm{km}\ {{\rm{s}}}^{-1}$ (Blanchard et al. 2017). This feature can be attributed to the blueshifted absorption of Mg ii $\lambda \lambda 2800$ doublet and suggests an outflow with velocity of $\gtrsim {10}^{4}\,\mathrm{km}\ {{\rm{s}}}^{-1}$. Can the outflow be driven by the radiation pressure amplified dramatically by the TDE?

First of all, the radiation pressure that the gas experienced becomes higher and higher along with the rising of the bolometric luminosity. At the Eddington luminosity, the radiative acceleration is significantly larger than the gravitational acceleration by a factor of f (100–1000), depending on the gas column density (Castor et al. 1975; Abbott 1982; Risaliti & Elvis 2010). For gas at around the original torus inner radius that is 10 light days away from the black hole, its escape velocity (${v}_{{\rm{e}}}=\sqrt{\tfrac{2{{GM}}_{\mathrm{BH}}}{R}}$) is $\sim {10}^{3}\,\mathrm{km}\,{{\rm{s}}}^{-1}$, and the dynamical timescale is 100–300 days (${t}_{{\rm{d}}}=\tfrac{R}{{f}^{1/2}{v}_{e}}$). Within ${t}_{{\rm{d}}}$, the gas can be accelerated to a velocity of ${f}^{1/2}$ times of the escape velocity, which is $\gtrsim {10}^{4}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. This may be sufficient to explain the observed BAL outflow.

Before PS16dtm, only three TDEs have been spectroscopically observed in UV, among which PTF15af and iPTF16fnl are X-ray weak and their UV spectra show BALs, while ASASSN-14li is X-ray bright and its UV spectrum does not present BALs (Yang et al. 2017). PS16dtm shows the same coincidence. This behavior is exactly in analogy with quasars with and without BALs. Although still controversial, it is commonly assumed that soft X-rays from accretion disk are filtered by a thick shielding gas, which prevent over-ionization of the outer layer gas and ensure effective radiative acceleration via UV resonance absorption lines (Murray et al. 1995). This may be particularly true for TDE, whose X-ray spectra are generally very soft, thus a rather moderately thick gas will produce a strong absorption. More UV spectra and X-ray follow-ups of TDEs are necessary to verify the coincidence or not in the future.