EXTREME CORONAL LINE EMITTERS: TIDAL DISRUPTION OF STARS BY MASSIVE BLACK HOLES IN GALACTIC NUCLEI?

We examine the possible continuum variability of the ECLEs by comparing their fiber magnitudes obtained in the SDSS imaging survey and the spectral magnitudes obtained in the spectroscopic survey. The two surveys were four months to two years apart. The fiber magnitudes are measured within an aperture of the size of the SDSS fibers from the SDSS images assuming a typical seeing of 20. The spectral magnitudes are synthesized from the SDSS spectra, which are spectrophotometrically calibrated using standard stars in the three SDSS bands g, r, and i. This calibration can lead to a difference between fiber and spectral magnitude for extended sources even if there is no variability. This is because of different seeing during the spectroscopic observations and object-to-object differences in radial profiles, and so there are both systematic offsets and random scatter, which vary from plate to plate. We estimate the mean offset and random scatter from the distributions of their offsets in the g, r, and i bands using galaxies in the plates of the ECLEs (Figure 3), which can be well fitted with one Gaussian (outliers are likely those containing AGNs). Based on the results, the probability and amount of potential variations are estimated for the ECLEs, as listed in Table 1.

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Four out of seven objects show significant (⩾3σ) variations with amplitudes ranging from 0.1 to 0.3 mag in the g band and smaller at longer wavelengths between the SDSS spectroscopic and photometric observations. Assuming that the light at the lower state is solely from stars, we derive the minimum brightness of a variable non-stellar component at the higher state, which ranges from −16.0 to −18.0 mag in absolute magnitude in the g band (Table 1). We note that two ECLEs without [Fe vii] (SDSS J0748+4712 and SDSS J1350+2916 in Table 1) brightened between the two observations while two with [Fe vii] (SDSS J0952+2143 and SDSS J1055+5637) show the opposite trend. In the former case, the interval between the two observations can set an upper limit on the ages of the ECLEs during the spectroscopic observation; in the latter case, a lower limit can be obtained. Consequently, the continuum flares occurred within 120 and 701 days prior to the spectroscopic observation for SDSS J0748+4712 and SDSS J1350+2916, respectively, and happened more than 140 and 375 days prior to the spectroscopic observation for SDSS J1055+5637 and SDSS J0952+2143, respectively.

We have also checked archival UV data for potential variations. SDSS J0748+4712 was detected by the Galaxy Evolution Explorer in both the near- and far-UV bands on 2004 March 10, 20 days after the SDSS spectroscopic observation, and was re-observed in near-UV later on 2010 January 9. The NUV flux dropped by nearly a factor of two at the later epoch. This sets a lower limit to the non-stellar UV luminosity as 2.6 × 10⁴² erg cm⁻² s⁻¹ on 2004 March 10, assuming that the flux at the later epoch is mostly from stellar light.

It is evident that our ECLEs can be divided into two subclasses, with and without the detected [Fe vii] lines (Figure 1 and Table 2). As shown in Figure 4, the lower limits on [Fe vii] give [Fe x]λ6376/[Fe vii]λ6088  >  3 for objects without [Fe vii] lines, while those with detected [Fe vii] have [Fe x]λ6376/[Fe vii]λ6088  <  3. In Figure 4, we plot the [Fe x]λ6376 versus [Fe vii]λ6088 luminosities for our ECLEs; for comparison, those from a sample of Seyfert galaxies from Gelbord et al. (2009) are also overplotted. The ECLEs with [Fe vii] show [Fe x]λ6376/[Fe vii]λ6088 ratios higher than normal Seyfert galaxies, and similar to narrow-line Seyfert 1 galaxies, which are believed to have black holes of relatively small masses accreting at near the Eddington rate. The objects without detected [Fe vii] show much higher ratios.

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In Figure 5, we show the [Fe x]λ6376 versus [O iii]λ5007 luminosities. The [Fe x]λ6376/[O iii]λ5007 ratios of the ECLEs are 1–2 orders of magnitude higher than those of Seyfert galaxies that is expected from our selection criteria. The ECLEs are outliers, offset from the smooth distribution of the Seyfert galaxies. There is no significant difference in the ratios between ECLEs with and without [Fe vii], although the latter show systematically lower [O iii]λ5007 luminosity.

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To determine whether they are actually Seyfert galaxies, we plot in Figure 6 their locations in the BPT diagrams involving a set of narrow line ratios (Baldwin et al. 1981; Veilleux & Osterbrock 1987; Kewley et al. 2006) which are diagnostics of the ionizing continuum. For comparison, overlaid are the contours of the distributions of narrow emission line galaxies in the SDSS DR4 (Xiao et al. 2012). It can be seen that six of the seven objects lie within the H ii locus on the [S ii]/Hα versus [O iii]λ5007/Hβ diagram, and the remaining one (SDSS J0952+2143) borders LINER and H ii regions. On the [N ii]/Hα versus [O iii]/Hβ diagram, three (SDSS J0748+4712, SDSS J1241+4426, and SDSS J1341+0530) locate within the H ii (star-forming galaxies) locus, while the other four objects locate in the near H ii end of the composite region. However, among those four, the line ratios of three objects are indistinguishable from being H ii galaxies due to their relative large uncertainties. For comparison, other galaxies with reliable detections of coronal lines in SDSS DR4 spectroscopic data locate usually far away from the demarcating line (blue points in Figure 6; T. G. Wang et al., in preparation). These results suggest that the bulk of our ECLEs differs largely from Seyfert galaxies, and the conventional narrow-line regions in their galactic nuclei did not see the hard ionizing continuum radiation that produces the strong CLs. The classifications appear to be diverse when the [O i]λ6300/Hα versus [O iii]λ5007/Hβ diagram is considered, where three objects (SDSS J1055+5637, SDSS J1241+4426, and SDSS J0952+2143) are located in the AGN locus and one (SDSS J0938+1353) at the demarcation of H ii and Seyfert galaxies. We note that the [O i]λ6300 line is, compared to other narrow lines (e.g., [O iii], [N ii], [S ii] and Hα), generally broader and more difficult to accurately measure due to its weakness. In fact, given the high critical density of [O i], it is possible that a significant part of the [O i] emission is non-permanent, i.e., is contributed by the continuum flare which also produces the (variable) iron lines, and may come from a region cospatial with the coronal line region. The He ii λ4686 line is also prominent in the spectra of most of the ECLEs, suggesting that it is produced in the CL region.

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We also compare the profiles of the CLs with those of the other narrow lines (Figure 7). The CLs usually display similar profiles, except that a narrow core is occasionally absent in high-ionization species, such as [Fe x]λ6376, [Fe xi]λ7894, and [Fe xiv]λ5304. In most cases, the CLs and [O i] are broader than low-ionization lines (Figure 8). He ii λ4686 has a similar profile to the CLs (Figure 2). For quantitative comparisons we calculate the FWHM from the best-fitted model. Note that some of the lines have apparently two components, and the FWHM may only crudely reflect the kinematics of the line-emitting gas. The FWHM of [Fe x]λ6376 has a range from 200 to 1000 km s⁻¹, and a median of 480 km s⁻¹. In comparison, [O iii]λ5007 has a median FWHM of 230 km s⁻¹ and a range from 90 to 340 km s⁻¹, and [N ii]λ6583 has similar values of a median 240 km s⁻¹ and a range from 110 to 340 km s⁻¹. There appears to be no correlation of the line widths between the CLs and the low-ionization lines such as [O iii]λ5007 and [N ii]λ6583; however, the sample is too small for a meaningful test.

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Broad emission lines are significantly detected in five out of the seven objects. For the three objects with relatively high signal-to-noise ratio (S/N), the broad Hα and Hβ lines have very similar profiles with complicated structures, such as wiggles and extra peaks (left panels of Figure 7). It should be noted that extra peaks are very rare among Seyfert galaxies, whereas they are present in two of the three objects in our study. One object is SDSS J0952+2143, which has already been presented in Komossa et al. (2008, 2009). Another one, SDSS J1350+2916, shows a red peak and a blue peak at slightly larger velocities than SDSS J0952+2143. Due to their weakness, the broad He ii λ4686 lines are detected only in SDSS J0938+1353, SDSS J0952+2143, and SDSS J1350+2916. The broad Hα lines have a median FWHM around 1400 km s⁻¹ and a range from 880 to 2600 km s⁻¹. They are much broader than the CLs, suggesting a different emission region. Very broad bumps are also detected in SDSS J0748+4712, which were argued by Wang et al. (2011) as being attributed also to the He ii λ4686 and Balmer lines. The unusually strong He ii λ4686 is probably due to the high helium abundance in the debris of an evolved star that is tidally disrupted. In the follow-up observations carried out thus far, these broad lines either disappeared completely or became considerably weaker. The strong fading and profile wiggle suggest that they are not of AGN origin.

Figure 9 shows the SDSS images of the ECLEs. Most of these appear to be disk galaxies with the Petrosian radii in the range of 3–5 arcsec, except for SDSS J1241+2240, which shows a relatively large low surface brightness disk. The Petrosian magnitudes are brighter than the point-spread function magnitudes by more than 2 mag in all these galaxies. Therefore, we estimate the absolute magnitude of the host galaxies using the Petrosian magnitudes. The absolute magnitudes in the i band are in the range of −21.3 < M_i < −18.8, suggesting that they are sub-L_* disk galaxies in the local universe (e.g., Blanton et al. 2003; Shao et al. 2007).

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The stellar velocity dispersions, measured by fitting the starlight templates to the continuum (Section 2), are mostly below 70 km s⁻¹, consistent with marginally resolved or unresolved absorption lines. While all are small, we did not perform precise measurements, since they are close to (or even below) the spectral resolution of SDSS (69 km s⁻¹) and the templates used are derived from a stellar population library of low spectral resolution. The small stellar velocity dispersions are also consistent with the narrowness of the [N ii] lines: σ_line < 40 km s⁻¹ in four objects and only one exceeding 100 km s⁻¹ albeit the large scatter in the σ_*–σ_[N ii] relation (Greene & Ho 2005).

Spectroscopic follow-ups have been carried out for three objects of our sample, and the high-ionization CLs were found to be fading ubiquitously. In the case of SDSS J0952+2143, the lines of [Fe x]λ6376, [Fe xi]λ7894, and [Fe xiv]λ5304 had decreased dramatically several years after the initial SDSS spectroscopic observation. In contrast, the low-ionization lines [Fe VII] remained nearly constant and [O iii]λ5007 even brightened in the very last observation (Komossa et al. 2009; H. Y. Zhou et al. 2012, in preparation). The broad lines decreased with time as well. A similar trend was also observed in SDSS J1241+4426 in an MMT spectrum taken four years after the SDSS observation (H. Y. Zhou et al. 2012, in preparation). In SDSS J0748+4712, all the CLs disappeared while [O iii]λ5007 increased by a factor of 10 in spectra taken 4–5 years later (Wang et al. 2011). To summarize, in all the cases with follow-up observations thus far, the high-ionization CLs and the broad lines were fading on timescales of several years. The ionization of the line spectrum decreases with time.

In this section, we show that the [Fe vii] cannot be collisionally ionized, and argue that it is photoionized. For objects with detected [Fe vii], the ratios of the [Fe vii] lines can be used to constrain the electron temperature and density. The [Fe vii]5160/[Fe vii]6088 ratios range from 0.1 to 0.3, while the [Fe vii]3759/[Fe vii]6088 ratios range within 0.5 and 1.0, suggesting a range of the temperature and density values. We calculate the theoretical line ratios for a grid of temperatures and densities using the atomic database CHIANTI (Dere et al. 2009), which are used to constrain the temperature and density of the CL region in each object. The χ² at each grid is computed for the observed line ratios and their uncertainties. In Figure 10, we show the confidence contours at the 68% (Δχ² = 2.7) and 90% (Δχ² = 4.6) levels in the density and temperature plane.

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In three of the four objects, the gas temperature is constrained to be within a few 10⁴ K to 10⁵ K, while it is poorly constrained in the remaining object. These temperatures are less than what is required for collisional ionization (T > 10⁶ K), thus photoionization is favored. An upper limit on the gas density is set to be 10⁷ cm⁻³ for three objects, while a lower limit of 10⁷ cm⁻³ is set for the other. Note that these ratios are not sensitive to densities below 10⁵ cm⁻³ or above 10⁸ cm⁻³. Obviously, spectra with higher S/N are required for better constraints on the density and temperature.

Lower limits on the line emissivity, defined as n_en_ionV, are estimated for different ions using the collisional strengths from CHIANTI, assuming that collisional de-excitation is not important. Because [Fe x]λ6376 and [Fe xi]λ7894 have the critical densities one order of magnitude higher than [Fe vii], objects with detected [Fe vii] are less likely affected by collisional de-excitation. For objects without [Fe vii] detections, there is no good temperature and density diagnostics in the optical band. In this case, we assume a gas temperature of 10⁵ K. Adopting a higher gas temperature will result in a higher emissivity. Assuming these ions are dominant species and the solar abundance, we can estimate a lower limit on the total emissivity ∫n_en_HdV. These numbers are in the range of (5–50) × 10⁶⁰ cm⁻³ (Table 2). Combing the line emissivity with the density, one can estimate the mass of the line-emitting gas. The typical value is from a few tenths to several solar masses, assuming a gas density of 10⁴ cm⁻³.

The ions responsible for the CLs are created by ionizing photons in the soft X-ray band, ranging from energies >125 eV for [Fe vii], >361 eV for [Fe xiv], and to >650 eV for [Ar xiv]. Therefore, the soft X-ray luminosity incident on the coronal line region (CLR) can be estimated with a detailed photoionization model. Instead, in this paper, we will use the observed relation between the soft X-ray emission and the CLs in Seyfert galaxies to infer the soft X-ray luminosity, and leave detailed photoionization modeling to future work.

It was found that the fluxes of [Fe x]λ6376 and [Fe xi]λ7894 are well correlated with the soft X-ray flux in Seyfert galaxies¹⁰ (Gelbord et al. 2009). The CLs to X-ray flux ratios are log(f_[Fe x]/f_X) = −3.43 ± 0.55 and log(f_[Fe xi]/f_X) = −3.52 ± 0.38 for both broad and narrow-line Seyfert 1 galaxies. These lines are thought to form in the inner edge of a dusty torus (Murayama & Taniguchi 1998a, 1998b; Rodríguez-Ardila et al. 2002), which has a covering factor about 0.6–0.7 based on the fraction of type 2 Seyfert galaxies. As shown in Figure 3, the observed [Fe x]λ6376 luminosities of the ECLEs are in the range of 39.2 (dex)–40.5 (dex) in erg s⁻¹, similar to those of the CLs detected in AGNs. With the above flux ratios, we estimate the soft X-ray luminosities to be in the range of 42.5 (dex)–43.9 (dex) erg s⁻¹. Soft X-rays with a luminosity of 10⁴¹ erg s⁻¹ (0.1–10 keV) were detected in SDSS J0952+2143 in 2009 (Komossa et al. 2009). Since the emission line fluxes were almost as high as the quasi-simultaneously measured X-ray flux, the authors suggested that the lines must be the echo of a past X-ray flare with a much higher luminosity. We note in passing that objects in Gelbord et al. (2009) are classical Seyfert galaxies, which are persistent sources, and so they are not affected by the fading effects seen in these ECLEs.

To estimate how much energy in soft X-rays is required, we integrate the CL energy over time. Assuming a lifetime for [Fe x]λ6376 and [Fe xi]λ7894 of one year, the integrated [Fe x]λ6376 or [Fe xi]λ7894 line energies is in the range of 46.7–48.0 (dex) erg. With the above L([Fe x]λ6376)/L_X and L([Fe xi]λ7894)/L_X, the total energy in soft X-rays is estimated to be around 50 (dex)–51.4 (dex) erg.

We estimate the event rate from the number of ECLEs, the lifetime of CLs and the number of galaxies observed. From the follow-up observations of the three objects, we find that extreme coronal lines are visible for 3–5 years. This gives a lifetime of the order of three years. We found seven ECLEs from 676,881 galaxies and quasars at redshifts less than 0.20 in the SDSS DR7 spectroscopic sample. This gives an event rate of 2 × 10⁻⁶ galaxy⁻¹ yr⁻¹.

The event rate is dependent on galaxy luminosity. As mentioned above, the host galaxy luminosities of the ECLEs are clustered in a relatively narrow luminosity range (−21.5 < M_i < −18.5; see Figure 11). This dependence may be related to the physical conditions which are required to produce the CLs observed, such as the central black hole mass or the gas environment. Furthermore, in practice there is a lower limit on the spectral S/N ratio for the detection of CLs. Considering this effect, we set a lower S/N cutoff to the spectra as the lowest spectral S/N ratio (S/N = 14.8 in the i band) among the detected ECLEs. As a result, we obtain an event rate of about 1.5 × 10⁻⁵ galaxy⁻¹ yr⁻¹ for all the galaxies with the absolute magnitudes in the range of −21.5 < M_i < −18.5. Despite a large number of more luminous galaxies that meet the S/N ratio constraints, we did not detect any ECLEs among them.

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We do not detect [Fe vii] in three of the seven objects. As clearly seen in both Figure 4 and Table 2, the non-detection is not due to the low S/N of the spectra, but due to the weakness or absence of the [Fe vii] lines. The [Fe vii] lines have significantly lower critical densities (10⁶–10⁷ cm⁻³) and lower ionization potentials than [Fe x]λ6376, [Fe xi]λ7894, and [Fe xiv]λ5304. The lack of [Fe vii] in the three objects may be due to one or both of the following two factors: [Fe vii] is collisionally de-excited in high-density gas, while [Fe x]λ6376 and [Fe xi]λ7894 are not because of their higher critical densities; the gas is overionized under intense soft X-ray radiation. In Section 3.1, we showed that in one object with [Fe vii] detection the CLR density is close to the critical density of [Fe vii]. Therefore, it is possible that some objects may have the densities even higher so that [Fe vii] is collisionally de-excited. On the other hand, it is also plausible that objects without [Fe vii] have higher ionization parameters. All the three objects without [Fe vii] show the [S xii]λ7612 lines, while only two of the four objects with [Fe vii] do. However, we cannot verify this as there is no good density indicator in the optical band for objects without [Fe vii] lines. Below, we investigate several possibilities in order to understand the origin of this difference.

We examine other line ratios, [Fe xi]λ7894/[Fe xiv]λ5304, [O iii]λ5007/[Fe xi]λ7894, and He ii λ4686_n/Hβ_n and find no significant difference between objects with and without the [Fe vii] lines. The intensity of [Fe xiv]λ5304 is comparable to those of [Fe x]λ6376 and [Fe xi]λ7894 in both subclasses. However, the [O iii]λ5007 luminosities for objects without [Fe vii] are one order of magnitude lower than those with [Fe vii]. The host galaxies of ECLEs with the [Fe vii] lines appear to be more luminous than those without. All the host galaxies of the ECLEs with [Fe vii] are brighter than −19.6 mag in the i band, whereas those without are fainter than this value. Among the four objects showing continuum variations between the SDSS photometric and spectroscopic observations, the two with [Fe vii] have higher non-stellar luminosities (M_{g, var} < −17.5) than the two without [Fe vii] (M_{g, var} > −17.0), as seen in Table 1. However, these results should be tested with a larger sample in the future.

The strong CLs clearly require a strong soft X-ray ionizing source. In galactic nuclei, a number of processes may produce strong soft X-ray emission: an SN explosion, episodic accretion onto a supermassive black hole following a TDE or disk instability, or encountering a molecular cloud (Komossa et al. 2008, 2009; Wang et al. 2011). Given the large mass and size of a stable molecular cloud, events of a random encounter of a molecular cloud likely last for a much longer timescale. The fact that most of the objects avoid the AGN region in the BPT diagram suggests that the normal narrow-line region did not see the hard ionizing continuum from the accretion disk. This implies that the last nuclear activity was either at least several 10³ years ago (the light crossing time of traditional Narrow Line Region; NLR) or at a very low level. The decay timescales are much shorter than those of limit-cycle outbursts driven by local thermal instability (Lin & Shields 1986) in accretion disks. Thus, episodic feeding by a molecular cloud, a persistent AGN and disk instability are very unlikely.

CLs are observed in a few SNe of type IIn, mostly at a late evolutionary stage. They are produced in pre-shocked regions ionized by radiative shocks from an expanding shell running into clumpy circumstellar medium (Smith et al. 2009). However, the CL luminosities in these SNe are factors of tens to hundreds lower than observed in the ECLEs studied here. Furthermore, the spectra of these SNe also display rich, strong low-ionization lines such as Fe ii at late stages, or strong He i emission lines in the early spectrum of SN 2005ip (Smith et al. 2009); these features are very different from the ECLE spectra. In addition, the current models of SNe do not predict sufficient energy in soft X-rays either. Nakar & Sari (2010) calculated the X-ray light-curves of core-collapsed SN breakouts for various initial masses. Integrating these light-curves yields a total soft X-ray energy about one to several orders of magnitude lower than those estimated in the last section. The X-rays produced in late shocks are also one order of magnitude lower than the those required to power the coronal line luminosity, even in strongly interacting objects (Fabian & Terlevich 1996; Chevalier & Fransson 1994). Finally, as discussed in Section 3.1, the UV magnitudes of SDSS J0748+4712 measured 20 days after the detection of the CLs was brighter than −17 mag, which is too bright for any current SN model predictions (e.g., Nakar & Sari 2010). For these reasons, we consider SNe to be unlikely either.

Most of the observed properties can be reconciled in the context of tidal disruption of stars by massive black holes at galactic centers (Komossa et al. 2009). Fallback of the bounded tidal debris forms an optically thick accretion torus around the black hole. The luminosity is peaked at or near super-Eddington on the accretion timescale, and then decreases as t^−5/3 (Rees 1988; Evans & Kochanek 1989; cf. Lodato et al. 2009). If 10% of the radiation goes into soft X-rays, it gives an integrated soft X-ray energy of ∼0.01M_*c² ≃ 10⁵² erg, which is sufficient to power the CLs, assuming 10% radiation efficiency in the accretion disk. A TDE can explain naturally (e.g., Strubbe & Quataert 2009) the bright UV source detected in SDSS J0748+4712 at least 20 days after the CL detection.

Broad emission lines can be produced via reprocessing the disk emission by bound and unbound stellar debris (Eracleous et al. 1995; Bogdanović et al. 2004; Komossa et al. 2008; Strubbe & Quataert 2009). Blueshifted, very broad lines, seen in SDSS J0748+4712, can form in winds driven by super-Eddington accretion during the initial flare (Strubbe & Quataert 2009). As in SNe, unbound material with high velocities may interact with the surrounding ISM, and produce broad emission lines as well (e.g., Khokhlov & Melia 1996; Ayal et al. 2000). In that case, material emitting the Balmer lines can be collisionally excited, rather than photoionized. The debris has a range of orbits and may be dynamically unsettled. This produces variable broad lines with complex profiles, as seen in the observed spectra. As a consistence check, the mass of the line-emitting gas should be smaller than that of the disrupted debris. Assuming the broad Balmer lines are produced via recombination, the minimum mass of the H ii region can be written as M_min = 1.3m_HN_pL_Hα/(4πj_{Hα, br}) ≃ 0.03n⁻¹_{e, 10}L_{Hα, br, 41} M_☉ using the Hα line emissivity from Osterbrock & Ferland (2006) for a temperature T = 10,000 K, where n_{e, 10} is the electron density in units of 10¹⁰ cm⁻³. The observed L_{Hα, br, 41} luminosities (in units of 10⁴¹ erg s⁻¹) are in the range of 0.03–3.0, which are consistent with stellar debris of a few tenths solar mass as line-emitting gas for a reasonable gas density.

CLs may come from interstellar medium photoionized by a flare. Typically a flare lasts for a few months, which are longer than the recombination time for the gas density inferred from the [Fe vii] line ratios.¹¹ At any given time, emission lines come from a region within two parabolic iso-delay surfaces of a delay interval of months at large scales as well as from the nuclear region (Figure 12). The ionizing photons, i.e., soft X-rays, must reach a distance of a few light-years in order to explain the presence of the CLs for a few years. In the last section, we have shown that there is a quite large range of densities, from object to object, from a few 10⁴ cm⁻³ to > a few 10⁷ cm⁻³ for the coronal line emitters (CLEs) with [Fe vii]. If the line-emitting gas fills completely the region, it would be optically thick to the soft X-rays. Thus, the emission-line region must be clumpy. Only the dense clouds produce the CLs and some recombination lines such as the Balmer lines and He ii line, while the low-density gas is probably completely ionized in the strong radiation field of the flare and is transparent to the soft X-rays.

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Tidal disruption may leave significant imprints on the kinematics of the line-emitting gas. Gas exposed to the intense radiation will receive a radial acceleration, and over the period of the passage of the flare, gas will gain a radial velocity of the order k(Δt/1 month)(t/1 month)⁻² km s⁻¹, where k = [(κ/σ_T)(L/L_Edd) − 1] is the ratio between the radiation force and gravity, and Δt the duration of the UV/X-ray flare. k can be on the order of 10², even if the gas contains a small amount of dust. This may explain the blueshifts seen in some of the CLs. The radial velocity decreases rapidly with time, thus we expect that the blueshifts become smaller as the flare evolves. Also the line width becomes smaller with time as gas farther out contributes to the CLs. However, the distribution of the line-emitting gas is likely not affected much by TDEs. This is because the timescale of density adjustment is the sound-traveling time within individual clouds, and the timescale for cloud migration is r/v, where v ∼ 10² km s⁻¹ is estimated from the emission line widths. A decrease of ionization with time was observed in three objects analyzed so far. Such a behavior is expected in a number of cases: gas density falls less steep than r⁻², so the ionization parameter decreases as the emission-line region moves out; if the optical depth to soft X-ray absorption is moderate, the ionizing continuum may be diluted on the way outward. In addition, as the mass accretion rate decreases with time, the ionization parameter in the inner region decreases and the continuum may be softened, too. Detailed photoionization modeling is needed to understand this problem.

If these ECLEs are indeed associated with TDEs, the question arises as to whether any TDEs, regardless whether they were discovered in X-ray, UV, or optical surveys, show strong coronal lines. To answer this question, we searched for post-flare spectra of the TDE candidates reported in the literature. The optical spectra of the ROSAT TDE candidates were mostly taken 5–10 years after the flares, and no high-ionization emission lines were detected in dedicated searches¹² (Komossa & Bade 1999; Komossa & Greiner 1999; Gezari et al. 2003). We found post-flare spectra within less than five years of the flares for eight objects among the most recent candidates identified from X-ray, UV, and optical surveys (Gezari et al. 2008, 2009; Esquej et al. 2008; van Velzen et al. 2011; Cenko et al. 2012), but no strong CLEs were detected. These results suggest that most TDE candidates identified so far do not show strong coronal lines. However, Gezari et al. and Cenko et al. rejected objects either with a broad line or with [O iii]λ5007/Hβ > 3 to remove AGN, while most objects in our sample do show (possibly transient) broad lines and two have [O iii]λ5007/Hβ >3. Therefore, by definition, they also excluded any potential TDEs with strong coronal lines. Furthermore, their absorption-line-dominated TDEs do not produce coronal lines as discussed later. We checked their rejected spectra. In fact, among eight objects with UV flares and with optical follow-up spectra in their sample, we find that one object, D2-9 (J100002.0+024216), displayed a very strong [Fe xiv]λ5304 line (see Figure 7 of Gezari et al. 2008). This object was classified as Seyfert 2 based on [O iii]λ5007/Hβ  >  3 by those authors. If its [Fe xiv]λ5304 line turns out to be fading in future observations, it would be one TDE candidate. For most of the other objects, however, the spectra are of too low S/N or do not cover the coronal line regime. Thus, the fraction of TDEs with strong CLs is not constrained.

To produce strong CLs, tidal disruption must occur in an environment of rich cold gas. Note that all objects in our sample show narrow emission lines from a region different from the coronal line region as indicated by their widths and/or low-ionization levels, demonstrating the presence of cold gas. The non-detection of coronal lines in absorption-line galaxies appears to be a natural outcome of depletion of cold gas in their nuclei. Whether or not a gas-rich galaxy (i.e., H ii-type galaxy) does show strong CLs after a nuclear flare would also depend on the amount of gas near the nucleus that is capable of producing CLs. In addition, it is also necessary to have strong soft X-ray emission from the accretion disk to ensure extreme coronal line emission. While most high-energy flares were indeed characterized by very luminous soft X-ray emission, some UV-detected flares may have been weak in X-rays (Gezari et al. 2009), and the broadband spectral energy distribution depends on the details of the stellar debris evolution, and on possible effects of self-absorption.

As we discussed in Section 3.4, ECLEs are hosted in intermediate-luminosity disk galaxies. Besides, these galaxies do not show apparent bulges in their SDSS images, indicating that the bulge luminosity would be much lower than that of the whole galaxy. This can be seen most clearly in the nearest object, SDSS J1241+4426, where we found only a faint light concentration in the very center of the galaxy. Thus the black hole masses in these galaxies are likely small according to the black hole and bulge mass relation. A similar conclusion can be reached from the M_BH–σ_* relation (Tremaine et al. 2002). If we use the stellar velocity dispersion in Section 3.4, the black hole masses would be at most around 10⁶M_☉. Because a high soft X-ray luminosity is required to power luminous CLs, the black hole mass is not likely much below 10⁵ M_☉.

Wang et al. (2011) speculated that ECLEs with and without [Fe vii] are at different evolution stages based on the variations of [Fe x] and [Fe vii] in three objects with follow-up observations so far. The high-ionization lines faded much faster than [Fe vii]. Thus, we expected higher ionization in earlier stages. The relative fraction of each subclass depends on the time spent in each stage, i.e., the similar numbers detected for each subclass indicate similar time periods spent in each stage. However, this cannot explain their difference in the luminosity of host galaxies, in [O iii] luminosity and possibly in the luminosity of variable components, if confirmed.

Alternatively, these differences may be understood in terms of the differences in black hole mass, and host galaxy properties. Objects with the [Fe vii] emission lines appear to be systematically more massive than those without. Less massive galaxies tend to host smaller black holes, which may result in a hotter accretion torus and a harder soft X-ray spectrum (Montesinos Armijo & de Freitas Pacheco 2011). This may lead to overionization of the line-emitting gas, and thus very weak [Fe vii]. Furthermore, if more massive host galaxies have a different gas distribution in their cores (gas mass, density, and column density), it is conceivable that the [Fe vii] emission would be affected in a systematic way.