Revisiting Optical Tidal Disruption Events with iPTF16axa

Due to the long-lived nature of TDE, we were not able to obtain a host galaxy spectrum of iPTF16axa for this analysis before it went behind the Sun in October.

We perform synthetic stellar population template fitting to the SDSS broadband photometry cmodelMag in ugriz as well as the WISE 3.4 and 4.6 μm photometry with Fitting and Assessment of Synthetic Templates (FAST) by Kriek et al. (2009). Assuming an exponentially declining star-formation history with the Bruzual & Charlot (2003) templates, a Salpeter IMF, the Cardelli et al. (1989) dust extinction law, and A_V = 0.12 from the Schlafly & Finkbeiner (2011) dust map, the fitting program yields a ${\chi }_{\nu }^{2}$ of 1.57. The results of the fit suggest that star formation has quenched in the galaxy with an SFR of 10^−6.6 M_⊙ yr⁻¹. In 2017 February, we obtained a high-resolution spectrum of iPTF16axa with the Echellette Spectrograph and Imager (ESI) mounted on the Keck-II telescope (PI Gezari). We observed the host galaxy and a template GIII star BD+332423 with the 05 slit for a total integration time of 3600 s and 120 s, respectively. The data is reduced with the MAuna Kea Echelle Extraction (MAKEE ¹⁶ ) package, while the wavelength is calibrated with IRAF.

We measure a stellar velocity dispersion of 101.3 ± 1.9 km s⁻¹ with the Mg ib λλ5167, 5173, 5184 triplet (Figure 1) by broadening the GIII stellar template to match the linewidths in the host spectrum. The velocity dispersion translates to a black hole mass of ${5.0}_{-2.9}^{+7.0}\times {10}^{6}$ M_⊙ (McConnell & Ma 2013). Despite the large intrinsic scatter in the M–σ relation (0.38 dex), the black hole mass estimated from velocity dispersion is within the range of allowable black hole masses able to disrupt a solar-type star outside of its event horizon.

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The follow-up photometric observations of iPTF16axa are described in this section. These measurements are presented in Table A1.

4.1.1. P48 and P60 Photometry

4.1.2. LCO Photometry

4.1.3. Swift UVOT and XRT Photometry

4.2.1. Keck DEIMOS

4.2.2. Keck LRIS

4.2.3. Discovery Channel Telescope (DCT) DeVeny

Classical calculations assume a uniform distribution in specific energy so that the bound stellar debris returns to the pericenter at a rate of t^−5/3 (Rees 1988; Phinney 1989). For more realistic energy distributions, there are deviations from t^−5/3 at early times, but the light curve eventually approaches a t^−5/3 power law at late times (Lodato et al. 2009), or approaches a power-law index within a range of values that brackets −5/3 (Guillochon & Ramirez-Ruiz 2013). The t^−5/3 power law can be expressed as

$$\begin{eqnarray}&&L(t)\propto \dot{M}(t)\propto {(t-{t}_{D})}^{-5/3},\end{eqnarray} \tag{ 1 }$$

where t_D is the time of disruption. We fit the light curves in both g and r bands simultaneously with data taken by P48 and P60 telescopes. With a fixed power-law index of −5/3, we can rewrite Equation (1) as

$$\begin{eqnarray}&&{m}_{\mathrm{obs}}=N+\displaystyle \frac{5}{2}\cdot \displaystyle \frac{5}{3}(t-{t}_{D}),\end{eqnarray} \tag{ 2 }$$

where m_obs is the observed magnitude and N is a normalization constant. We derived a disruption time (t_D) of MJD 57482.9 ± 1.1 using emcee (Foreman-Mackey et al. 2013), a python implementation of the Affine invariant Markov chain Monte Carlo (MCMC) ensemble sampler. The corner plot for 1000 MCMC simulations is shown in Figure 2. If we loosen the fitting parameter constraints further by allowing the power-law index to change freely, we obtain a best-fit power-law index of $-{1.44}_{-0.12}^{+0.09}$ and a t_D of 57494.7 ± 0.1. The derived values imply the rise time to peak light is shorter than 49 rest-frame days assuming the peak was reached some time before the discovery of iPTF16axa.

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The light curve is fitted well by a t^−5/3 power law in all the UV and optical bands, with a constant color between the bands with time. The model fit shown in Figure 3 has the colors UVW2 − r = −1.05 mag and g − r = −0.34. The lack of color evolution and the observed t^−5/3 power-law decline in the UV and optical bands requires a fixed temperature over time to be consistent with the expected t^−5/3 evolution of the bolometric luminosity.

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In Figure 4, we show the best-fit blackbody spectrum implied by these colors using the magnitudes extrapolated from the power law in Figure 3 to the time of discovery MJD 57537.4 in UVW2, UVM2, UVW1, u, g, r, and i bands. The best-fit blackbody temperature implied by the light-curve model is 2.85 × 10⁴ K. Using the X-ray upper limit, we also place an upper limit of 1.85 × 10⁵ K on the blackbody temperature of the TDE, which is shown in the green dashed line in Figure 4.

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Given the archival SDSS u-band magnitude of the host is ∼21.4 mag, we assume that the host light contribution is negligible in UVOT filters with shorter wavelengths (UVW2, UVM2, UVW1, u). The data in B and V bands are excluded for data analysis since the contribution from the host galaxy is unknown. We also collected the host-subtracted photometry in gri from P48 and P60, which use images from IPAC and SDSS as references, respectively.

To construct UV–optical SEDs at different epochs, we interpolate the host-subtracted flux in g and r bands using the t^−5/3 light curves in Figure 3 to the epoch of Swift observations. The uncertainties of the interpolated magnitudes in g and r are estimated to be the weighted residual of the light-curve fit with the t^−5/3 power law.

The SEDs are fit with a blackbody using the Markov chain Monte Carlo (MCMC) method. Shown in Figure 5 are the best-fit blackbody spectra. The 1σ uncertainties of the model parameter are shown by the two gray lines in each panel, representing the upper and the lower bound of the best-fit temperature. The best-fit blackbody temperatures are plotted as a function of time in the top panel of Figure 6. The blackbody temperatures of iPTF16axa remained at nearly constant temperature $\bar{T}$ = (3.0 ± 0.33) × 10⁴ K over the 80 days of Swift monitoring.

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In Figure 6, we also plot the time evolution of the UV–optical integrated luminosity and the blackbody radius in the middle and the bottom panels. We calculate the luminosity by integrating the area under the best-fit blackbody for each SED, which follows the theoretical t^−5/3 law. Given that there is no detection in the X-ray, we assume that the bolometric luminosity of the transient is dominated by the emission in the UV and optical. The observed peak luminosity of 1.1 × 10⁴⁴ erg s⁻¹ corresponds to an Eddington ratio of 17.4% for a 5 × 10⁶ M_⊙ black hole and a mass accretion rate (${\dot{M}}_{0}$) of 1.8 × 10⁻² (/0.1)⁻¹ M_⊙ yr⁻¹, where is the accretion efficiency. The total energy integrated under the model fit from from t_disc to ${{\rm{t}}}_{\infty }$ is 5.5 × 10⁵⁰ erg, which corresponds to a total mass accreted of 3.1 × 10⁻³ (/0.1)⁻¹ M_⊙. Note, that this is a small fraction of the 0.5 M_⋆ of mass expected to remain bound to the black hole in a TDE (Rees 1988) unless the radiative efficiency () is low .

We also calculate the emitting radius of the blackbody using the Stefan–Boltzmann law:

$$\begin{eqnarray}&&L=4\pi {R}_{{bb}}^{2}\sigma {T}_{e}^{4},\end{eqnarray} \tag{ 3 }$$

where L is the luminosity integrated from the best-fit blackbody spectrum to the SED, R_bb is the blackbody radius, and T_e is the effective temperature, which is set to be equal to the blackbody temperature derived from the SED fit. In Table 1, we list our fits for the blackbody temperature, luminosity, and photospheric radius for each of our photometric observations. In the bottom panel of Figure 6, we plot our fit for the photospheric radius as a function of time, where the y-axis on the right hand side of Figure 6 shows the radius in units of the tidal radius (R_T) assuming the disrupted star is a solar mass star. The tidal radius, R_T = R_⋆ (M_BH/M_⋆)^1/3, is 1.19 × 10¹³ cm for a 5 × 10⁶ M_⊙ black hole.

Five follow-up spectra are shown in Figure 7. We also show the best-fit host spectrum from FAST fit with SDSS fiberMag (flux enclosed in a 3'' diameter fiber) in ugriz filters as described in Section 3.1. In Figure 7, we rescale all the new spectra to the synthetic magnitude in the r band (m_r,syn), which is defined as

$$\begin{eqnarray}&&{m}_{r,\mathrm{syn}}=-2.5{\mathrm{log}}_{10}({10}^{-{m}_{r,0}/2.5}+{10}^{-{m}_{r,\mathrm{sub}}/2.5}),\end{eqnarray} \tag{ 4 }$$

where m_r,0 is the fiber magnitude of the host and m_r,sub is the host-subtracted r-band magnitude derived from the t^−5/3 power-law fit at the time of the observation.

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In order to measure the broad emission lines in the spectra, we first subtract off the instrumental broadened host template spectrum from the FAST fit in Section 3.1, where $\sigma =\sqrt{{\sigma }_{\mathrm{instrument}}^{2}-{\sigma }_{\mathrm{lib}}^{2}}$, for each spectrum. The FWHM resolution of the Bruzual & Charlot (2003) template library is 3 Å. The host-subtracted spectra are shown in Figure 8.

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It is known that the spectroscopic signatures of optically discovered TDEs consist of a strong blue continuum and a combination of broad He ii and Hα emission (Arcavi et al. 2014). We select the regions outside of the Balmer lines and the He ii emission line in the host-subtracted spectrum to estimate the continuum. The line-free regions are fit with a fifth-order Legendre polynomial. A blackbody spectrum with T_bb = 3.0 × 10⁴ (K) is shown in red in Figure 9, which is the mean blackbody temperature from the SED fit. The blackbody spectrum shows a depature from the host-subtracted spectrum at rest wavelength λ > 4500 Å.

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We approximate the continuum with the Legendre polynomial because it fits the spectra better than the blackbody spectrum and does not require an assumption of the physical origin for the continuum. The line profiles of He iiλ4686 and Hα are measured after host and TDE continuum subtraction. The best-fit results are shown as red lines in Figure 10, where the gray solid line is the flux of the subtracted spectrum centered at the indicated line in velocity space. We simultaneously fit the He iiλ4686 (orange) and Hβ (green) emissions as two individual Gaussian profiles. The Hα line is modeled as a single Gaussian. The linewidths and line luminosities are listed in Table 2.

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The color evolution and the spectroscopic signatures of the flare are not consistent with any known supernova. Supernovae exhibit a much faster color evolution due to cooling in the expanding ejecta and can only remain bright in the UV for a few days. In addition, we do not detect any P-Cygni profile indicative of outflow in the spectra of iPTF16axa.

Although the nuclear position of the flare may connect it to AGN activity, we do not see any evidence of the host galaxy harbouring an active nucleus. First, common AGN lines such as [O iii] and [N ii] are not present in the spectra. Although the Balmer lines Hα and Hβ were detected, the broad Balmer lines have faded almost entirely from 2016 June to September, which indicates the presence of broad Balmer lines is associated with the transient instead of the host galaxy. In fact, in the rare case of a changing-look AGN, we may see broad emission lines in an AGN suddenly appear or disappear on the timescale of a few years (e.g., Shappee et al. 2014; LaMassa et al. 2015; Ruan et al. 2016; Gezari et al. 2017). However, the lack of X-ray emission in iPTF16axa does not support the changing-look AGN scenario. Furthermore, AGNs are known to vary on various timescales across the electromagnetic spectrum. As mentioned in Section 2, the position of iPTF16axa does not have any historical PTF detection signposting AGN activity between 2011 and 2014.

The photometric and spectroscopic properties bear a stronger resemblance to previous events classified as optical TDE candidates. We compare and discuss their temperatures, luminosities, and spectral line ratios in Sections 6.3, 6.5, and 6.4.

We derive the shortest rise time (t₀–t_D) by setting the derivative of Equation (A2) (in Guillochon & Ramirez-Ruiz 2013) with respect to the impact parameter β to zero. The minimum theoretical timescale implied by a 5 × 10⁶ M_⊙ black hole is 63 days for β = 1.9 assuming a γ = 4/3 and a solar-type star. Since the TDE was discovered on the decline, we can only place an upper limit on the rise time derived from the observed light curve. The upper limit on the rise time is Δt < 49 rest-frame days assuming that the peak light occurred some time before the iPTF discovery. This rise time is consistent with a black hole mass of less than 3 × 10⁶ M_⊙, which is within the intrinsic scatter (0.38 dex) of the M–σ relation in McConnell & Ma (2013) given in Section 3.1.

The blackbody temperature of iPTF16axa remained constant (T_bb ∼ 3.0 × 10⁴ K) over the three-month monitoring period. This temperature is similar to what was found in PS1-10jh (Gezari et al. 2012), which was also reported to have constant temperature on the timescale of about a year.

The TDE candidates discovered by GALEX (D1-9, D3-13), which were also detected in the optical with CFHTLS, have higher blackbody temperatures than the other optical TDE candidates in Figure 11. However, the difference is much less significant than the difference between X-ray-detected TDE candidates and optical TDE candidates, where the former is usually one to two orders of magnitude hotter than the latter.

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TDE candidates found in the ASASSN, ASASSN-14ae, and ASASSN-14li, the SDSS TDEs TDE1 and TDE2, PS1-10jh, PS1-11af, and PTF09ge also have blackbody temperatures that remain roughly constant over months (Figure 11). The only outlier here is ASASSN-15oi, which features an ∼100% increase in blackbody temperature on the timescale of less than a month.

Figure 12 shows the integrated Helium-to-Hα line ratio of iPTF16axa and the other TDE candidates discovered in the optical. PS1-10jh, PTF09ge, and ASASSN-15oi do not have Hα emission. A lower limit of 4.7 was reported for PS1-10jh (Gezari et al. 2015), a lower limit of ∼1 was reported for ASASSN-15oi (Holoien et al. 2016a), and we measure a lower limit of 1.9 for PTF09ge from fitting its spectrum obtained from the Double Spectrograph mounted on the Palomar 200-inch (P200) telescope on 2009 May 20.

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We measure the line ratios for ASASSN-14ae and ASASSN-14li by performing Gaussian line fitting on the spectra on the open TDE catalog¹⁹ in a similar fashion as described in Section 5.3. The continuum is modeled as a fifth-order Legendre polynomial and subtracted before measuring the lines. ASASSN-14ae did not develop He iiλ4686 until later epochs.

Throughout the spectroscopic epochs, the Hα line was readily detected in iPTF16axa except for the last epoch. iPTF16axa did not show significant Hα suppression as was observed in PS1-10jh and PTF09ge. From Figure 12, the spectroscopic signatures of TDE candidates can be divided into two groups based on the presence/absence of Hα emission. The sources that show both He iiλ4686 and Hα emission appear to have similar He ii/Hα ratios, with the exception of iPTF16fnl near peak, which shows a high He iiλ4686-to-Hα ratio that rapidly evolves to the lower ratio observed in the other sources.

The nebular He iiλ4686 to Hα line ratio can be expressed as

$$\begin{eqnarray}&&\displaystyle \frac{L(\mathrm{He}\,{\rm{II}}\lambda 4686)}{L({\rm{H}}\alpha )}=\displaystyle \frac{n({\mathrm{He}}^{++}){n}_{e}{\alpha }_{\lambda 4686}^{\mathrm{eff}}h{\nu }_{\lambda 4686}}{{n}_{p}{n}_{e}{\alpha }_{\lambda {\rm{H}}\beta }^{\mathrm{eff}}({j}_{{\rm{H}}\alpha }/{j}_{{\rm{H}}\beta })h{\nu }_{\lambda {\rm{H}}\beta }},\end{eqnarray} \tag{ 5 }$$

where n(He⁺⁺) is the density of He⁺⁺, n_p is the proton density, n_e is the electron density, and ${\alpha }_{\lambda }^{\mathrm{eff}}$ is the effective recombination coefficient. For a typical T = 10⁴ K nebular gas, ${\alpha }_{\lambda 4686}^{\mathrm{eff}}\,$= 3.57 ×10⁻¹³ cm³ s⁻¹, ${\alpha }_{{{\rm{H}}}_{\beta }}^{\mathrm{eff}}\,$= 3.02 × 10⁻¹⁴ cm³ s⁻¹, and j_Hα/j_Hβ is 2.87 (Osterbrock p80). Substituting in these values, the He iiλ4686 to Hα line ratio can be expressed as 3.98 n(He⁺⁺)/n_p for an electron density of 10² cm⁻³ in case B recombination. Assuming the solar helium abundance Y_⊙ = 0.2485 (Serenelli & Basu 2010), the number abundance of helium n(He⁺⁺)/n_p is ≈0.08. This results in a line ratio of 0.32($\tfrac{{n}_{\mathrm{He}}}{{n}_{\mathrm{He},\odot }}$), which is denoted by the dotted line in Figure 12.

It is noticed that the nebular arguments, while still commonly used in the literature, are not valid for most of the TDE spectra. Figure 12 demonstrates that all measurements of the helium-to-hydrogen line ratio in TDEs, with the exception of the early epochs of ASASSN-14ae, display a helium enhancement compared to the nebular prediction assuming solar abundance. While stellar composition may be affecting these ratios in some events, this pattern also suggests that nebular arguments along the lines of Equation (5) may break down for TDEs. A likely explanation is that high gas densities (>10¹⁰ cm⁻³) are leading to the suppression of the Balmer lines as these transitions become optically thick. This possibility was first suggested by Bogdanović et al. (2004), and has been recently studied with CLOUDY caclulations (Gaskell & Rojas Lobos 2014; Strubbe & Murray 2015; Saxton et al. 2016) and full radiative transfer calculations (Roth et al. 2016).

Shown in Figure 13 is the time evolution of the UV–optical integrated luminosity of iPTF16axa from the blackbody model. Also shown in this plot are the UV/optical integrated luminosities of ASASSN-14ae, ASASSN-14li, ASASSN-15oi, PS1-10jh, PS1-11af, TDE1, TDE2, D1-9, and D3-13.

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In Figure 13, all of the TDE candidates except iPTF16fnl follow a power-law decline with a decline rate more or less consistent with t^−5/3. It is also interesting that, based on our blackbody fit, all of these TDEs except iPTF16fnl are confined to a small range of luminosities, with the peak luminosities ranging from log(L [erg s⁻¹]) = 43.4–44.4. We must caution, however, that a substantial fraction of the total radiated energy, especially if originally emitted at FUV and EUV wavelengths, may be missing in our observations, as was demonstrated by van Velzen et al. (2016b) in the case of PTF09ge based on infrared light echo observations.

Figure 14 shows the evolution of blackbody radius for iPTF16axa and other optically bright TDE candidates. The blackbody radius of iPTF16axa decreased steadily from 4 × 10¹⁴ to 2 × 10¹⁴ cm as the luminosity decreases with time. The blackbody radius of PS1-10jh is derived assuming a t^−5/3 decay in luminosity and constant temperature. Since the tidal radius is weakly dependent on the black hole mass (${R}_{T}\propto {M}_{\mathrm{BH}}^{1/3}$), Figure 14 shows that the derived radii are at least 10 times farther away from the R_T for all the TDE candidates.

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Due to the non-varying temperature evolution of TDE emission, the photospheric radius must decline at late times in order to match the fading light curve. The physical meaning of this decline remains unclear. One explanation is that the density of the optically emitting gas drops over time, allowing the observer to see light emitted from increasingly deeper regions, even if the gas is continuously outflowing (Strubbe & Murray 2015). Another possibility is that the optically emitting gas is in fact moving closer to the black hole over time, and may be related to the decreasing apocenter radius of the circularizing debris stream (Bonnerot et al. 2017).

The FWHMs of He iiλ4686 and Hα are plotted in Figure 15. The triangles denote the linewidths of He iiλ4686 lines, while the dots denote the linewidths of Hα emission. The He iiλ4686 linewidths for ASASSN-14ae and ASASSN-14li were measured using the spectra on the open TDE catalog. The He iiλ4686 linewidth of PTF09ge is measured from its P200 spectrum and the value for PS1-10jh is provided in Gezari et al. (2012).

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In Figure 15, the FWHMs of He ii and Hα emission lines evolve in the same trend. Throughout the observations of iPTF16axa, the He iiλ4686 linewidth remains comparable, sometimes even narrower, than the linewidths of Hα. The fact that the linewidths of He ii are not wider than that of Hα suggests that the line emitting material is not virially bound. In the scenario of a stratified broad line region, because the photoionization energy of He is higher than hydrogen, helium has to be emitted at a smaller radius and therefore would have a wider linewidth. As pointed out in Holoien et al. (2016a, 2016b), in reverberation mapping studies, the linewidths would increase while the luminosity decreases due to recombination at outer radii. This trend is also not observed until the last epoch when the line detection was weak.

In Figure 16, we plot the peak luminosity reported in the literature as a function of the black hole mass. The circle symbols show black hole masses reported in the literature while the diamond symbols show black hole masses estimated from the r-band scaling relation in Tundo et al. (2007), which has a 1σ scatter of 0.33 dex. We obtain the black hole mass of ASASSN-14ae from Holoien et al. (2014), ASASSN-14li from Holoien et al. (2016b), ASASSN-15oi from Holoien et al. (2016a), PS1-11af from Chornock et al. (2014), PTF09ge from Arcavi et al. (2014), D1-9 and D3-13 from Gezari et al. (2009), and TDE1 and TDE2 from van Velzen et al. (2011).

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We show four different ratios of Eddington luminosity, L_Edd, 0.1 L_Edd, 10⁻² L_Edd, and 10⁻³ L_Edd, as a function of the black hole mass with the black dotted lines. The black dashed line in Figure 16 shows the theoretical scaling of ${L}_{\mathrm{peak}}\propto {\dot{M}}_{\mathrm{peak}}\,\propto {M}_{\mathrm{BH}}^{-1/2}$ (Lodato & Rossi 2011; Guillochon & Ramirez-Ruiz 2013) normalized to Equation (A1) in Guillochon & Ramirez-Ruiz (2013) assuming a star with solar mass and radius, γ = 4/3, β = 1, and an accretion efficiency of 0.1. The dashed line does not extend below M_BH ∼ 10^6.6 M_⊙ since the emergent luminosity should be Eddington limited. Below this threshold, the luminosity scales with the Eddington luminosity, L_peak ∝ L_Edd ∝ M_BH. We do not see a clear trend in the data that suggests the peak luminosity and the black hole mass are correlated, though we emphasize again that undetected emission originally at FUV and EUV wavelengths may alter this conclusion and that many of the TDE candidates plotted were discovered post-peak, and thus their luminosity at discovery may be underestimating the true peak luminosity.