Seventeen Tidal Disruption Events from the First Half of ZTF Survey Observations: Entering a New Era of Population Studies

Our search for new TDEs is done exclusively using ZTF data. The strength of ZTF (Graham et al. 2019) is a combination of depth (limiting magnitude of m ≈ 20.5 per visit) and area (47 deg² field of view). Most of our sources originate from the public MSIP survey, which aims (Bellm et al. 2019a) to visit the entire visible northern sky every three nights in both the g and r filters. The use of two filters is an essential ingredient to our TDE selection pipeline, as it allows for efficient photometric filtering (Figure 1) to narrow down the number of targets for spectroscopic follow-up observations.

Zoom In Zoom Out Reset image size

We use the information from the data stream (Patterson et al. 2019) of ZTF alerts, which is produced at IPAC and contains the difference-imaging photometry and astrometry of transients and variable sources (Masci et al. 2019).

We place no requirement on the host-galaxy type or color. However, we reject galaxies that can be spectroscopically classified as broad-line AGNs. This rejection step implies that our sample will not contain TDE candidates in broad-line AGNs, such as PS16dtm (Blanchard et al. 2017). For AGN identification we use the Million Quasars Catalog (Flesch 2015, v5.2.). In addition, we construct a light curve from the NeoWISE (Mainzer et al. 2011) photometry and reject any galaxies with significant variability (${\chi }^{2}/\mathrm{dof}\gt 10$) or a mean W1 − W2 color that exceeds the AGN threshold of Stern et al. (2012). Our filter is executed by Ampel (Nordin et al. 2019), which includes fast catalog matching by catsHTM (Soumagnac & Ofek 2018), and we use the GROWTH marshal (Kasliwal et al. 2019) to coordinate our follow-up observations and spectroscopic classifications.

Compared to our TDE search in ZTF commissioning data (van Velzen et al. 2019e), we use a more liberal cut on the star–galaxy score (Tachibana & Miller 2018) of <0.8. This increases the galaxy sample at the cost of a much higher background due to bright variable stars (these often have a score equal to 0.5 due to issues with the PS1 photometry for bright and variable objects). We therefore veto the star–galaxy score if the source has a detected parallax in Gaia DR2 (Gaia Collaboration et al. 2016, 2018) or if the ratio of the Gaia G-band flux to the PS1 PSF g, r, i flux (converted to the G band) is consistent with a point source. Because we require a match to a known source in the ZTF reference image, we can use a relatively liberal cut on the real–bogus score (Mahabal et al. 2019) of 0.3.

As demonstrated in Figure 1, TDEs can be discriminated from SNe and AGNs based on their rise/fade timescale, g – r color, and lack of color evolution. We rank photometric TDE candidates for spectroscopic follow-up based on their distance from the locus of photometric properties of SNe. In general, we rejected transients that are significantly off-center (mean offset >04), or have significant g − r color evolution (${\rm{\Delta }}(g-r)/{dt}\gt 0.015$ day⁻¹), or show only a modest flux increase when comparing the difference flux to the PSF flux in the ZTF reference image (${m}_{\mathrm{diff}}-{m}_{\mathrm{ref}}\gt 1.5$). We also rejected all objects that can be classified as SNe or broad-line AGNs in our spectroscopic follow-up observations. The details of our photometric selection, including estimates for the completeness and selection effects which are required to compute event rates, will be presented in a forthcoming publication.

In Table 1, we list the IAU name, the ZTF name, our internal nickname,²² the name given by other optical transient surveys, and reference to the first public spectroscopic classification of this transient as a TDE. The table is sorted by the date of the first ZTF detection and credit for discovery of the transient, based on the first report to the Transient Name Server (TNS), is indicated using boldface.

Our TDE discovery pipeline does not use the TNS as input; we read and filter the ZTF alerts directly from their source (Patterson et al. 2019). The TNS reporting of ZTF alerts is mainly provided by AMPEL (Nordin et al. 2019) and by the Redshift Completeness Factor project (Fremling et al. 2020), plus more recently by a filter implemented in the ALeRCE broker. For 10 of the 17 sources in our sample, ZTF was the first survey to report a detection to TNS. As listed in Table 1, ATLAS provided three discoveries, ASAS-SN two discoveries, and Gaia and PS1 each claim one more discovery.

In order to classify the TDEs into spectroscopic subclasses, we use the "best" spectrum, namely high signal-to-noise and prominent line features, for each of our TDEs from our various follow-up programs with the 4.3 m Discovery Channel Telescope De Veny Spectrograph (DCT/De Veny, PI: Gezari), the 200 inch Palomar Telescope Double Spectrograph (P200/DBSP, PI: Kulkarni), the 10 m Keck Low Resolution Imaging Spectrograph (Keck/LRIS, PI: Kulkarni), and the 3 m Lick Kast Double Spectrograph (Lick/Kast, PI: Foley). Spectra were reduced with PyRAF using standard long-slit spectroscopy data reduction procedures. For those spectra not corrected for telluric absorption, we show the spectra in Figure 2 with those wavelength regions masked out. In three cases, we use publicly available spectra from the TNS. In Table 2, we indicate the IAU name, date, phase in days since peak, and telescope and instrument of the spectrum we use for determining the spectroscopic subclassification shown in Figure 2, the TDE class, and the redshift. In all cases, the redshift is measured from host-galaxy absorption features.

Zoom In Zoom Out Reset image size

We find that our ZTF TDE sample can be divided into three spectroscopic classes:

• 1.  
  TDE-H: broad Hα and Hβ emission lines.
• 2.  
  TDE-H+He: broad Hα and Hβ emission lines and a broad complex of emission lines around He ii λ4686. The majority of the sources in this class also show N iii λ4640 and emission at λ4100 (identified as N iii λ4100 instead of Hδ), plus and in some cases also O iii λ3760.
• 3.  
  TDE-He: no broad Balmer emission lines, a broad emission line near He ii λ4686 only.

In our flux-limited sample of TDEs with ZTF observations, the relative ratios of the classes are H:H+He:He = 8:7:1. In Section 7, we will elaborate on how the rarity of the TDE-He class might be an important clue to understand what conditions are needed to provide the spectroscopic properties of TDEs. Two of the TDEs (AT2019meg and AT2019dsg) also have strong narrow emission lines from star formation in their host galaxies.

These classifications are based on a single spectral epoch obtained near the peak of the flare. There is at least one case in which a TDE showed the late-time disappearance of Hα emission (Nicholl et al. 2019a), which according to our classification scheme, would result in a change of spectral class from TDE-H+He to TDE-He.

A detailed analysis of the spectroscopic evolution of the ZTF TDEs and their line features with time will be presented in a future paper (T. Hung et al. 2021, in preparation). For one of our TDEs, AT2019eve, a follow-up spectrum obtained 6 months after peak, demonstrated the appearance of strong, narrow He i lines, potentially a signature of a Type Ibn SN (although the presence of strong Balmer lines is inconsistent with this classification). We therefore label the spectral class of AT2019eve as "Unknown" until more careful analysis of the host-galaxy contribution to the emission-line spectrum. We note also that the rise time of the flare and the blackbody temperature are also outliers compared to the rest of the TDEs in our sample, the blackbody temperature of AT2019eve is below the threshold for TDE identification established by van Velzen et al. (2020).

For a few TDEs, we acquired multiband images with P60/SEDM (Blagorodnova et al. 2018; Rigault et al. 2019) and/or the optical imager (IO:O) on the Liverpool Telescope (LT; Steele et al. 2004). For LT data, image reductions were provided by the IO:O pipeline. For both LT and SEDM, image subtraction was performed versus PS1 ($g$, $r$, $i$, $z$ bands) or SDSS ($u$ band) reference imaging, following the techniques of Fremling et al. (2016). PSF photometry was performed relative to PS1/SDSS photometric standards.

All of our 17 ZTF TDEs have Neil Gehrels Swift Observatory (Gehrels et al. 2004) follow-up observations in the UV and X-ray from UVOT (Roming et al. 2005) and XRT (Burrows et al. 2005), respectively, with a typical cadence of 3–5 days, and in most cases triggered within 2 weeks of the peak. Some of the fainter TDEs have only a few epochs of Swift observations, but they are sufficient to measure the average temperature of the UV/optical component, given that the optical colors of these TDEs are relatively constant with time.

The Swift photometry was measured using the uvotsource package with an aperture of 5'', in the AB system, and corrected for the enclosed energy within the aperture (for AT2019azh, AT2018bsi, and AT2019dsg, we use a larger aperture to make sure we capture all the flux of the host galaxy). We estimate the host-galaxy flux in the UVOT bandpass from the posterior distribution of the population synthesis models. The uncertainty on this baseline level is propagated into our measurement of the TDE flux. Our host-subtracted UVOT aperture photometry, as well as the ZTF, SEDM, and LT photometry, is displayed in Figure 5 and the data is available online.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The 0.3–10 keV X-ray light curves for the four TDEs with XRT detections were produced using the UK Swift Data center online XRT data products tool, which uses the HEASOFT v6.22 software (Arnaud 1996). We used a fixed aperture at the ZTF coordinate of the transient and converted to flux using the best-fit blackbody model to the stacked XRT spectrum. The XRT stacked spectra were processed by the XRT Products Page (Evans et al. 2009), with Galactic extinction fixed to values from the HI4PI survey (HI4PI Collaboration et al. 2016): ${N}_{{\rm{H}}}/{10}^{20}\,$ cm⁻² = 2.59, 6.46, 1.42, and 4.16, for AT2018hyz, AT2019dsg, AT2019ehz, and AT2019azh, respectively. The resulting temperatures are kT/keV = 0.131 ± 0.026, 0.071 ± 0.003, 0.101 ± 0.004, and 0.053 ± 0.001, again for AT2018hyz, AT2019dsg, AT2019ehz, and AT2019azh, respectively (uncertainties correspond to the 90% confidence levels). These soft blackbody temperatures are similar to the previously known X-ray-detected optically selected TDEs: ASASSN-14li (kT = 0.050 keV; Miller et al. 2015), ASASSN-15oi (kT = 0.045 keV; Gezari et al. 2017), AT2018zr/PS18kh (kT = 0.10 keV; van Velzen et al. 2019e), and AT2018fyk/ASASSN-18ul (kT = 0.12 keV; Wevers et al. 2019b).

Finally, we note that, while this paper was under review, a fifth source in our sample, AT2019qiz, was shown to yield a significant detection of X-ray photons when multiple XRT observations are binned together (Nicholl et al. 2020).

We consider two models to describe the TDE light curve. First, for the first 100 days after maximum light, we use a Gaussian rise and exponential decay:

$$\begin{eqnarray}\begin{array}{rcl}{L}_{\nu }(t) & = & {L}_{{\nu }_{0}\mathrm{peak}}\,\displaystyle \frac{{B}_{\nu }({T}_{0})}{{B}_{{\nu }_{0}}({T}_{0})}\\ & & \times \ \left\{\begin{array}{ll}{e}^{-{\left(t-{t}_{\mathrm{peak}}\right)}^{2}/2{\sigma }^{2}} & t\leqslant {t}_{\mathrm{peak}}\\ {e}^{-(t-{t}_{\mathrm{peak}})/\tau } & t\gt {t}_{\mathrm{peak}}.\end{array}\right.\end{array}\end{eqnarray} \tag{ 2 }$$

Here, ${L}_{{\nu }_{0}\mathrm{peak}}$ is the peak luminosity, measured at the reference frequency ν₀ (in the rest frame of the source). To predict the luminosity in other bands, we assume the spectrum follows a blackbody, B_ν(T₀), with a constant temperature T₀. We pick the g band (6.3 × 10¹⁴ Hz) as our reference frequency. We adopt T₀ as our default temperature measurement, and we use this temperature to estimate the peak bolometric luminosity (L_bb) and blackbody radius (R).

One advantage of Equation (2) is simplicity: measuring the rise/decay timescale independently with multiband observations would not be possible with fewer free parameters. However, for observations longer than 100 days, all TDEs show deviations from an exponential decay. A power law is required to properly describe the light curve, and this introduces an extra free parameter. In our second light-curve model, we therefore use a power-law decay and also allow for evolution of the blackbody temperature:

$$\begin{eqnarray}\begin{array}{rcl}L(t,\nu ) & = & {L}_{\mathrm{peak}}\,\displaystyle \frac{\pi {B}_{\nu }(T(t))}{{\sigma }_{\mathrm{SB}}{T}^{4}(t)}\\ & & \ \times \ \left\{\begin{array}{ll}{e}^{-{\left(t-{t}_{\mathrm{peak}}\right)}^{2}/2{\sigma }^{2}} & t\leqslant {t}_{\mathrm{peak}}\\ {\left[(t-{t}_{\mathrm{peak}}+{t}_{0})/{t}_{0}\right]}^{p} & t\gt {t}_{\mathrm{peak}}.\end{array}\right.\end{array}\end{eqnarray} \tag{ 3 }$$

Here σ_SB is the Stephan–Boltzmann constant. While this model allows for temperature evolution, we cannot measure this at the same cadence as the observations because (1) the Swift and ZTF observations were not obtained simultaneously, and (2) the uncertainty on the temperature estimated from a single epoch are often very large. We therefore first try a simple linear relation for the postpeak temperature evolution:

$$\begin{eqnarray}&&T(t)=({T}_{0})+{dT}/{dt}\times (t-{t}_{\mathrm{peak}}).\end{eqnarray} \tag{ 4 }$$

Here, dT/dt is a free parameter with units K day⁻¹, and we use a flat prior with 10⁴ < T/K < 10⁵. This simple model works well for most TDEs, because they only show very modest temperature evolution (about 50 K day⁻¹, which corresponds to a 20% increase over 100 days; see Figure 6).

Zoom In Zoom Out Reset image size

However, for some sources, more rapid temperature changes have been observed (e.g., Holoien et al. 2018), and to allow for more flexibility in our description of temperature evolution, we use a linear interpolation of the temperature on a grid of fixed points in time. The points on this grid are the free parameters of our fit. The grid starts at the time of the peak, and the spacing is ±30 days. At each grid point, we use a log-normal Gaussian prior with a dispersion of 0.1 dex centered on the best-fit mean temperature from our simplest light-curve model (Equation (2)). We adopt this nonparametric approach as our default model to estimate the parameters of the power law (p, and t₀) as well as the rise timescale.

We apply our single power-law decay model (Equation (3)) only to the first year of data (measured after maximum light) because at later times, many TDE light curves show significant flattening that is not consistent with the early-time power-law decay (van Velzen et al. 2019c), likely due to the contribution of an accretion disk to the optical/UV light.

5.1.1. Light-curve Parameter Inference

To estimate the parameters of our two models we use the emcee sampler (Foreman-Mackey et al. 2013). Following van Velzen et al. (2019c), we use a Gaussian likelihood function that includes a "white-noise" term, $\mathrm{ln}(f)$, which allows for additional variance in the data that is not captured by the reported measurement uncertainty. We use 100 walkers and 2000 steps, discarding the first 1500 steps to ensure convergence. We use a flat prior for all parameters (except for the grid points that anchor the temperature evolution): the boundaries of the parameters are listed in Table 5.

An exception is made for sources with no detections prior to maximum light, i.e., TDEs discovered postpeak. For these, we force t_peak = 0 when measuring L_peak using Equation (2). However, we always use the default priors (Table 5) when estimating the best-fit parameters of the power-law decay (Equation (3)), because this allows the uncertainty on the true time of peak to enter the posterior distributions of the power-law parameters. Finally, we also make an exception for the three TDEs from PTF (Table 3). These are the only sources with light curves that have no UV coverage in the first year, and we therefore keep their blackbody temperature fixed at the value measured from the optical spectrum by Arcavi et al.(2014).

To estimate the blackbody radius and blackbody luminosity at peak, we sample the posterior distribution of T₀ and L_peak as obtained from the model of Equation (2). For all parameters, the reported uncertainty follows from a credible interval of [0.16, 0.84], i.e., ±1σ for Gaussian statistics.

The ZTF light curve of two sources in our sample was included in the reference image, hence the IPAC difference-imaging light curves are compromised and excluded from the light-curve analysis. In one case (AT2018bsi), both r-band and g-band light curves are affected, but we were able to use alerts based on an earlier, TDE-free, r-band reference frame that had been created during the ZTF commission period. For the second source (AT2018hyz), only the g-band light curve is affected. For both sources, sufficient Swift/UVOT photometry is available to obtain a good estimate (uncertainty <0.1 dex) of the light-curve features.

We list the results for the 17 sources with ZTF data in Table 6, and we show the light-curve models in Figure 7. The rest-frame absolute r-band magnitude, and the evolution of the blackbody luminosity, radius, and temperature with time is shown in Figure 8. This study increases the number of TDEs with well characterized prepeak light curves by a factor of 3. We observe a homogeneity in the shape of the radius and temperature evolution. In particular, we point out that most sources show a (modest) increase of the temperature with time.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 6.  Light-curve Shape Parameters

Name	Lg	${L}_{\mathrm{bb}}$	T	dT/dt	${t}_{\mathrm{peak}/\max }$	σ	τ	p	t0	${t}_{0}{| }_{p=-5/3}$
	log erg s−1	log erg s−1	log K	102 K day−1	MJD	log day	log day		log day	log day
AT2018zr	${43.44}_{0.02}^{0.02}$	${43.78}_{0.02}^{0.02}$	${4.14}_{0.01}^{0.01}$	${0.46}_{0.05}^{0.05}$	${58180.7}_{1.0}^{1.1}$	${1.0}_{0.03}^{0.04}$	${1.88}_{0.03}^{0.03}$	$-{0.8}_{0.1}^{0.0}$	${1.23}_{0.12}^{0.15}$	${2.14}_{0.03}^{0.03}$
AT2018bsi	${43.08}_{0.03}^{0.03}$	${43.87}_{0.08}^{0.08}$	${4.37}_{0.03}^{0.03}$	${0.21}_{0.30}^{0.63}$	58217.2	⋯	${1.94}_{0.10}^{0.12}$	$-{1.9}_{0.6}^{0.4}$	${1.92}_{0.21}^{0.25}$	${1.83}_{0.07}^{0.09}$
AT2018hco	${43.41}_{0.02}^{0.02}$	${44.25}_{0.04}^{0.04}$	${4.39}_{0.01}^{0.01}$	${0.05}_{0.09}^{0.10}$	${58401.8}_{1.9}^{1.7}$	${0.9}_{0.04}^{0.04}$	${2.03}_{0.04}^{0.04}$	$-{1.2}_{0.2}^{0.2}$	${1.73}_{0.15}^{0.16}$	${2.00}_{0.07}^{0.06}$
AT2018iih	${44.15}_{0.03}^{0.03}$	${44.62}_{0.03}^{0.04}$	${4.23}_{0.01}^{0.01}$	${0.19}_{0.05}^{0.05}$	${58442.2}_{0.8}^{1.6}$	${1.2}_{0.01}^{0.01}$	${2.05}_{0.04}^{0.04}$	$-{0.9}_{0.1}^{0.1}$	${1.61}_{0.07}^{0.11}$	${2.06}_{0.05}^{0.06}$
AT2018hyz	${43.56}_{0.01}^{0.01}$	${44.11}_{0.01}^{0.01}$	${4.25}_{0.01}^{0.01}$	${0.18}_{0.05}^{0.05}$	58428.0	⋯	${1.72}_{0.01}^{0.01}$	$-{1.1}_{0.1}^{0.1}$	${1.29}_{0.06}^{0.07}$	${1.71}_{0.01}^{0.01}$
AT2018lni	${43.26}_{0.03}^{0.03}$	${44.21}_{0.17}^{0.29}$	${4.44}_{0.07}^{0.09}$	${0.48}_{0.47}^{0.46}$	${58460.3}_{5.8}^{3.6}$	${0.8}_{0.50}^{0.18}$	${2.16}_{0.12}^{0.16}$	$-{1.4}_{1.6}^{0.8}$	${2.46}_{0.45}^{0.37}$	${2.23}_{0.19}^{0.22}$
AT2018lna	${43.22}_{0.02}^{0.02}$	${44.56}_{0.06}^{0.06}$	${4.60}_{0.02}^{0.03}$	${0.93}_{0.92}^{0.72}$	${58508.3}_{2.0}^{2.2}$	${1.2}_{0.07}^{0.06}$	${1.65}_{0.03}^{0.03}$	$-{2.1}_{0.7}^{0.7}$	${1.79}_{0.21}^{0.24}$	${1.66}_{0.15}^{0.16}$
AT2019cho	${43.59}_{0.02}^{0.01}$	${43.98}_{0.01}^{0.01}$	${4.19}_{0.01}^{0.01}$	${0.84}_{0.23}^{0.21}$	${58535.3}_{1.6}^{3.0}$	${0.8}_{0.11}^{0.10}$	${1.94}_{0.03}^{0.03}$	$-{1.0}_{0.5}^{0.4}$	${1.83}_{0.13}^{0.25}$	${2.19}_{0.16}^{0.13}$
AT2019bhf	${43.50}_{0.04}^{0.05}$	${43.91}_{0.05}^{0.04}$	${4.20}_{0.02}^{0.02}$	${0.74}_{0.14}^{0.15}$	${58539.3}_{5.7}^{4.4}$	${0.6}_{0.35}^{0.23}$	${1.70}_{0.03}^{0.04}$	$-{1.3}_{0.4}^{0.4}$	${1.70}_{0.20}^{0.23}$	${1.96}_{0.09}^{0.07}$
AT2019azh	${43.33}_{0.01}^{0.01}$	${44.50}_{0.02}^{0.02}$	${4.53}_{0.01}^{0.01}$	${0.98}_{0.19}^{0.21}$	${58558.6}_{1.6}^{1.5}$	${1.3}_{0.04}^{0.05}$	${1.83}_{0.01}^{0.01}$	$-{1.8}_{0.1}^{0.2}$	${1.87}_{0.08}^{0.08}$	${1.96}_{0.04}^{0.05}$
AT2019dsg	${43.22}_{0.05}^{0.06}$	${44.26}_{0.05}^{0.04}$	${4.49}_{0.01}^{0.01}$	$-{0.07}_{0.12}^{0.14}$	${58600.2}_{10.0}^{8.2}$	${1.2}_{0.12}^{0.06}$	${1.80}_{0.02}^{0.02}$	$-{1.5}_{0.1}^{0.1}$	${1.51}_{0.10}^{0.11}$	${1.59}_{0.06}^{0.06}$
AT2019ehz	${43.33}_{0.01}^{0.01}$	${44.03}_{0.02}^{0.01}$	${4.33}_{0.01}^{0.01}$	$-{0.40}_{0.03}^{0.03}$	${58611.4}_{0.6}^{0.6}$	${0.9}_{0.02}^{0.03}$	${1.67}_{0.01}^{0.01}$	$-{1.8}_{0.1}^{0.1}$	${1.73}_{0.09}^{0.06}$	${1.61}_{0.04}^{0.04}$
AT2019eve	${42.89}_{0.02}^{0.02}$	${43.14}_{0.03}^{0.02}$	${4.07}_{0.01}^{0.01}$	${0.07}_{0.07}^{0.08}$	${58610.5}_{0.3}^{0.5}$	${0.1}_{0.07}^{0.09}$	${2.36}_{0.16}^{0.26}$	$-{0.8}_{1.7}^{0.2}$	${1.70}_{0.31}^{0.87}$	${2.25}_{0.10}^{0.10}$
AT2019mha	${43.39}_{0.01}^{0.01}$	${44.05}_{0.05}^{0.06}$	${4.32}_{0.03}^{0.03}$	${0.36}_{1.07}^{0.88}$	${58704.0}_{0.8}^{0.7}$	${1.1}_{0.02}^{0.02}$	${1.23}_{0.02}^{0.03}$	$-{4.0}_{0.5}^{0.7}$	${1.63}_{0.12}^{0.11}$	${1.21}_{0.09}^{0.10}$
AT2019meg	${43.41}_{0.01}^{0.01}$	${44.34}_{0.04}^{0.03}$	${4.43}_{0.01}^{0.01}$	${1.94}_{0.10}^{0.04}$	${58696.4}_{0.6}^{0.5}$	${0.9}_{0.03}^{0.02}$	${1.72}_{0.02}^{0.03}$	$-{0.5}_{1.1}^{0.4}$	${2.69}_{0.53}^{0.23}$	${2.42}_{0.14}^{0.14}$
AT2019lwu	${43.33}_{0.03}^{0.02}$	${43.60}_{0.04}^{0.03}$	${4.09}_{0.01}^{0.01}$	${0.64}_{0.19}^{0.14}$	${58690.2}_{0.7}^{1.0}$	${0.4}_{0.21}^{0.17}$	${1.68}_{0.05}^{0.06}$	$-{1.5}_{0.5}^{0.4}$	${1.56}_{0.18}^{0.20}$	${1.67}_{0.08}^{0.09}$
AT2019qiz	${42.86}_{0.01}^{0.01}$	${43.44}_{0.01}^{0.01}$	${4.28}_{0.01}^{0.01}$	$-{0.17}_{0.09}^{0.10}$	${58761.4}_{0.4}^{0.4}$	${0.8}_{0.01}^{0.01}$	${1.48}_{0.01}^{0.01}$	$-{2.0}_{0.1}^{0.1}$	${1.40}_{0.06}^{0.06}$	${1.26}_{0.03}^{0.02}$

Download table as:  ASCIITypeset image

We find that the typical value of the power-law index of the bolometric luminosity is close to the canonical p = −5/3 = −1.67, albeit with large scatter. For the entire sample of 39 TDEs, we find $\bar{p}=-1.56;$ restricting the sample to the 31 spectroscopic TDEs yields a similar value of $\bar{p}=-1.57$ with an rms of 0.64. To conclude, the mean power-law index is consistent with p = −5/3, but we also find some significant deviations.

In Figure 9, we show a comparison of the 0.3–10 keV X-ray luminosity measured by Swift/XRT to the luminosity of the UV/optical component derived from our light-curve model, for the four new ZTF TDEs with Swift/XRT detections in a single-epoch observation. A fifth ZTF source with X-ray detections was recently presented by Nicholl et al. (2020), obtained after combining multiple XRT epochs. Unlike the UV/optical luminosity, which has a smooth evolution over time and is well described with a single power-law decline post peak, the soft X-ray component shows variability on several timescales (Figure 10). Both large-amplitude flaring on the timescale of just a few days (AT2019ehz) and a dramatic increase in luminosity over a timescale of a few months (AT2019azh) have been observed.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

There are only three other TDEs with well-sampled soft X-ray light curves from Swift: ASASSN-14li (Holoien et al. 2014), ASASSN-15oi (Gezari et al. 2017; Holoien et al. 2018), and AT2018fyk/ASASSN-18ul (Wevers et al. 2019b). While ASASSN-14li showed a soft X-ray flare that followed the general power-law decline of the UV/optical component, with a characteristic ratio of L_opt/L_X ∼ 1 for over a year, the other two TDEs show quite dramatic variability, with a variability and a systematic brightening in the soft X-rays at late times. The first TDE in our ZTF sample, AT2018zr/PS18kh (Holoien et al. 2019b), was detected with a soft X-ray component (kT ≈ 100 eV) in XMM-Newton observations (van Velzen et al. 2019e), but this component was weak relative to the optical luminosity, L_opt/L_X ∼ 100.

We use the Anderson–Darling (AD²³ ) statistic to assess whether our three TDE spectral classes show different distributions of light-curve or host properties. The results are summarized in Table 7, and examples of cumulative distributions are shown in Figure 11.

Zoom In Zoom Out Reset image size

Table 7.  p Value of the Anderson–Darling Test Comparing Distributions Separated by TDE Spectral Classes

	H-only versus H+He	H-only versus He-only	H+He versus He-only
Blackbody radius	$p\lt 0.001$ (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Blackbody temperature	p = 0.005 (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
g-band luminosity	$p\lt 0.001$ (13 versus 14)	$p\gt 0.1$   (13 versus 4)	p = 0.025 (14 versus 4)
Blackbody luminosity	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Rise e-folding time	$p\gt 0.1$   (9 versus 9)	p = 0.049 (9 versus 3)	$p\gt 0.1$   (9 versus 3)
Decay e-folding time	$p\gt 0.1$   (11 versus 14)	$p\gt 0.1$   (11 versus 4)	$p\gt 0.1$   (14 versus 4)
Fallback time	$p\gt 0.1$   (11 versus 14)	$p\gt 0.1$   (11 versus 3)	$p\gt 0.1$   (14 versus 3)
Power-law index	p = 0.078 (8 versus 8)	$p\gt 0.1$   (8 versus 3)	$p\gt 0.1$   (8 versus 3)
Redshift	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host mass	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host rest-frame u − r	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Time since peak SFR	$p\gt 0.1$  (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
SFH τ	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host metallicity	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host dust $E(B-V)$	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host population synthesis PC1	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host population synthesis PC2	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host population synthesis PC3	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host population synthesis PC4	$p\gt 0.1$   (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)
Host population synthesis ${{\rm{C}}}_{\max }$	p = 0.002 (13 versus 14)	$p\gt 0.1$   (13 versus 4)	$p\gt 0.1$   (14 versus 4)

Note. Parameter distributions that show a significant difference ($p\lt 0.05$) are highlighted in green. The p values have been corrected for the number of trials (see Section 6.1. The number of sources in each class are listed in the brackets.

Download table as:  ASCIITypeset image

6.1.1. Separation of TDE Photometric Properties with TDE Spectral Class

6.1.2. Separation of TDE Host-galaxy Properties with TDE Spectral Class

After noticing that the He-only TDEs appear to have redder host-galaxy u − r colors, we also investigated differences between the TDE spectroscopic classes and their host properties as derived from our population synthesis model. The population parameters are stellar mass, metallicity, age since the peak of star formation, e-folding time of the star formation rate (τ_sfh), and the dust optical depth. Because we only have five to seven observables (the GALEX FUV and NUV flux or upper limits, plus five bands from SDSS or PS1) the stellar population parameters have large uncertainties and degeneracies. We therefore also consider a principal component analysis (PCA) of these parameters, which should capture the main correlations between the population synthesis parameters (e.g., the age–metallicity degeneracy). We find that the fourth principal component of the galaxy population parameters (PC4 hereafter) yields an apparent separation of the TDE-H and TDE-H+He TDE populations. The weights of PC4 are dominated by the dust parameter and τ_sfh.

Motivated by the results of the PCA, we also estimated the combination of population synthesis parameters that yields the maximum separation of the TDE-H and TDE-H+He class. We normalized the five population synthesis parameters by dividing out the median value of each parameter and define

$$\begin{eqnarray}&&{C}_{\max }={c}_{1}{C}_{\mathrm{dust}}+{c}_{2}{C}_{\mathrm{age}}+{c}_{3}{C}_{\tau }+{c}_{4}{C}_{Z}+{c}_{5}{C}_{\mathrm{mass}},\end{eqnarray} \tag{ 5 }$$

with C the normalized population synthesis parameters and c₁ to c₅ a set of free parameters. We used a basin-hopping algorithm to estimate the value of these coefficients that yields the highest AD statistic. We find c₁ = 1.00, c₂ = 0.80, c₃ = −0.35, c₄ = 0.04, and c₅ = −0.43. In the next section, we will compute the significance of the difference in the C_max distribution of TDE-H and TDE-H+He class.

The look elsewhere effect can cause one to overestimate the significance when multiple trials have been made to search for effects that pass a given threshold for significance. Here we make a correction for this effect on the p values of a single AD test.

If each of the N properties is counted as a trial, and each property is independent, the p value for a single AD test should be increased by $N{(1-p)}^{N-1}$. However, our photometric properties are not independent, and we therefore need to use the data directly to estimate the importance of the look elsewhere effect. In our case, N = 12, namely 7 parameters of our light-curve model, 5 host-galaxy population synthesis parameters.

To estimate the look elsewhere effect, we repeat the AD test after randomly reordering the spectroscopic TDE labels. On this shuffled data set, we compute the AD statistic for the parameters that describe the photometric properties of the TDE and its host galaxy. After we repeat this procedure many times, each time shuffling the spectroscopic labels, we obtain a new distribution of the AD statistic of these parameters. We use this trial-corrected distribution to compute the p value of the AD statistic for the parameters listed in Table 7.

As explained in the previous section, the parameter C_max (Equation (5)) is a linear combination of the five host-galaxy population synthesis parameters that yields the largest separation of the TDE-H and TDE-H+He class. To obtained a distribution of the AD statistic that accounts for the trials due to the optimization step, we repeat the computation of C_max each time after shuffling the spectroscopic labels. We find (Figure 12) that for only 2 in 1000 shuffled data sets is the difference between the TDE-H and TDE-H+He C_max distribution equal to or larger than the observed value (i.e., the hypothesis that C_max values of TDE-H and TDE-H+He class are drawn from the same distribution can be rejected with p = 0.002).

Zoom In Zoom Out Reset image size

In the previous two sections, we presented differences between the TDE spectroscopic classes. We now focus on correlations between TDE light-curve properties, using all 39 TDEs in our sample. When considering the correlation between a pair of parameters, we remove sources with an uncertainty larger than 0.3 dex. The results of a Kendall's tau test are listed in Table 8. This test only considers the rank of pairs of data points, which is useful because the resulting p value is not disproportionately weighted by large outliers (e.g., ASASSN-15lh). If we instead use a Pearson's test, which assumes the data follow a normal distribution, we typically find lower (i.e., more significant) p values.

Table 8.  Kendall's tau p-Value Comparing Photometric and Host-galaxy Properties

	R	T	${L}_{\mathrm{bb}}$	Rise	Decay	z	Host Mass	Host u − r	Host ${C}_{\max }$
R	...	<0.001(39)	>0.1   (39)	>0.1   (26)	>0.1   (36)	>0.1   (39)	>0.1   (39)	>0.1   (39)	0.014(39)
T	...	...	0.017(39)	0.047(26)	>0.1   (36)	>0.1   (39)	>0.1   (39)	>0.1   (39)	0.025(39)
${L}_{\mathrm{bb}}$	...	...	...	0.086(26)	>0.1   (36)	0.051(39)	0.093(39)	>0.1   (39)	>0.1   (39)
Rise	...	...	...	...	>0.1   (23)	>0.1   (26)	>0.1   (26)	>0.1   (26)	0.030(26)
Decay	...	...	...	...	...	0.021(36)	0.005(36)	>0.1   (36)	>0.1   (36)
z	...	...	...	...	...	...	0.011(39)	>0.1   (39)	>0.1   (39)
Host mass	...	...	...	...	...	...	...	<0.001(39)	0.061(39)
Host u − r	...	...	...	...	...	...	...	...	0.008(39)
Host ${C}_{\max }$	...	...	...	...	...	...	...	...	...

Note. Parameter sets that show a significant correlation ($p\lt 0.05$) are highlighted in green. The number of sources in each set is listed in brackets. The parameter ${C}_{\max }$ is a linear combination of the host-galaxy population synthesis parameters that yields a maximum separation of the TDE-H and TDE-H+He class.

Download table as:  ASCIITypeset image

When considering the correlations between a given set of parameters, we need to keep in mind that our data set as a whole shows a large degree of correlation. If all parameters would be uncorrelated, the 36 p values of the correlation test in Table 8 should follow a uniform distribution between 0 and 1, and for a given limit on the significance p < p_test, we should find p_test × 36 parameter pairs. Instead, we find that 26/36 = 0.72 pairs have p < 0.5, 16/36 = 0.44 have p < 0.1, and 9/36 = 0.25 have p < 0.05. This means that, similar to what we found in the previous section, spurious correlations due to a larger number of trials are unlikely to be important. However, the large degree of correlation makes it harder to find the causal relation between the parameters.

We find a significant correlation between the blackbody radius and blackbody temperature (p < 0.001). The two properties follow the relation expected for a single blackbody spectrum ${L}_{\mathrm{bb}}\propto {R}^{2}{T}^{4}$, with L_bb ≈ 10⁴⁴ erg s⁻¹. This correlation simply confirms that our TDEs are well described by a blackbody spectrum and have a similar luminosity. The scatter around the median luminosity is only 0.3 dex. Because most sources are selected based on optical observations and the bolometric luminosity is largely determined by the temperature estimated from UV follow-up observations, the relatively small scatter cannot be entirely explained by Malmquist bias in our flux-limited sample. As expected, we also find a positive correlation between the blackbody temperature and the blackbody luminosity.

As shown in Figure 13, the rise time of the flare appears to be correlated with the bolometric luminosity. If we consider the ratio of the bolometric luminosity to the blackbody radius, L_bb/R, we find a significant correlation with rise time (p = 0.02). In Section 7.1, we find that this could be explained by a longer diffusion time at higher densities.

Zoom In Zoom Out Reset image size

Notably, we find no correlation between the rise timescale and the exponential decay timescale (τ in Equation (2)) or the fallback timescale (t₀ with p = −5/3 in Equation (3)).

A correlation of TDE light-curve features with host-galaxy properties is anticipated because the black hole mass and the density of the disrupted star should influence the TDE light curve. Black hole mass estimates from the stellar velocity dispersion are not (yet) available for most TDEs in our sample, and we therefore use the total host-galaxy mass obtained from the host photometry (Section 3) as a proxy for black hole mass.

In Figure 14, we show a number of TDE properties as a function of total galaxy mass, and in Table 8, we list the significance. Using a Kendall's tau test, a significant correlation is found for the monochromatic decay timescale measured during the first 100 days (τ, p = 0.005). The host-galaxy mass also appears to be correlated with the fallback timescale, but the scatter is larger the correlation is weaker.

Zoom In Zoom Out Reset image size

We also investigated correlations between the photometric TDE properties and the combination of host-galaxy properties that separates the TDE-H and TDE-H+He class, ${C}_{\max }$ (Equation (5)). Using all 39 TDEs, we find a significant correlation between C_max and the three photometric properties: rise time (p = 0.03), blackbody temperature (p = 0.03), and radius (p = 0.01); see Table 7. We also find an correlation (p = 0.01) between the second host-galaxy PCA component, which is dominated by the mass and metallicity parameters, and the TDE rise time. This is interesting because the correlation between rise time and stellar mass alone is not significant (see Figure 14).

In the model by Metzger & Stone (2016), the optical radiation will be advected through an outflowing wind until it reaches the trapping radius (R_tr), the location at which the radiative diffusion time through the remaining debris is shorter than the outflow expansion time. It is useful to introduce the trapping time t_tr, which is the time photons are losing a significant amount of energy from being trapped in the wind and adiabatically transferring energy to the outflow. For low-mass black holes, M_BH ≲ 7 × 10⁶M_⊙, Metzger & Stone (2016) find that t_tr > t_fb, and thus adiabatic losses suppress and delay the peak of the TDE light curve. In this case, the predicted correlation between the peak luminosity L_pk and M_BH is extremely weak, ${L}_{\mathrm{pk}}\propto {M}_{\mathrm{BH}}^{0.06}$. This results from a cancellation of effects: for larger M_BH, the longer t_fb causes the accretion rate powering the outflow to be lower, but the photons are also less trapped in the outflow and so retain more of their energy. This weak correlation between L_pk and M_BH also manifests as a weak correlation between t_pk and M_BH, again for these lower black hole masses. At higher black hole mass, the relations ${L}_{\mathrm{pk}}\propto {M}_{\mathrm{BH}}^{-1/2}$ and ${t}_{\mathrm{pk}}\propto {M}_{\mathrm{BH}}^{1/2}$, as expected from the mass fallback relations, should reappear.

Alternatively, in the description of Piran et al. (2015), there is no outflow, and the size of the UV/optical emitting region is tied to the apocenter of the most bound stellar debris. For sufficiently low-mass black holes, the diffusion time t_diff for photons to escape the shock-heated debris will provide a timescale that must be convolved with the shock-heating rate set by t_fb to produce the final light curve. For sufficiently low black hole mass, t_diff may become long enough that the black hole mass dependence inherent in t_fb may be washed out by the diffusion time, which is itself more strongly correlated with the mass and structure of the disrupted star than with the black hole mass. For higher-mass black holes, as was the case for Metzger & Stone (2016), these radiative transfer effects should diminish in importance; we again expect the mass fallback relations to dictate the shape of the light curve.

To conclude, the lack of significant correlations between light-curve rise time and host-galaxy stellar mass in our sample of TDEs could be explained by photon advection or diffusion, because these will interfere with seeing an unmitigated signal from the mass fallback rate.

The diffusion timescale for electron scattering scales as t_diff ∝ ρR² (e.g., Metzger & Stone 2017). For a spherical distribution of mass within the photosphere radius R, we find t_diff ∝ M/R. If the peak blackbody luminosity (L_bb) is proportional to this mass, we obtain t_diff ∝ L_bb/R. This scaling of the diffusion time and the ratio of blackbody luminosity and radius could explain the observed correlation between L_bb/R and the rise timescale (Figure 13).

An important property of the TDE-H+He class is their low optical luminosity. Because they are detected in numbers equal to the H-only class, this low luminosity implies a higher intrinsic rate. To estimate the magnitude of this effect, we use the empirical g-band luminosity function of TDEs (van Velzen 2018) to assign a rate to each TDE based on its observed g-band luminosity. In Figure 15, we show the result as a function of blackbody radius; we find a steep dependence on radius, ${dN}/{dR}\propto {R}^{-3}$.

Zoom In Zoom Out Reset image size

If the optical/UV blackbody radius would be proportional to the mass of the star, we obtain a potential explanation for steep decline of the event rate with blackbody radius (Figure 15). Such a scaling is in fact expected if the photosphere is proportional to the self-intersection radius of stream. In Figure 16, we show the radius of an accretion disk created from energy dissipated at the self-intersection radius as a function of black hole mass and stellar mass, obtained using the formalism²⁴ of Dai et al. (2015) and the mass–radius relations for high-/low-mass main-sequence stars from Kippenhahn & Weigert (1990). If we assume that the blackbody photospheric radius R is proportional to the disk size, from Figure 16 we see that, all else being equal, lower mass stars are associated with smaller values of R; at ${M}_{\mathrm{BH}}={10}^{6.5}\,{M}_{\odot }$, $\mathrm{log}(R)\approx 0.8\mathrm{log}({M}_{* })$. Using this result, we find that smaller blackbody radii imply higher blackbody temperatures, consistent with the observed scaling T ∝ R^−1/2 (Figure 6). On the Rayleigh–Jeans tail, we have ${L}_{\nu }\propto {L}_{\mathrm{bb}}^{1/4}{R}^{2}T\propto {L}_{\mathrm{bb}}^{1/4}{R}^{3/2}\propto {L}_{\mathrm{bb}}^{1/4}{M}_{* }^{1.2}$. For a typical initial mass function (${dN}/{{dM}}_{* }\,\propto {M}_{* }^{-2.3}$), the higher number density of low-mass stars thus provides a simple explanation for the steep decrease of the event rate with blackbody radius (${dN}/{dR}\,\propto {R}^{-3}$, Figure 15).

Zoom In Zoom Out Reset image size

The greatest distinction between the TDE-H and TDE-H+He classes is that the latter is characterized by smaller radii (e.g., Figures 13 or 11). Here we recall that almost all sources in the TDE-H+He class show evidence for Bowen lines and that this fluorescence mechanism requires both a high flux of EUV photons and a high gas density. Because the observed blackbody luminosity is similar for the TDE-H+He and TDE-H class, we may infer that the small radii of the TDE-H+He class can be explained by the high-density conditions that enable their fluorescent lines. If we again assume that the optical/UV blackbody radius is related to the stream self-intersection radius (Figure 16), the density within a spherical emission region ($\rho \sim {M}_{* }/{R}^{3})$ will decrease with stellar mass. It thus appears that we can explain both higher density within the photosphere and the higher rate of the TDE-H+He class with the disruption of lower mass stars.

The TDE-He class presents an interesting case to test the idea that the photosphere radius is set by properties of the disrupted star. The He-only class has the longest rise times and highest luminosities, yet relatively large photosphere radii (Figure 13). We either need a high-mass star that is relatively dense, or a high-mass star and a high impact parameter. Both of these scenarios would explain why this spectroscopic class is rare. The lack of H emission would then be a signature either of the lack of hydrogen in a dense He star (Gezari et al. 2012) or the radiative transfer effects in a dense reprocessing region (Guillochon et al. 2014; Roth et al. 2016).

The observation that the TDE-H and TDE-H+He classes show significant differences in the distribution of stellar population parameters (Table 7) could in principle be used to shed light on which stellar properties (e.g., density, composition, or impact parameter) influence the TDE light curve and spectrum. Unfortunately, the interpretation of the population parameters is not straightforward.

The superposition of the host-galaxy stellar population synthesis parameters that yields the largest separation of the TDE-H and TDE-H+He class is mainly driven by the dust optical depth (C_dust) plus the age of the stellar population (C_age), minus e-folding time of the star formation (C_τ), such that the TDE-H+He class has higher values of C_dust + C_age − C_τ. Yet the Bowen TDEs also have the highest blackbody temperatures, implying that they are not systematically affected by dust in their host galaxies. We therefore expect that the dust parameter absorbs the imperfections of our simple single-age stellar population model. At this point, we can speculate that the age of the stellar population is the underlying cause for the difference between the TDE spectroscopic classes. But the correct path forward is to improve our inference of the stellar population by including additional information, such as the WISE photometry and the absorption-line diagnostics (e.g., French et al. 2017). This will be the subject of future work.

Most models that use reprocessing of photons from close to the black hole to explain the observed optical emission of TDEs predict that at some point, the reprocessing layer becomes transparent to X-rays. In the outflow model by Metzger & Stone (2017), the inner wind becomes transparent to X-ray radiation once it is fully ionized by emission from the inner accretion disk, which happens at ${t}_{\mathrm{ion}}\,\approx 0.8{t}_{\mathrm{fb}}{({M}_{\mathrm{BH}}/{10}^{6}{M}_{\odot })}^{-0.8}{({M}_{* }/{M}_{\odot })}^{0.4}$. At this point, the reprocessing efficiency decreases, and one would expect an increase of the ratio of the X-ray to optical/UV luminosity (${L}_{{\rm{X}}}/{L}_{\mathrm{bb}}$). Alternatively, if our view of the inner accretion disk is unobscured and the optical emission originates from the stream intersection point (Piran et al. 2015), an increase of the X-ray importance is evidence for delayed accretion onto the black hole (as seen in the simulations of Shiokawa et al. 2015).

Because the inner accretion disk itself should also produce optical/UV emission (Cannizzo et al. 1990; Strubbe & Quataert 2009; Lodato & Rossi 2011), the optical luminosity is unlikely to completely vanish when the reprocessing layer is fully ionized. Indeed, late-time observations of TDEs (∼few years after peak) show a near-constant luminosity that is consistent with an accretion disk (van Velzen et al. 2019c; Jonker et al. 2020; Mummery & Balbus 2020).

The dramatic brightening of AT2019azh in the soft X-rays 7 months after peak is similar to the behavior of TDE ASASSN-15oi (Liu et al. 2019), which was interpreted by Gezari et al. (2017) as a result of delayed accretion. However, the faint flux in the soft X-rays could also be explained by a suppression from adiabatic losses due to electron scattering (Dai et al. 2018). In contrast to the preferential suppression of soft X-rays associated with atomic absorption, these adiabatic losses leave a subtler imprint on the spectral slope of the attenuated X-ray spectrum, potentially consistent with the lack of strong evolution in the X-ray spectra when L_bb/L_X decreases.

One TDE in our sample (AT2019ehz) shows a remarkable, and hitherto unseen, evolution of L_bb/L_X. We observe three X-ray flares during the first months of post-peak observation (Figure 9), increasing its X-ray luminosity by almost two orders of magnitude to L_X ≈ 5 × 10⁴⁴ erg s⁻¹ on a timescale of days. The peak X-ray luminosity of the flares is just below the optical/UV blackbody luminosity measured at the same time (Figure 10). If stream collisions are the main power source of early-time optical TDE emission (i.e., accretion is energetically unimportant), the X-ray flares of AT2019ehz could in principle be explained by parcels of gas that are deflected toward the black hole from the stream collision site. However, the short timescale of the observed flare implies these discrete parcels would have to be aimed very precisely, which is not expected; the simulation by Shiokawa et al. (2015) does show fluctuations in the mass accretion rate, but these occur on a timescale that is longer than the fallback time. We also note that it would be a coincidence that for each of the three flares, the X-rays from the gas deflected by shocks reach ${L}_{\mathrm{bb}}/{L}_{{\rm{X}}}\sim 1$. On the other hand, an equal amount of intrinsic accretion luminosity and observed optical/UV luminosity is a generic feature of a reprocessing layer with a high covering factor. In this scenario, the X-ray flares are not due to an increase of the accretion rate but to a decrease of the optical depth to our line of sight of the compact X-ray emitting region.

Obtaining a few brief glimpses of the central soft X-ray emission would be possible for a reprocessing region that is moderately patchy. Because the size of this accretion disk is ∼100 times smaller than the optical photosphere, our hypothetical patchy reprocessing layer can have many small "gaps" that provide a view of the disk while the reprocessing efficiency remains high. Adapting the equation for the orbital timescale of a gas cloud at r_orb from LaMassa et al. (2015), we get a crossing timescale of

$$\begin{eqnarray}&&{t}_{\mathrm{cross}}=0.22{\left[\displaystyle \frac{{r}_{\mathrm{orb}}}{\mathrm{lt} \mbox{-} \mathrm{day}}\right]}^{3/2}{\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{10}^{7}{M}_{\odot }}\right)}^{-1/2}\arcsin \left[\displaystyle \frac{{r}_{\mathrm{src}}}{{r}_{\mathrm{orb}}}\right]\,\mathrm{yr}.\end{eqnarray} \tag{ 6 }$$

For a small gap, the distance of the optical photosphere of 10^14.5 cm = 0.1 lt-day, we get a crossing time of 2.5 days, in agreement with the duration of the soft X-ray flares.