Long-term X-ray evolution of SDSS J134244.4+053056.1: A more than 18
  year-old, long-lived IMBH-TDE candidate
  SDSS J134244.4+053056 is a tidal disruption event candidate with strong
temporal coronal line emitters and a long fading, mid-infrared dust echo. We
present detailed analyses of X-ray emission from a Swift/XRT observation in
2009 and the most recent XMM-Newton/pn observation in 2020. The two spectra can
be modeled with hard and soft components. While no significant variability is
detected in the hard component above 2 keV between these two observations, the
soft X-ray emission in 0.3-2 keV varies by a factor of $\sim5$. The luminosity
of this soft component fades from $\sim1.8\times10^{41}$ to
$\sim3.7\times10^{40}$ erg s$^{-1}$ from the observation in Swift to that of
XMM-Newton, which are 8 and 19 years after the outburst occurred, respectively.
The evolution of luminosity matches with the $t^{-5/3}$ decline law well; there
is a soft X-ray peak luminosity of 10$^{44}$ erg s$^{-1}$ at the time of the
optical flare. Furthermore, the spectra of the soft component harden slightly
in the decay phase, in which the photon index $\Gamma$ varies from
$4.8^{+1.2}_{-0.9}$ to $3.7\pm0.5$, although they are consistent with each
other if we consider the uncertainties. Additionally, by comparing the BH mass
estimate between the $M-\sigma$ correlation, the broad H$\alpha$ emission, and
the fundamental plane relation of BH accretion, we find that a value of
$\sim10^{5}$Msun is favored. If so, taking its X-ray spectral variation,
luminosity evolution, and further support from theory into account, we suggest
that SDSS J134244.4+053056 is a long-lived tidal disruption event candidate
lasting more than 18 years with an intermediate-mass black hole.
