A Time-Dependent Solution for GSN 069 Disk Evolution and the Nature of Long-Lived Tidal Disruption Events

TL;DR

This work tackles constraining time-dependent accretion-disk physics in transient events by developing a fully relativistic, time-evolving disk model. The authors implement the model in a pyXspec-compatible FitTeD framework, enabling simultaneous fitting of multi-epoch X-ray and UV data with a small set of free parameters describing the black hole and initial disk, while evolution follows the dynamical equations of motion for an evolving accretion flow. The approach quantifies the evolution through the diffusion-like equation for $\Sigma(r,t)$ in the Kerr metric and leverages a Green's function $G_\Sigma$ with a stress law $W^r_{\ \phi}$ to connect initial disk mass and radius to observable spectra, incorporating relativistic transfer via the energy shift $g$ and color correction $f_c$. Application to GSN 069 across 2010–2019 shows that long-lived, X-ray-bright TDEs can be explained within the same framework as shorter-lived events, with the primary difference encoded in the viscous timescale $t_{\rm visc}$ (tied to angular momentum transport efficiency). The analysis yields time-resolved disk properties such as mass surface density $\Sigma(r,t)$ and accretion rate, informs QPE modeling by revealing tensions between observed eruptions and disk-property evolution (e.g., the 2014 eruption absence), and underscores the value of time-dependent spectral fitting for interpreting X-ray TDEs.

Abstract

We present the implementation of a fully time-dependent relativistic disk model-based on the light curve fitting package FitTeD-into the X-ray spectral fitting environment, pyXspec. This implementation enables simultaneous fitting of multi-epoch and multi-wavelength spectral data, where the only free parameters are those describing the black hole and the initial conditions, while the subsequent evolution is governed by the dynamical equations of an evolving accretion flow. We use it fit seven epochs of X-ray spectra and two epochs of UV spectra of the 'long-lived' tidal disruption event (TDE) and quasi-periodic eruption (QPE) source GSN 069, from 2010 through late-2019. Our results show that such 'long-lived', X-ray-bright TDEs-of which GSN 069 is a prime, but not unique, example-can naturally be explained within the same framework as events with shorter-lived X-ray emission, like ASASSN-14li and AT2019dsg. Their distinction lies in the `viscous' timescale parameter-tied to the disk's angular momentum transport efficiency-which should be treated as a free parameter when modeling the disk evolution of transient events. We examine the implications for QPE models by tracking the time evolution of disk properties such as mass surface density and accretion rate. We argue that existing QPE models may not be able to reproduce the observed connection between the presence (2018) or absence (2014) of eruptions and the disk properties. In the context of orbiter-disk collision models, the change in mass surface density appears insufficient to explain the needed variation in the eruption's temperature. The absence of eruptions in GSN 069 in 2014 remains a challenge for QPE models.

Figures (2)

• Figure 1: Schematics of the ray tracing geometry. The coordinates $b_x$ and $b_y$ lie in the observer plane; $x$ and $y$ in the disk plane. A schematic photon trajectory from the inner disk is shown, observer-disk inclination angle is denoted $i$.
• Figure 2: Schematics of the implementation of relativist time-dependent disk framework into FitTeD; from the seven free parameters, to the disk's spectral energy distribution as a function of time. See text in §\ref{['sec:theory']} for details.