Late-Time Evolution of Magnetized Disks in Tidal Disruption Events

TL;DR

This work addresses the apparent stability of late-time TDE disks despite standard radiative-instability expectations by adopting a magnetized, magnetic-pressure–dominated 1D α-disk model. The authors solve the nonlinear diffusion equation with ν determined by magnetic stresses, and they also derive a self-similar solution to capture late-time behavior, then compare with a conventional linear viscosity prescription. They find that magnetized disks produce UV light curves that decay roughly as a power law in time, with UV emission persisting for decades, and show that a linear viscosity model with μ_l = 0 can reproduce these light curves, revealing a degeneracy that aids analytical modeling. The study also explores observational prospects, including the potential to detect fossil TDEs with ULTRASAT, and discusses a possible link between TDE disks and quasi-periodic eruptions via disk–EMRI interactions, offering a framework to extract SMBH and stellar parameters from late-time data and motivating future work that couples gas, radiation, and magnetic pressures.

Abstract

In classic time-dependent 1D accretion disk models, the inner radiation pressure dominated regime is viscously unstable. However, late-time observations of accretion disks formed in tidal disruption events (TDEs) do not exhibit evidence of such instabilities. The common theoretical response is to modify the viscosity parametrization, but typically used viscosity parametrization are generally ad hoc. In this study, we take a different approach, and investigate a time-dependent 1D $α$-disk model in which the pressure is dominated by magnetic fields rather than photons. We compare the time evolution of thermally stable, strongly magnetized TDE disks to the simpler linear viscosity model. We find that the light curves of magnetized disks evolve as $L_{\rm UV}\propto t^{-5/6}$ for decades to centuries, and that this same evolution can be reproduced by the linear viscosity model for specific parameter choices. Additionally, we show that TDEs remain UV-bright for many years, suggesting we could possibly find fossil TDEs decades after their bursts. We estimate that ULTRASAT could detect hundreds of such events, providing an opportunity to study late-stage TDE physics and supermassive black hole (SMBH) properties. Finally, we explore the connection between TDE disks and quasi-periodic eruptions (QPEs) suggested by recent observations. One theoretical explanation involves TDE disks expanding to interact with extreme mass ratio inspirals (EMRIs), which produce X-ray flares as the EMRI passes through the disk. Our estimates indicate that magnetized TDE disks should exhibit QPEs earlier than those observed in AT2019qiz, suggesting that the QPEs may have begun before their first detection.

Figures (14)

• Figure 1: Late-time UV light curve observations from Swift/UVOT for various TDEs Mummery+2024. Data are presented for the uvw2 filter. The light curves have been binned and averaged over $20$-day intervals, with error bars representing (asymmetric) 1$\sigma$ uncertainties. The observations generally show smoothly evolving late-time emission without the dramatic instabilities predicted by unmagnetized $\alpha$-disk models (ShenMatzner2014PiroMockler2024, with the possible exception of AT2018dyb).
• Figure 2: A comparison between the Gaussian initial condition (solid) to the source function (dashed). The top panel shows the surface density as a function of radius at different times, while the bottom panel presents the light curves at different wavelengths (NUV: $\lambda=250 \text{nm}$, FUV: $\lambda=150 \text{nm}$, and X-ray: $hf=300 \text{eV}$). The masses of the SMBH and the disrupted star are $M_\bullet=10^6M_\odot$ and $M_\star=0.3M_\odot$ respectively, and $\alpha=0.1$.
• Figure 3: Surface density $\Sigma$ plotted against dimensionless radius $R/r_{\rm g}$ at late times. The solid curves are the numerical solution of the disk diffusion equation while the dashed curves are the self-similar solution (Eq. \ref{['eq:similaritysol']}). The masses of the SMBH and the disrupted star are $M_\bullet=10^6M_\odot$ and $M_\star=0.3M_\odot$ respectively, and $\alpha=0.1$. The self-similar solutions provide a good match to numerical integration of the disk diffusion equation at late times and large radii.
• Figure 4: Surface densities plotted against radius at different times, for the magnetized viscosity (solid) and the linear viscosity (dashed). The power laws of the linear viscosity are $\mu_{\rm l}=\{3/2,5/9,0,-3/2\}$ from the top panel to the bottom panel. The normalization factor of the linear parametrization $\nu_{0,\rm l}$ is determined by equating the outer radius of the two disks after 1 year. The choice of $M_\bullet$, $M_\star$, and $\alpha$ is the same as in \ref{['fig:self-similar solution']}. The best match between the surface densities occurs for $\mu_{\rm l}=5/9$ in the inner regions of the disk and $\mu_{\rm l}=0$ in the outer regions.
• Figure 5: Light curves for near-UV, far-UV and X-ray bands (top panel to bottom panel) with Gaussian initial conditions for magnetized viscosity solutions (solid red) and linear viscosity solutions (dashed), with $\mu_{\rm l}=\{3/2,5/9,0,-3/2\}$ (green, black, blue, brown). The normalization factor of the linear parametrization $\nu_{0,\rm l}$ is determined by equating the outer radius of the disk after 1 year. The choice of $M_\bullet$, $M_\star$, and $\alpha$ is the same as in \ref{['fig:self-similar solution']}. The light curves of the linear and magnetized viscosity models appear very similar for $\mu_{\rm l}=0$, but quite distinct for other values of $\mu_{\rm l}$.