X-ray Variability and Photosphere Evolution during Accretion Disk Formation in Tidal Disruption Events

TL;DR

The paper addresses how TDEs transition from initial debris-stream interactions to a formed accretion disk and how this evolution shapes multi-wavelength emission. It employs 3D radiation-hydrodynamic simulations, including a gray, frequency-integrated run and subsequent multi-group runs across 16–20 photon groups, to track the disk formation at about $t\approx 24$ days and the associated emission. The key findings are that a rapid, optically thick reprocessing layer forms due to strong apsidal precession, the optical-UV light is largely shock-driven before disk formation, the disk forms around the circularization radius and remains geometrically thick with radiation pressure dominating, and soft X-ray emission is highly viewing-angle dependent with pre-peak variability largely due to obscuration. These results provide a cohesive picture linking debris dynamics, disk formation, and multi-wavelength observables, with implications for inferring geometry from early X-ray/optical ratios and for interpreting pre-peak color evolution in optical TDEs.

Abstract

The early time emission in tidal disruption events (TDEs) originates from both accretion and shocks, which produce photons that eventually emerge from an inhomogeneous photosphere. In this work, we model the disk formation following the debris stream self-intersection in a TDE. We track the multi-band emission using three-dimensional, frequency-integrated and multi-group radiation hydrodynamic simulations. We find a more circularized disk forms about 24 days following the initial stream-stream collision, after the mass fallback rate peaks and once the debris stream density decreases. Despite the absence of a circularized disk at early times, various shocks and the asymmetric photosphere are sufficient to drive a wide range of optical-to-X-ray ratios and soft-X-ray variability. We find that with strong apsidal precession, the first light is from the stream-stream collision. It launches an optically-thick outflow, but only produces modest prompt emission. The subsequent optical and ultraviolet (UV) light curve rise is mainly powered by shocks in the turbulent accretion flow close to the black hole. The optical-UV luminosity peaks roughly when the disk forms and shock-driven outflows subside. The disk is optically and geometrically thick, extending well beyond the circularization radius. Radiation pressure clears the polar region and leaves optically-thin channels. We obtain the broad-band spectral energy distribution (SED) directly from multi-group simulations with 16-20 frequency groups. The SED has a black body component that peaks in the extreme UV. The soft X-ray component either resembles a thermal tail, or can be described by a shallower power law associated with bulk Compton scattering. The blackbody parameters are broadly consistent with observed optical TDEs and vary weakly with viewing angle. In contrast, soft X-ray emission is highly angle-dependent.

Figures (18)

• Figure 1: Snapshots at the orbital-plane, which show gas density averaged for $\theta=90^{\circ}\pm10^{\circ}$. From left to right, and top to bottom, the times are t=2.3, 2.5, 4.8, 6.8, 15.5 and 24.9 days from the beginning of simulation, indicated by the white text in each panel. The stream-stream collision happens at around t=2.2 days. The orbital period at the injected stream pericenter radius is $P_{\rm peri}\approx0.88$ hours. In each panel, the white curve in the inset plot shows the shape of the fallback rate, and the blue marker labels the current time.
• Figure 2: First row: frequency-integrated luminosity from gray simulation. The red horizontal line labels the Eddington luminosity for $M_{\rm bh}=3\times10^{6}M_{\odot}$ assuming $10\%$ efficiency. The dotted line shows the kinetic energy flux carried by unbound gas. In all panels, the vertical dashed line marks the first stream-stream collision time. On the top, we label the three dynamical stages discussed in Section \ref{['sec:result']} : stream-stream collision, asymmetric accretion flow, disk formation . The small black triangle roughly labels the time when the polar region is cleared by radiation pressure after disk formation. Second row: the black solid line is the accretion rate estimated by the mass flux measured at ISCO. The blue solid line shows the mass fallback rate of the injected stream. In the third row, the solid black line is the total mass flux measured at the outer boundary radius, the dotted black line is the unbound mass flux. The blue solid line shows the mass fallback rate of the injected stream. The mass fluxes are normalized to the Eddington accretion rate. The fourth row shows radiation efficiency: the black solid line is using the accretion rate, and the blue solid line is using the mass fallback rate (Equation \ref{['eq:efficiency']}
• Figure 3: Gas density (upper panels) and radiation temperature (lower panels) snapshots. The plotted variables are averaged for $\phi=180^{\circ}\pm10^{\circ}$. The first, second, third columns are t=6.8, 15.5 and 24.9 days. The stream-stream collision happens at around t=2.2 days, the orbital period at the injected stream pericenter radius is $P_{\rm peri}\approx0.88$ hours. In the upper panel plots, the white arrows show the direction of velocity field, the velocity arrows are uniform and not scaled to their magnitude. In the lower panel, the beam pattern in t=6.8 day radiation temperature is due to the ray effect in the low optical depth region, which is associated with angular discretization of the radiation field.
• Figure 4: The eccentricity (Equation \ref{['eq:ecc']}) calculated at the pericenter radius $R=r_{\rm T}=5.3r_{\rm S}$ (the blue solid line), the stream-stream collision radius $R=r_{\rm SI}=76.2r_{\rm S}$ (the cyan solid line) and an outer radius of $R=250r_{\rm S}=2\times10^{14}$cm (the red solid line). With the defined $|\mathbf{e}|$, the non-negligible $\theta$ and $\phi$ velocity components can lead to eccentricity greater than unity. The stream-stream collision and post-collision happen about $t=2.2-6.8$ day, the asymmetric accretion flow stage lasts $t=6.8-24.9$ days, and after which the flow evolves into the circularization accreting stage.
• Figure 5: Schematic annotation of the azimuthal- and vertical- asymmetric accretion flow structure. The snapshots are gas density, the arrows show the projected direction of flow velocity. The upper panel is the "face-on" view averaged over $\theta=90^{\circ}\pm10^{\circ}$, lower panel is an "edge-on" view averaged over $\phi=\phi_{\rm SI}\pm10^{\circ}$, where $\phi_{\rm SI}$ is the initial stream self-intersection angle. In the upper panel, the dashed line shows $\phi_{\rm SI}+90^\circ$. We defined the region of $\phi_{\rm SI}\pm90^\circ$ as the "outflow region", where the interaction of incoming fallback stream and accretion flow drives outflow. Opposite to the outflow region is the inflow region, where the outflow converges to the orbital plane. In the lower panel, the tilted dashed lines correspond to $\theta=90\pm30^{\circ}$, which roughly separates the disk and polar region. The $\theta$ and $\phi$ range for each angular section is summarized in Table \ref{['tab:angular_sec']}