Stellar Stripping and Disruption in Disks around Supermassive Black Hole Binaries: Repeating nuclear transients prior to LISA events

Schematic of the circumbinary disk (CBD) plus star around a 3:1 mass ratio supermassive black hole binary at the critical separation $a_{\crit}$ (Eq. \ref{Eq:acrit}), where the maximum extent of the tidal radius of the binary (red-dashed line) is equal to the distance to the edge of the circumbinary cavity. At this separation the star begins to be tidally stripped once per conjunction of the secondary black hole and star. Each binary component may have its own accretion disk (minidisk) not shown.

\textbf{Left, Fiducial:} Critical semi-major axes for disruption ($a_{\crit}$, cyan line) compared to those for binary-disk decoupling ($a_{\dec D}$, orange) and binary-stellar migration decoupling ($a_{\dec M}$, purple), for fiducial values and the \citealt{Sirko_Goodman:2003} disk models. $a_{\crit}$ is also drawn for different mass ratios (q=0.1, dotted cyan and $q=0.39$ dashed cyan), but the variation is within the width of the $q=1$ line. {\em Disruption is allowed when the cyan line falls above the purple and orange lines.} \textbf{Right, Parameter Dependence:} Critical disruption separations drawn for three stellar densities parameterized by the stellar radius. The shaded regions indicate ranges of possible decoupling separations given a range of disk parameters. The solid (dashed) lines show decoupling radii for fiducial disk parameters for the \citealt{Sirko_Goodman:2003} (\citealt{SS73}) disk model. Dotted orange and purple lines denote disk models with the same parameters in the extremes of the shaded regions, highlighting the inverse dependence of the two types of decoupling on disk parameters.

\textbf{Left, Fiducial:} Gravitational wave properties of the SMBHB when stellar-stripping begins. The solid black line represents the sensitivity of LISA while the gray lines are SMBHB inspiral tracks for the labeled binary masses, mass ratio, and redshift. The vertical cyan line is the critical rest-frame frequency where the fiducial star at $\rcav=2a$ ($N_{\cav}=2$) will begin to be stripped, for all SMBH masses (corresponding to the cyan lines in Fig. \ref{Fig:acrit}). The dotted cyan lines show how this moves down and to the left with increasing redshift. The cyan stars show where disruption would begin for the different binary masses at $z=1$ (the largest star being the fiducial case). Above the purple-orange dashed line, disk-or migrator-decoupling may occur before the disruption begins (Fig. \ref{Fig:acrit}). \textbf{Right, Parameter Dependence:} The same as the left panel but demonstrating dependence on source redshift, lower stellar density (thin cyan $R=3 R_{\mathrm{MS}}$ line), or increased CBD cavity size (dashed $\rcav=4a$ vertical line).

Timescale to strip material from the star $\tau_*$, Time between stripping events $T_{\rep}$, and the SMBH binary orbital period at the onset of stripping $P_{\crit}$ vs. cavity size. Each of the plotted quantities is independent of SMBHB mass. The shaded blue range represents the weak binary mass ratio ($q \in [0.1,1]$) dependence of the time between stripping events.

Result of solving Eq. (\ref{Eq:mDEQ}) including tidal stripping from both the primary and secondary SMBHs, up to the point of full disruption, for a $\gamma=5/3$ polytropic star and the fiducial system (Table \ref{Table:Fid}). This shows the last $32$ encounters (stripping events) representing the final $\approx 27$ days before full disruption, during which time the majority of the star is stripped. The onset of tidal stripping begins at $t=0$, $\approx21$ years before full disruption at time $t_c$. The SMBHB will merge $\approx246$ years after the full disruption. Times are in the source frame. Results are representative of solutions with $N_{\cav}=2$ and intermediate binary mass ratios (see \S\ref{Ss:scalings}).

Result of solving Eq. (\ref{Eq:mDEQ}) including tidal stripping from both the primary and secondary SMBHs, up to the point of full disruption, for a $\gamma=5/3$ polytropic star and the fiducial system (Table \ref{Table:Fid}). This shows the last $32$ encounters (stripping events) representing the final $\approx 27$ days before full disruption, during which time the majority of the star is stripped. The onset of tidal stripping begins at $t=0$, $\approx21$ years before full disruption at time $t_c$. The SMBHB will merge $\approx246$ years after the full disruption. Times are in the source frame. Results are representative of solutions with $N_{\cav}=2$ and intermediate binary mass ratios (see \S\ref{Ss:scalings}).

\textbf{Left:} The average stellar-stripping rate (black line) and solution to Eq. (\ref{Eq:Mring}) for the amplitude of the accretion rate onto the binary (orange), computed from the beginning of the disruption process to full stellar disruption (grey-dashed line). \textbf{Left:} Continuation of the left panel after full stellar disruption and the final decay. We use fiducial system parameters (Table \ref{Table:Fid}) corresponding to the event modeled in Fig. \ref{Fig:disrupt}.

\textbf{Left:} The average stellar-stripping rate (black line) and solution to Eq. (\ref{Eq:Mring}) for the amplitude of the accretion rate onto the binary (orange), computed from the beginning of the disruption process to full stellar disruption (grey-dashed line). \textbf{Left:} Continuation of the left panel after full stellar disruption and the final decay. We use fiducial system parameters (Table \ref{Table:Fid}) corresponding to the event modeled in Fig. \ref{Fig:disrupt}.

Purple-yellow colored contours (with highlighted values in black) of log$_{10}$ of the maximum accretion rate enhancement for a steady-state $\alpha$-disk and the system parameters labeled in the figure. Thick solid lines show the limits of where disk properties allow consistent migration of the star to the critical disruption radius. Red lines delineate the space via condition (\ref{Eq:mstr-mdisk-conditions}), green is the gap opening condition of \citep{Crida+2006}, orange is for disk-decoupling and purple is for migrator-decoupling (See \S\ref{S:Setup}). Arrows point in the direction where consistent solutions exist. The upper-right region with 100s-1000s$\times$ enhancements in the accretion rate is allowed for the parameters chosen here. The cyan star denotes the fiducial system, for which Figures \ref{Fig:disrupt} and \ref{Fig:Acc_Mdodel_Ex} show example evolutions.