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<jats:title>Abstract</jats:title> <jats:p>The astrophysical origin of gravitational wave (GW) events discovered by LIGO/VIRGO remains an outstanding puzzle. In active galactic nuclei (AGNs), compact-object binaries form, evolve, and interact with a dense star cluster and a gas disk. An important question is whether and how binaries merge in these environments. To address this question, we have performed one-dimensional <jats:italic>N</jats:italic>-body simulations combined with a semianalytical model that includes the formation, disruption, and evolution of binaries self-consistently. We point out that binaries can form in single–single interactions through the dissipation of kinetic energy in a gaseous medium. This “gas-capture” binary formation channel contributes up to 97% of gas-driven mergers and leads to a high merger rate in AGN disks even without preexisting binaries. We find the merger rate to be in the range of ∼0.02–60 Gpc<jats:sup>−3</jats:sup> yr<jats:sup>−1</jats:sup>. The results are insensitive to the assumptions on the gaseous hardening processes: we find that once they are formed, binaries merge efficiently via binary–single interactions even if these gaseous processes are ignored. We find that the average number of mergers per black hole (BH) is 0.4, and the probability for repeated mergers in 30 Myr is ∼0.21–0.45. High BH masses due to repeated mergers, high eccentricities, and a significant Doppler drift of GWs are promising signatures that distinguish this merger channel from others. Furthermore, we find that gas-capture binaries reproduce the distribution of low-mass X-ray binaries in the Galactic center, including an outer cutoff at ∼1 pc due to the competition between migration and hardening by gas torques.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The role of ideal-MHD instabilities in a prominence eruption is explored through 2D and 3D kinematic analysis of an event observed with the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory between 22:06 UT on 2013 February 26 and 04:06 UT on 2013 February 27. A series of 3D radial slits are used to extract height–time profiles ranging from the midpoint of the prominence leading edge to the southeastern footpoint. These height–time profiles are fit with a kinematic model combining linear and nonlinear rise phases, returning the nonlinear onset time (<jats:italic>t</jats:italic> <jats:sub>nl</jats:sub>) as a free parameter. A range (1.5–4.0) of temporal power indices (i.e., <jats:italic>β</jats:italic> in the nonlinear term <jats:inline-formula> <jats:tex-math> <?CDATA ${(t-{t}_{\mathrm{nl}})}^{\beta }$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjab92a0ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) are considered to prevent prescribing any particular form of nonlinear kinematics. The decay index experienced by the leading edge is explored using a radial profile of the transverse magnetic field from a PFSS extrapolation above the prominence region. Critical decay indices are extracted for each slit at their own specific values of height at the nonlinear phase onset (<jats:italic>h</jats:italic>(<jats:italic>t</jats:italic> <jats:sub>nl</jats:sub>)) and filtered to focus on instances resulting from kinematic fits with <jats:inline-formula> <jats:tex-math> <?CDATA ${\chi }_{\mathrm{red}}^{2}\lt 2$?> </jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjab92a0ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> (restricting <jats:italic>β</jats:italic> to 1.9–3.9). Based on this measure of the critical decay index along the prominence structure, we find strong evidence that the torus instability is the mechanism driving this prominence eruption. Defining any single decay index as being “critical” is not that critical because there is no single canonical or critical value of decay index through which all eruptions must succeed.</jats:p>