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tokens: y ∈ [−50, 50] L 0 yieldswhich is in good agreement with the growth rate shown in Figure 16 . Evidently, the growth rate for this instability derived in the Boussinesq regime, which is admittedly inapplicable in our simulation, produces values that are in good agreement with our simulation results. Thus, both the fastest growing parallel and perpendicular wavenumbers and growth rates of the instability observed in our simulation are in reasonable agreement with theoretical predictions of these same quantities in the undular instability. 3.6. Interaction of the Lobes The emergence of magnetic lobes was found by Archontis et al. ( 2013 ) to result in significant reconnection and a jet-like disturbance in the corona. In our simulation, we see a similar event around t = 820 t 0 that may affect the linear evolution of the undular mode, which stops around the same time. Figure 17 shows the magnetic energyand kinetic energyin the corona as a function of time. The decrease in the magnetic energy that starts around t = 824 t 0 (green line) corresponds approximately to the same magnitude increase in the kinetic energy which peaks at t = 864 t 0 (blue line). In Figure 18 , we plot a series of field lines, seeded along a vertical line at ( x = y = 0, z > 0) in the corona on top of vertical cuts of the vertical velocity V z . The field lines are colored by B z . Early in the interaction, at t = 824 t 0 , the field lines only barely extend above the photosphere. They slowly rise, and it is clear that by t = 860 t 0 , the two primary lobes are interacting, and field lines with opposite signs of B z begin to reconnect. This creates a significant upflow, as the newly reconnected concave up field lines release their tension. This upflow is only seen low down in the corona before t = 860 t 0 , and with much smaller magnitude, since the field is not significantly expanding into the corona, but by t = 880 t 0 and t = 900 t 0 there is a clear upflow visible in the corona along with a concave-down arcade overlying the interacting loops. This type of event likely represents an Ellerman bomb, which is associated with this type of topology (Pariat et al. 2004 , 2006 , 2009 ; Isobe et al. 2007 ; Archontis Hood 2009 ; Danilovic 2017 ). Figure 17. Magnetic energy (black) and kinetic energy (red) in the corona as a function of time. The green (blue) line at t = 824 t 0 ( t = 864 t 0 ) shows the local maximum of the magnetic (kinetic) energy. Figure 18. Field lines colored by B z overplotted on a vertical plane of V z and a photospheric magnetogram at several times before and during the reconnection event. 4. Conclusions In this paper, we simulated the buoyant rise and emergence of an untwisted toroidal flux rope from deep in the convection zone. The flux rope is able to rise coherently through the convection zone, emerge through the photosphere, and form a relatively large (≈40 Mm across) active region. The emergence mechanism of our flux rope is identified to be the undular