The Arctic is estimated to have warmed up to four times faster than the rest of the globe since the 1980s. There is significant interest in understanding the mechanisms by which such warming may impact weather and climate at lower latitudes. One such mechanism is the "stratospheric pathway"; Arctic warming is proposed to induce a wave-driven weakening of the stratospheric polar vortex, which may subsequently impact large-scale tropospheric circulation. However, recent comprehensive model studies have found systematic differences in both the magnitude and sign of the stratospheric response to Arctic warming. Using a series of idealized model simulations, we show that this response is sensitive to characteristics of the warming and mean polar vortex strength. In all simulations, imposed polar warming amplifies upward wave propagation from the troposphere, consistent with comprehensive models. However, as polar warming strength and depth increases, the region through which waves can propagate is narrowed, inducing wave breaking and deceleration of the flow in the lower stratosphere. Thus, the mid-stratosphere is less affected, with reduced sudden stratospheric warming frequency for stronger and deeper warming compared to weaker and shallower warming. We also find that the sign of the stratospheric response depends on the mean strength of the vortex, and that the stratospheric response in turn plays a role in the magnitude of the tropospheric jet response. Our results help explain the spread across multimodel ensembles of comprehensive climate models. In the last four decades, the Arctic has warmed significantly faster than the rest of the world. Such warming has been suggested to generate waves in the atmosphere that move up into the stratosphere, where they break. If this were particularly powerful, it could disrupt and slow the typically strong and stable band of stratospheric winds encircling the winter pole, with potential consequences for surface weather and climate. However, state-of-the-art models disagree on how this "stratospheric polar vortex" responds to Arctic warming, even in terms of whether it will become weaker or stronger. In this study, our simplified climate model simulations indicate that the stratospheric response depends on certain characteristics of the Arctic warming. As it increases in strength and vertical extent, upward-moving waves are confined and forced to break lower down, resulting in fewer disruptions of the vortex above. We also find that the state of the vortex influences whether it weakens or strengthens, with implications for near-surface winds. Our results help explain the range of stratospheric responses simulated by more complex models. In a simple GCM, the sign and magnitude of the stratospheric polar vortex response to Arctic warming is highly sensitive to the basic state The stratospheric response also depends on the strength and vertical extent of Arctic warming in the troposphere Stronger/deeper warming narrows the lower stratospheric waveguide, slowing winds at lower levels than with weaker/shallower warming
