Dynamics of the Upwind Heliosphere Due to Data-Driven, Solar Wind and Magnetic Field Variations and Implications for Wave Propagation into the Very Local Interstellar Medium

We introduce an updated, time-dependent treatment to the split-tail ("croissant-like") heliosphere model with data-driven solar wind conditions at 1 au, to study the evolution of the heliosphere with solar-cycle variations in plasma speed, plasma density, and magnetic field intensity. The model produces a sub-Alfv\'enic and low beta region, not observed by the Voyagers, ~15 au ahead of the heliopause. The simulated magnetic field and radial flow depart from Voyager observations in this region, indicating that time-dependent effects alone are not sufficient to understand this regime of the heliosheath. We decompose fast and slow magnetosonic wave modes from time-dependent plasma pulse structures in the heliosheath, using a linear Riemann variable analysis, for the first time. Fast mode waves can both reflect at the heliopause and transmit into the interstellar medium, and their speeds are unaffected by the low beta plasma regime in front of the heliopause. The model reproduces the pf2 jump in the magnetic field at ~2020 in the interstellar medium and we attribute the source of pressure fronts observed by Voyager 1 in the interstellar medium, and pressure pulses observed by Voyager 2 in the heliosheath, to fast mode waves that are commonly recurring solar-cycle features. The presence of fast mode waves drive a highly variable termination shock, with average radial speeds of 6.05 au yr$^{-1}$ $\pm$ 5.37 au yr$^{-1}$ in the New Horizons direction. We find that the termination shock has a sinusoidal-like oscillatory motion in the rising phase of the solar cycle, and broad inward motions during the declining phase.