Exploring the Future of Soft X-ray Polarimetry: the Capabilities of the REDSoX Instrument for XDINS and Magnetar Studies

X-ray polarimetry offers a unique window into neutron star physics and can provide answers to questions that cannot otherwise be probed. The up-and-coming REDSoX sounding rocket mission will be the first experiment equipped with a detector able to explore polarized X-rays below 1 keV, observing in the 0.2-0.4 keV range. Although REDSoX will only be capable of short, one-off observations, it will crucially test the instrument performance. In this paper we investigate how a fully-fledged orbital mission with longer lifetime, based on an instrument design similar to REDSoX, will allow us to study thermal emission from the X-ray dim isolated neutron stars (XDINSs) and magnetars, probing their magnetic field and the physics of their outer surface layers, including vacuum effects and QED mode conversion at the vacuum resonance. We discuss the potentially observable features for promising values of the star's surface temperature, magnetic field, and viewing geometry. Assuming emission from the whole surface, we find that, for a source with a magnetic field B=5x10^{13} G and surface temperature T~10^7 K, the instrument can resolve a proton-cyclotron absorption feature in the spectrum with high significance when collecting ~25,000 counts across a single observation. Similarly, for a source with B=10^{14} G and T~10^7 K, a switch in the dominant polarization mode, caused by mode conversion at the vacuum resonance, can be detected by collecting ~25,000 counts, allowing for a long-sought observational test of the presence of QED effects. We then present two case studies for XDINS targets: RX J1856.5-3754 and RX J0720.4-3125.