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X-ray binaries are known to launch powerful accretion disk winds that canhave significant impact on the binary systems and their surroundings. Toquantify the impact and determine the launching mechanisms of these outflows,we need to measure the wind plasma number density, an important ingredient inthe theoretical disk wind models. While X-ray spectroscopy is a crucial tool tounderstanding the wind properties, such as their velocity and ionization, innearly all cases, we lack the signal-to-noise to constrain the plasma numberdensity, weakening the constraints on outflow location and mass outflow rate.We present a new approach to determine this number density in the X-ray binaryHercules X-1 by measuring the speed of the wind ionization response totime-variable illuminating continuum. Hercules X-1 is powered by a highlymagnetized neutron star, pulsating with a period of 1.24 s. We show that thewind number density in Hercules X-1 is sufficiently high to respond to thesepulsations by modeling the ionization response with the time-dependentphotoionization model TPHO. We then perform a pulse-resolved analysis of thebest-quality XMM-Newton observation of Hercules X-1 and directly detect thewind response, confirming that the wind density is at least $10^{12}$cm$^{-3}$. Finally, we simulate XRISM observations of Hercules X-1 and showthat they will allow us to accurately measure the number density at differentlocations within the outflow. With XRISM we will rule out $\sim3$ orders ofmagnitude in density parameter space, constraining the wind mass outflow rate,energetics, and its launching mechanism.

Constraining the Number Density of the Accretion Disk Wind in Hercules X-1 Using its Ionization Response to X-ray Pulsations