Time-Dependent Photoionization of Gaseous Nebulae: The Pure Hydrogen Case

Abstract

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full time-dependent energy balance, ionization balance, and radiation transfer equations in a selfconsistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionization/thermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and non-linearly from the illuminated face of the cloud to the ionization front (IF). Ionization/thermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud.Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solutions. Moreover, even the time average ionization and temperature is different from any steady-state case. This time average is characterized by over-ionization and a broader IF with respect to the steadystate solution for a mean value of the radiation flux. Around the time average of physical conditions there is large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations.Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of non-linear propagation times for thermal/ionization fronts and equilibration times.

Multi-time-scale X-ray reverberation mapping of accreting black holes

“…In reality, the reflected flux will take some finite time to increase when the illuminating flux increases (on top of the light-crossing time). García et al (2013b) showed, albeit with a very simple model, that the reflection spectrum for a stellar-mass black hole should indeed respond very quickly (∼ 1 ns) to a rise in the illuminating flux, but the response to a drop in illuminating flux could take as long as ∼ 1 ms for a very low disc density. The different timescales occur because the rise time depends on photoionisation, but the fall time depends on recombination.…”

Disk, Corona, Jet Connection in the Intermediate State of MAXI J1820+070 Revealed by NICER Spectral-timing Analysis

“…need to be taken with caveats, such as possible contribution from thermalization time in the disk (García et al 2013) which we will implement in reltrans the near future, or even the effects from returning radiation that are shown to increase the reverberation lags by ∼50% (Wilkins et al 2020). With all this in mind, we stress that within the reverberation model, the relative trend of increasing coronal height during the state transition comes fundamentally from the change in the reverberation lag frequency.…”

Resonant Temperature Fluctuations in Nebulae Ionized by Short-period Binary Stars

“…This equation shows that RTFs increase with the amplitude of ionizing flux variations and are inversely proportional to the equilibrium temperature of the nebula T 0 and to the binary occultation period. A lower limit to k i is ω/v r , where v r is propagation velocity of radiation fronts, which is of the order of 0.1 × c (see García et al 2013). As per the results shown in Figure 2, L 1 ∼ 5 × 10 −20 ergs.s −1 .…”

“…Clearly, the qualitative results are the same for nebulae with different ionization parameters, densities, and compositions. The simulation was done with the time-dependent version of the photoionization modeling code XSTAR (Ahmed 2017; García et al 2013;Kallman and Bautista 1999).…”

“…The simulations show clear phase shifts in the heating-cooling wave for different radii in the nebula. This shift is determined by the radiation propagation time (see García et al 2013).…”