Formation and X-ray emission from hot bubbles in planetary nebulae - III. The impact of [Wolf-Rayet]-type winds

TL;DR

The paper assesses how H-deficient [Wolf-Rayet]-type winds reshape hot-bubble formation and X-ray emission in planetary nebulae by coupling self-consistent MESA wind tracks with 1D and 2D radiation-hydrodynamical simulations. Using two cooling curves for H-rich and H-deficient gas and a DEM-based X-ray synthesis that accounts for mixing between wind and nebular gas, the authors find that [WR] winds yield higher X-ray luminosities but the emissivity-weighted X-ray temperature converges to about $1$–$3 imes10^6$ K in the mixing-dominated regime, independent of the post-AGB path. Hot bubbles form later in [WR]-wind models due to enhanced radiative cooling, with the delay increasing for lower-mass progenitors; multidimensional instabilities drive mixing that regulates the bubble temperature, aligning predictions with observed soft X-ray PNe. The work reinforces the view that hydrodynamical mixing, rather than thermal conduction, is the primary mechanism shaping X-ray properties, and it highlights the importance of using self-consistent WR wind prescriptions in PN evolution studies. This has implications for interpreting X-ray detections and for understanding the late-stage evolution of low-mass stars with [WR]-type winds.

Abstract

We use radiation-hydrodynamical simulations to investigate the formation and synthetic X-ray emission of hot bubbles within planetary nebulae (PNe) driven by the powerful winds of H-deficient, [Wolf-Rayet]([WR])-type stars. Our models, based on {\sc mesa} stellar evolution tracks for 1--3 M$_{\odot}$ progenitors, adopt a recent mass-loss rate prescription for [WR] stars and incorporate the enhanced radiative cooling of their C-rich material, comparing the results against standard H-rich PN models. The enhanced mass-loss in the [WR] models leads to an accelerated post-AGB evolution and a subsequent delay in hot bubble formation compared to their H-rich counterparts, as suggested by a previous work. By computing synthetic X-ray spectra that account for the mixed H-rich and H-deficient gas phases, we find that models incorporating [WR] winds exhibit significantly higher X-ray luminosities ($L_\mathrm{X}$) than their H-rich counterparts, but the emissivity-weighted plasma temperature of the X-ray-emitting gas converge to values of $T_\mathrm{X} = [1-3] \times 10^{6}$~K, regardless of whether the system follows a [WR]-type or an H-rich post-AGB evolutionary path. Our results reinforce previous suggestions that mixing is a key mechanism in generating the observed soft X-ray emission even for PN hosting [WR] central stars.

Figures (22)

• Figure 1: Cooling rates as function of gas temperature used in the pluto simulations presented in this work. The dashed-line curve was computed adopting standard H-rich PNe abundances while the solid line represents a cooling function computed for H-deficient, C-rich [WR] abundances.
• Figure 2: HR diagram of the 1, 2, and 3 M$_\odot$ stellar evolution models created with mesa. Symbols on the tracks represent times into the evolution of the post-AGB phase. Filled and open symbols correspond to [WR] and H-rich post-AGB evolution, respectively.
• Figure 3: Mass-loss rate ($\dot{M}$, top-left), stellar wind velocity ($\varv_\infty$, top-right), ionising photon rate ($Q_0$, bottom-left), and wind mechanical luminosity ($L_\mathrm{wind}$, bottom-right) during the first 10 kyr of post-AGB evolution. Solid and dashed lines represent [WR] and H-rich models, respectively. Different colours represent different initial masses as indicated in the top-left panel.
• Figure 4: Evolution of the stellar wind luminosity ($L_\mathrm{wind}$ - top left), stellar luminosity ($L$ - top right), mass-loss rate ($\dot{M}$ - bottom left), and stellar wind velocity ($\varv_\infty$ - bottom right) as functions of the effective temperature $T_\mathrm{eff}$. Solid and dashed lines represent [WR] and H-rich post-AGB models, respectively. The dotted (blue) lines in the left panels represent the wind-momentum and mass-loss rate for a Post-AGB star with an increased mass-loss by a factor of 100 used in Schonberner2024. The properties of CSPN from the literature are shown with different symbols: stars -- [WR] CSPN, bullets -- O(H) CSPN, and crossed-circle -- Of-WR (only NGC 6543). See Table \ref{['tab:XPN']} for details.
• Figure 5: Radial profiles of the number density ($n$, upper panels) and plasma temperature ($T$, lower panels) for the post-AGB models 500 yr after the beginning of the formation of the hot bubble. Left panels show the H-rich PNe evolution while the right panels correspond to the [WR] case. Different colours correspond to different ZAMS stellar masses.