Modeling Emission-Line Surface Brightness in a Multiphase Galactic Wind: An O VI Case Study

Abstract

We present a fast and robust analytic framework for predicting surface brightness (SB) of emission lines in galactic winds as a function of radius up to $\sim 100$ kpc out in the circum-galactic medium. We model multi-phase structure in galactic winds by capturing emission from both the volume-filling hot phase (T $\sim 10^{6-7}$ K) and turbulent radiative mixing layers that host intermediate temperature gas at the boundaries of cold clouds (T $\sim 10^4$ K). Our multi-phase framework makes significantly different predictions of emission signatures compared to traditional single-phase models. We emphasize how ram pressure equilibrium between the cold clouds and hot wind in supersonic outflows, non-equilibrium ionization effects, and energy budgets other than mechanical energy from core-collapse supernovae affect our SB predictions and allow us to better match OVI observations in the literature. Our framework reveals that the optimal galactic wind properties that facilitate OVI emission observations above a detection limit of $\sim 10^{-18} \ \rm{erg \ s^{-1} \ cm^{-2} \ arcsec^{-2}}$ are star formation rate surface density $1 \lesssim \dotΣ_{\ast} \lesssim 20 \ M_{\odot}\ \rm{yr^{-1}\ kpc^{-2}}$, hot phase mass loading factor $η_{\rm M,hot} \sim 0.2 - 0.4$, and thermalization efficiency factor $η_{\rm E} \gtrsim 0.8$. These findings are consistent with existing observations and can help inform future target selections.

Figures (14)

• Figure 1: O VI SB profile predictions at different $\eta_{\rm{M,hot}}$ for the single-phase galactic wind model in Thompson_2016 (dashed) and the multiphase framework presented in this work based on FB_2022 and Chen_2023 (solid). The single-phase model predicts a region of constant O VI SB at small radius. The multiphase framework does not exhibit this feature and instead produces a profile that declines smoothly with radius. We explain key features in detail and compare these two setups in \ref{['subsec:single_vs_multi']}. Emission signatures like SB profiles can serve as diagnostics for the phase structure of galactic winds seen in observations and help distinguish between single- and multi-phase models.
• Figure 2: O VI SB profile predictions from our multiphase galactic wind framework is sensitive to hot-phase parameters including SFR (left), $\eta_{\rm{M,hot}}$ (middle), and $\eta_{\rm{E}}$ (right). The fiducial parameter choices are SFR = $40 \ \rm{M_{\odot} \ yr^{-1}}$, $\eta_{\rm{M,hot}}=0.2$, $\eta_{\rm{E}}=1.0$, $\eta_{\rm{M,cold}}=0.1$, and $M_{\rm cloud} = 10^5 \ M_{\odot}$ except when a parameter is explicitly varied. We motivated these fiducial parameter choices in \ref{['sec:results']}. The black curves across the 3 panels are identical and show the O VI SB profile generated using the fiducial parameters. We explain how O VI SB profile depend on these hot-phase parameters in \ref{['subsec:hot_phase_pars']}. These dependencies have profound consequences on observations, which will be explored in \ref{['sec:discussions']}.
• Figure 3: Similar to \ref{['fig:SB_profile_vs_hot_phase_params']}, but here we vary cold-phase parameters in our multiphase framework including the cold phase mass loading factor $\eta_{\rm{M,cold}}$ (left) and single cloud mass $M_{\rm{cloud}}$ (right). Increasing $\eta_{\rm{M,cold}}$ steepens the slope of the SB profiles, while increasing $M_{\rm{cloud}}$ has the opposite effect. These trends are explained in detail in \ref{['subsec:cold_phase_pars']}.
• Figure 4: The ratio of ram and thermal pressure $\left. P_{\rm ram}\right/ P_{\rm th}$ profile computed from the FB_2022 model with different $\eta_{\rm M,hot}$ (top; $\eta_{\rm{E}} = 1.0$ and SFR = 40 $M_{\odot} \ \rm{yr^{-1}}$) and SFR (bottom; $\eta_{\rm{E}} = 1.0$ and $\eta_{\rm{M,hot}} = 0.2$). $\left. P_{\rm ram}\right/ P_{\rm th} = \gamma \mathcal{M}_{\rm rel}^2$, where $\mathcal{M}_{\rm rel} = v_{\rm{rel}} / c_{\rm{s,hot}}$ is the relative Mach number between the cold clouds and the hot wind, and $\gamma$ is the adiabatic index. Both panels indicate that ram pressure is always a crucial component of the pressure balance between the cold cloud and the hot wind. Since O VI SB $\propto n^2 \propto P^2$, accounting for ram pressure significantly boosts O VI SB and is crucial for explaining observational results in Hayes_2016.
• Figure 5: Comparison between O VI SB profiles generated by our multiphase wind framework and observational result in Hayes_2016 (black). In solid blue, we plot the O VI SB profile generated by our framework using fiducial parameters (SFR = $40 \ \rm{M_{\odot} \ yr^{-1}}$, $\eta_{\rm{M,hot}}=0.2$, $\eta_{\rm{M,cold}}=0.1$, and $M_{\rm cloud} = 10^5 \ M_{\odot}$) and only accounting for thermal pressure. This under-predicts the observation by more than 2 orders of magnitude. As discussed in \ref{['subsec:ram_pressure']} and \ref{['fig:fb22_pressure_mrel_profiles']}, accounting for ram pressure significantly boosts O VI SB. This is verified by the dotted blue curve, which is much closer to observation but still off by a factor of $\sim 3$. One way to bridge this difference is to choose $\eta_{\rm E}=2.0$ (yellow), which yields excellent agreement with observation. Physically, $\eta_{\rm E}=2.0$ means there are energy sources other than the mechanical energy of supernova explosions that powers the emission. In \ref{['subsec:extra_energy']}, we discuss possible energy source including radiation and merger-induced thermal energy and argue that $\eta_{\rm E}=2.0$ is reasonable.