A local, topology-independent parameterization of quasar IGM damping wings

TL;DR

The paper addresses the stochasticity in quasar damping wings caused by IGM topology during reionization and introduces two local pre-quasar HI labels, $N_\mathrm{HI}^\mathrm{DW}$ and $r_\mathrm{bubble}$, plus the quasar lifetime $t_\mathrm{Q}$, to form a topology-independent three-parameter framework. It demonstrates that the damping-wing shape is effectively determined by these local quantities, yielding a one-parameter-like behavior when evaluated at a fixed reference velocity and dramatically reducing sightline-to-sightline scatter compared with global$\,$$\langle x_\mathrm{HI} \rangle$ parameterizations. The authors validate their approach with realistic Nyx+semi-numerical simulations and an analytic toy bubble model, showing strong agreement in the damping-wing region across reionization topologies. This framework enables robust, topology-agnostic extraction of local information from damping wings and, when paired with a topology-specific prior, can constrain both the timing and topology of reionization, with potential extension to galaxy damping wings.

Abstract

Lyman-$α$ damping wings towards quasars provide a unique probe of reionization because their strength correlates strongly with the global volume-averaged neutral hydrogen (HI) fraction of the intergalactic medium (IGM). Cosmic variance in the IGM, however, is a major source of stochasticity since the local neutral environment around a quasar varies significantly even at fixed global neutral fraction. We show that the IGM damping wing carries additional information about this local ionization topology, unexploited by current analysis frameworks. We introduce a set of two new physically motivated summary statistics encoding the local information about the HI distribution in the IGM before it is altered by ionization radiation from the quasar, encompassing 1) the HI column density, weighted by a Lorentzian profile mimicking the frequency dependence of the Lyman-$α$ cross section, and 2) the distance from the quasar to the first neutral patch. This description, when combined with the quasar's lifetime as a third parameter, reduces the IGM transmission scatter in the damping wing region of the spectrum to $\lesssim 1\,\%$ across the full range of physical parameter space. We introduce a simple procedure for generating synthetic HI sightlines around quasars and demonstrate that the resulting damping wing profiles are statistically indistinguishable from a realistic reionization topology. This opens the door for optimally extracting the salient local information encoded in the imprint in a model-independent fashion. In the context of a specific reionization model, measurements of these local parameters can be translated into constraints on the global timing of reionization, but in addition, they provide information about the reionization topology, hitherto unused. A marginally modified version of our framework can also be employed in the context of damping wings towards galaxies.

Figures (10)

• Figure 1: Lyman-$\alpha$ transmission and physical fields for an example Nyx sightline combined with a semi-numerical $x_\mathrm{HI}$ skewer extracted from a $\langle x_\mathrm{HI} \rangle = 0.65$ topology (left panels/blue lines; see Section \ref{['sec:sims']}) and an analytical $x_\mathrm{HI}$ skewer generated according to our toy bubble prescription (right panels/red lines; see Section \ref{['sec:bubble_model']}), before (dark) and after (light colors) a quasar has been shining for $t_\mathrm{Q} = 10^6\,\mathrm{yr}$. The panels show from top to bottom the Lyman-$\alpha$ transmission field, the distance-weighted HI column density $N_\mathrm{HI}^\mathrm{DW}$ as a function of the upper integration limit $r_\mathrm{max}$, the HI density field $n_\mathrm{HI}$ (also shown in units of $x_\mathrm{HI} \cdot \Delta$), including its distance-weighted pre-quasar version (black dash-dotted line), the HI fraction $x_\mathrm{HI}$, the overdensity field $\Delta$, and the temperature field $T$. Our fiducial integration range for the distance-weighted HI column density $N_\mathrm{HI}^\mathrm{DW}$ is highlighted by the grey-shaded region, and the horizontal dashed line marks the value of $\log_{10}N_\mathrm{HI}^\mathrm{DW}/\mathrm{cm}^{-2} = 20.1$ corresponding to this integration range. The vertical dotted lines mark the location $r_\mathrm{bubble} = 8\,\mathrm{cMpc}$ of the first neutral bubble in the pre-quasar sightline.
• Figure 2: IGM transmission values at the fixed reference velocity offset $v_\mathrm{T} = 2000\,\mathrm{km}/\mathrm{s}$ versus transmission values at a number of velocities offsets $v = v_\mathrm{T} + \Delta v$ away from this reference offset. Solid curves and shaded regions depict the median as well as the $68$- and $95$-percentile scatter of these transmission values, respectively, among $852 \times 21 \times 51$ realistic IGM transmission profiles simulated according to the description in Section \ref{['sec:sims']}. For reference, we are also showing the trivial one-to-one relation for $v = v_\mathrm{T}$ as a dashed black line.
• Figure 3: Median and $68$-percentile scatter of the simulated IGM transmission profiles based on our semi-numerical reionization topology in the global $(\langle x_\mathrm{HI} \rangle, t_\mathrm{Q})$ parameterization. The profiles are shown on a representative grid of $(\langle x_\mathrm{HI} \rangle, t_\mathrm{Q})$ parameter values.
• Figure 4: Median and $68$-percentile scatter of the simulated IGM transmission profiles based on our semi-numerical reionization topology in the local $(N_\mathrm{HI}^\mathrm{DW}, r_\mathrm{bubble}, t_\mathrm{Q})$ parameterization. The profiles are shown on a representative grid of $(N_\mathrm{HI}^\mathrm{DW}, r_\mathrm{bubble}, t_\mathrm{Q})$ parameter values for the most typical combinations of $N_\mathrm{HI}^\mathrm{DW}$ and $r_\mathrm{bubble}$ across the full parameter space.
• Figure 5: Sightline-to-sightline scatter of the IGM damping wing as a function of astrophysical parameter space in the global $(\langle x_\mathrm{HI}\rangle, t_\mathrm{Q})$-parameterization. The scatter is quantified as half the $68$-percentile width $\sigma(t(v = v_\mathrm{T}))$ of the distribution of IGM transmission values at $v = v_\mathrm{T}$ among all sightlines at a given location in $(\langle x_\mathrm{HI}\rangle, t_\mathrm{Q})$-parameter space.