Mapping reionization bubbles in the JWST era II: inferring the position and characteristic size of individual bubbles

The James Webb Space Telescope (JWST) is discovering an increasing number of galaxies well into the early stages of the Epoch of Reionization (EoR). Many of these galaxies are clustered with strong Lyman alpha (Ly$\alpha$) emission, motivating the presence of surrounding cosmic HII regions that would facilitate Ly$\alpha$ transmission through the intergalactic medium (IGM). Detecting these HII "bubbles" would allow us to connect their growth to the properties of the galaxies inside them. Here we develop a new forward-modeling framework to estimate the local HII region size and location from Ly$\alpha$ spectra of galaxy groups in the early stages of the EoR. Our model takes advantage of the complementary information provided by neighboring sightlines through the IGM. Our forward models sample the main sources of uncertainty, including: (i) the global neutral fraction; (ii) EoR morphology; (iii) emergent Ly$\alpha$ emission; and (iv) NIRSpec instrument noise. Depending on the availability of complementary nebular lines, $\sim$ 0.006 $\unicode{x2013}$ 0.01 galaxies per cMpc$^3$, are required to be $\gtrsim$95\% confident that the HII bubble location and size recovered by our method is accurate to within $\sim$ 1 comoving Mpc. This corresponds roughly to tens of galaxies at $z\sim7\unicode{x2013}8$ in $\sim$2x2 tiled pointing with JWST NIRSpec. Such a sample is achievable with a targeted survey with completeness down to $M_{\rm UV}^{\rm min}\lesssim$ -19 $\unicode{x2013}$ -17, depending on the over-density of the field. We test our method on 3D EoR simulations as well as misspecified equivalent width distributions, in both cases accurately recovering the HII region surrounding targeted galaxy groups.