Direct Collapse Pre-supermassive Black Hole Objects as Ly$\alpha$ Emitters

The Direct Collapse scenario to form the supermassive black hole (SMBH) seeds offers the most promising way to explain the origin of quasars at $z>7$. Assuming atomic primordial gas, can Ly$\alpha$ photons escape from the central regions of the collapse and serve as a diagnostic for the detection of these pre-SMBH objects? Models of spherical collapse have found these photons to be trapped and destroyed. We use Ly$\alpha$ radiation transfer within the inflow-outflow geometry, based on earlier zoom-in cosmological modeling involving radiation transfer and magnetic forces. Adopting geometry that includes ongoing disk and spherical accretion, and formation of a biconical outflow funnel, we obtain the formation of a dense radiatively driven expanding shell. The Ly$\alpha$ transfer is performed using a Monte Carlo algorithm, accounting for the destruction of Ly$\alpha$ photons and the emergence of two-photon emission. We find that a substantial fraction of Ly$\alpha$ photons can escape through the funnel and calculate the line profiles, the line peak velocity shift, asymmetry, and cuspiness, by varying basic model parameters. The escaping Ly$\alpha$ emission is anisotropic and sensitive to the overall inflow-outflow geometry. The escaping fraction of Ly$\alpha$ radiation exceeds 95% from a $z=10$ pre-SMBH object -- in principle detectable by the JWST NIRSpec in the MOS mode, during $\sim 10^4$ seconds for a $10\sigma$ signal-to-noise ratio. Moreover, comparisons with line shapes from high-$z$ galaxies and quasars allow us to separate them from pre-SMBH objects based on the line shape: the pre-SMBH lines show a profound asymmetry and extended red tail.