Understanding the Reconstruction of the Biased Tracer

Recent development in the reconstruction of the large-scale structure (LSS) has seen significant improvement in restoring the linear baryonic acoustic oscillation (BAO) from at least the non-linear matter field. This outstanding performance is achieved by iteratively solving the Monge-Ampere equation of the mass conservation. However, this technique also relies on several assumptions that are not valid in reality, namely the longitudinal displacement, the absence of shell-crossing and homogeneous initial condition. In particular, the conservation equation of the tracers comprises the biasing information that breaks down the last assumption. Consequently, direct reconstruction would entangle the non-linear displacement with complicated bias parameters and further affect the BAO. In this paper, we formulate a theoretical model describing the reconstructed biased map by matching the tracer overdensity with an auxiliary fluid with vanishing initial perturbation. Regarding the performance of the reconstruction algorithm, we show that even though the shot noise is still the most significant limiting factors in a realistic survey, inappropriate treatment of the bias could also shift the reconstructed frame and therefore broaden the BAO peak. We suggest that, in principle, this bias-related BAO smearing effect could be used to independently self-calibrate the bias parameters.