Application of the space-based optical interferometer towards measuring cosmological distances of quasars

Abstract

Measuring the quasar distance through joint analysis of spectroastrometry (SA) and reverberation mapping (RM) observations is a new method for driving the development of cosmology. In this paper, we carry out detailed simulation and analysis to study the effect of four basic observational parameters (baseline length, exposure time, equivalent diameter and spectral resolution) on the data quality of differential phase curves (DPCs), furthermore on the accuracy of distance measurement. In our simulation, we adopt an axis symmetrical disc model of broad line region (BLR) to generate differential phase signals. We find that the differential phases and their Poisson errors could be amplified by extending the baseline, while the influence of OPD (optical path difference) errors can be reduced during fitting the BLR model. Longer exposure time or larger equivalent diameter helps reduce the absolute Poisson error. Therefore, the relative error of DPCs could be reduce by increasing any of the above three parameters, then the accuracy of distance measurement could be improved. In contrast, the uncertainty of $D_{\rm{A}}$ ( absolute angular distances) could be improved with higher spectral resolution, although the relative error of DPCs would be amplified. We show how the uncertainty of distance measurement varies with the relative error of DPCs. For our specific set of model parameters, without considering more complicated structures and kinematics of BLRs in our simulation, it is found that the relative error of DPCs $<$ 20$\%$ is a limit for accurate distance measurement. The relative error of DPCs have a lower limit (roughly 5$\%$) and the uncertainty of distance measurement can be better than 2$\%$.