A method of calibrating effective area of focusing X-ray detector by using normal spectrum of Crab pulsar

X-ray detector is a core component for X-ray astronomical observation and pulsar navigation. The on-orbit observation performance of X-ray detector will change gradually, owing to the influences of emission vibration, radiation damage of high-energy particles, and the aging of the components. The on-orbit calibration of X-ray detector facilitates the accurate acquisition and the precise modeling of X-ray radiation of the observation celestial bodies. In this paper a new method of calibrating the performance of X-ray detector is studied by using the radiation spectrum of the pulsar, which can effectively eliminate the influences from detector background and space environment noise. The on-orbit performance of the first focusing X-ray detector in China has been evaluated by analyzing the observations of the X-ray pulsar-based navigation satellite-1 (XPNAV-1) for the Crab pulsar. The XPNAV-1 was launched in November 2016, with the aim of conducting the test of the feasibility of applying the regular emission of X-ray signals from pulsars to spacecraft navigation. Now, the first batch of scientific data about the Crab pulsar observations gained by the focusing X-ray detector for almost one month has been released. The pulse profiles of 124 observations and the total observational spectrum of Crab pulsar are achieved from those data. According to the international accurate X-ray radiation parameters of Crab pulsar, which have been determined by other X-ray space satellites, together with the absorption effect of the neutral hydrogen gas in the universe, the effective area of the focusing X-ray detector is estimated. The result shows that the effective area of the focusing X-ray detector on XPNAV-1 in an energy range of 0.6-1.9 keV is better than 2 cm(2). The maximum effective area is 3.06 cm(2) at an energy of 0.7 keV, which means that its detection efficiency is about 10%. As the observed energy increases, the effective area decreases. The area of the focusing X-ray detector in an energy range of 2-3.5 keV is about 1 cm(2), and it is about 0.1 cm(2) at energies above 5 keV, and its estimation accuracy is affected seriously by the statistical errors of X-ray photons. At the same time, another method of calibrating the effective area is studied by considering the energy response matrix of detector. The energy response matrix of the focusing X-ray detector is estimated by using the five ground test values of energy resolution. The effective area of the focusing X-ray detector is re-calibrated. However, the result shows that the energy response matrix exerts little effect on the effective area of the focusing X-ray detector. Finally, we suggest that the XPNAV-1 should observe some supernova remnants to monitor the changes of energy resolution and energy linearity and so on.