Mitigating the impact of fiber assignment on the measurement of galaxy-lensing cross correlation

We examine the impact of fiber assignment on the measurement of galaxy clustering and its cross correlation with weak lensing fields. Unlike the past spectroscopic galaxy surveys such as Baryon Oscillation Spectroscopic Survey (BOSS), currently ongoing spectroscopic galaxy surveys such as Prime Focus Spectrograph (PFS) and Dark Energy Spectroscopic Instrument (DESI) suffer from the fiber assignment artifacts more severely because there are more target galaxies than available fibers. The previous studies found that the fiber assignment suppresses the amplitude of the galaxy power spectrum at all scales. We newly find that the fiber assignment introduces the artificial correlation of structure at different redshifts, which suppresses the amplitude of the galaxy-lensing cross power spectrum. We show that the fiber assignment effects on the cross power spectrum can be mitigated at all scales with accuracy better than $\sim 1\%$, by up-weighting observed galaxies with the probability to be observed. This is not the case for the galaxy power spectrum, which is not fully corrected at $k \gtrsim 0.2$ [$h$/Mpc]. We find that the galaxy-lensing cross power spectrum is not affected by the pairwise probability of galaxies to be observed, and thus the correction method based on the individual probability is sufficient at all scales.