Self-calibration method for II and GI types of intrinsic alignments of galaxies

We introduce a self-calibration method that can be applied to the intrinsic ellipticity--intrinsic ellipticity (II) and gravitational shear -- intrinsic ellipticity (GI) types of intrinsic alignment of galaxies. The method combines previous self-calibration techniques with modifications to one of them in order to use auto-spectra in addition to cross-spectra between redshift bins. This allows one to use the self-calibration while preserving all the constraining power of cosmic shear from surveys. We show that the new method provides more flexibility in using various redshift bin widths. We perform cosmological parameter constraint forecast when this method is applied to the Large Synoptic Survey Telescope (LSST). Compared to the original self-calibration, we find that the new method provides further significant reduction in any residual shift in the cosmological parameters (e.g. factors of $2-4$ for the dark energy equation of state) which is promising for accurate cosmology.