The LIS for CR protons (top), He (middle), and all electrons (e− + e+; bottom). The latest AMS-02 measurements from Aguilar et al. (2014, 2015a, 2015b) are shown with red squares. The green dashed line shows the results from Boschini et al. (2017, 2018a), which we employ GALPROP and HelMod together in an iterative manner to derive the LIS. We adopt their derived GALPROP CR parameters, and the LIS for our IEM (M31 IEM: solid black line) are roughly the same. The thin dotted black line shows the LIS modulated with HelMod (Boschini et al. 2017, 2018a). Yellow triangles show the Voyager 1 p and He data in the local interstellar medium (Cummings et al. 2016). Voyager 1 electron data are below 100 MeV and therefore are not shown. In addition, we show the LIS for the (“Yusifov”) IEM in Ajello et al. (2016), which we use as a reference model in our study of the systematics for the M31 field (see Appendix B.2).