tokens: An additional effect, therefore, will be required to explain the orbital variation of the GeV emissions of LMC LP3 and especially for 4FGL J1405.1−6119. In addition to the effect of the anisotropic soft-photon field, we will explore the orbital modulation caused by the dependence of travel distance of the unshocked pulsar wind that moves toward the observer on the orbital phase. This effect is introduced in Sierpowska-Bartosik Bednarek ( 2008 ) for the PSR B1259−63/SS2883 system and in Sierpowska-Bartosik Torres ( 2008 ) and Khangulyan, Aharonian Bosch-Ramon ( 2008 ) for the very high-energy emission (TeV emission) of LS 5039. Since the interaction between the pulsar wind and stellar wind/disc will produce a termination-shock with cone-like structure (Canto, Raga Wilkin 1996 ), the distance from the pulsar to the termination shock ( r s in Fig. 2 ) increases with the angle measured from the axis created by the pulsar and the companion star. This causes a dependence of the distance from the pulsar to the termination shock in the direction of the observer on the orbital phase and results in the orbital dependent intensity of the ICS of the unshocked pulsar wind. For the gamma-ray binary with O-type star, the GeV light curve is not well studied with the effect of the shock geometry and the system parameters. In this paper, therefore, we will perform an investigation for the modulation of the GeV emission with the shock-cone model, and will apply the model to two gamma-ray binaries, LMC P3 and 4FGL J1405.1−6119. LMC P3 is the first gamma-ray binary outside Milky Way and it is discovered in the Large Magellanic Cloud (LMC) (Corbet et al. 2016 ), which is a neighbour galaxy located at about 50 kpc from the Earth (Macri et al. 2006 ; Pietrzyński et al. 2013 ; de Grijs, Wicker Bono 2014 ). The companion star in the LMC P3 system is an O-type star, but the compact object has not been identified yet. In the LMC, ∼50 supernova remnants (SNRs) are known to emit X-rays (Seward et al. 2012 ), and LMC P3 is associated with SNR 0535−67.5 in the H ii region DEM L241 (Davies, Elliott Meaburn 1976 ). Long, Helfand Grabelsky ( 1981 ) report the first detection of the X-ray emission from the SNR 0535−67.5. Seward et al. ( 2012 ) find a compact X-ray source (CXOU J053600.0−673507) with a luminosity of ∼2–3 × 10 35 erg s −1 in 0.3–10 keV energy bands and an optical counterpart, O5III(f) star. They therefore suggest that CXOU J053600.0−673507 is the high-mass X-ray binary hosting neutron star or black hole. Corbet et al. ( 2016 ) analyse the GeV counter part (LMC P3) of CXOU J053600.0−673507 in data of Fermi Large Area Telescope ( Fermi -LAT) and find a 10.3-d periodic modulation, which reveals that LMC P3/ CXOU J053600.0−673507 is the binary system with a orbital period of P orb ∼ 10.3 d. They also confirm the orbital modulation of the X-ray emission. HESS Collaboration et al. ( 2018 ) subsequently detect the TeV emission from LMC P3. van Soelen et al. ( 2019 ) find
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