superfluidity of Λ hyperons exists in the core of neutron stars depends on the ΛΛ interaction used. With weaker ΛΛ interactions, such as NSC97b and NSC97f, the Λ superfluidity does not appear inside neutron stars. For the NSC97e, NFs, NSC97s, and Urbana interactions, although we obtain the pairing gaps of the order of 10 − 4 MeV in the TM1 case, it is unlikely that Λ superfluidity can exist in observed neutron stars because of its low superfluid critical temperature T$_{c}$ ≃ 0 . 57Δ$_{F}$ /κ$_{B}$ ∼ 10 6 K [24, 29]. With stronger ΛΛ interactions, such as ESC00, ND1, and ND2, the $^{1}$S$_{0}$ superfluidity of Λ hyperons may exist in massive neutron stars, as shown in Figs. 5 and 6. In the case of TM1 (NL3) with the ESC00 potential, Λ hyperons do not appear in neutron stars with M < 1 . 37 M ⊙ ( M < 1 . 50 M ⊙ ). For neutron stars with 1 . 37 M ⊙ < M < 1 . 63 M ⊙ (1 . 50 M ⊙ < M < 1 . 82 M ⊙ ), Λ hyperons in the core of neutron stars form a $^{1}$S$_{0}$ superfluid. However, when M > 1 . 63 M ⊙ ( M > 1 . 82 M ⊙ ), not only superfluid Λ but also normal (nonsuperfluid) Λ can exist in the core of neutron stars because the central baryon density exceeds the upper limit of the range where Λ superfluidity exists. The presence of nonsuperfluid Λ hyperons in the core of massive stars would lead to a more rapid cooling than the case with only superfluid Λ hyperons. The mass region, where only superfluid Λ hyperons exist in the core of neutron stars, is shaded in Figs. 5 and 6. It is shown that the region with the ESC00 potential is the widest among all cases in these figures. This is because the ESC00 potential has the strongest attraction, and its pairing gap covers the widest density range, as shown in Fig. 2. We note that this region depends both on the ΛΛ interaction and on the EOS of neutron star matter. 

## V. SUMMARY 

We have studied the $^{1}$S$_{0}$ superfluidity of Λ hyperons in neutron star matter and neutron stars. In this article, we employ the RMF model with the parameter sets TM1 and NL3 to calculate the properties of neutron star matter, which is composed of a chemically equi- librated and charge-neutral mixture of nucleons, hyperons, and leptons. The RMF theory has been successfully and widely used for the description of nuclear matter and finite nuclei, including unstable nuclei. In the RMF approach, baryons interact through the exchange of scalar and vector mesons. The baryons considered in this article are nucleons ( p and n ) and hyperons (Λ, Σ, and Ξ). The exchanged mesons include isoscalar scalar and vector mesons ( σ and ω ), an isovector vector meson ( ρ ), and two additional hidden-strangeness 

