tokens: Σ after core collapse stops. The disk lifetime is close to that shown in Figure 6 . See the text for details. In Figure 8 , we show M disk and M * as functions of t for the disk evolutions ( ω = 0.3 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M ) with and without external FUV fields. The evolutions of M disk and M * are similar to those shown in Figure 3 . Since ω is smaller, more material of the core falls onto the star, which causes the star to grow faster and the disk to grow relatively slower. When the collapse ends, M * is about 0.86 M and M disk is about 0.14 M . Therefore, the gravitational potential well is deeper, which results in the weaker external FUV photoevaporation. Finally, the difference between the final star masses shown in Figure 8 is smaller (0.002 M ). Figure 8. Evolution of M disk (top panel) and M * (bottom panel) as functions of t for the same core properties as those shown in Figures 6 and 7 . The solid lines represent the case for including both internal X-ray and external FUV photoevaporations. The dashed lines represent the case for including internal X-ray photoevaporation only. Figure 9 shows R disk as a function of t for the disk evolutions ( ω = 0.3 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M ). The evolutions of R disk are similar to those shown in Figure 4 . However, the lower ω means that the location of core mass falling onto the disk is closer to the star. So, R disk for the disk without external FUV fields shown in Figure 9 is smaller than that shown in Figure 4 . As discussed in previous paragraphs, the star gets more mass during the core collapse for the case of ω = 0.3 × 10 −14 s −1 . Therefore, R g of the disk with external FUV photoevaporation grows quickly and it can finally reach ∼372 au. Although external FUV photoevaporation is very weak in this case, the gravitational potential well is shallow at the large radius of the disk. The external photoevaporation can still cut off the disk and decrease R disk effectively, as shown in Figure 9 . Figure 9. Evolution of R disk and R g as a function of t for the same core properties as those shown in Figures 6 and 7 . The solid line represents the evolution of R disk in the disk, including both internal X-ray and external FUV photoevaporations. The dashed line represents the evolution of R disk in the disk, including internal X-ray photoevaporation only. The dotted line represents the evolution of R g in the disk, including both internal X-ray and external FUV photoevaporations. Next, we discuss the evolution of external FUV photoevaporating disks with high ω . We first present the results of the disk evolution, including internal X-ray photoevaporation only. Figure 10 shows the evolution of Σ of the internal X-ray photoevaporating disk for the high low ω case that ω = 5.0 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M . In this case, the angular momentum of the pre-stellar core is very high. Most material of the core collapses onto the disk and is far
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O