The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well ionized disks, the predominant form of disk viscosity originates from the mag-netorotational instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate, the so-called dead zone, turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-rays, cosmic rays, and radioactive elements) and determined the size of a dead zone for the total ionization rate by using a radiative, hydrostatic equilibrium disk model developed by Chiang and coworkers. We studied a range of surface mass density (∑_0 = 10~3-10~5 g cm~(-2)) and X-ray energy (kT_X = 1-10 keV). We also compared the ionization rate of such a disk by X-rays with cosmic rays and find that the latter dominate X-rays in ionizing protostellar disks unless the X-ray energy is very high (5-10 keV). Among our major conclusions are that for typical conditions, dead zones encompass a region extending out to several AU, the region in which terrestrial planets are found in our solar system. Our results suggest that the division between low- and high-mass planets in exosolar planetary systems is a consequence of the presence of a dead zone in their natal protoplanetary disks. We also find that the extent of a dead zone is mainly dependent on the disk's surface mass density. Our results provide further support for the idea that Jovian planets in exosolar systems must have migrated substantially inward from their points of origin.
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机译：当木星施加在其周围的原恒星盘上的潮汐扭矩足以在盘形粘性表面上打开缝隙，从而阻止任何进一步的积聚时，它们便达到了最终的质量。在离子化程度足够好的磁盘中，磁盘粘度的主要形式源自驱动水磁磁盘湍流的磁旋转不稳定性（MRI）。在电离率足够低的区域，即所谓的死区，湍流得到了抑制，我们表明将形成质量较小的行星。我们考虑了三个电离源（X射线，宇宙射线和放射性元素），并使用Chiang和他的同事开发的辐射静水平衡盘模型确定了总电离率的盲区大小。我们研究了表面质量密度（∑_0 = 10〜3-10〜5 g cm〜（-2））和X射线能量（kT_X = 1-10 keV）的范围。我们还将X射线与宇宙射线的这种磁盘的电离速率进行了比较，发现除非X射线能量非常高（5-10 keV），否则后者在电离的原恒星磁盘中将主导X射线。我们的主要结论是，在典型情况下，死区包括一个延伸到几个AU的区域，该区域是我们太阳系中发现地行星的区域。我们的结果表明，太阳系外行星系统中低质量和高质量行星之间的划分是其原初行星盘中存在死区的结果。我们还发现，死区的范围主要取决于磁盘的表面质量密度。我们的结果进一步支持了系外行星系统中的木星行星必须从其起源点基本向内迁移的观点。
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