原行星盘演变的粘滞扩散阶段
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摘要
太阳星云的演变可以分为三个阶段:下落,粘滞耗散和清除阶段。每个阶段的盘子结构由不同的物理过程决定。当从分子云坍塌而汇合的物质下落到盘子的表面时,物质在盘子表面受到薄层吸积冲击而以次音速稳定下来时太阳星云就形成了。这种吸积冲击过程给星云表面提供了大量的热量。汇流的气体的角动量在吸积冲击薄层的下面的湍流剪切层上将会被调整到开普勒盘的角动量值并且有可能提供局部的粘滞。在本文我们集中讨论粘滞耗散阶段。我们认为盘子的演化主要决定于盘子内部所产生的粘滞压。在这个阶段,粘滞机制将重新分布星云的质量和角动量。盘子的物质往里流而角动量往外流,星云逐渐向外扩展。与以往的均匀粘滞考虑不同,在此我们加入不均匀粘滞来研究原始太阳星云粘滞耗散阶段。计算中应用了目前最新的不均匀粘滞。在粘滞的计算中,我们加入了磁转动不稳效应。星云面密度和其它物理量的径向分布与以往的考虑均匀粘滞的星云模型中有显著不同。我们认为不均匀粘滞的结果更符合星云演变的历史真实。
The origin of the solar system is one of the most important questions in science. The standard theory of the origin of the solar system in the solar era is the nebular hypothesis.
The current knowledge suggests that the viscosity in the solar nebular is not uniform and calculations of the nebular evolution with constantαmay miss usefull information about the history of solar system. It is pointed out that the angular momentum transport mechanism can be the magnetohydrodynamic turbulence driven by the magnetorotational instability. Considering the effect of ohmic diffusion on the magnetorotational instability in the solar nebular, it is pointed out that in the outer region of the nebular, the suface density is low enough for cosmic rays to penetrate and the ionization is high enough that the magnetorotational instability can survive. The magnetorotational instability can survive in the inner region due to thermal ionization. But the magnetorotational instability can not survive in the intermediate region between the inner region and the outer region, and the viscosity drops significantly. The angular momentum transport is not nonuniform and can not be described with a uniformα.
In this paper, we present complete radial, time-dependent calculations of the structure and evolution of the protoplanetary disks during the viscous diffusion stage. The viscous stress is derived from the model of the vertical nebular structure based on detailed grain opacities. we investigate the viscous diffusion stage of evolution of protoplanetary disks by including nonuniform viscosity. The calculations are done by using currently accepted viscosity, which is nonuniform. In the calculation of viscosity, we include the effect of magnetorotational instability. The radial distributions of the suface density and other physical quantities of the nebular are significantly different from nebular models with constantαviscosity.
We present complete radial, time-dependent calculations of the structure and evolution of the protoplanetary disks during the viscous diffusion stage. The viscous stress is derived from the model of the vertical nebular structure based on detailed grain opacities.
The origin of the solar system is one of the most important questions in science. The standard theory of the origin of the solar system in the solar era is the nebular hypothesis.
The current knowledge suggests that the viscosity in the solar nebular is not uniform and calculations of the nebular evolution with constantαmay miss usefull information about the history of solar system. It is pointed out that the angular momentum transport mechanism can be the magnetohydrodynamic turbulence driven by the magnetorotational instability. Considering the effect of ohmic diffusion on the magnetorotational instability in the solar nebular, it is pointed out that in the outer region of the nebular, the suface density is low enough for cosmic rays to penetrate and the ionization is high enough that the magnetorotational instability can survive. The magnetorotational instability can survive in the inner region due to thermal ionization. But the magnetorotational instability can not survive in the intermediate region between the inner region and the outer region, and the viscosity drops significantly. The angular momentum transport is not nonuniform and can not be described with a uniformα.
In this paper, we present complete radial, time-dependent calculations of the structure and evolution of the protoplanetary disks during the viscous diffusion stage. The viscous stress is derived from the model of the vertical nebular structure based on detailed grain opacities. we investigate the viscous diffusion stage of evolution of protoplanetary disks by including nonuniform viscosity. The calculations are done by using currently accepted viscosity, which is nonuniform. In the calculation of viscosity, we include the effect of magnetorotational instability. The radial distributions of the suface density and other physical quantities of the nebular are significantly different from nebular models with constantαviscosity.
We present complete radial, time-dependent calculations of the structure and evolution of the protoplanetary disks during the viscous diffusion stage. The viscous stress is derived from the model of the vertical nebular structure based on detailed grain opacities.
引文
[1] Cameron, A. G. W. Physics of the primitive solar accretion disk [J].Moon and Planets, 1978, 18: 5-40.
[2] Lin, D. N. C., & Papaloizou, J. On the structure and evolution of the primordial solar nebula [J].Monthly Notices of the Royal Astronomical Society, 1980, 191: 37-48.
[3] Lin, D. N. C., & Papaloizou, J. On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction [J].The Astrophysical Journal, 1986, 307: 395-409.
[4] Cassen, P., & Moosman, A. On the formation of protostellar disks [J].Icarus, 1981, 48: 353-376.
[5] Cassen, P., & Summers, A. Models of the formation of the solar nebula [J].Icarus, 1983, 53: 26-40.
[6] Cameron, A. G. W. Physics of the primitive solar accretion disk [J].Moon and Planets, 1978, 18: 5-40.
[7] Elmegreen, B. G. On the interaction between a strong stellar wind and a surrounding disk nebula [J].Moon and Planets, 1978, 19: 261-277.
[8] Strom, K. M., Strom, S. E., Edwards, S., Cabrit, S., & Skrutskie, M. F. Circumstellar material associated with solar-typepre-main-sequence stars - A possible constraint on the timescale for planet building [J].The Astronomical Journal, 1989, 97: 1451-1470.
[9] Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. A survey for circumstellar disks around young stellar objects [J].The Astronomical Journal, 1990, 99: 924-945.
[10] Skrutskie, M. F., Dutkevitch, D., Strom, S. E., Edwards, S., Strom, K. M., & Shure, M. A. A sensitive 10-micron search for emission arising from circumstellar dust associated with solar-type pre-main-sequence stars [J].The Astronomical Journal, 1990, 99: 1187-1195.
[11] Strom, S. E., Edwards, S., & Skrutskie, M. F. Evolutionary time scales for circumstellar disks associated with intermediate- and solar-type stars [J].Protostars and Planets III, 1993, 837-866.
[12] Jensen, E. L. N., Mathieu, R. D., & Fuller, G. A. A connection between submillimeter continuum flux and separation in young binaries [J].The Astrophysical Journal, 1994, 429: L29-L32.
[13] Jensen, E. L. N., Mathieu, R. D., & Fuller, G. A. The Connection between Submillimeter Continuum Flux and Binary Separation in Young Binaries: Evidence of Interaction between Stars and Disks [J].The Astrophysical Journal, 1996, 458: 312
[14] Osterloh, M., & Beckwith, S. V. W. Millimeter-wave continuummeasurements of young stars [J].The Astrophysical Journal, 1995, 439: 288-302.
[15] Koerner, D. W., Sargent, A. I., & Beckwith, S. V. W. A rotating gaseous disk around the T Tauri star GM Aurigae [J].Icarus, 1993, 106: 2
[16] Koerner, D. W., & Sargent, A. I. Imaging the Small-Scale Circumstellar Gas Around T Tauri Stars [J].The Astronomical Journal, 1995, 109: 2138
[17] Koerner, D. W., Chandler, C. J., & Sargent, A. I. Aperture Synthesis Imaging of the Circumstellar Dust Disk around DO Tauri [J].The Astrophysical Journal, 1995, 452: L69
[18] Lay, O. P., Carlstrom, J. E., Hills, R. E., & Phillips, T. G. Protostellar accretion disks resolved with the JCMT-CSO interferometer [J].The Astrophysical Journal, 1994, 434: L75-L78.
[19] Mundy, L. G., et al. Imaging the HL Tauri Disk at lambda = 2.7 Millimeters with the BIMA Array [J].The Astrophysical Journal, 1996, 464: L169
[20] Dutrey, A., Guilloteau, S., Duvert, G., Prato, L., Simon, M., Schuster, K., & Menard, F. Dust and gas distribution around T Tauri stars in Taurus-Auriga. I. Interferometric 2.7mm continuum and ^13^CO J=1-0 observations [J].Astronomy and Astrophysics,1996, 309: 493-504.
[21] Simon, M., Dutrey, A., & Guilloteau, S. Dynamical Masses of T Tauri Stars and Calibration of Pre-Main-Sequence Evolution [J].The Astrophysical Journal, 2000, 545: 1034-1043.
[22] Kenyon, S. J., & Hartmann, L. Spectral energy distributions of T Tauri stars - Disk flaring and limits on accretion [J].The Astrophysical Journal, 1987, 323: 714-733.
[23] Chiang, E. I., & Goldreich, P. Spectral Energy Distributions of T Tauri Stars with Passive Circumstellar Disks [J].The Astrophysical Journal, 1997, 490: 368
[24] D'Alessio, P., Calvet, N., Hartmann, L., Lizano, S., & Cantó, J. Accretion Disks around Young Objects. II. Tests of Well-mixed Models with ISM Dust [J].The Astrophysical Journal, 1999, 527: 893-909.
[25] Bertout, C., Basri, G., & Bouvier, J. Accretion disks around T Tauri stars [J].The Astrophysical Journal, 1988, 330: 350-373.
[26] Bertout, C. T Tauri stars - Wild as dust [J].Annual Review of Astronomy and Astrophysics, 1989, 27: 351-395.
[27] Lynden-Bell, D., & Pringle, J. E. The evolution of viscous discs and the origin of the nebular variables. [J].Monthly Notices of the Royal Astronomical Society, 1974, 168: 603-637.
[28] Hartigan, P., Hartmann, L., Kenyon, S. J., Strom, S. E., &Skrutskie, M. F. Correlations of optical and infrared excesses in T Tauri stars [J].The Astrophysical Journal, 1990, 354: L25-L28.
[29] Edwards, S. Observational Evidence for the Importance of Magnetospheres in the Evolution of T Tauri Accretion Disk Systems [J].Revista Mexicana de Astronomia y Astrofisica Conference Series, 1995, 1: 309
[30] Kenyon, S. J., & Hartmann, L. Pre-Main-Sequence Evolution in the Taurus-Auriga Molecular Cloud [J].The Astrophysical Journal Supplement Series, 1995, 101: 117
[31] Camenzind, M. Magnetized Disk-Winds and the Origin of Bipolar Outflows. [J].Reviews in Modern Astronomy, 1990, 3: 234-265.
[32] Koenigl, A. Disk accretion onto magnetic T Tauri stars [J].The Astrophysical Journal, 1991, 370: L39-L43.
[33] Ostriker, E. C., & Shu, F. H. Magnetocentrifugally Driven Flows from Young Stars and Disks. IV. The Accretion Funnel and Dead Zone [J].The Astrophysical Journal, 1995, 447: 813
[34] Calvet, N., & Hartmann, L. Balmer line profiles for infalling T Tauri envelopes [J].The Astrophysical Journal, 1992, 386: 239-247.
[35] Hartmann, L., Boss, A., Calvet, N., & Whitney, B. Protostellar collapse in a self-gravitating sheet [J].The Astrophysical Journal, 1994, 430: L49-L52. 46
[36] Basri, G., & Bertout, C. Accretion disks around T Tauri stars. II - Balmer emission [J].The Astrophysical Journal, 1989, 341: 340-358.
[37] Hartigan, P., Kenyon, S. J., Hartmann, L., Strom, S. E., Edwards, S., Welty, A. D., & Stauffer, J. Optical excess emission in T Tauri stars [J].The Astrophysical Journal, 1991, 382: 617-635.
[38] Hartigan, P., Edwards, S., & Ghandour, L. Disk Accretion and Mass Loss from Young Stars [J].The Astrophysical Journal, 1995, 452: 736
[39] Valenti, J. A., Basri, G., & Johns, C. M. T Tauri stars in blue [J].The Astronomical Journal, 1993, 106: 2024-2050.
[40] Gullbring, E., Hartmann, L., Briceno, C., & Calvet, N. Disk Accretion Rates for T Tauri Stars [J].The Astrophysical Journal, 1998, 492: 323
[41] Lynden-Bell, D., & Pringle, J. E. The evolution of viscous discs and the origin of the nebular variables. [J].Monthly Notices of the Royal Astronomical Society, 1974, 168: 603-637.
[42] Shakura, N. I., & Sunyaev, R. A. Black holes in binary systems. Observational appearance. [J].Astronomy and Astrophysics, 1973, 24: 337-355.
[43] Lynden-Bell, D. Galactic Nuclei as Collapsed Old Quasars [J].Nature, 1969, 223: 690-694.
[44] Lüst, R. Die Entwicklung einer um einen Zentralkörper rotierenden Gasmasse. I. Lösungen der hydrodynamischen Gleichungen mit turbulenter Reibung [J].Zeitschrift Naturforschung Teil A, 1952, 7: 87
[45] Weizsäcker, C. F. V. Über die Entstehung des Planetensystems. Mit 2 Abbildungen. [J].Zeitschrift fur Astrophysik, 1943, 22: 319
[46] Lin, D. N. C. Convective accretion disk model for the primordial solar nebula [J].The Astrophysical Journal, 1981, 246: 972-984.
[47] Lin, D. N. C., & Bodenheimer, P. On the evolution of convective accretion disk models of the primordial solar nebula [J].The Astrophysical Journal, 1982, 262: 768-779.
[48] Shakura, N. I., & Sunyaev, R. A. Black holes in binary systems. Observational appearance. [J].Astronomy and Astrophysics, 1973, 24: 337-355.
[49] Umebayashi, T. The Densities of Charged Particles in Very Dense Interstellar Clouds [J].Progress of Theoretical Physics, 1983, 69: 480-502.
[50] Reyes-Ruiz, M. Evolution of protoplanetary discs driven by the MRI, self-gravity and hydrodynamical turbulence [J].Monthly Notices of the Royal Astronomical Society, 2007, 380: 311-319.
[51] Ruden, S. P., & Lin, D. N. C. The global evolution of theprimordial solar nebula [J].The Astrophysical Journal, 1986, 308: 883-901.
[52] Jin, L., & Sui, N. The Evolution of the Solar Nebula I. Evolution of the Global Properties and Planet Masses [J].The Astrophysical Journal, 2010, 710: 1179-1194.
[53] Jin, L., Arnett, W. D., Sui, N., & Wang, X. An Interpretation of the Anomalously Low Mass of Mars [J].The Astrophysical Journal, 2008, 674: L105-L108.
[54] J.E. Pringle, Accretion discs in astrophysics [J].Ann. Rev. Astr. Ap.,1981, 19: 137.
[55] Balbus, S. A.,& Hawley, J. F. A powerful local shear instability in weakly magnetized disks. [J].The Astrophysical Journal, 1991, 376: 214-233..
[2] Lin, D. N. C., & Papaloizou, J. On the structure and evolution of the primordial solar nebula [J].Monthly Notices of the Royal Astronomical Society, 1980, 191: 37-48.
[3] Lin, D. N. C., & Papaloizou, J. On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction [J].The Astrophysical Journal, 1986, 307: 395-409.
[4] Cassen, P., & Moosman, A. On the formation of protostellar disks [J].Icarus, 1981, 48: 353-376.
[5] Cassen, P., & Summers, A. Models of the formation of the solar nebula [J].Icarus, 1983, 53: 26-40.
[6] Cameron, A. G. W. Physics of the primitive solar accretion disk [J].Moon and Planets, 1978, 18: 5-40.
[7] Elmegreen, B. G. On the interaction between a strong stellar wind and a surrounding disk nebula [J].Moon and Planets, 1978, 19: 261-277.
[8] Strom, K. M., Strom, S. E., Edwards, S., Cabrit, S., & Skrutskie, M. F. Circumstellar material associated with solar-typepre-main-sequence stars - A possible constraint on the timescale for planet building [J].The Astronomical Journal, 1989, 97: 1451-1470.
[9] Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. A survey for circumstellar disks around young stellar objects [J].The Astronomical Journal, 1990, 99: 924-945.
[10] Skrutskie, M. F., Dutkevitch, D., Strom, S. E., Edwards, S., Strom, K. M., & Shure, M. A. A sensitive 10-micron search for emission arising from circumstellar dust associated with solar-type pre-main-sequence stars [J].The Astronomical Journal, 1990, 99: 1187-1195.
[11] Strom, S. E., Edwards, S., & Skrutskie, M. F. Evolutionary time scales for circumstellar disks associated with intermediate- and solar-type stars [J].Protostars and Planets III, 1993, 837-866.
[12] Jensen, E. L. N., Mathieu, R. D., & Fuller, G. A. A connection between submillimeter continuum flux and separation in young binaries [J].The Astrophysical Journal, 1994, 429: L29-L32.
[13] Jensen, E. L. N., Mathieu, R. D., & Fuller, G. A. The Connection between Submillimeter Continuum Flux and Binary Separation in Young Binaries: Evidence of Interaction between Stars and Disks [J].The Astrophysical Journal, 1996, 458: 312
[14] Osterloh, M., & Beckwith, S. V. W. Millimeter-wave continuummeasurements of young stars [J].The Astrophysical Journal, 1995, 439: 288-302.
[15] Koerner, D. W., Sargent, A. I., & Beckwith, S. V. W. A rotating gaseous disk around the T Tauri star GM Aurigae [J].Icarus, 1993, 106: 2
[16] Koerner, D. W., & Sargent, A. I. Imaging the Small-Scale Circumstellar Gas Around T Tauri Stars [J].The Astronomical Journal, 1995, 109: 2138
[17] Koerner, D. W., Chandler, C. J., & Sargent, A. I. Aperture Synthesis Imaging of the Circumstellar Dust Disk around DO Tauri [J].The Astrophysical Journal, 1995, 452: L69
[18] Lay, O. P., Carlstrom, J. E., Hills, R. E., & Phillips, T. G. Protostellar accretion disks resolved with the JCMT-CSO interferometer [J].The Astrophysical Journal, 1994, 434: L75-L78.
[19] Mundy, L. G., et al. Imaging the HL Tauri Disk at lambda = 2.7 Millimeters with the BIMA Array [J].The Astrophysical Journal, 1996, 464: L169
[20] Dutrey, A., Guilloteau, S., Duvert, G., Prato, L., Simon, M., Schuster, K., & Menard, F. Dust and gas distribution around T Tauri stars in Taurus-Auriga. I. Interferometric 2.7mm continuum and ^13^CO J=1-0 observations [J].Astronomy and Astrophysics,1996, 309: 493-504.
[21] Simon, M., Dutrey, A., & Guilloteau, S. Dynamical Masses of T Tauri Stars and Calibration of Pre-Main-Sequence Evolution [J].The Astrophysical Journal, 2000, 545: 1034-1043.
[22] Kenyon, S. J., & Hartmann, L. Spectral energy distributions of T Tauri stars - Disk flaring and limits on accretion [J].The Astrophysical Journal, 1987, 323: 714-733.
[23] Chiang, E. I., & Goldreich, P. Spectral Energy Distributions of T Tauri Stars with Passive Circumstellar Disks [J].The Astrophysical Journal, 1997, 490: 368
[24] D'Alessio, P., Calvet, N., Hartmann, L., Lizano, S., & Cantó, J. Accretion Disks around Young Objects. II. Tests of Well-mixed Models with ISM Dust [J].The Astrophysical Journal, 1999, 527: 893-909.
[25] Bertout, C., Basri, G., & Bouvier, J. Accretion disks around T Tauri stars [J].The Astrophysical Journal, 1988, 330: 350-373.
[26] Bertout, C. T Tauri stars - Wild as dust [J].Annual Review of Astronomy and Astrophysics, 1989, 27: 351-395.
[27] Lynden-Bell, D., & Pringle, J. E. The evolution of viscous discs and the origin of the nebular variables. [J].Monthly Notices of the Royal Astronomical Society, 1974, 168: 603-637.
[28] Hartigan, P., Hartmann, L., Kenyon, S. J., Strom, S. E., &Skrutskie, M. F. Correlations of optical and infrared excesses in T Tauri stars [J].The Astrophysical Journal, 1990, 354: L25-L28.
[29] Edwards, S. Observational Evidence for the Importance of Magnetospheres in the Evolution of T Tauri Accretion Disk Systems [J].Revista Mexicana de Astronomia y Astrofisica Conference Series, 1995, 1: 309
[30] Kenyon, S. J., & Hartmann, L. Pre-Main-Sequence Evolution in the Taurus-Auriga Molecular Cloud [J].The Astrophysical Journal Supplement Series, 1995, 101: 117
[31] Camenzind, M. Magnetized Disk-Winds and the Origin of Bipolar Outflows. [J].Reviews in Modern Astronomy, 1990, 3: 234-265.
[32] Koenigl, A. Disk accretion onto magnetic T Tauri stars [J].The Astrophysical Journal, 1991, 370: L39-L43.
[33] Ostriker, E. C., & Shu, F. H. Magnetocentrifugally Driven Flows from Young Stars and Disks. IV. The Accretion Funnel and Dead Zone [J].The Astrophysical Journal, 1995, 447: 813
[34] Calvet, N., & Hartmann, L. Balmer line profiles for infalling T Tauri envelopes [J].The Astrophysical Journal, 1992, 386: 239-247.
[35] Hartmann, L., Boss, A., Calvet, N., & Whitney, B. Protostellar collapse in a self-gravitating sheet [J].The Astrophysical Journal, 1994, 430: L49-L52. 46
[36] Basri, G., & Bertout, C. Accretion disks around T Tauri stars. II - Balmer emission [J].The Astrophysical Journal, 1989, 341: 340-358.
[37] Hartigan, P., Kenyon, S. J., Hartmann, L., Strom, S. E., Edwards, S., Welty, A. D., & Stauffer, J. Optical excess emission in T Tauri stars [J].The Astrophysical Journal, 1991, 382: 617-635.
[38] Hartigan, P., Edwards, S., & Ghandour, L. Disk Accretion and Mass Loss from Young Stars [J].The Astrophysical Journal, 1995, 452: 736
[39] Valenti, J. A., Basri, G., & Johns, C. M. T Tauri stars in blue [J].The Astronomical Journal, 1993, 106: 2024-2050.
[40] Gullbring, E., Hartmann, L., Briceno, C., & Calvet, N. Disk Accretion Rates for T Tauri Stars [J].The Astrophysical Journal, 1998, 492: 323
[41] Lynden-Bell, D., & Pringle, J. E. The evolution of viscous discs and the origin of the nebular variables. [J].Monthly Notices of the Royal Astronomical Society, 1974, 168: 603-637.
[42] Shakura, N. I., & Sunyaev, R. A. Black holes in binary systems. Observational appearance. [J].Astronomy and Astrophysics, 1973, 24: 337-355.
[43] Lynden-Bell, D. Galactic Nuclei as Collapsed Old Quasars [J].Nature, 1969, 223: 690-694.
[44] Lüst, R. Die Entwicklung einer um einen Zentralkörper rotierenden Gasmasse. I. Lösungen der hydrodynamischen Gleichungen mit turbulenter Reibung [J].Zeitschrift Naturforschung Teil A, 1952, 7: 87
[45] Weizsäcker, C. F. V. Über die Entstehung des Planetensystems. Mit 2 Abbildungen. [J].Zeitschrift fur Astrophysik, 1943, 22: 319
[46] Lin, D. N. C. Convective accretion disk model for the primordial solar nebula [J].The Astrophysical Journal, 1981, 246: 972-984.
[47] Lin, D. N. C., & Bodenheimer, P. On the evolution of convective accretion disk models of the primordial solar nebula [J].The Astrophysical Journal, 1982, 262: 768-779.
[48] Shakura, N. I., & Sunyaev, R. A. Black holes in binary systems. Observational appearance. [J].Astronomy and Astrophysics, 1973, 24: 337-355.
[49] Umebayashi, T. The Densities of Charged Particles in Very Dense Interstellar Clouds [J].Progress of Theoretical Physics, 1983, 69: 480-502.
[50] Reyes-Ruiz, M. Evolution of protoplanetary discs driven by the MRI, self-gravity and hydrodynamical turbulence [J].Monthly Notices of the Royal Astronomical Society, 2007, 380: 311-319.
[51] Ruden, S. P., & Lin, D. N. C. The global evolution of theprimordial solar nebula [J].The Astrophysical Journal, 1986, 308: 883-901.
[52] Jin, L., & Sui, N. The Evolution of the Solar Nebula I. Evolution of the Global Properties and Planet Masses [J].The Astrophysical Journal, 2010, 710: 1179-1194.
[53] Jin, L., Arnett, W. D., Sui, N., & Wang, X. An Interpretation of the Anomalously Low Mass of Mars [J].The Astrophysical Journal, 2008, 674: L105-L108.
[54] J.E. Pringle, Accretion discs in astrophysics [J].Ann. Rev. Astr. Ap.,1981, 19: 137.
[55] Balbus, S. A.,& Hawley, J. F. A powerful local shear instability in weakly magnetized disks. [J].The Astrophysical Journal, 1991, 376: 214-233..