II型超新星的物态方程与爆发能量
摘要
本工作探讨物态方程中κ0对II型超新星瞬时爆发的影响,并且对超新星爆发能量的四种定义进行了研究。
综述了II型超新星的相关理论。包括大质量恒星的演化、超新星的分类、超新星的爆发机制、引起恒星不稳定坍缩的物理因素等;同时论述了Ⅱ型超新星爆发所应用的数值模拟相关物理因素和数值处理方法,包括电子俘获的一般分析方法、“四粒子”模型的物态方程、广义相对论流体动力学方法和数值模拟差分方法。
本文通过使用2002年Woosley提供的新前身星模型数据,计算前身星为11Μ、13Μ、15Μ、20Μ、25Μ、30Μ、35Μ、40Μ的超新星,重新探讨了物态方程中κ0对超新星铁核坍缩、激波传播时间、爆发能量、整个铁核的温度( t 4时刻)的影响及详细讨论超新星爆发能量的四种定义。研究结果表明:1.在星核坍缩阶段,κ0越大,τc(1o)llap时间越短,但对τc(o2l)lap的影响不大。发现爆发能量越大,τt 4 ? t11越短;2.κ0越大,ρmcax值越小, cYL、Ye c、Yνc的值随κ0的增大而增大,但中心的熵却减小(变化都不大);3. t 4时刻,调节κ0的值,发现κ0越大,在内核,则温度越低,在外核,温度几乎不变;4.考察κ0的变化对不同太阳质量模型的爆发能量影响时,我们发现对于不同太阳质量模型时,最佳的对称物质的压缩模量κ0的取值不一样,通过对8个模型的对比,发现:κ0=210MeV较为合适;5.在探讨爆发能量的四种定义时,通过对八个不同太阳质量模型的考察, E x(p2)是较为合适的选择。这些结论说明κ0对超新星铁核坍缩、激波传播时间、爆发能量、整个铁核的温度( t 4时刻)等有重要的影响。这对于超新星爆发的研究有着重要的意义。
In this paper,κ0 in the equation of state effects on the prompt explosin of type II supernova and the four definitions of explosion energy are investigated.
The theory related toⅡsupernova is summarized. Including the evolution of massive stars,the reason of causing collapsing instability in stars.Explosion mechanism of type II supernova,the classify characters of SN are introduced,the physical factors relevant to SNII explosion numerrical simulation and numerical simulation methods are introduced,which include electron capture(EC),four model state equation ,general relativity hydrodynamic method,numerical simulation me- thods.
In this paper, we study the effects ofκ0in the equation of state on the core collapse ,shock propagation ,explosion energy and temperature of iron core at t 4, using the data of presupernova given by Woosley in 2002.The presupernova models which we are studied are11Μ,13Μ,15Μ,20Μ,25Μ,30Μ,35Μand40Μ, and also make a discussion in detail about the four definitions of explosion energy. The results of this paper are these:First,at the stage of the core collapse,the augmenttation ofκ0 shorten the collapse time(τc(1o)llap),but there is a little influence on collapse time(τc(o2l)lap),in the same time,the augmentation of explosion energy lowers the time ofτt 4 ? t11.Second,when we augment the value ofκ0,the inner density (ρmcax) and entropy are reduced,lepton abundance( YL c),electron abundance( Ye c) and neutrion abundance( Yνc ) of the inner core are augmentted.Third,at t 4,regulating the value ofκ0,we find that the augmentation ofκ0 lowers the internal core tempera- ture,but there is a little effect on the exterior core temperature.Fourth,we abserve that the change ofκ0 influences the explosion energy,found that the most suitableκ0 is different for 8 models,from the comparison of the eight models,foud that the suitable value is 210 MeV .Fifth,when we use 8 models to discuss the definition of explosion energy,found that the definition of E x(p2) is more suitable than others.The above conclusions show thatκ0 has a great effect on the core collapse ,shock propagation,explosion energy and core temerature(at t 4),and it is significance for the research of supernova.
综述了II型超新星的相关理论。包括大质量恒星的演化、超新星的分类、超新星的爆发机制、引起恒星不稳定坍缩的物理因素等;同时论述了Ⅱ型超新星爆发所应用的数值模拟相关物理因素和数值处理方法,包括电子俘获的一般分析方法、“四粒子”模型的物态方程、广义相对论流体动力学方法和数值模拟差分方法。
本文通过使用2002年Woosley提供的新前身星模型数据,计算前身星为11Μ、13Μ、15Μ、20Μ、25Μ、30Μ、35Μ、40Μ的超新星,重新探讨了物态方程中κ0对超新星铁核坍缩、激波传播时间、爆发能量、整个铁核的温度( t 4时刻)的影响及详细讨论超新星爆发能量的四种定义。研究结果表明:1.在星核坍缩阶段,κ0越大,τc(1o)llap时间越短,但对τc(o2l)lap的影响不大。发现爆发能量越大,τt 4 ? t11越短;2.κ0越大,ρmcax值越小, cYL、Ye c、Yνc的值随κ0的增大而增大,但中心的熵却减小(变化都不大);3. t 4时刻,调节κ0的值,发现κ0越大,在内核,则温度越低,在外核,温度几乎不变;4.考察κ0的变化对不同太阳质量模型的爆发能量影响时,我们发现对于不同太阳质量模型时,最佳的对称物质的压缩模量κ0的取值不一样,通过对8个模型的对比,发现:κ0=210MeV较为合适;5.在探讨爆发能量的四种定义时,通过对八个不同太阳质量模型的考察, E x(p2)是较为合适的选择。这些结论说明κ0对超新星铁核坍缩、激波传播时间、爆发能量、整个铁核的温度( t 4时刻)等有重要的影响。这对于超新星爆发的研究有着重要的意义。
In this paper,κ0 in the equation of state effects on the prompt explosin of type II supernova and the four definitions of explosion energy are investigated.
The theory related toⅡsupernova is summarized. Including the evolution of massive stars,the reason of causing collapsing instability in stars.Explosion mechanism of type II supernova,the classify characters of SN are introduced,the physical factors relevant to SNII explosion numerrical simulation and numerical simulation methods are introduced,which include electron capture(EC),four model state equation ,general relativity hydrodynamic method,numerical simulation me- thods.
In this paper, we study the effects ofκ0in the equation of state on the core collapse ,shock propagation ,explosion energy and temperature of iron core at t 4, using the data of presupernova given by Woosley in 2002.The presupernova models which we are studied are11Μ,13Μ,15Μ,20Μ,25Μ,30Μ,35Μand40Μ, and also make a discussion in detail about the four definitions of explosion energy. The results of this paper are these:First,at the stage of the core collapse,the augmenttation ofκ0 shorten the collapse time(τc(1o)llap),but there is a little influence on collapse time(τc(o2l)lap),in the same time,the augmentation of explosion energy lowers the time ofτt 4 ? t11.Second,when we augment the value ofκ0,the inner density (ρmcax) and entropy are reduced,lepton abundance( YL c),electron abundance( Ye c) and neutrion abundance( Yνc ) of the inner core are augmentted.Third,at t 4,regulating the value ofκ0,we find that the augmentation ofκ0 lowers the internal core tempera- ture,but there is a little effect on the exterior core temperature.Fourth,we abserve that the change ofκ0 influences the explosion energy,found that the most suitableκ0 is different for 8 models,from the comparison of the eight models,foud that the suitable value is 210 MeV .Fifth,when we use 8 models to discuss the definition of explosion energy,found that the definition of E x(p2) is more suitable than others.The above conclusions show thatκ0 has a great effect on the core collapse ,shock propagation,explosion energy and core temerature(at t 4),and it is significance for the research of supernova.
引文
[1] Luo Z Q, Liu M Q, Peng Q H et al. Collapsing Velocity and Prompt Explosion of Supernova for Presupernova Model Ws15Μ[J], Chin.J.A.A., 2006,accepted
[2] Bahcall J N. Electron Capture in Stellar Interiors [J]. ApJ, 1964, 139,318.
[3] Baade W, Zwicky F. Proc.Natl.Acad.Sci., USA,1934,20:254;20:259;Phys.Rew., 45:138;46:76
[4] Colgate S A,.Johnson M H.Phys.Rev.Letts.,1960,5(6):235
[5]彭秋和,恒星演化和超新星爆发理论中某些重要的核物理问题,物理学进展,2001,21:225
[6] Clayton D D.Principles of Stellar Evolution and Nucleosynthesis,NewYork :McGraw Hill,1968,Chap.7.
[7] Woosley S E.In:Hauck.,Maeder A. and Meynet Geds. Nucleosynthesis and Chem- ical Evolution.Switzerland:Geneva Observatory,1986,1
[8]黄润乾。恒星物理[M].北京:科学出版社,1998
[9] Shapiro S L and Teukolsky S A.Black Holes, White Dwarfs,and Neutron Stars.A wiley Intersience Publication1984.
[10]李宗伟.核坍缩超新星.天文研究与技术—国家天文台台刊.2004,1(3):163
[11]罗志全.核心坍缩型超新星的相关物理过程及爆发机制的研究[D].2006
[12] Weaver T A, Woosley S E(WW93).Phys.Rep.1993,227:65
[13] Weaver T A, Woosley S E(WW95).APJ Suppl.,1995,101:181
[14] Weaver T A,Heger., Woosley S E.,Reviews of Modern Physics,2002,74, 1015
[15] Nieuwenhuijzen H.,DeJager C.,Astrophs.1990,231,134
[16] Schaller, G.,Schaerer,D.,Meynet,G.,Maeder,A.1992&AS,96,269
[17] Iglesias,C.A.,and F.J.Rogers,1996,Astrophys.J.464,943.
[18] Weaver,T.A.,Zimmermann,G.B., Woosley S E.1978,ApJ,225,1021
[19] Langanke K.,Martinez-Pinedo G.,Nucl.Phys.A673,2000,481
[20] Hoffman,R.D.,S.E. Woosley,and T.A. Weaver,2001,Astrophs. J.549, 1085
[21] Lliadis,C.,D,Auria,J.,Sumner,S.,Thompson,W.,Wiescher,M.2001,ApJS,134,151
[22] Caughlan G A,Folwer W A.At.Data.Tables,1988,40:238
[23] Wilson J.In:Proc.Univ.Illinois Meeting on Numerical Astrophysics. [s.n.],1982
[24] Dai Zigao,Peng Qiuhe,Lu Tan,ApJ,1995,440,815
[25] Anand J D,et. ApJ.,1997,481:954
[26] Chandrasekhar S.APJ(Astrophsics Journal),1931,74:81
[27]刘门全,罗志全,彭秋和谢佐恒,压强梯度对Ws12Μ模型瞬时爆发能量的影响,计算物理,2006,23(4):494
[28]王贻仁,张锁春,谢佐恒,汪惟中,超新星爆发机制和数值模拟[M].郑州:河南科学出版社,2003.
[29] Bahcall J N.Electron Capture in Stellar Interiors[J].ApJ,1964,139, 318.
[30] Bahcall J N.Beta Decay in Stellar Interiors[J].Phys.Rev.,1962,126, 1143
[31] Fuller G M.,Flower W A,W J.Stellar weak interaction rates mass nuclei II. ApJ,1982,252:715
[32]王贻仁,李鸿,姚进。物态方程对恒星星核区坍缩的影响[J].计算物理,1989,6,257
[33] Bonche P,Vantherin D.A&A,1982,112:268
[34] Bethe H A,Brown G E,Cooperstein J,Wilson J R.Nucl.Phys.A.,1983,403:625
[35] Baym G,Bethe H A,Pethick C J.Nucl Phys.A,1971,175:225
[36] May M M,White R H. Phys.Rev.,1966,141(4):1232
[37] May M M,White R H.Meth.Comp.Phys.,1967,7:219
[38] Weaver,T.A.,Zimmerman G.B.,Woosley S E.,APJ,1978,225,10
[39] Hillebrandt W.,Nomoto K.,Wolff R.G.,A&A,1984,122,175
[40] Bruenn S.W.,ApJPS,1985,58,771
[41] Baron E.,Cooperstein J.,Kashana S.,Phy.Rev.Lett.,1985,55,1
[42] Burrows A.,Lattimer J.M.,APJ,1983,270,735
[43] Burrows S.W(B89).APJ,1989,340:955;341:385
[44]汪惟中,王贻仁,张锁春,超新星爆发的前身星模型研究,天体物理学报,1996,16(2):161
[45]张锁春,谢佐恒,王贻仁,II型超新星瞬发爆炸的激波传播,天体物理学报,1997,17(1):43
[46]张锁春,谢佐恒,王贻仁,II型超新星瞬发爆炸成功的简单判据,天体物理学报,1999,19(2):163
[47] Wilson J R.In:Centrella J M,LeBlane J M, Bower R L,ed.Numerical Astrop- hysics.Boston:Jones& Bartlett,1985.422
[48] Lamb D Q,Lattimer J M,Pethick C J,Ravenhall D G.Nucl.Phys.A.,1981,360:459
[2] Bahcall J N. Electron Capture in Stellar Interiors [J]. ApJ, 1964, 139,318.
[3] Baade W, Zwicky F. Proc.Natl.Acad.Sci., USA,1934,20:254;20:259;Phys.Rew., 45:138;46:76
[4] Colgate S A,.Johnson M H.Phys.Rev.Letts.,1960,5(6):235
[5]彭秋和,恒星演化和超新星爆发理论中某些重要的核物理问题,物理学进展,2001,21:225
[6] Clayton D D.Principles of Stellar Evolution and Nucleosynthesis,NewYork :McGraw Hill,1968,Chap.7.
[7] Woosley S E.In:Hauck.,Maeder A. and Meynet Geds. Nucleosynthesis and Chem- ical Evolution.Switzerland:Geneva Observatory,1986,1
[8]黄润乾。恒星物理[M].北京:科学出版社,1998
[9] Shapiro S L and Teukolsky S A.Black Holes, White Dwarfs,and Neutron Stars.A wiley Intersience Publication1984.
[10]李宗伟.核坍缩超新星.天文研究与技术—国家天文台台刊.2004,1(3):163
[11]罗志全.核心坍缩型超新星的相关物理过程及爆发机制的研究[D].2006
[12] Weaver T A, Woosley S E(WW93).Phys.Rep.1993,227:65
[13] Weaver T A, Woosley S E(WW95).APJ Suppl.,1995,101:181
[14] Weaver T A,Heger., Woosley S E.,Reviews of Modern Physics,2002,74, 1015
[15] Nieuwenhuijzen H.,DeJager C.,Astrophs.1990,231,134
[16] Schaller, G.,Schaerer,D.,Meynet,G.,Maeder,A.1992&AS,96,269
[17] Iglesias,C.A.,and F.J.Rogers,1996,Astrophys.J.464,943.
[18] Weaver,T.A.,Zimmermann,G.B., Woosley S E.1978,ApJ,225,1021
[19] Langanke K.,Martinez-Pinedo G.,Nucl.Phys.A673,2000,481
[20] Hoffman,R.D.,S.E. Woosley,and T.A. Weaver,2001,Astrophs. J.549, 1085
[21] Lliadis,C.,D,Auria,J.,Sumner,S.,Thompson,W.,Wiescher,M.2001,ApJS,134,151
[22] Caughlan G A,Folwer W A.At.Data.Tables,1988,40:238
[23] Wilson J.In:Proc.Univ.Illinois Meeting on Numerical Astrophysics. [s.n.],1982
[24] Dai Zigao,Peng Qiuhe,Lu Tan,ApJ,1995,440,815
[25] Anand J D,et. ApJ.,1997,481:954
[26] Chandrasekhar S.APJ(Astrophsics Journal),1931,74:81
[27]刘门全,罗志全,彭秋和谢佐恒,压强梯度对Ws12Μ模型瞬时爆发能量的影响,计算物理,2006,23(4):494
[28]王贻仁,张锁春,谢佐恒,汪惟中,超新星爆发机制和数值模拟[M].郑州:河南科学出版社,2003.
[29] Bahcall J N.Electron Capture in Stellar Interiors[J].ApJ,1964,139, 318.
[30] Bahcall J N.Beta Decay in Stellar Interiors[J].Phys.Rev.,1962,126, 1143
[31] Fuller G M.,Flower W A,W J.Stellar weak interaction rates mass nuclei II. ApJ,1982,252:715
[32]王贻仁,李鸿,姚进。物态方程对恒星星核区坍缩的影响[J].计算物理,1989,6,257
[33] Bonche P,Vantherin D.A&A,1982,112:268
[34] Bethe H A,Brown G E,Cooperstein J,Wilson J R.Nucl.Phys.A.,1983,403:625
[35] Baym G,Bethe H A,Pethick C J.Nucl Phys.A,1971,175:225
[36] May M M,White R H. Phys.Rev.,1966,141(4):1232
[37] May M M,White R H.Meth.Comp.Phys.,1967,7:219
[38] Weaver,T.A.,Zimmerman G.B.,Woosley S E.,APJ,1978,225,10
[39] Hillebrandt W.,Nomoto K.,Wolff R.G.,A&A,1984,122,175
[40] Bruenn S.W.,ApJPS,1985,58,771
[41] Baron E.,Cooperstein J.,Kashana S.,Phy.Rev.Lett.,1985,55,1
[42] Burrows A.,Lattimer J.M.,APJ,1983,270,735
[43] Burrows S.W(B89).APJ,1989,340:955;341:385
[44]汪惟中,王贻仁,张锁春,超新星爆发的前身星模型研究,天体物理学报,1996,16(2):161
[45]张锁春,谢佐恒,王贻仁,II型超新星瞬发爆炸的激波传播,天体物理学报,1997,17(1):43
[46]张锁春,谢佐恒,王贻仁,II型超新星瞬发爆炸成功的简单判据,天体物理学报,1999,19(2):163
[47] Wilson J R.In:Centrella J M,LeBlane J M, Bower R L,ed.Numerical Astrop- hysics.Boston:Jones& Bartlett,1985.422
[48] Lamb D Q,Lattimer J M,Pethick C J,Ravenhall D G.Nucl.Phys.A.,1981,360:459
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