长周期变星的演化及振动
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摘要
长周期变星的演化和振动一直是引人入胜的课题。这不仅仅是因
为在它们的变化过程中有丰富的物理内容，更重要的是可以用它们来做
河外星系距离的定标者。在本文中详细的计算了在z=0.0005，z=0.001，
z=0.005，z=0.01和z=0.02这样一个大的金属丰度跨度下，质量为15M
_⊙，20M_⊙和30M_⊙恒星的演化和振动。在计算中采用了最新的不透明度，
考虑了星风损失对大质量星的影响，对于每一个模型都从零年龄主序演
化到了中心氦燃烧结束。在本文中仔细研讨了混合长参数以及中心对流
核的对流超射对演化模型的影响，同时在中心氦燃烧阶段蓝超巨星和红
超巨星的比值被用来限定模型的参数（尤其是混合长和对流起射）。尽管
在本文中并没有得到和观测一致的结论，即随着金属丰度的增加B/R增
加。但是，通过在低金属丰度区采用对流超射，而在高金属丰度区放弃
对流超射这一方法得到了与观测更相符合的比值。
在新的演化模型的基础上，对于大质量星的振动进行了详细的计算。
各项振动的性质用来和LMC，M33以及MW中的RSGs做比较。对于LMC和
M33中长周期变星，理论的周光关系和观测在基频振动模式下很好的符
合；而对于MW中长周期变星，它们更可能在一阶模式下振动。最终，得
到了金属丰度和周光关系的之间的联系，即随着金属丰度的增加，有周
期增加、光度下降的趋势。一个近似的改正δM_(bol)～0.831gZ，对于决定
河外星系的距离相信应该有所改善。
In this thesis we have calculated the evolution models and the
pulsating property of 15M? 2OM0and 30M畇tars under different
metal I icity, in order to understand the dependence of the
per iod條uminosity relation on metal I icity. Up梩o梔ate opacities,
overshootingfrom the convective core and mass loss through the
stellar wind was included in our evolution models. In order to get
better agreement with the observed blue梩o梤ed ratio of supergiant
numbers, we adopted 1.0 and 1.8 as the ratio of the mixing條ength
to local pressure scale height in the convection zone. We find that
normal models without overshooting seems to produce too many blue
supergiants while overshooting models seems to produce too many red
supergiants, but neither of them can correctly predict the tendency
of increasing the B/R ratios with increasing the metal abundance
observed in many stellar systems. This result seems to indicate that
the overshooting from the convective core is strong in extremely
metal梡oor stars and fades gradually away with the increase of the
metal abundance. With a proper combination of model parameters we
have constructed a series of stellar models with a1.0 that give
theoretical B/R ratios in better agreement with the observations,
and these models have been used to calculate the period條uminosity
relation of the RSG long梡eriod variables.
We have compared the theoretical P桳 relations with observed
long梡eriod variables in the LMC, M33 and our Milky Way. The
observed LPVs are in good agreementwith the P桳 relations of the
fundamental mode for the LMC and M33, but the LPVs in the M~I seems
to have shorter periods and more likely to be the first overtone
pulsators. We have found that the period條uminosity relations under
different metal I icity show a tendency of decreasing the luminosity
and increasing the period with the increase of the metal abundance,
3
and the correction of the luminosity at a given period is ~Mb0I
0.836 lgZ.
为在它们的变化过程中有丰富的物理内容，更重要的是可以用它们来做
河外星系距离的定标者。在本文中详细的计算了在z=0.0005，z=0.001，
z=0.005，z=0.01和z=0.02这样一个大的金属丰度跨度下，质量为15M
_⊙，20M_⊙和30M_⊙恒星的演化和振动。在计算中采用了最新的不透明度，
考虑了星风损失对大质量星的影响，对于每一个模型都从零年龄主序演
化到了中心氦燃烧结束。在本文中仔细研讨了混合长参数以及中心对流
核的对流超射对演化模型的影响，同时在中心氦燃烧阶段蓝超巨星和红
超巨星的比值被用来限定模型的参数（尤其是混合长和对流起射）。尽管
在本文中并没有得到和观测一致的结论，即随着金属丰度的增加B/R增
加。但是，通过在低金属丰度区采用对流超射，而在高金属丰度区放弃
对流超射这一方法得到了与观测更相符合的比值。
在新的演化模型的基础上，对于大质量星的振动进行了详细的计算。
各项振动的性质用来和LMC，M33以及MW中的RSGs做比较。对于LMC和
M33中长周期变星，理论的周光关系和观测在基频振动模式下很好的符
合；而对于MW中长周期变星，它们更可能在一阶模式下振动。最终，得
到了金属丰度和周光关系的之间的联系，即随着金属丰度的增加，有周
期增加、光度下降的趋势。一个近似的改正δM_(bol)～0.831gZ，对于决定
河外星系的距离相信应该有所改善。
In this thesis we have calculated the evolution models and the
pulsating property of 15M? 2OM0and 30M畇tars under different
metal I icity, in order to understand the dependence of the
per iod條uminosity relation on metal I icity. Up梩o梔ate opacities,
overshootingfrom the convective core and mass loss through the
stellar wind was included in our evolution models. In order to get
better agreement with the observed blue梩o梤ed ratio of supergiant
numbers, we adopted 1.0 and 1.8 as the ratio of the mixing條ength
to local pressure scale height in the convection zone. We find that
normal models without overshooting seems to produce too many blue
supergiants while overshooting models seems to produce too many red
supergiants, but neither of them can correctly predict the tendency
of increasing the B/R ratios with increasing the metal abundance
observed in many stellar systems. This result seems to indicate that
the overshooting from the convective core is strong in extremely
metal梡oor stars and fades gradually away with the increase of the
metal abundance. With a proper combination of model parameters we
have constructed a series of stellar models with a1.0 that give
theoretical B/R ratios in better agreement with the observations,
and these models have been used to calculate the period條uminosity
relation of the RSG long梡eriod variables.
We have compared the theoretical P桳 relations with observed
long梡eriod variables in the LMC, M33 and our Milky Way. The
observed LPVs are in good agreementwith the P桳 relations of the
fundamental mode for the LMC and M33, but the LPVs in the M~I seems
to have shorter periods and more likely to be the first overtone
pulsators. We have found that the period條uminosity relations under
different metal I icity show a tendency of decreasing the luminosity
and increasing the period with the increase of the metal abundance,
3
and the correction of the luminosity at a given period is ~Mb0I
0.836 lgZ.
引文
黄润乾，恒星物理，1998，科学出版社
黄润乾，李焱，恒星振动理论，1990，科学出版社
李焱，博士论文，1992，云南天文台
李焱，天文学进展，1998，16，92
Aikawa, T., Antonello, E., 2000a, A&A, 363, 593
Aikawa, T., Antonello, E., 2000a, A&A, 363, 601
Arnett W.D., 1991, APJ 383,295
Becker, S.A., 1987, Stellar Pulsation, Lecture Notes in Physics, vol. 274, eds. A.N. Cox, W.M. Sparks, S.G. Starrfiled, Springer verlag, Proceddings, Los Alomos, p. 16
Blaha, C., Humphreys, R.M., 1989, AJ 98, 1598
Bowen, G.H., 1988, Pulsation And Mass Loss In stars, eds. R. Stalio, L.A. Willsion, Kluwer Academic Publisher, p. 3
Bracoto, E., Castellani V., 1993, APJ 410,99
Bressan, A., Fagotto F.,BertelliG., ChiosiC., 1993, A&AS 100,647
Brunish, W.M., Gallagher J.S., Truran J.W., 1986, AJ 91,598
Brunish, W.M.,&TRURAN, J.W., 1982, APJs 49,447
Cassinellii, J.P., 1979, Ann. Rev. Astro. Astrophys 17,275
Catchpole, R.M., Feast, M.W., 1981, mnras 197, 385
Catchpole, R.M., Feast, M.W., 1981, MNRAS 197, 385
Chin C.-W., Stothers R.B., 1991, APJS 77,299
Choisi, C., Meader, A., 1986, Ann. Rev. Astron. Astrophys. 24,329
Chiosi,C., Nasi, E., Sreenivasan, S.R., 1978, A&A 63,103
Dambis, A.K., (1990a), Astron. Tsirk., 1545, 17
Dambis, A.K., (1990b), Astron. Tsirk., 1545, 19
Dambis, A.K., (1990c), Astron. Tsirk., 1546, 19
Dambis, A.K., (1993), Astron. Lett., 19, 172
de Jager c., 1980, The Brightest stars, D. Reidel
de Jager C., Nieuwenhuijzen, H., 1988, Atmospheric Diagnostics of
Stellar Evolution: Chmical Peculiarity, Mass, and Explosion, Ed. K. Nomoto, Lecture Notes in Physics, No. 305, p. 102
El Eid, M.F., 1995, MNRAS, 275, 983
Feast, M. W., 1992, Instabilies in evolved super-and hypergiant, Eds. C. de Jager, H. Nieuwenhui jzen, p. 18
Feast, M.W., 1996, MNRAS 278, 11;
Feast, M. W., Catchpole, R. M., Carter, B. S., Robters, G., 1980, MNRAS 193, 377
Feast, M. W., Whitelock, P. A., 1987, Late Stages Of Stellar Evolution, eds. S. Kowk, S. R. Pottasch, D. Reidel, p. 33
Fitzpatrick, B..L., Garmany, C. D., 1990, APJ 363, 119
Fox, M.W., Wood, P. R., 1982, APJ 259, 198
Frogel, J. A. ,Mould, J. R., Blanco, V.M., 1990, APJ 352, 96
Fusi-Pecci, FR., Renzini, A., 1976, A&A 46,447
Glass, I.S., 1979, MNRAS 186, 317
Goldberg, L., 1979, Q. J. R. Astro. Soc. 20,361
Habing, H. J., 1987, Late Stages Of Stellar Evolution, eds. s. Kwok, S. R. Pottasch, D. Reidel, p. 291
Habing, H. J., te Lintel Hekkert P., van der veen W. E. C. J., 1989, Planetary Nebulae, IAU Symp. No. 131, eds. Torres-Peimbert, p. 359
Haniff, C. A., Scholz, M., Tuthill, P. G., 1995, MNRAS 212, 783;
Herman, J., 1985, Moss Loss From Red Giant, eds. M. Morries, B. Zuckerman, D. Reidel, p. 55
Hinkle, K.H., 1978, APJ 220, 210
Hughes, S.M. G., Wood, P. R., 1990, AJ 99, 784
Humphreys, R. M., 1986, Luminous Stars and Associations in Galaxies, IAU Symp. NO. 116, eds.C.W. H. de Loore, A.J.Willis, P.Laskarides, D. Reidel, p. 45
Jones, T. J., 1987, Late Stages Of Stellar Evolution, eds. s. Kwok,
Kinman, T. D., Mould, J. R., and Wood, P. R., 1987, AJ 93, 833 Kwok, S., Purton, C. R., 1979, Mass Loss and Evolution of 0-Type srars, IAU Symp. No. 83, eds. P. S. Conti, C. W. H. de Loore, D.Redel, p. 151
Kwok, S., 1980, J. R. Astro. Soc. Can. 47,216
Kwok, S., 1984, InRelations Between Chromosphetic Coronal Heating and Mass Loss in Stars, Trieste Workshoip, 3rd
Li, Y., 1992a, A&A 257, 133
Li, Y., 1992b, A&A 257, 145
Li, Y., Gong, Z. G., 1994, A&A 289,449
Limongi, M., Straniero, 0． , Chieffi, A., 2000, APJs, 129,625
Linsky, J. L., 1981, Effects of Mass Loss On Stellar Evolution, IAU Collo. No. 59, eds.C. Chiosi, R. Stalio, D. Reidel, p. 187
Lovy, D., Maeder, A., No?ls, A., Gabriel, M., 1984, A&A 133, 307
Maeder, A., 1980, A&A 90,311
Maeder, A., 1981a, A&A 99,97
Maeder, A., 1981b, A&A 102,401
Meader, A., 1984 in Observational Tests of the Stellar Evolution Theory, eds. A. Meader and A. Renzini, Dordrecht: reidel, p. 299
Meader, A., Meynet, G., 1987 A&A 187, 243
Meader, A., Meynet, G., 1989 A&A 210, 155
Merrill, K. M., 1978, In The Interaction of Varible Stars With Their Enviroment, ed. R. Kippenhehn, J. Rahe, W. Strohmeeir, p. 446． Dordrecht: Reidel
Meynet G., 1992, in The Feedback of chemical evolution on stellar content of galaxies , Eds. D. Alloin and G. Skasinska, Obs. Paris, p. 40
Meynet G., Maeder, A., Schaller, D., Schaerer, D., Charbonnel, C., 1994, A&As 103, 97
Moran, J.M., 1976, In Frontiers of Astrophysics, ed. E. H. Avrett,
p. 385, Cambridge Univ. Press
Mould, J., 1987, PASP 99, 1127
Mould, J., Graham, J. R., Matthews, K., Neugerbauer, G., 1990, APJ 349, 503
Ger, N., Meader, A., 1995, A&A 295, 685
Petit, M., 1987, Variable Stars, John Wiley & Sons, p.65, p.53
Pierce, M. J., Jucevic, J. S., Crabtree, D., 2000, mnras 313, 271
Pottasch, S. R., 1984, Planetary Nebulae, D. Reidel. p. 242
Reimers, D., 1975, Mem. Soc. R. Sci. Liege, 6 Ser., 8, 369
Reimers, D., 1978, In The Interaction of Varible Stars With Their Envrioment, ed. R. Kippenhahn, J. Rahe, W. Strohmeir, p. 559, Dordrecht: Reidel
Reimers, D., 1981, In physical Processes in Red Giants, ed.I.Iben Jr., A. Renzini, p. 269． Dordrecht: Reidel
Renzini, A., 1981, In Physical Processes In Red Giants, ed.I. Iben Jr.,
Renzini, p. 431． Dordrecht: Reidel
Salasnich, B., Bressan, A., Chiosi, C., 1999, APJ, 342, 131
Schaller, D., Meynet.G., Maeder, A., Schaller, G., 1993, A&As 98, 523
Smith V.V, Lambert, D. L., McWilliam, A., 1987, APJ 320, 862
Stothers, R., 1969, APJ 156,541
Stothers, R., Leung, K. C., 1971, A&A 10, 290;
Stothers R. B., Chin C.-W., 1992, APJ 390,136
Stothers R. B., Chin C.-W., 2000, APJ 540,1041
Tuchman, Y., 1983, Planetary Nebulae, IAU Symp. NO. 103, ed. D. r. flower, p. 281
Tuchman, Y., 1999, IAU, Symp, 191, 123
Tuchman, Y., Sack, N. , Barkat, Z., 1979, APJ 234, 217
Van Leeuwen, F., Feast, M.W., Whitelock, P. A., Yudin, B., 1997,
MNRAS 287, 1027
Vas.siliadis, E., Wood, P. R., 1992, Proc. ASA 10(1) , 30 Wannier, P.G., 1984, Cool Stars, Stellar Systems, and the Sun, eds. H. Araki et al., p. 296
Whitelock, P. A., Pottasch, S. R., Feast, M. W., 1987, Late Stages Of Stellar Evolution, eds. S. Kwok, S. R. Pottasch, D.Reidel, p. 269
Willson, L. A., 1986, JAAVSO, vol.15, No. 2, p. 228 S. R. Pottasch, D.Reidel, p. 3
Willson, L. A., 1987, Late Stages Of Stellar Evolution, eds. s. Kwok, S. R. Pottasch, D.Reidel, p. 253
Wood, P.R., 1974, APJ 190, 609
Wood, P.R., 1990a, Confrontation between stellar pulsation and Evolution, Astronomical Society of the Pacific Confrence Series, vol.11, eds. C. Cacciari, C. Glementini, p. 355
Wood , P.R., 1990b, From Miras to Planetary Nebulae, eds. M. O. Mennessier, Omont, p. 67
Wood, P. R., Bessell, M.S., Fox, M.W., 1983, APJ 272,99
Wood, P. R., Moore, G. L G., Hughes, S. M. G., 1991, in The Magellanic Clouds, IAU Symp, 148, eds. R. Haynes, D.Miline, P. 245
Wood, P. R., Vassiliadis, E., 1992, Highlighes of Astronomy, Vol. 9, Ed. J. Bergron, p. 617
Wood, P.R., et al. 1992, APJ 397, 552
Wood, P.R. et. al, 1991, The Magallanic Clouds, IAU Symp. NO. 148, Eds. R. Haynes, D.Milne, p. 386;
黄润乾，李焱，恒星振动理论，1990，科学出版社
李焱，博士论文，1992，云南天文台
李焱，天文学进展，1998，16，92
Aikawa, T., Antonello, E., 2000a, A&A, 363, 593
Aikawa, T., Antonello, E., 2000a, A&A, 363, 601
Arnett W.D., 1991, APJ 383,295
Becker, S.A., 1987, Stellar Pulsation, Lecture Notes in Physics, vol. 274, eds. A.N. Cox, W.M. Sparks, S.G. Starrfiled, Springer verlag, Proceddings, Los Alomos, p. 16
Blaha, C., Humphreys, R.M., 1989, AJ 98, 1598
Bowen, G.H., 1988, Pulsation And Mass Loss In stars, eds. R. Stalio, L.A. Willsion, Kluwer Academic Publisher, p. 3
Bracoto, E., Castellani V., 1993, APJ 410,99
Bressan, A., Fagotto F.,BertelliG., ChiosiC., 1993, A&AS 100,647
Brunish, W.M., Gallagher J.S., Truran J.W., 1986, AJ 91,598
Brunish, W.M.,&TRURAN, J.W., 1982, APJs 49,447
Cassinellii, J.P., 1979, Ann. Rev. Astro. Astrophys 17,275
Catchpole, R.M., Feast, M.W., 1981, mnras 197, 385
Catchpole, R.M., Feast, M.W., 1981, MNRAS 197, 385
Chin C.-W., Stothers R.B., 1991, APJS 77,299
Choisi, C., Meader, A., 1986, Ann. Rev. Astron. Astrophys. 24,329
Chiosi,C., Nasi, E., Sreenivasan, S.R., 1978, A&A 63,103
Dambis, A.K., (1990a), Astron. Tsirk., 1545, 17
Dambis, A.K., (1990b), Astron. Tsirk., 1545, 19
Dambis, A.K., (1990c), Astron. Tsirk., 1546, 19
Dambis, A.K., (1993), Astron. Lett., 19, 172
de Jager c., 1980, The Brightest stars, D. Reidel
de Jager C., Nieuwenhuijzen, H., 1988, Atmospheric Diagnostics of
Stellar Evolution: Chmical Peculiarity, Mass, and Explosion, Ed. K. Nomoto, Lecture Notes in Physics, No. 305, p. 102
El Eid, M.F., 1995, MNRAS, 275, 983
Feast, M. W., 1992, Instabilies in evolved super-and hypergiant, Eds. C. de Jager, H. Nieuwenhui jzen, p. 18
Feast, M.W., 1996, MNRAS 278, 11;
Feast, M. W., Catchpole, R. M., Carter, B. S., Robters, G., 1980, MNRAS 193, 377
Feast, M. W., Whitelock, P. A., 1987, Late Stages Of Stellar Evolution, eds. S. Kowk, S. R. Pottasch, D. Reidel, p. 33
Fitzpatrick, B..L., Garmany, C. D., 1990, APJ 363, 119
Fox, M.W., Wood, P. R., 1982, APJ 259, 198
Frogel, J. A. ,Mould, J. R., Blanco, V.M., 1990, APJ 352, 96
Fusi-Pecci, FR., Renzini, A., 1976, A&A 46,447
Glass, I.S., 1979, MNRAS 186, 317
Goldberg, L., 1979, Q. J. R. Astro. Soc. 20,361
Habing, H. J., 1987, Late Stages Of Stellar Evolution, eds. s. Kwok, S. R. Pottasch, D. Reidel, p. 291
Habing, H. J., te Lintel Hekkert P., van der veen W. E. C. J., 1989, Planetary Nebulae, IAU Symp. No. 131, eds. Torres-Peimbert, p. 359
Haniff, C. A., Scholz, M., Tuthill, P. G., 1995, MNRAS 212, 783;
Herman, J., 1985, Moss Loss From Red Giant, eds. M. Morries, B. Zuckerman, D. Reidel, p. 55
Hinkle, K.H., 1978, APJ 220, 210
Hughes, S.M. G., Wood, P. R., 1990, AJ 99, 784
Humphreys, R. M., 1986, Luminous Stars and Associations in Galaxies, IAU Symp. NO. 116, eds.C.W. H. de Loore, A.J.Willis, P.Laskarides, D. Reidel, p. 45
Jones, T. J., 1987, Late Stages Of Stellar Evolution, eds. s. Kwok,
Kinman, T. D., Mould, J. R., and Wood, P. R., 1987, AJ 93, 833 Kwok, S., Purton, C. R., 1979, Mass Loss and Evolution of 0-Type srars, IAU Symp. No. 83, eds. P. S. Conti, C. W. H. de Loore, D.Redel, p. 151
Kwok, S., 1980, J. R. Astro. Soc. Can. 47,216
Kwok, S., 1984, InRelations Between Chromosphetic Coronal Heating and Mass Loss in Stars, Trieste Workshoip, 3rd
Li, Y., 1992a, A&A 257, 133
Li, Y., 1992b, A&A 257, 145
Li, Y., Gong, Z. G., 1994, A&A 289,449
Limongi, M., Straniero, 0． , Chieffi, A., 2000, APJs, 129,625
Linsky, J. L., 1981, Effects of Mass Loss On Stellar Evolution, IAU Collo. No. 59, eds.C. Chiosi, R. Stalio, D. Reidel, p. 187
Lovy, D., Maeder, A., No?ls, A., Gabriel, M., 1984, A&A 133, 307
Maeder, A., 1980, A&A 90,311
Maeder, A., 1981a, A&A 99,97
Maeder, A., 1981b, A&A 102,401
Meader, A., 1984 in Observational Tests of the Stellar Evolution Theory, eds. A. Meader and A. Renzini, Dordrecht: reidel, p. 299
Meader, A., Meynet, G., 1987 A&A 187, 243
Meader, A., Meynet, G., 1989 A&A 210, 155
Merrill, K. M., 1978, In The Interaction of Varible Stars With Their Enviroment, ed. R. Kippenhehn, J. Rahe, W. Strohmeeir, p. 446． Dordrecht: Reidel
Meynet G., 1992, in The Feedback of chemical evolution on stellar content of galaxies , Eds. D. Alloin and G. Skasinska, Obs. Paris, p. 40
Meynet G., Maeder, A., Schaller, D., Schaerer, D., Charbonnel, C., 1994, A&As 103, 97
Moran, J.M., 1976, In Frontiers of Astrophysics, ed. E. H. Avrett,
p. 385, Cambridge Univ. Press
Mould, J., 1987, PASP 99, 1127
Mould, J., Graham, J. R., Matthews, K., Neugerbauer, G., 1990, APJ 349, 503
Ger, N., Meader, A., 1995, A&A 295, 685
Petit, M., 1987, Variable Stars, John Wiley & Sons, p.65, p.53
Pierce, M. J., Jucevic, J. S., Crabtree, D., 2000, mnras 313, 271
Pottasch, S. R., 1984, Planetary Nebulae, D. Reidel. p. 242
Reimers, D., 1975, Mem. Soc. R. Sci. Liege, 6 Ser., 8, 369
Reimers, D., 1978, In The Interaction of Varible Stars With Their Envrioment, ed. R. Kippenhahn, J. Rahe, W. Strohmeir, p. 559, Dordrecht: Reidel
Reimers, D., 1981, In physical Processes in Red Giants, ed.I.Iben Jr., A. Renzini, p. 269． Dordrecht: Reidel
Renzini, A., 1981, In Physical Processes In Red Giants, ed.I. Iben Jr.,
Renzini, p. 431． Dordrecht: Reidel
Salasnich, B., Bressan, A., Chiosi, C., 1999, APJ, 342, 131
Schaller, D., Meynet.G., Maeder, A., Schaller, G., 1993, A&As 98, 523
Smith V.V, Lambert, D. L., McWilliam, A., 1987, APJ 320, 862
Stothers, R., 1969, APJ 156,541
Stothers, R., Leung, K. C., 1971, A&A 10, 290;
Stothers R. B., Chin C.-W., 1992, APJ 390,136
Stothers R. B., Chin C.-W., 2000, APJ 540,1041
Tuchman, Y., 1983, Planetary Nebulae, IAU Symp. NO. 103, ed. D. r. flower, p. 281
Tuchman, Y., 1999, IAU, Symp, 191, 123
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