Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(4): 040401    DOI: 10.1088/1674-1056/20/4/040401
GENERAL Prev   Next  

Determining the long living quasi-normal modes of relativistic stars

Lü Jun-Li(吕君丽)a)† and Suen Wai-Mo(孙纬武)b)c)
a College of Physics and Information Science, Hunan Normal University, Changsha 410081, China; b Department of Physics, Washington University, One Brookings Drive, St. Louis, MO 63130, USAc Department of Physics, Chinese University of Hong Kong, Shatin, Hong Kong, China
Abstract  Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio (M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1) provide detailed steps in our treatment to facilitate future effort in this direction; 2) correct mistakes in the literature on the formulation; and 3) analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.
Keywords:  relativistic stars      non-radial perturbations      gravitational wave      quasi-normal modes  
Received:  13 September 2010      Revised:  06 November 2010      Accepted manuscript online: 
PACS:  04.20.-q (Classical general relativity)  
  04.25.D- (Numerical relativity)  
  04.30.-w (Gravitational waves)  
Fund: Project supported by the Science Foundation of the Education Department of Hunan Province of China (Grant No. 07c578) and in part by the US National Science Foundation NRAC, the McDonnell Center for the Space Sciences of the Washington University (Grant No. MCA93S025).

Cite this article: 

Lü Jun-Li(吕君丽) and Suen Wai-Mo(孙纬武) Determining the long living quasi-normal modes of relativistic stars 2011 Chin. Phys. B 20 040401

[1] http://www.ligo.caltech.edu
[2] http://lisa.nasa.gov
[3] http://www.virgo.infn.it
[4] Thorne K S and Campolattaro A 1967 Astrophys. J. 149 591
[5] Price R and Thorne K S 1969 Astrophys. J. 155 163
[6] Thorne K S 1969a Astrophys. J. 158 1
[7] Thorne K S 1969b Astrophys. J. 158 997
[8] Campolattaro A and Thorne K S 1970 Astrophys. J. 159 847
[9] Lindblom L and Detweiler S L 1983 Astrophys. J. Suppl. 53 73
[10] Detweiler S L and Lindblom L 1985 Astrophys. J. 292 12
[11] Chandrasekhar S and Ferrari V 1991 Proc. R. Soc. Lond. A 432 247
[12] Ferrari V 1992 Phil. Trans. R. Soc. Lond. A 340 423
[13] Balbinski E, Detweiler S and Schutz B F 1985 Mon. Not. R. Astron. Soc. 213 553
[14] Ipser J R and Thorne K S 1973 Astrophys. J. 181 181
[15] Detweiler S L 1975 Astrophys. J. 201 440
[16] Lindblom L and Splinter R S 1989 Astrophys. J. 345 925
[17] Chandrasekhar S and Ferrari V 1991 Proc. R. Soc. Lond. A 434 449
[18] Price R H and Ipser J R 1991 Phys. Rev. D 44 307
[19] Chandrasekhar S and Ferrari V 1992 Proc. R. Soc. Lond. A 437 133
[20] Kokkotas K D and Schutz B F 1992 Mon. Not. R. Astron. Soc. 255 119
[21] Leins M, Noller H P and Soffel M H 1993 Phys. Rev. D 48 3467
[22] Kokkotas K D 1994 Mon. Not. R. Astron. Soc. 268 1015
[23] Andersson N and Kokkotas K D 1996 Phys. Rev. Lett. 77 4134
[24] Andersson N, Kokkotas K D and Schutz B F 1995 Mon. Not. R. Astron. Soc. 274 1039
[25] Andersson N, Kokkotas K D and Schutz B F 1996 Mon. Not. R. Astron. Soc. 280 1230
[26] Andersson N and Kokkotas K D 1998 Mon. Not. R. Astron. Soc. 299 1059
[27] Allen G, Andersson N, Kokkotas K D and Schutz B F 1998 Phys. Rev. D 58 124012
[28] Kokkotas K D and Stergioulas N 1999 Astron. Astrophys. 341 110
[29] Andersson N and Kokkotas K D 1999 Mon. Not. R. Astron. Soc. 320 307
[30] Benhar O, Berti E and Ferrari V 1999 Mon. Not. R. Astron. Soc. 310 797
[31] Yip C W, Chu M C and Leung P T 1999 Astrophys. J. 513 849
[32] Kokkotas K D and Ruoff J 2001 Astron. Astrophys. 366 565
[33] Ruoff J and Kokkotas K D 2001 Mon. Not. R. Astron. Soc. 328 678
[34] Kojima Y and Sakata K 2002 Prog. Theor. Phys. 108 801
[35] Sotani H and Harada T 2003 Phys. Rev. D 68 024019
[36] Sotani H, Khori K and Harada T 2004 Phys. Rev. D 69 084008
[37] Benhar O, Ferrari V and Gualtieri L 2004 Phys. Rev. D 70 124015
[38] Kokkotas K D 2005 Nucl. Phys. Proc. Suppl. 138 433
[39] Samuelsson L, Andersson N and Maniopoulos A 2007 Class. Quantum Grav. 24 4147
[40] Finn L S 1987 Mon. Not. R. Astron. Soc. 227 265
[41] McDermott P N 1990 Mon. Not. R. Astron. Soc. 245 508
[42] Strohmayer T E 1993 Astrophys. J. 417 273
[43] Miniutti G, Pons J A, Berti E, Gualtieri L and Ferrari V 2003 Mon. Not. R. Astron. Soc. 338 389
[44] Ferrari V, Miniutti G and Pons J A 2003 Mon. Not. R. Astron. Soc. 342 629
[45] Ferrari V, Gualtieri L, Pons J A and Stavridis A 2004 Mon. Not. R. Astron. Soc. 350 763
[46] Ferrari V, Gualtieri L and Pons J A 2007 Class. Quantum Grav. 24 5093
[47] Ferrari V, Gualtieri L and Marassi S 2007 Phys. Rev. D 76 104033
[48] Gaertig E and Kokkotas K D 2008 Phys. Rev. D 78 064063
[49] Gaertig E and Kokkotas K D 2009 Phys. Rev. D 80 064026
[50] Lau H K, Leung P T and Lin L M 2010 Astrophys. J. 714 1234
[51] Stergioulas N 1996 http://ads.bao.ac.cn/abs/1996PhDT.........4S
[52] Ott C D, Burrows A, Dessart L and Livne E 2006 Phys. Rev. Lett. 96 201102
[53] Fu W J, Wei H Q and Liu Y X 2008 Phys. Rev. Lett. 101 181102
[54] Cowling T G 1942 Mon. Not. R. Astron. Soc. 101 367
[55] Zerilli F J 1970 Phys. Rev. Lett. 24 737
[56] Fackerell E D 1971 Astrophys. J. 166 197
[57] Chandrasekhar S and Detweiler S 1975 Proc. R. Soc. Lond. A 344 441
[58] http://www.vni.com/products/imsl/
[59] http://www.netlib.org/linpack/ endfootnotesize
[1] Estimation of far-field wavefront error of tilt-to-length distortion coupling in space-based gravitational wave detection
Ya-Zheng Tao(陶雅正), Hong-Bo Jin(金洪波), and Yue-Liang Wu(吴岳良). Chin. Phys. B, 2023, 32(2): 024212.
[2] Simulation of the gravitational wave frequency distribution of neutron star-black hole mergers
Jianwei Zhang(张见微), Chengmin Zhang(张承民), Di Li(李菂), Xianghan Cui(崔翔翰), Wuming Yang(杨伍明), Dehua Wang(王德华), Yiyan Yang(杨佚沿), Shaolan Bi(毕少兰), and Xianfei Zhang(张先飞). Chin. Phys. B, 2021, 30(12): 120401.
[3] Gravitational quasi-normal modes of static R2 Anti-de Sitter black holes
Hong Ma(马洪), Jin Li(李瑾). Chin. Phys. B, 2017, 26(6): 060401.
[4] Orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period
Wang Gang (王刚), Ni Wei-Tou (倪维斗). Chin. Phys. B, 2015, 24(5): 059501.
[5] Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris
Wang Gang (王刚), Ni Wei-Tou (倪维斗). Chin. Phys. B, 2013, 22(4): 049501.
[6] High-frequency gravitational waves having large spectral densities and their electromagnetic response
Li Fang-Yu (李芳昱), Wen Hao (文毫), Fang Zhen-Yun (方祯云). Chin. Phys. B, 2013, 22(12): 120402.
[7] Gravitational waves from the axial perturbations of hyperon stars
Wen De-Hua(文德华), Yan Jing(燕晶), and Liu Xue-Mei(刘雪梅) . Chin. Phys. B, 2012, 21(6): 060402.
[8] Impact of neutron star crust on gravitational waves from the axial  w-modes
Wen De-Hua(文德华), Fu Hong-Yang(付宏洋), and Chen Wei(陈伟). Chin. Phys. B, 2011, 20(6): 060402.
[9] Noise in a coupling electromagnetic detecting system for high frequency gravitational waves
Li Jin(李瑾), Li Fang-Yu(李芳昱), and Zhong Yuan-Hong(仲元红). Chin. Phys. B, 2009, 18(3): 922-926.
[10] Improved calculation of relic gravitational waves
Zhao Wen(赵文). Chin. Phys. B, 2007, 16(10): 2894-2902.
[11] A special form of electrodynamical response to a gravitational wave: outgoing and imploding photon fluxes
Li Fang-Yu (李芳昱), Su Xun (苏荀), Long Bing-Wei (龙炳蔚), Tang Meng-Xi (唐孟希). Chin. Phys. B, 2002, 11(5): 461-466.
No Suggested Reading articles found!