Helically Reduced Wave Equations and Binary Neutron Stars

  • Stephen R. LauEmail author
  • Richard H. Price
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)


We describe ongoing work towards construction—via multidomain, modal, spectral methods—of helically symmetric spacetimes representing binary neutron stars. In particular, we focus on the influence of both the helically reduced wave operator and boundary conditions on the self-consistent field method, a widely used iterative scheme for the construction of stellar models.



We gratefully acknowledge support by NSF grant no. DMS-1216866.


  1. 1.
    S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover, New York, 1967)zbMATHGoogle Scholar
  2. 2.
    I. Hachisu, A versatile method for obtaining structures of rapidly rotating stars. Astrophys. J. Suppl. Ser. 61, 479–507 (1986)CrossRefGoogle Scholar
  3. 3.
    J.P. Ostriker, J.W.-K. Mark, Astrophys. J. 151, 1075–1088 (1968)CrossRefGoogle Scholar
  4. 4.
    M. Beroiz, T. Hagstrom, S.R. Lau, R.H. Price, Multidomain, sparse, spectral-tau method for helically symmetric flow. Comput. Fluids 102, 250–265 (2014)CrossRefMathSciNetGoogle Scholar
  5. 5.
    S.R. Lau, R.H. Price, Sparse modal tau-method for helical binary neutron stars, in Proceedings of Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol. 106 (Springer, Cham, 2015), pp. 315–323Google Scholar
  6. 6.
    S.R. Lau, Stellar surface as low-rank modification in iterative methods for binary neutron stars. J. Comput. Phys. 348, 460–481 (2017)CrossRefMathSciNetGoogle Scholar
  7. 7.
    S.R. Lau, Second-order formalism for helically symmetric spacetimes describing binary neutron stars (2017, in preparation)Google Scholar
  8. 8.
    S.R. Lau, R.H. Price, Multidomain spectral method for the helically reduced wave equation. J. Comput. Phys. 227, 1126–1161 (2007). We regret an error in Eq. (42). The correct expressions are \(\nu ^{\pm } = \left [T_{0}^{{\prime}}(\pm 1),T_{1}^{{\prime}}(\pm 1),T_{2}^{{\prime}}(\pm 1),T_{3}^{{\prime}}(\pm 1),T_{4}^{{\prime}}(\pm 1),\cdots \,\right ] = \left [0,1,\pm 4,9,\pm 16,\cdots \,\right ].\) The right-hand side of the second equation of (69) is also off by a signGoogle Scholar
  9. 9.
    S.R. Lau, R.H. Price, Sparse spectral-tau method for the three-dimensional helically reduced wave equation on two-center domains. J. Comput. Phys. 231(2), 7695–7714 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    C. Beetle, B. Bromley, N. Hernández, R. H. Price, Periodic standing-wave approximation: Post-Minkowski computations. Phys. Rev. D 76, 084016 (2007)CrossRefGoogle Scholar
  11. 11.
    I. Hachisu, A versatile method for obtaining structures of rapidly rotating stars. II. Three-dimensional self-consistent field method. Astrophys. J. Suppl. Ser. 62, 461–499 (1986)Google Scholar
  12. 12.
    I. Hachisu, Y. Eriguchi, K. Nomoto, Fate of merging double white dwarfs. II. Numerical method. Astrophys. J. 311, 214–225 (1986)CrossRefGoogle Scholar
  13. 13.
    C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations (SIAM, Philadelphia, 1995)CrossRefzbMATHGoogle Scholar
  14. 14.
    H.P. Pfeiffer, L.E. Kidder, M.A. Scheel, S.A. Teukolsky, A multidomain spectral method for solving elliptic equations. Comput. Phys. Commun. 152(3), 253–273 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    E.A. Coutsias, T. Hagstrom, J.S. Hesthaven, D. Torres, Integration preconditioners for differential operators in spectral τ-methods. Houst. J. Math. (Special Issue), 21–38 (1996)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA
  2. 2.Department of PhysicsUniversity of Massachusetts at DartmouthDartmouthUSA

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