Discrete Scale Relativity and SX Phoenicis Variable Stars

Author(s)
Robert L Oldershaw

ABSTRACT

Discrete Scale Relativity proposes a new symmetry principle called discrete cosmological self-similarity which relates each class of systems and phenomena on a given Scale of nature’s discrete cosmological hierarchy to the equivalent class of analogue systems and phenomena on any other Scale. The new symmetry principle can be understood in terms of discrete scale invariance involving the spatial, temporal and dynamic parameters of all systems and phenomena. This new paradigm predicts a rigorous discrete self-similarity between Stellar Scale variable stars and Atomic Scale excited atoms undergoing energy-level transitions and sub-threshold oscillations. Previously, methods for demonstrating and testing the proposed symmetry principle have been applied to RR Lyrae, δ Scuti and ZZ Ceti variable stars. In the present paper we apply the same analytical methods and diagnostic tests to a new class of variable stars: SX Phoenicis variables. Double-mode pulsators are shown to provide an especially useful means of testing the uniqueness and rigor of the conceptual principles and discrete self-similar scaling of Discrete Scale Relativity. These research efforts will help theoretical physicists to understand the fundamental discrete self-similarity of nature, and to model both stellar and atomic systems with one unified physics.

Discrete Scale Relativity proposes a new symmetry principle called discrete cosmological self-similarity which relates each class of systems and phenomena on a given Scale of nature’s discrete cosmological hierarchy to the equivalent class of analogue systems and phenomena on any other Scale. The new symmetry principle can be understood in terms of discrete scale invariance involving the spatial, temporal and dynamic parameters of all systems and phenomena. This new paradigm predicts a rigorous discrete self-similarity between Stellar Scale variable stars and Atomic Scale excited atoms undergoing energy-level transitions and sub-threshold oscillations. Previously, methods for demonstrating and testing the proposed symmetry principle have been applied to RR Lyrae, δ Scuti and ZZ Ceti variable stars. In the present paper we apply the same analytical methods and diagnostic tests to a new class of variable stars: SX Phoenicis variables. Double-mode pulsators are shown to provide an especially useful means of testing the uniqueness and rigor of the conceptual principles and discrete self-similar scaling of Discrete Scale Relativity. These research efforts will help theoretical physicists to understand the fundamental discrete self-similarity of nature, and to model both stellar and atomic systems with one unified physics.

Cite this paper

nullR. Oldershaw, "Discrete Scale Relativity and SX Phoenicis Variable Stars,"*International Journal of Astronomy and Astrophysics*, Vol. 1 No. 2, 2011, pp. 39-44. doi: 10.4236/ijaa.2011.12006.

nullR. Oldershaw, "Discrete Scale Relativity and SX Phoenicis Variable Stars,"

References

[1] R. L. Oldershaw, “The Self-Similar Cosmological Paradigm―A New Test and Two New Predictions,” Astrophysical Journal, Vol. 322, No. 1, 1987, pp. 34-36. doi:10.1086/165699

[2] R. L. Oldershaw, “Self-Similar Cosmological Model: Introduction and Empirical Tests,” International Journal of Theoretical Physics, Vol. 28, No. 6, 1989, pp. 669-694. doi:10.1007/BF00669984

[3] R. L. Oldershaw, “Self-Similar Cosmological Model: Technical Details, Predictions, Unresolved Issues and Implications,” International Journal of Theoretical Physics, Vol. 28, No. 12, 1989, pp. 1503-1532. doi:10.1007/BF00671591

[4] R. L. Oldershaw, “Mass Estimates for Galactic Dark Matter Objects as a Test of a Fractal Cosmological Paradigm,” Fractals, Vol. 10, No. 1, 2002, pp. 27-38. doi:10.1142/S0218348X02000987

[5] R. L. Oldershaw, “Discrete Scale Relativity,” Astrophy- sics and Space Science, Vol. 311, No. 4, 2007, pp. 413- 433. doi:10.1007/s10509-007-9557-x

[6] R. L. Oldershaw, “Fractal Cosmology Website,” 2007. http://www.amherst.edu/~rloldershaw

[7] R. L. Oldershaw, “The Meaning of the Fine Structure Constant,” Electronic Journal of Theoretical Physics, Vol. 5, No. 17, 2008, pp. 207-214.

[8] I. Soszynski, et al., “The Optical Gravitational Lensing Experiment. Catalog of RR Lyrae Stars in the Large Magellanic Cloud,” Acta Astronomica, Vol. 53, 2003, pp. 93-116. www.arxiv.org/pdf/astro-ph/0306041

[9] R. L. Oldershaw, “Discrete Self-Similarity of RR Lyrae Stars: II. Period Spectrum for a Very Large Sample,” 2008. http://www.arxiv.org/ftp/astro-ph/papers/0606/0606128.pdf

[10] R. L. Oldershaw, “Discrete Cosmological Self-Si- milarity and Delta Scuti Stars,” 2008. http://www.arxiv.org/ftp/astro-ph/papers/0601/0601038.pdf

[11] R. L. Oldershaw, “ZZ Ceti Stars: Fractal Analogues of Excited He+ Ions,” 2009. http://www.arxiv.org/ftp/astro-ph/papers/0602/0602451.pdf

[12] E. G. Hintz, M. D. Joner and M. Ivanushkina, “Period Changes in the SX Phoenicis Star DY Pegasi,” Publications of the Astronomical Society of the Pacific, Vol. 116, No. 820, 2004, pp. 543-553. doi:10.1086/420858

[13] J. N. Fu, et al., “Pulsations and Period Changes of the SX Phoenicis Star DY Pegasi,” Publications of the Astronomical Society of the Pacific, Vol. 121, No. 877, 2009, pp. 251-259. doi:10.1086/597829

[14] Y. B. Jeon, et al., “Discovery of an SX Phoenicis Type Pulsating Component in the Algol-Type Semidetached Eclipsing Binary QU Sagittae in M71,” The Astrophys Journal Letters, Vol. 636, No. 2, 2006, pp. 129-132. doi:10.1086/500263

[15] S. Fauvaud, et al., “A Comprehensive Study of the SX Phoenicis Star BL Camelopardalis,” Astron & Astrophy- sics, Vol. 451, No. 3, 2006, pp. 999-1008. doi:10.1051/0004-6361:20053841

[1] R. L. Oldershaw, “The Self-Similar Cosmological Paradigm―A New Test and Two New Predictions,” Astrophysical Journal, Vol. 322, No. 1, 1987, pp. 34-36. doi:10.1086/165699

[2] R. L. Oldershaw, “Self-Similar Cosmological Model: Introduction and Empirical Tests,” International Journal of Theoretical Physics, Vol. 28, No. 6, 1989, pp. 669-694. doi:10.1007/BF00669984

[3] R. L. Oldershaw, “Self-Similar Cosmological Model: Technical Details, Predictions, Unresolved Issues and Implications,” International Journal of Theoretical Physics, Vol. 28, No. 12, 1989, pp. 1503-1532. doi:10.1007/BF00671591

[4] R. L. Oldershaw, “Mass Estimates for Galactic Dark Matter Objects as a Test of a Fractal Cosmological Paradigm,” Fractals, Vol. 10, No. 1, 2002, pp. 27-38. doi:10.1142/S0218348X02000987

[5] R. L. Oldershaw, “Discrete Scale Relativity,” Astrophy- sics and Space Science, Vol. 311, No. 4, 2007, pp. 413- 433. doi:10.1007/s10509-007-9557-x

[6] R. L. Oldershaw, “Fractal Cosmology Website,” 2007. http://www.amherst.edu/~rloldershaw

[7] R. L. Oldershaw, “The Meaning of the Fine Structure Constant,” Electronic Journal of Theoretical Physics, Vol. 5, No. 17, 2008, pp. 207-214.

[8] I. Soszynski, et al., “The Optical Gravitational Lensing Experiment. Catalog of RR Lyrae Stars in the Large Magellanic Cloud,” Acta Astronomica, Vol. 53, 2003, pp. 93-116. www.arxiv.org/pdf/astro-ph/0306041

[9] R. L. Oldershaw, “Discrete Self-Similarity of RR Lyrae Stars: II. Period Spectrum for a Very Large Sample,” 2008. http://www.arxiv.org/ftp/astro-ph/papers/0606/0606128.pdf

[10] R. L. Oldershaw, “Discrete Cosmological Self-Si- milarity and Delta Scuti Stars,” 2008. http://www.arxiv.org/ftp/astro-ph/papers/0601/0601038.pdf

[11] R. L. Oldershaw, “ZZ Ceti Stars: Fractal Analogues of Excited He+ Ions,” 2009. http://www.arxiv.org/ftp/astro-ph/papers/0602/0602451.pdf

[12] E. G. Hintz, M. D. Joner and M. Ivanushkina, “Period Changes in the SX Phoenicis Star DY Pegasi,” Publications of the Astronomical Society of the Pacific, Vol. 116, No. 820, 2004, pp. 543-553. doi:10.1086/420858

[13] J. N. Fu, et al., “Pulsations and Period Changes of the SX Phoenicis Star DY Pegasi,” Publications of the Astronomical Society of the Pacific, Vol. 121, No. 877, 2009, pp. 251-259. doi:10.1086/597829

[14] Y. B. Jeon, et al., “Discovery of an SX Phoenicis Type Pulsating Component in the Algol-Type Semidetached Eclipsing Binary QU Sagittae in M71,” The Astrophys Journal Letters, Vol. 636, No. 2, 2006, pp. 129-132. doi:10.1086/500263

[15] S. Fauvaud, et al., “A Comprehensive Study of the SX Phoenicis Star BL Camelopardalis,” Astron & Astrophy- sics, Vol. 451, No. 3, 2006, pp. 999-1008. doi:10.1051/0004-6361:20053841