We investigate the gravitational Higgs mechanism in the inspiraling scalarized neutron star-white dwarf (NS-WD) binaries, whose dynamics are described by the scalar-tensor theory. Because of the difference in binding energy of NS and WD, the orbital decay of scalarized NS-WD system actually sources an emission of dipolar gravitational scalar radiation, in addition to the tensor gravitational waves, which breaks the Lorentz invariance constructed in the framework of general relativity. The resulted gravitational scalar radiation field obtains a scalar-energy-density-dependent effective mass, arising from a gravitational scalar potential that consists of a monotonically decreasing self-interactions of gravitational scalar field and an increasing exponential coupling between the scalar field and the NS/WD matter. Owing to a thin-ring-orbit effect, the gravitational interactions encoded by the massive scalar field are screened in the region of binary orbit, with high density of stars’ scalar energy, which gives us the estimation for scalar masses of about 10−21 eV/c2 and leads to a Yulkawa-like correction to the Newtonian potential of the binary system. We demonstrate that the radiated gravitational tensor waves, propagating in the Yukawa type of potential, gain a scalar-background-dependent mass term of the order of 10−23 eV/c2.
References
[1]
Zhang, C.M., Wang, J., Zhao, Y.H., Yin, H.X., Song, L.M., Menezes, D.P., Wickramasinghe, D.T., Ferrario, L. and Chardonnet, P. (2011) Study of Measured Pulsar Masses and Their Possible Conclusions. Astronomy & Astrophysics, 527, A83. https://doi.org/10.1051/0004-6361/201015532
[2]
Demorest, P.B., Pennucci, T., Ransom, S.M., Roberts, M.S.E. and Hessels, J.W.T. (2010) A Two-Solar-Mass Neutron Star Measured Using Shapiro Delay. Nature, 467, 1081-1083. https://doi.org/10.1038/nature09466
[3]
Antoniadis, J., Freire, P.C.C., Wex, N., Tauris, T.M., Lynch, R.S., van Kerkwijk, M.H., Kramer, M., Bassa, C., Dhillon, V.S., Driebe, T., Hessels, J.W.T., Kaspi, V.M., Kondratiev, V.I., Langer, N., Marsh, T.R., McLaughlin, M.A., Pennucci, T.T., Ransom, S.M., Stairs, I.H., van Leeuwen, J., Verbiest, P.W. and Whelan, D.G. (2013) A Massive Pulsar in a Compact Relativistic Binary. Science, 340, 448. https://doi.org/10.1126/science.1233232
[4]
Wang, J., Zhang, C.M., Zhao, Y.H., Kojima, Y., Yin, Y.H. and Song, L.M. (2011) Spin Period Evolution of a Recycled Pulsar in an Accreting Binary. Astronomy & Astrophysics, 526, A88. https://doi.org/10.1051/0004-6361/201015190
[5]
Damour, T. and Esposito-Farese, G. (1993) Nonperturbative Strong Field Effects in Tensor—Scalar Theories of Gravitation. Physical Review Letters, 70, 2220. https://doi.org/10.1103/PhysRevLett.70.2220
[6]
Damour, T. and Esposito-Farese, G. (1996) Tensor-Scalar Gravity and Binary Pulsar Experiments. Physical Review D, 54, 1474. https://doi.org/10.1103/PhysRevD.54.1474
[7]
Palenzuela, C., Barausse, E., Ponce, M. and Lehner, L. (2014) Dynamical Scalarization of Neutron Stars in Scalar-Tensor Gravity Theories. Physical Review D, 89, Article ID: 044024. https://doi.org/10.1103/PhysRevD.89.044024
[8]
Damour, T. and Esposito-Farese, G. (1992) Tensor Multiscalar Theories of Gravitation. Classical and Quantum Gravity, 9, 2093. https://doi.org/10.1088/0264-9381/9/9/015
[9]
Freire, P.C.C., Wex, N., Esposito-Farese, G., Verbiest, J.P.W., Bailes, M., Jacoby, B.A., Kramer, M., Stairs, I.H., Antoniadis, J. and Janssen, G.H. (2012) The Relativistic Pulsar-White Dwarf Binary PSR J1738+0333-II. The Most Stringent Test of Scalar-Tensor Gravity. Monthly Notices of the Royal Astronomical Society, 423, 3328-3343. https://doi.org/10.1111/j.1365-2966.2012.21253.x
[10]
Khoury, J. and Weltman, A. (2004) Chameleon Cosmology. Physical Review D, 69, Article ID: 044026. https://doi.org/10.1103/PhysRevD.69.044026
[11]
Damour, T., Gibbons, G.W. and Gundlach, C. (1990) Dark Matter, Time Varying G, and a Dilaton Field. Physical Review Letters, 64, 123. https://doi.org/10.1103/PhysRevLett.64.123
[12]
Salgado, M., Sudarsky, D. and Nucamendi, U. (1998) On Spontaneous Scalarization. Physical Review D, 58, Article ID: 124003. https://doi.org/10.1103/PhysRevD.58.124003
[13]
Maggiore, M. (2008) Gravitational Waves Volume 1: Theory and Experiments. Oxford University Press, London.
[14]
Will, C.M. (1993) Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511564246
[15]
Alsing, J., Berti, E., Will, C.M. and Zaglauer, H. (2012) Gravitational Radiation from Compact Binary Systems in the Massive Brans-Dicke Theory of Gravity. Physical Review D, 85, Article ID: 064041. https://doi.org/10.1103/PhysRevD.85.064041
[16]
Wagoner, R.V. (1970) Scalar Tensor Theory and Gravitational Waves. Physical Review D, 1, 3209. https://doi.org/10.1103/PhysRevD.1.3209
[17]
Damour, T. and Esposito-Farese, G. (1998) Gravitational Wave versus Binary—Pulsar Tests of Strong Field Gravity. Physical Review D, 58, Article ID: 042001. https://doi.org/10.1103/PhysRevD.58.042001
[18]
Abbott, B.P., Abbott, R., Abbott, T.D., et al. (2016) Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters, 116, Article ID: 061102. https://doi.org/10.1103/PhysRevLett.116.061102
[19]
Fierz, M. (1939) Uber die relativistische Theorie krvftefreier Teilchen mit beliebigem Spin. Helvetica Physica Acta, 12, 3-37. https://doi.org/10.1002/hlca.19390220102
[20]
Fierz, M. and Pauli, W. (1939) On Relativistic Wave Equations for Particles of Arbitrary Spin in an Electromagnetic Field. Proceedings of the Royal Society of London. Series A, 173, 211. http://www.jstor.org/stable/97457
[21]
Van Dam, H. and Veltman, M. (1970) Massive and Mass-Less Yang-Mills and Gravitational Fields. Nuclear Physics B, 22, 397-411.
[22]
Zakharov, V.I. (1970) Linearized Gravitation Theory and the Graviton Mass. ZhETF Pisma Redaktsiiu, 12, 447.
[23]
Zakharov, V.I. (1970) Linearized Gravitation Theory and the Graviton Mass. Soviet Journal of Experimental and Theoretical Physics Letters, 12, 312.
[24]
Boulware, D.G. and Deser, S. (1972) Can Gravitation Have a Finite Range? Physical Review D, 6, 3368. https://doi.org/10.1103/PhysRevD.6.3368
[25]
Hinterbichler, K. (2012) Theoretical Aspects of Massive Gravity. Reviews of Modern Physics, 84, 671. https://doi.org/10.1103/RevModPhys.84.671
[26]
De Rham, C. (2014) Massive Gravity. Living Reviews in Relativity, 17, 7. https://doi.org/10.12942/lrr-2014-7
[27]
Chamseddine, A.H. and Mukhanov, V. (2010) Higgs for Graviton: Simple and Elegant Solution. JHEP, 1008, 011. https://doi.org/10.1007/JHEP08(2010)011
[28]
Oda, I. (2010) Remarks on Higgs Mechanism for Gravitons. Physics Letters B, 690, 322.
[29]
Coates, A., Horbartsch, M.W. and Sotiriou, T.P. (2017) Gravitational Higgs Mechanism in Neutron Star Interiors. Physical Review D, 95, Article ID: 084003. https://doi.org/10.1103/PhysRevD.95.084003
