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Gravitational waves from quasicircular extreme mass-ratio inspirals as probes of scalar-tensor theories

Nicolás Yunes1, Paolo Pani2, and Vitor Cardoso2,3

  • 1Department of Physics, Montana State University, Bozeman, Montana 59717, USA
  • 2CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade Técnica de Lisboa—UTL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
  • 3Department of Physics and Astronomy, The University of Mississippi, University, Mississippi 38677, USA

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Phys. Rev. D 85, 102003 – Published 21 May, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.102003

Abstract

A stellar-mass compact object spiraling into a supermassive black hole, an extreme mass-ratio inspiral, is one of the targets for future space-based gravitational-wave detectors. Such inspirals offer a unique opportunity to learn about astrophysics and test general relativity in the strong field. Here we study whether scalar-tensor theories in asymptotically flat spacetimes can be further constrained with these inspirals. In the extreme mass-ratio limit, and assuming analyticity of the coupling functions entering the action, we show that all scalar-tensor theories universally reduce to massive or massless Brans-Dicke theory. We also show that in this limit, black holes do not emit dipolar radiation to all orders in post-Newtonian theory. For massless theories and quasicircular orbits, we calculate the scalar energy flux in the test-particle Teukolsky formalism to all orders in post-Newtonian theory and fit it to a high-order post-Newtonian expansion. We then derive the post-Newtonian corrections to the scalar-tensor modified, Fourier transform of the gravitational-wave response function and map it to the parametrized post-Einsteinian framework. With the Teukolsky flux at hand, we use the effective-one-body framework adapted to extreme mass-ratio inspirals to calculate the scalar-tensor modifications to the gravitational waveform. We find that such corrections are smaller than those induced in the early inspiral of comparable-mass binaries, leading to projected bounds on the Brans-Dicke coupling parameter that are worse than current Solar System ones. This is because Brans-Dicke theory modifies the weak field, leading to deviations in the energy flux that are largest at small velocities. For massive theories, superradiance can produce resonances in the scalar energy flux that can lead to quasicircular floating orbits outside the innermost stable circular orbit and that last until the supermassive black hole loses enough mass and spin-angular momentum. If such floating orbits occur in the frequency band of a LISA-like mission, they would lead to a large dephasing (typically ∼106  rads) that would prevent detection of such modified inspirals using general relativity templates. A detection that is consistent with general relativity would then rule out the presence of floating resonances at frequencies lower than the lowest inspiral frequency observed, allowing for the strongest constraints yet on massive scalar-tensor theories.

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Phys. Rev. D 85, 102003– Published 21 May, 2012
  • Received 12 December 2011
Article part of CHORUS

© 2012 American Physical Society

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