Apsidal-Motion Constants for Polytropic Models

Brooker, R. A.; Olle, T. W.

doi:10.1093/mnras/115.1.101

Cited by 53 publications

(61 citation statements)

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“…[8,12]. The parameter depends on the EOS via both the NS radius R and a dimensionless quantity k 2 , called the Love number [13][14][15]: ¼ 2=ð3GÞk 2 R 5 . The relativistic Love numbers of polytropic 1 EOS were examined first by Flanagan and Hinderer [11,16] and later by others in more detail [17,18].…”

Section: Introductionmentioning

confidence: 99%

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

et al. 2010

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The early part of the gravitational wave signal of binary neutron-star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability , which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate for a wide range of equations of state and find that the value of spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron-star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in increases steeply with the total mass of the binary. Comparing the errors with the expected range of , we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature.

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Section: Introductionmentioning

confidence: 99%

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

et al. 2010

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“…BDs may rather be treated as polytropes of order n = 3/2 (Baraffe, private communication). We infer the Love number from the relation k 2 = 2k aps (Mardling & Lin 2002) and use the tables of apsidal motion constants k aps given in Brooker & Olle (1955). These authors provide numerical calculations for k aps for a polytrope of n = 3/2.…”

Section: Tidal Modelsmentioning

confidence: 99%

Tidal effects on brown dwarfs: application to the eclipsing binary 2MASS J05352184-0546085

Heller¹,

Jackson²,

Barnes

et al. 2010

A&A

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Context. 2MASS J05352184−0546085 (2M0535−05) is the only known eclipsing brown dwarf (BD) binary, and so may serve as a benchmark for models of BD formation and evolution. However, theoretical predictions of the system's properties seem inconsistent with observations: i) the more massive (primary) component is observed to be cooler than the less massive (secondary) one; ii) the secondary is more luminous (by ≈10 24 W) than expected. Previous explanations for the temperature reversal have invoked reduced convective efficiency in the structure of the primary, connected to magnetic activity and to surface spots, but these explanations cannot account for the enhanced luminosity of the secondary. Previous studies also considered the possibility that the secondary is younger than the primary. Aims. We study the impact of tidal heating to the energy budget of both components to determine if it can account for the observed temperature reversal and the high luminosity of the secondary. We also compare various plausible tidal models to determine a range of predicted properties. Methods. We apply two versions of two different, well-known models for tidal interaction, respectively: i) the "constant-phase-lag" model; and ii) the "constant-time-lag" model and incorporate the predicted tidal heating into a model of BD structure. The four models differ in their assumptions about the rotational behavior of the bodies, the system's eccentricity and putative misalignments ψ between the bodies' equatorial planes and the orbital plane of the system. Results. The contribution of heat from tides in 2M0535−05 alone may only be large enough to account for the discrepancies between observation and theory in an unlikely region of the parameter space. The tidal quality factor Q BD of BDs would have to be 10 3.5 and the secondary needs a spin-orbit misalignment of 50 • . However, tidal synchronization time scales for 2M0535−05 restrict the tidal dissipation function to log(Q BD ) 4.5 and rule out intense tidal heating in 2M0535−05. We provide the first constraint on Q for BDs. Conclusions. Tidal heating alone is unlikely to be responsible for the surprising temperature reversal within 2M0535−05. But an evolutionary embedment of tidal effects and a coupled treatment with the structural evolution of the BDs is necessary to corroborate or refute this result. The heating could have slowed down the BDs' shrinking and cooling processes after the birth of the system ≈1 Myr ago, leading to a feedback between tidal inflation and tidal heating. Observations of old BD binaries and measurements of the Rossiter-McLaughlin effect for 2M0535−05 can provide further constraints on Q BD .

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“…In Newtonian gravity, apsidal constants can be computed by a standard method for different polytropic indices n or Γ = 1 + 1/n and different values of l using the numerical method described in [22]. The results are listed, for example, in the classical monographs by Kopal [23,24].…”

Section: Apsidal Constants In Newtonian Gravitymentioning

confidence: 99%

“…Since these values are needed for neutron stars, we report here results of our own numerical calculations. In Newtonian gravity, apsidal constants are defined by the relation (see Appendix B of [6] for a detailed discussion) [22] and Table II in [23]); l is the angular harmonic index, Γ and n are adiabatic indices, with Γ = 1 + 1/n. where R is the stellar radius and the function η l is a solution of the Clairaut-Radau differential equation…”

Section: Apsidal Constants In Newtonian Gravitymentioning

confidence: 99%

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Post-Newtonian diagnosis of quasiequilibrium configurations of neutron star–neutron star and neutron star–black hole binaries

Berti¹,

Iyer²,

Will³

2008

Phys. Rev. D

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We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for non-spinning double neutron star and neutron star-black hole binary systems. The PN equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of "apsidal" constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are becoming extreme. We show that the differences could be interpreted as representing small residual eccentricity in the initial orbits. In comparing the diagnostic with preliminary numerical data on neutron star-black hole binaries, we find less agreement.

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Apsidal-Motion Constants for Polytropic Models

Cited by 53 publications

References 0 publications

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

Tidal effects on brown dwarfs: application to the eclipsing binary 2MASS J05352184-0546085

Post-Newtonian diagnosis of quasiequilibrium configurations of neutron star–neutron star and neutron star–black hole binaries

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