Approximate universal relations among tidal parameters for neutron star binaries

Abstract

One of largest uncertainties in nuclear physics is the relation between the pressure and density of supranuclear matter: the equation of state. Some of this uncertainty may be removed through future gravitational wave observations of neutron star binaries by extracting the tidal deformabilities (or Love numbers) of neutron stars, a novel way to probe nuclear physics in the high-density regime. Previous studies have shown that only a certain combination of the individual (quadrupolar) deformabilities of each body (the so-called chirp tidal deformability) can be measured with second-generation, gravitational wave interferometers, such as Adv. LIGO, due to correlations between the individual deformabilities. To overcome this, we search for approximately universal (i.e. approximately equation-of-state independent) relations between two combinations of the individual tidal deformabilities, such that once one of them has been measured, the other can be automatically obtained and the individual ones decoupled through these relations. We find an approximately universal relation between the symmetric and the anti-symmetric combination of the individual tidal deformabilities that is equation-of-state-insensitive to 20% for binaries with masses less than 1.7M . We show that these relations can be used to eliminate a combination of the tidal parameters from the list of model parameters, thus breaking degeneracies and improving the accuracy in parameter estimation. A simple (Fisher) study shows that the universal binary Love relations can improve the accuracy in the extraction of the symmetric combination of tidal parameters by as much as an order of magnitude, making the overall accuracy in the extraction of this parameter slightly better than that of the chirp tidal deformability. These new universal relations and the improved measurement accuracy on tidal parameters not only are important to astrophysics and nuclear physics, but also impact our ability to probe extreme gravity with gravitational waves and cosmology.Approximate Universal Relations among Tidal Parameters for NS Binaries * See e.g. [63][64][65][66][67][68][69][70] for other possibilities of probing cosmology with GW observations alone. † The signs of the terms proportional toλ a are opposite those in [46] because we use the convention m 1 ≤ m 2 (so thatλ a ≥ 0), while Ref.[46] used m 1 ≥ m 2 . ‡ The PN expansion is a series in powers of the ratio of the orbital velocity v of the binary to the speed of light c. A term of nPN order in a PN series corresponds to one that is of O[(v/c) 2n ] or equivalently O(x n ), relative to the leading order term in the series. * For rotating NSs, tidal effects enter first through their quadrupole moment, which appear at lower PN order than λ in the gravitational waveform. The effect of the quadrupole, however, is suppressed for * In [78], we show a similar figure for q = 0.75, in which one sees that the error bars for the stiff (soft) EoS classes decreases (increases) compared to those when q = 0.9. Thus, distinguishing betwe...

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“…Lacking enough sensitivity in current GW observations, one is forced to only estimate the mass-weighted tidal deformability, but this prevents the independent extraction of Λ 1 and Λ 2 . Yagi and Yunes [22,23] proposed a solution to this problem by finding "approximately universal" or "EoS-insensitive" relations between the symmetric and anti-symmetric combinations of the tidal deformabilities Λ s,a = 1 2 (Λ 1 ± Λ 2 ), the so-called "binary Love relations." These relations can be used to analytically express Λ s in terms of Λ a (or vice-versa), making the mass-weighted tidal deformability a function of only Λ a .…”