Mega-Hertz Gravitational Waves from Neutron Star Mergers

2025-05-02 0 0 733.48KB 14 页 10玖币

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Mega-Hertz Gravitational Waves from Neutron Star

Mergers

Jorge Casalderrey-Solana,aDavid Mateos,b,a Mikel Sanchez-Garitaonandiaa,c

aDepartament de F´ısica Qu`antica i Astrof´ısica and Institut de Ci`encies del Cosmos (ICC), Uni-

versitat de Barcelona, Mart´ı i Franqu`es 1, ES-08028, Barcelona, Spain.

bInstituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA), Passeig Llu´ıs Companys 23, ES-

08010, Barcelona, Spain.

cCPHT, CNRS, ´

Ecole Polytechnique, IP Paris, F-91128 Palaiseau, France

Abstract: Neutron star mergers provide a unique laboratory for the study of strong-

ﬁeld gravity coupled to Quantum Chromodynamics in extreme conditions. The frequencies

and amplitudes of the resulting gravitational waves encode invaluable information about

the merger. Simulations to date have shown that these frequencies lie in the kilo-Hertz

range. They have also shown that, if Quantum Chromodynamics possesses a ﬁrst-order

phase transition at high baryon density, then this is likely to be accessed during the merger

dynamics. Here we show that this would result in the nucleation of superheated and/or

supercompressed bubbles whose subsequent dynamics would produce gravitational waves

in the Mega-Hertz range. We estimate the amplitude of this signal and show that it may fall

within the expected sensitivity of future superconducting radio-frequency cavity detectors

for mergers at distances up to tens of Mega-parsecs.

arXiv:2210.03171v1 [hep-th] 6 Oct 2022

Contents

1 Introduction 1

2 Frequency 3

3 Characteristic strain 8

4 Discussion 10

1 Introduction

The revolutionary discovery of gravitational waves (GW) has opened two unprecedented

windows into the Universe: one into the strong-ﬁeld regime of gravity, and another one

into the dynamics of quantum matter. These two aspects are often intertwined. This is

beautifully illustrated by neutron star (NS) mergers, in which quarks and gluons described

by Quantum Chromodynamics (QCD) interact in the strong gravitational ﬁeld sourced by

the quarks and gluons themselves.

Most of the merger dynamics can be accurately described by numerical simulations

of magneto-hydrodynamics coupled to general relativity (for a review, see e.g. [1]). One

robust conclusion of these simulations is that the characteristic lifetime of the system is

of order of several, possibly 10, milliseconds (ms). These simulations take as an input the

properties of QCD, in particular its Equation of State (EoS). At zero baryon density the

EoS can be reliably determined via the lattice formulation of QCD. In contrast, the famous

sign problem [2] renders this tool inapplicable at the baryon densities of interest for NS

physics. In particular, it is unknown whether QCD possesses ﬁrst-order phase transitions

(FOPT) in this region. Nevertheless, a variety of arguments suggest that at least two FOPT

may be present [3–6], as sketched in Fig. 1. One is the transition from hadronic matter

to deconﬁned, quark matter. The other is the transition from a non-superconducting to

a color-superconducting phase. We emphasize that, while these transitions are well moti-

vated, at the theoretical level their existence cannot be rigorously established at present.

NS mergers have the potential to establish this experimentally, possibly in combination

with heavy ion collision experiments. To realise this potential, a theoretical understanding

of the imprints of a phase transition on the GW spectrum is indispensable.

Numerical simulations of NS mergers based on EoS with a hadronic-quark matter phase

transition include [7–12]. These studies have shown that the dynamics of the merger results

in the formation of regions in which the matter is suﬃciently heated and/or compressed so

that the thermodynamically preferred phase is the quark-matter phase. We will generically

– 1 –

Hadronic Quark Matter

in the cosmological case the metastable phase is supercooled. In this ﬁrst paper we will take

advantage of the physical picture that emerges from the large body of work devoted to the

cosmological case to give an order-of-magnitude estimate of the frequency and amplitude

of the GW signal in a neutron star merger. A more reﬁned analysis will be presented

elsewhere [14].

In the cosmological case the separation of scales is provided by the fact that the

expansion rate of the Universe, H1,withHthe Hubble rate, is much longer than the

microscopic time scale given by the inverse of the local temperature, T1. As the Universe

expands and cools down it eventually enters the metastable phase. At some point bubbles

of the stable phase begin to nucleate. These bubbles then grow and collide and eventually

leave behind a superposition of long-lived sound waves propagating on the stable phase.

At suﬃciently late times turbulence may also develop. Although each of these processes

contributes to the GW spectrum, it is believed that the dominant contribution comes from

collisions of sound waves with one another. As a ﬁrst approximation, we will assume that

the same may be true in a NS merger. We will ﬁrst determine the peak frequency of the

GWs and then we will estimate their characteristic strain.

The peak wavelength of the produced GWs is given by the characteristic wavelength

of the sound waves, which in turn is determined by the mean bubble separation, R.To

estimate the latter we recall that, once the system is in the metastable phase, the bubble

nucleation rate per unit volume takes the form

(t)

V=µ(t)4eS[µ(t)] ,(2.1)

where Sis the action of the critical bubble at the chemical potential µ

. This scale, which is the dominant one in NS, would be replaced by the temperature in

the cosmological case. The phase transition starts when the nucleation rate in the available

volume of metastable phase becomes comparable to the characteristic evolution rate of the

system. NS merger simulations show that the typical size of a HoCS is L⇠1 km. In the

cosmological case this would be the Hubble radius, H1. The evolution rate has units of

inverse time and measures the rate at which the physical properties of the system change,

for example 1

⌧=1

dµ

dt .(2.2)

NS simulations show that this is of order ⌧⇠1 ms. In the cosmological case this would be

the Hubble expansion rate, H1. Using these values, together with µ⇠1 GeV, we see that

the phase transition starts when the action of the critical bubble reaches the numerical

value

S⇠

for the HoCS with a characteristic time scale set by the merger ⌧⇠1ms. Its relation

to the heating/compression rate is,

Recent NS merger simulations show that a typical size LHoCS ⇠1km for the HoCS

with a characteristic time scale set by the merger ⌧⇠1ms. Its relation to the heat-

ing/compression rate is,

–3–

Non-superconducting

Superconducting