J. Astrophys. Astr. (2018) 39:45 © Indian Academy of Sciences https://doi.org/10.1007/s12036-018-9536-3 Neutron star mergers in the context of the hadron–quark phase transition MATTHIAS HANAUSKE1,2,∗ and LUKE BOVARD1 1Institut für Theoretische Physik, Max-von-Laue-Straße 1, 60438 Frankfurt, Germany. 2Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438 Frankfurt, Germany. ∗Corresponding author. E-mail: [email protected] MS received 5 June 2018; accepted 6 July 2018; published online 14 August 2018 Abstract. The long awaited event of the detection of a gravitational wave from a binary neutron star merger and its electromagnetic counterparts marked the beginning of a new era in observational astrophysics. The brand- new field of gravitational wave astronomy combined with multi-messenger observations will uncover violent, highly energetic astrophysical events that could not be explored before by humankind. This article focuses on the presumable appearance of a hadron–quark phase transition and the formation of regions of deconfined quark matter in the interior of a neutron star merger product. The evolution of density and temperature profiles inside the inner region of the produced hypermassive/supramassive neutron star advises an incorporation of a hadron–quark phase transition in the equation of state of neutron star matter. The highly densed and hot neutron star matter of the remnant populate regions in the QCD phase diagram where a non neglectable amount of deconfined quark matter is expected to be present. If a strong hadron–quark phase transition would happen during the post-merger phase, it will be imprinted in the spectral properties of the emitted gravitational wave signal and might give an additional contribution to the dynamically emitted outflow of mass. Keywords. Binary neutron star mergers—hadron–quark phase transition. 1. Introduction the equation of state (EoS) of dense matter (Bauswein et al. 2017; Rezzolla et al. 2018; Margalit & Metzger One hundred years after Albert Einstein developed 2017; Paschalidis et al. 2018; Most et al. 2018; De et al. the field equations of general relativity and predicted 2018; Abbott et al. 2018a,b). However, the main differ- the existence of gravitational waves, his theory tri- ence between GWs originating from a merger of two umphantly corroborates all experimental and observa- BHs or NSs is the possibility of an existence of a post- tional tests it has been put through to date. Not even merger phase after the collisions of the two objects. two years after the first detection of a gravitational wave Indeed, the most interesting part of the high density and (GW) emanated from the inward spiral and merger of a temperature regime of the EoS is solely imprinted in the pair of black holes by LIGO (Abbott et al. 2016), GWs post-merger GW emission from the remnant hypermas- from a binary neutron star (BNS) merger have been sive/supramassive neutron star (HMNS/SMNS). The recently discovered. In August 2017, the GWs (Abbott GWs produced by a merger of two NSs are by far et al. 2017a), a 1.7 s delayed gamma-ray burst (Abbott more interesting as the GWs resulting from a binary et al. 2017b and the electromagnetic counterparts of an black hole merger. As in the case of an existence of a associated kilonova (Abbott et al. 2017c) were detected post-merger phase, the high density regime of the EOS from a BNS merger by the LIGO/Virgo collaboration might be deduceable by a frequency analysis of the and numerous observatories around the world. This observed GW (Rezzolla & Takami 2016). This post- long-awaited event (GW170817) marks the beginning merger emission was not observed in GW170817, but of the new field of multi-messenger gravitational wave will possibly be detected in forthcoming events within astronomy. Exploiting the extracted tidal deformations the next observing run (Abbott et al. 2017d). of the two neutron stars from the late inspiral phase A large number of numerical-relativity simulations and other properties of GW170817, it is now possible of BNS mergers have been investigated long before to severely constrain several global characteristics of the detection of GW170817 and the emitted GWs, the 45 Page 2 of 11 J. Astrophys. Astr. (2018) 39:45 interior structure of the generated HMNS/SMNS, the 2. Relativistic hydrodynamics and numerical impact of initial spin and mass ratio (Kastaun et al. general relativity 2017; Dietrich et al. 2017), the accurate measurement of the amount of ejected material from the merger, the Einstein’s theory of general relativity and the synthetic light curves of the produced kilonova signal, resulting general relativistic conservation laws for the distribution of the abundances of heavy-elements, energy-momentum in connection with the rest mass the impact of magnetic fields, and last but not the least, conservation are the theoretical groundings of BNS the temperature and density distributions of the pro- mergers: duced remnant have been analysed in detail (Baiotti & 1 Rezzolla 2017). The merger is an extremely disruptive Rμν − gμν R = 8π Tμν 2 process and mass can be ejected either very rapidly – via μν μ ∇μT = 0 , ∇μ ρ u = 0. (1) tidal torques at the time of the dynamically merger or encounter – or more slowly – via winds that can be due Tμν describes the energy-momentum tensor, Rμν is the to a number of different processes, which range from Ricci tensor, which contains first and second deriva- shock-heating to neutrino emission. This gravitationally tives of the space–time metric gμν, ∇μ is the covariant unbound matter represents the perfect site for r-process derivative and uμ is the four velocity of the star’s nucleosynthesis and, if it contains sufficient mass, can fluid. The Einstein equation (first equation in equa- also lead to a bright electromagnetic signal, known as tion (1)) describes in which way the space-time structure a kilonova, as the material decays radioactively. In the need to bend (left-hand side of the equation) if energy- follow-up observations of GW170817, a bright kilonova momentum is present (right-hand side of the equation). was observed providing the first definitive and undis- These highly non-linear differential equations describe puted confirmation of a kilonova and the formation of on the one hand how matter moves in a curved space– r-process elements from merging neutron stars. Several time and on the other hand formulates in which way the numerical simulations demonstrate that the r-process amounts of energy-momentum bends the space–time elements created from mergers is almost independent of structure. In the ideal-fluid energy-momentum tensor the initial masses, mass ratios or EoS. However, when Tμν = (e + p) uμuν + pgμν enters the energy and comparing the produced light curves from the differ- pressure densities of the nuclear and elementary parti- ent simulations with those observed, it shows that the cle physics contributions of the underlying neutron star simulated results are significantly dimmer than those matter and uμ = dxμ/dτ describes the four velocity observed, which was due to a lower amount of ejected of the star’s fluid which is defined as the derivative of material and lack of lanthanides. This suggests that the the coordinates xμ = (t, x, y, z) by the proper time dynamical ejecta is not the major source of ejecta from τ. a merger, but places a secondary role to other forms of In order to solve the evolution of a merging neutron secular ejecta, such as from neutrino-driven winds, vis- star binary system numerically, equation (1) needs to cous ejecta from a disk or it might come from a second be rewritten, because its structure is not well posed. burst caused by a rearrangement of a compact star due To reformulate equation (1), the so-called (3+1)-split to the quark core formation (Hanauske et al. 2018b). is used, which starts by slicing the 4-dimensional man- A similar effect has been recently found in numerical ifold M into 3-dimensional space-like hypersurfaces simulations of supernova explosions of massive blue- t . The space–time metric gμν is then sub-classified supergiant stars (Fischer et al. 2017). into a purely spatial metric γij, a lapse function α and This article is structured as follows: section 2 gives a shift vector βi (μ, ν = 0, 1, 2, 3andi, j = 1, 2, 3): a short introduction to the mathematical and numerical −α2 + β βi β = i i . setup of a simulation of BNS mergers. The temperature gμν β γ (2) and density structure of a neutron star merger product i ij will be analysed in section 3. A new way of presenting Figures 1(a)–(d) illustrate a typical time dependence the results will be used, which shows the evolution of of the rest-mass density ρ and lapse function α in the the hot and dense matter inside the HMNS in a (T − ρ) equatorial plane reached during the late inspiral and QCD phase diagram. It will be illustrated that the tem- early post-merger phase of a BNS merger. The lapse perature and density values reached inside the HMNS function α describes the difference between the coor- requires an incorporation of a hadron–quark phase tran- dinate time t and the proper time τ of a fluid particle sition (HQPT) in the EoS. Section 4 gives a summary (dτ = α dt). The shift vector βi measures how the and an outlook. coordinates are shifted on the spatial slice if the fluid J. Astrophys. Astr. (2018) 39:45 3of11 Page (a) (b) (c) (d) Figure 1. Logarithm of the rest mass density log(ρ [g/cm3]) and lapse function α in the xy-plane at two different time snap-shots within the late inspiral phase (t =−1.21 (a), −0.5ms(b)) and at merger and early post-merger time (t = 0 (c),0.77 ms (d)) within the LS220-M135 simulation (for details, see Hanauske et al.