Neutron Star Mergers in the Context of the Hadron–Quark Phase Transition

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 Page 3 of 11 45 ; 2017a et al. Hanauske while the white density ] ,... 65 . 0 , 6 . 0 , 55 . 0 ) =[ d (b) ( α -plane at two different time snap-shots within the late inspiral phase xy )) within the LS220-M135 simulation (for details, see while the white density contours have a logarithmic distance to indicate the d 0 ρ ] in the α 77 ms ( ,... . 5 . ,0 1 , (c) 1 , 0 5 . = 0 t =[ ρ ]) and lapse function 3 [g/cm ])). The black contour lines of the lapse function were taken at 3 ρ ) a (c) ( log([g/cm ] 14 , 10 ∈[ ) ρ )) and at merger and early post-merger time ( b 5. . 0 5ms( . = ). The black density contour lines were taken at 0 α − ), 2017 a Logarithm of the rest mass density log( ( 21 . et al. 1 =− t low density crust matter (log( ( Bovard Figure 1. contour indicate 45 Page 4 of 11 J. Astrophys. Astr. (2018) 39:45 particle moves an infinitesimal time step further. The φ nucleons begin to overlap at densities ρ 3ρ0 and -component of the shift vector βφ describes the drag- a transition from hadronic to quark-gluon degrees of ging of local inertial frames within the highly differ- freedom needs to be accounted in such dense systems. entially rotating BNS merger product (Hanauske et al. At high densities and moderate temperatures, the phase 2017a). diagram of quantum chromodynamics (QCD phase dia- By inserting the metric (equation (2)) into the gram) predicts a first order HQPT while lattice gauge Einstein equation (equation (1)) one can restate the theory prognosticate a cross-over transition for mod- equations into a system of first-order differential equa- erate densities and high temperatures. Simulations of tions, the so-called Arnowitt–Deser–Misner (ADM) BNS mergers including a HQPT, with a strong soften- equations. As the ADM equations are still not ‘well ing of the EoS within the mixed phase region, have not posed’, they need to be further transformed using a been performed until now. In this section the results of conformal traceless formulation (for details, see Rez- a BNS merger simulation will be used to justify that zolla & Zanotti 2013). The numerical simulations a HQPT is expected to happen during the post-merger have been performed in full general relativity using phase of a BNS merger. the Einstein Toolkit, where the BSSNOK conformal Figures 2(a)–(c) illustrate the time dependence of traceless formulation of the Einstein equations using the spatial allocation of the density and temperature a‘1+ log’ slicing condition and a ‘Gamma-driver’ values reached during the late inspiral phase (t = shift condition were used. The covariant conservation −1.21, −0.83, −0.5 ms) while Fig. 3 shows the pop- of energy, momentum and rest mass, formulated within ulated area of (T − ρ)-values at the time of the merger the general-relativistic hydrodynamics equations (see (t = 0 ms). Before the merger happens, the temperature second and third equations in equation (1)), are cast in the low density regime, near to the region where the in the conservative Valencia formulation. The evolu- two NSs touch each other, increases rapidly (see Fig. 2) tion of these hydrodynamics equations was done using and at merger time, the temperature hot spot of the newly the WhiskyTHC code (Radice et al. 2014). A numer- born remnant reaches values up to T ≈ 75MeV (see ical grid with an adaptive mesh refinement approach triangle in Fig. 3). The maximum value of the density at based on the Carpet mesh-refinement driver was used to t =−0.5msisbelow2.5 ρ0 and its spatial position is increase both resolution and extend the spatial domain. located in the center of the still separated two NSs (see In the next section, the results of a BNS merger Fig. 1(b) and the diamond symbol in the green region simulation will be presented which bases on a ‘hot’, in Fig. 2(c)). At merger time t = 0, where the emitted i.e., temperature dependent, Lattimer–Swesty (LS220) gravitational wave of the newly born remnant reaches EoS (Lattimer & Douglas 1991). The total gravitational its maximum value, the density maxima are almost at mass of the binary is 2 × 1.350 M andtherunwas the center of the numerical grid (see Fig. 1(c)) and the evolved without the assumption of π-symmetry (for high temperature regions are placed between them. The details, see Hanauske et al. 2017a; Bovard & Rezzolla following violent, early post-merger phase is character- 2017; Bovard et al. 2017). ized by a pronounced density double-core structure and hot temperature regions which are smeared out in areas 3. Hypermassive neutron stars and the phase between the double-core density maxima (see Fig. 4 and diagram of quantum chromodynamics Fig. 1(d)). Figure 4 shows the distribution of the rest-mass General relativistic astrophysics of BNS mergers and density (Fig. 4(a)) and temperature (Fig. 4(b)) at time nuclear physics are deeply connected and numerical t = 0.83 ms after merger. In order to track the motion simulations in both fields are strongly dependant on the of individual fluid cells, tracer particles have been used EoS of fundamental elementary matter. Hot and dense within the LS220-M135 simulation (for details, see matter created in high energy heavy ion collisions and Bovard & Rezzolla 2017; Bovard et al. 2017). The flow- mergers of a binary system of two neutron stars reach lines of several tracer particles that remain close to the values where strongly interacting matter is expected to equatorial plane are visualized using the method of a undergo the deconfinement phase transition (Hanauske ‘co-rotating frame’. In a co-rotating frame, each grid et al. 2017b). Hadrons, mesons and baryons are believed point is rotating at a frequency that is half the angu- to be the correct degrees of freedom for modelling lar frequency of the instantaneous emitted gravitational = strongly-interacting matter at densities around the satu- waves, GW . Initially placed at t 0 near the surface ration density of nuclear matter ρ0. However, following of the newly born remnant the tracer particles diffuse simple geometrical estimates (Mishustin et al. 2003), both spatially and in the (T − ρ)-plane. J. Astrophys. Astr. (2018) 39:45 Page 5 of 11 45

(a) (b)

(c)

Figure 2. Density-temperature proﬁles inside the inner area of the LS220-M135 simulation in the style of a (T − ρ)QCD phase diagram plot at three different time snapshots right before the merger of two neutron stars (t =−1.21 (a), −0.83 (b), −0.5ms(c)). The color-coding indicate the radial position r of the corresponding (T − ρ) ﬂuid element measured from the origin of the simulation (x, y) = (0, 0) on the equatorial plane (z = 0). The open triangle indicates the maximum value of the temperature while the open diamond indicates the maximum of the density.

Figure 5 depicts the populated area of the HMNS in the (T −ρ)-plane at t = 0.83 ms. Two separated, almost equally high temperature regions (T ≈ 50 MeV) are visible, whereas the position where these temperature hot spots occur differs (indicated in Fig. 5 by the green region (r ∼ 7 km) and the blue region (r ∼ 3 km)). The maximum value of the temperature is located near the origin, while the density maxima are placed in the two low temperature centers of the density double-core of the HMNS (see diamond symbol, which is located at the tip of the green cusp in Fig. 5). In the time interval 1.5ms< t < 3 ms, the double- core structure disappears and the maximum density value shifts to the central region of the HMNS. The high temperature regions transform to two temperature Figure 3. Same as Fig. 2 but at merger time t = 0ms. hot spots and they move further outwards. The density 45 Page 6 of 11 J. Astrophys. Astr. (2018) 39:45

Figure 4. Distribution of the rest-mass density (a) and temperature (b) at time t = 0.83 ms after merger. The density contour lines were taken at the same values as in Fig. 1. The black temperature contour lines were taken at [30, 40] MeV while the white contours indicate the low temperature values ([5, 10] MeV). The green triangle marks the maximum value of the temperature, while the magenta diamond indicates the maximum of the density. Additionally the flowlines of several tracer particles that remain close to the equatorial plane are visualized in Fig. 4(b). The final part of the tracer flowlines for the last t = 0.19 ms are shown and the small black dots indicate the tracer position at the time indicated in the frame. The initial parts of the trajectories have increasing transparency so as to highlight the final part of the trajectories.

of the maximum values of the density points at a given positionr (ρmax(r)) follow along the axis of the ‘peanut’ for increasing values of r. The axis of the ‘peanut’ represents the lowermost boundary of the populated colored surface in Fig. 7. This lower boundary is for most of the inner region inside the HMNS at quite low temperature values, or stated differently, the ρmax(r)-fluid elements are for r < 8 km at temperatures T < 2MeV.Inthe more outer regions (r > 8km)whereρmax(r)<2 ρ0 the low temperature boundary of the colored surface increases and reaches values T ≈ 10 MeV. The highest temperature values (Tmax(r)) are reached at the waistline of the ‘peanut’, 90 ◦ shifted off its axis (see Fig. 6(b)). For small r (r < 3 km) the maximum temperature values Tmax(r) increase steeply for increasing Figure 5. Same as Fig. 2 but at t = 0.83 ms. r until the maximum value of T ≈ 53MeV is reached at r 3 km. This sharp increase of Tmax(r) corre- distribution at this post-merger time has a pronounced sponds to the right boundary of the (T − ρ)diagram ‘peanut’ shape but the highest value of the density ρ is in Fig. 7. The flowlines of the tracers (see Fig. 6(a)) now placed in the center of the HMNS. Figure 6 visual- show that the fluid in the interior of the HMNS has two izes the density and temperature profiles reached inside pronounced vortices. The two centers of these swirls, the inner region of the HMNS at t = 3.69 ms while where the tracer particles are accelerated correspond to Fig. 7 shows the corresponding populated area in the the two temperature hot spots. The occurrence of these (T − ρ)-plane. The maximum density value (diamond hot spots and their spatial location is closely connected symbol) is located at the center of the HMNS, while with the rotational properties of the HMNS (for details, the temperature maximum (triangle) is placed in one of see Hanauske et al. 2017a). The angular velocity within the temperature hot spots at r 3 km. The spatial path the 3 + 1 split can be expressed as = αvφ − βφ, J. Astrophys. Astr. (2018) 39:45 Page 7 of 11 45

Figure 6. Distribution of the rest-mass density (a) and temperature (b). Same as Fig. 4 but at t = 3.69ms.

deconfine to quark matter within this time segment of the post-merger phase. Under the assumption of the ‘strange matter hypothesis’, where the strange-quark phase is the true ground state of elementary matter, the whole neutron star would suddenly transform into a pure-quark star after exceeding certain deconfinement barrier of the HQPT (Drago & Pagliara 2015; Bombaci et al. 2016). During such a process, a significant amount of energy would be released in the form of neutrinos and gamma-rays (Drago & Pagliara 2015). However, if the strange-matter hypothesis has not been adopted, a stable hybrid HMNS can be formed having only an inner core of deconfined strange quark matter. The properties of hybrid stars containing both the hadrons and quarks have been already studied for a long time in the Figure 7. Same as Fig. 7 but at t = 3.69ms. context of static (Hanauske & Greiner 2001; Mishustin et al. 2003; Shovkovy et al. 2003) and uniformly rotat- where vφ and βφ describes the φ-component of the ing hybrid stars (Banik et al. 2004; Bhattacharyya et al. three-velocity and shift vector. The temperature hot 2005) and the results show that tremendous changes spots overlap closely with the position of the max- in the star properties might occur including the exis- ima of the angular-velocity distribution, which is not tence of a third family of compact stars – the so-called surprising as in these regions, the fluid flow has the ‘twin stars’ (Glendenning & Kettner 2000). A twin star largest shear and compression (Hanauske et al. 2017a; behaviour is present, if the third stable sequence of Alford et al. 2018). compact stars is separated from the second one by an During the late inspiral, merger and early, transient unstable region. Such twin stars opens the possibility of post-merger phase, the maximum value of the density a catastrophic re-arrangement from one configuration does not exceed the threshold where a HQPT is expected to the other with a prompt burst of neutrinos followed to be present. However, for t ≥ 3.5 ms the maxi- by a gamma-ray burst (Mishustin et al. 2003; Hanauske mum value of the density in the central region of the et al. 2018a,b). Such an appearance of a HQPT in the HMNS is clearly above the onset of a HQPT (ρmax ≥ interior region of the HMNS will change the spectral 3.5 ρ0). As a result, within a realistic model of an properties of the emitted GW if it is strong enough. EoS, a considerable amount of hadronic matter should If the unstable twin star region is reached during the 45 Page 8 of 11 J. Astrophys. Astr. (2018) 39:45

Figure 8. Distribution of the rest-mass density (a) and temperature (b). Same as Fig. 4 but at t = 19.43ms.

‘post-transient’ phase, the f2-frequency peak of the GW signal will change rapidly due to the sudden speed up of the differentially rotating HMNS. However, within the LS220-M135 run no HQPT has been implemented and as a result none of the discussed astrophysical consequences has been observed within this simulation study. At late post-merger times (t > 15 ms), the temperature hot spots have smeared out to become a ring-like structure, the ‘peanut’ shape has been dissolved and the area populated in the (T − ρ) plane has been constricted to a small quasi stable region. The central region of the HMNS consists of highly densed matter (ρ/ρ0 ≈ 5) at moderate temperature values T ≈ 10 MeV while the maximum of the temperature is reached at the top of the temperature ring like structure at r ≈ 6 km at moderate density val- Figure 9. Same as Fig. 2 but at t = 19.43ms. ues ρ/ρ0 ≈ 2 (see Figures 8 and 9). The tracer particles have diffused over the entire inner region of the HMNS and populate almost the whole area of the Figure 10 summarizes the results presented so far HMNS. Some of these tracers circulate in the highly by showing the time evolution of the maximum value densed, cold inner region, others circulate near the high of the temperature (triangles) and the rest mass den- temperature ring and some are moving in the outer sur- sity (diamonds) of the BNS merger simulation in the face of the HMNS within the low density regime (see (T − ρ) QCD phase diagram. In this illustration, the Fig. 8(a)). spatial structure of the density and temperature profiles The results presented so far show that within the have been neglected and several points solely indicate first 20 ms, the matter inside the HMNS populate areas the evolution of the maximum values of the temperature in the QCD phase diagram where an inclusion of the and density. The temperature maxima reached during quark degrees of freedom in the EoS is necessary. Espe- the post-merger phase are in the range of 40 MeV ≤ T ≤ cially in the interior region of the HMNS for t > 3.5 80 MeV. As the position of these maxima is most of ms, the density reaches values where a non neglectable the time not placed in the central region of the HMNS, amount of deconfined quark matter is expected to be their corresponding density values do not exceed 3 ρ0. present. So far, no simulation of a binary compact Although these temperatures are quite high, it is not star merger containing a strong HQPT has been per- likely that in these (Tmax,ρ)-fluid elements a large formed. amount of deconfined quark matter is present. The J. Astrophys. Astr. (2018) 39:45 Page 9 of 11 45

(a) (b)

Figure 10. Time evolution of the maximum value of the temperature (a) and rest mass density (b) at the equatorial plane in the interior of a HMNS using the simulation results of the LS220-M135 run. The color coding of the points indicate the time of the simulation after merger. situation is different if one focuses on the central region reach T ∼ 40–80 MeV. The numerical simulations of the HMNS, where the maximum of the density is showed that — after the violent transient post-merger reached (see Fig. 10(b)). The time dependence of the phase — the HMNS stabilizes, after ≈10 ms, resulting maximum value of the density shows that values above in a quasi-stable configuration with a specific rotation 3 ρ0 are reached for most of the post-merger phase and profile (Hanauske et al. 2017a). This HMNS is sta- that for late times values near the ρ ≈ 5 ρ0 can be bilized by its differentially rotating nature which will achieved, which is clearly above the threshold where a become more uniform with time until the star gets unsta- HQPT is expected to take place. ble and collapses to a Kerr BH. The observation of the gamma-ray burst (GRB 170817A), which was detected with a time delay of 1.7 s with respect to the merger 4. Summary and outlook time, indicates the collapse of the HMNS at a post- merger time 1s.InHanauske et al. (2017a), the BNS The recent detection of a gravitational wave from merger scenarios within six different EoSs were anal- a BNS merger by the LIGO-VIRGO collaboration ysed and it was found that with the exception of the (GW170817) (Abbott et al. 2017a) marked the begin- APR4 and LS220 EoSs, all other binaries with masses ning of a new era in observational astrophysics. The (M = 1.35M) collapse to a black hole within t < 40 independently detected gamma-ray burst (GRB 1708 ms. During the late post-merger time of the simulation 17A) (Abbott et al. 2017b) and further electromagnetic (t ≈ 20 ms), the value of the central rest-mass density radiation (Abbott et al. 2017c) resulted in a neutron increases to ρc 5 ρnuc for the APR4-M135 and the star merger scenario which is in good agreement with LS220-M135 run. However, for such high densities the numerical simulations of BNS mergers performed in EoS is still poorly constrained. full general relativistic hydrodynamics. The extracted The main question which is still open is the lack constraints on the mass of the total system, in com- of knowledge what happens exactly in the time span bination with the limitations on the EoS, which were of 1.7 s between the merger of GW170817 and estimated using the extracted tidal deformation of the the detected gamma-ray burst GRB 170817A. The two neutron stars right before merger results in a neutron largely accepted opinion is that the created HMNS star merger scenario which is remarkably similar to the collapsed after approximately 1 s to a Kerr black APR4-M135 and LS220-M135 simulation discussed in hole and the infalling surrounding matter caused the detail in Hanauske et al. (2017a). After the detected delayed gamma-ray burst. However, within realistic GW, it is believed that a differentially rotating compact QCD-motivated EoSs this scenario might be differ- object, the HMNS had been produced. Matter in the ent. The astrophysical consequences of an appearance interior of this object reached densities of up to several of a HQPT in the interior region of the HMNS have times the normal nuclear matter, and temperatures could not been analysed until now using general relativistic 45 Page 10 of 11 J. Astrophys. Astr. (2018) 39:45

BNS merger simulations. The ALF2-EoS (Alford et al. at the Relativistic Heavy Ion Collider (RHIC) at 2005), which was used within the BNS merger sim- Brookhaven National Laboratory created the hottest, ulations, however, is a model which has implemented least viscous and most vortical fluid ever produced a phase transition to color-flavor-locked quark matter, in the laboratory. A remarkably different rotational but the properties of this EoS are hardly distinguishable behaviour is observed, compared to similarly dense from a neutron star matter EoS including hyperonic par- and hot hadronic matter. Hence, the ticles (Hanauske et al. 2017a). Hybrid stars within the differentially rotating inner region of the HMNS which ALF2-EoS masquerades as neutron stars. may consist of deconfined quark matter, can also act If the ‘strange matter hypothesis’ is true, the HMNS as a macroscopically vortical fluid with an intrinsic will promptly transform into a pure-quark star shortly angular momentum. A similar effect as found in non- after the first strange quark droplets were formed in central ultra-relativistic heavy ion collisions may be the star’s central region. Depending on the proper- present during the post-merger evolution of a HMNS. ties of the quark matter EoS, this transformation could For example, at t = 3.69ms (see Fig. 6), the evo- either be a collapse or an expansion of the HMNS. As lution of tracer particles show a swirling behaviour a result of such a violent process, a second burst of around two pronounced vortices which are centered in dynamically ejected matter is expected and a signifi- the two temperature hot spots of the HMNS. These trac- cant amount of energy would be released in the form ers describe trajectories of fluid elements that could of neutrinos and gamma-rays (Drago & Pagliara 2015), pass the deconfinement transition and confine again which could alternatively explain the observed gamma- within less than 0.3 ms. After the hadronization pro- ray burst GRB 170817A. cess, an alignment between the angular momentum of However, if the strange-matter hypothesis is not the HMNS and the spin of hadronic particles is expected realised in nature, a HQPT is expected to be formed and such an effect would slow down the slowly rotating during the evolution of the HMNS, resulting in a hybrid inner core of the HMNS even further. After hadroniza- HMNS having an inner core of deconfined pure quark tion, the polarized hadronic particles (e.g. , −,−) matter, surrounded by a mixed phase and a purely will pass regions where the frame dragging and Lense– hadronic region. The modelling of such a HQPT in the Thirring effect, quantified with βφ, is large and an interior of the hybrid HMNS depends strongly on the additional gravitomagnetic force would act on these properties of the used hadronic and quark model and on fluid cells. the surface tension of the quark matter droplets within Last but not least, it should be mentioned that within the mixed phase region. A strong HQPT might give the presented simulations the expected emission of neu- rise to a mass–radius relation with a twin star shape, trinos has only been implemented using a simplified where the third stable sequence of compact stars is neutrino-leakage scheme, and high energetic photons separated from the second one by an unstable region. or viscosity effects have not been implemented so far. The astrophysical consequences of a rearrangement of In order to simulate the discussed astrophysical impacts a HMNS due to the quark core formation, namely a of an appearance of a HQPT in the interior region of the twin star collapse or twin star oscillation, will be anal- HMNS, including a re-arrangement of the HMNS due ysed in a separate article (Hanauske et al. 2018b). If the to quark core formation, an incooperation of shear/bulk unstable twin star region is reached during the ‘post- viscosity and neutrino trapping might be important in transient’ phase, the f2-frequency peak of the GW future BNS merger simulations (Alford et al. 2018). signal will change rapidly due to the sudden speed up of the differentially rotating HMNS and this second burst could give an additional contribution to the Acknowledgements dynamically emitted outflow of mass and might additionally explain the observed gamma-ray burst GRB The authors would like to thank Luciano Rezzolla. 170817A. Without his profound knowledge and his comprehen- The high energy heavy ion collision data are sive expertise in the field of numerical relativity and compatible with a HQPT, which then shall also be general relativistic hydrodynamics, the presented sim- present in the interior of the HMNS. As predicted ulations and the whole article would not have been by Csernai et al. (2013), a strongly rotating quark- possible. They would like to thank Horst Stöcker who gluon plasma has been detected experimentally in built the scientific bridge between general relativity the non-central ultra-relativistic heavy ion collisions and elementary particle physics and arranged financial (Adamczyk et al. 2017). The STAR Collaboration support. MH would like to thank the Saha Institute of J. Astrophys. Astr. (2018) 39:45 Page 11 of 11 45

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