Binary neutron star mergers and the effect of onset of phase transition on gravitational wave signals Shamim Haque, ∗ Ritam Mallick, † and Shashikesh Kumar Thakur ‡ Department of Physics, Indian Institute of Science Education and Research Bhopal, India (Dated: August 1, 2022) We have performed simulations of equal and unequal mass binary neutron star mergers in this study. We have compared how the observational gravitational signals change depending upon the equation of state, which governs matter at high density. Mainly we have compared results between the hadronic and quark equation of state. The quark matter is modelled with Gibbs formalism, where a mixed-phase appears between the pure hadronic and pure quark state. We have varied the density where quark matter first appears. It is found that when two almost equal mass binaries merge, the final star attains a stable configuration (does not collapse) irrespective of the matter properties. However, if the post-merger scenario of the binary merger can be probed, a significant difference in the gravitational wave amplitude can be seen if quark matter appears at low densities. It is found that if the matter properties with hadronic and quark degrees differ significantly, it is reflected in the stability of the final merger product. Hadronic matter can give a stable remnant star, whereas if quark matter appears, it makes the collapse possible (assuming that the hadronic equation of state is stiffer than the quark equation of state). However, when unequal mass binaries (the mass difference is significant) merge, the difference in the observational signals depending on the equation of state (hadronic or quark) is evident just from the point of first contact. It is also seen that the difference in gravitational signal (depending on the equation of state) is more significant for unequal mass binary merging than for equal mass binary having the same total baryonic mass. I. INTRODUCTION The advancement of detection capabilities of astro- physical detectors and robust high-resolution numerical simulations of a large number of complicated astrophys- ical systems has given us the hope to resolve many as- trophysics problems, which has intrigued the scientific community for decades. One of the most sought-after questions is about the constituent particles and the fun- damental nature of the force that governs matter at high density. Quantum chromodynamics (QCD) predicts a transition (mostly believed as a first order) from hadronic matter (HM) to quark matter (QM) at high density [1]. Although the prediction was made a few decades ago, theoretical or experimental evidence regarding this hy- pothesis is yet to be found. In fact, constructing an ex- perimental setup to probe such high matter has proved challenging over the years. On the other hand, ab-initio calculations (like lattice QCD [2]) have failed due to the famous sign problem [3], and the perturbative QCD cal- culations [4] give reliable results only at asymptotically large densities. However, the phase transition (PT) is expected to occur at much lower densities. Earth-based experiments and particle theory calcula- tions fail in this regard; however, neutron star (NS) as- trophysics comes to the forefront. NSs are very dense objects with a mass of few solar masses (most NS mass lies between 1.2 ∼ 1.8 M ⊙ [5]) and a radius of ∼ 10 km. ∗ shamims@iiserb.ac.in † mallick@iiserb.ac.in ‡ shashikesh17@iiserb.ac.in Therefore, at the centre of such stars, the density is ex- pected to reach a few times that of nuclear density, which is considered an ideal condition where the PT can take place. However, the task is not easy, as the interior of the NSs are not directly visible to us. The detectors can only observe the surface and various emissions from the sur- face. Presently, the mass of the NS can be measured with high accuracy [6], and its radius with improved accuracy up to a few hundreds of meters [7, 8]. Earlier, this was insufficient to constrain the properties of matter (known as the equation of state (EoS)); however, the discovery of a few massive NSs in the last decade has changed the picture entirely. The discovery of heavy pulsars (highly rotating NSs) like PSR J0348+0432 (2.01 M ⊙ ) [9], and PSR J0740+6620 (2.08 M ⊙ ) [10], has ruled out soft EoSs which are unable to produce massive NSs. Furthermore, the recent observation of the pulsar PSR J0740+6620 by NICER has given a lower bound on the radius of the pulsar to be R  11 km [11, 12]. Such observations have put constraints on the EoS of NS to a great de- gree. While such observations are gaining momentum, additional constraints came from the observation of bi- nary NS merger (BNSM) GW170817 [13–15]. The grav- itational wave (GW) observation of the merger has put a severe constrain of the tidal deformability (Λ) of the stars [16–20]. The present bound on the tidal deforma- bility is Λ ≤ 720. The deformability of the star is directly proportional to the star compactness, which in turn de- pends on the EoS. Combining all these observations has narrowed down the EoS to a great extent. Although the observation of the pre-merger phase of GW170817 has helped constraining the EoS to a certain arXiv:2207.14485v1 [astro-ph.HE] 29 Jul 2022