Supported by ERC through Starting Grant no. 759253 Systematics of prompt black-hole formation in neutron star mergers Mathematical and Computational Approaches for the Einstein Field Equations with Matter Fields ICERM, virtual, 29/10/2020 Andreas Bauswein (GSI Darmstadt, HFHF) with N. Bastian, S. Blacker, D. B. Blaschke, K. Chatziioannou, M. Cierniak, J. A. Clark, T. Fischer, G. Lioutas, T. Soultanis, N. Stergioulas, V. Vijayan
Outline ► Overview and motjvatjon ► Collapse behavior and simulatjons ► EoS dependence of threshold binary mass → constraints on EoS/NS parameters ► Impact of binary mass ratjo ► QCD phase transitjon in NS mergers → signature in collapse behavior ► Summary and conclusions
Inspiral of NS binary ~100 Myrs Neutron star merger dependent on EoS, M tot ms ms Prompt formation of a Formation of a differentially BH + torus rotating massive NS dependent on EoS, M tot 10-100 ms Rigidly rotating Delayed collapse (supermassive) NS to a BH + torus (stable or long-lived)
Inspiral of NS binary ~100 Myrs Neutron star merger ? ms ms Prompt formation of a Formation of a differentially BH + torus rotating massive NS dependent on EoS, M tot 10-100 ms Rigidly rotating Delayed collapse (supermassive) NS to a BH + torus (stable or long-lived)
Collapse behavior ► Collapse movie Understanding of BH formatjon in mergers [e.g. Shibata et al. 2005, Baiottj et al. 2008, Hotokezaka et al. 2011, Bauswein et al. 2013, Bauswein et al 2017, Koeppel et al. 2019, Kiuchi 2019, Agathos et al. 2020, Bernuzzi et al. 2020, Bauswein et al. 2020]
Collapse behavior Total binary mass M tot Prompt collapse to BH + Threshold binary + Inspiral mass M thres No or delayed collapse to BH + strong postmerger GW emission + bright kilonova + …. M thres - EoS dependent (weakly on mass ratjo) !!!
Which (binary) mass can be supported against gravitational collapse ?
High-density EoS and NS propertjes ► Stellar propertjes of NSs uniquely determined by incompletely known high-density EoS ► Maximum mass (of non-rotatjng!) NSs, i.e. threshold for BH formatjon, not precisely known (but above ~1.95 Msun) ► In turn, NS observatjons constrain EoS and thus inform about fundamental constjtuents and interactjons of matuer Some constraints on radius available e.g. from GW170817 ruling out very large NS radii Bauswein et al., PRL 2020
Mmax and rotatjon ► Centrifugal support increases stability: - supermassive – hypermassive NSs ► Uniform rotatjon → about 20% (limited by mass shedding), e.g. Lasota et al. 1996 ► Difgerentjal rotatjon much more (depending on rotatjon law), e.g. Morrison et al. 2004 e.g. with RNS stellar equilibrium code (Stergioulas & Friedman 1995) Sequencies of const J Uniform rotatjon Difg. rotatjon J = 0 Friedman & Stergioulas 2013 Bauswein & Stergioulas 2017 ► Complex velocity fjeld in merger remnants → a priori maximum mass unclear and has to be determined by hydrodynamical simulatjons ► Maximum mass in mergers ≡ Mthres in the following
Motjvatjon and context ► Binary inspiral: chirp mass and mass ratjo → Mtot typically well measured, q less accurate ► Merger outcome leaves strong impact on observables: - mass ejectjon → kilonova propertjes (dim for prompt collapse) - presence of postmerger GW emission from oscillatjng NS remnant - gamma-ray burst (?) - … → Mthres measurable ► Mthres important to predict outcome and possible search strategies for em counterparts and postmerger GW and their interpretatjon ► Constraints on Mthres → EoS of high-density matuer (high-density regime) - later
Future determinatjon of M thres ► M tot accurately measured during inpiral (from chirp mass and mass ratjo q) ► Combing several detectjons provides M thres Total binary mass M tot ► Merger product NS vs BH { - kilonova propertjes Direct collapse - postmerger GWs Threshold binary { mass M thres * No direct collapse * determined by highest binary mass with no collapse and lowest mass with direct collapse
► Important questjons: How does Mthres depend on binary mass ratjo ? How does Mthres depend on EoS ?
Simulatjons and data ► 40 difgerent EoS models (grouped in 3 classes depending on possible assumptjons about a priori EoS knowledge: w/wo phase transitjon, “excluded” EoSs); most models temperature dependent ► 300-400 simulatjons with relatjvistjc smoothed partjcle hydrodynamics code (conformal fmatness approximatjon, temperature dependent EoSs – some EoS models with approximate thermal treatment, no initjal spin) ► Calculatjons for difgerent total masses to check outcome for fjxed binary mass ratjo (q=1 and q=0.7) → Mthres* within at least ± 0.025 Msun * determined by highest binary mass with no collapse and lowest mass with direct collapse Bauswein et al., PRL 2020
Bauswein et al., PRL 2020
Simulation results EoS/TOV properties arXiv:2010.04461 Maximum residual 0.04 M sun , on average 0.02 M sun deviatjon! Compatjble but betuer than older relatjon A.B., Baumgarte, Janka, PRL 111 (2013)
q=M 1 /M 2 =1 q=0.7 arXiv:2010.04461 ► Similarly tjght fjts for asymmetric mergers Other independent variables like Λ(1.4), R max , Λ_thretthres ► Bi-linear relatjons → simple to invert ► Similar relatjons for chirp mass
EoS constraints, i.e. NS TOV parameter Unknown EoS/TOV measurable properties ► Either measure X as well and get Y ► Or impose a relatjon between X and Y
► From causality or large set of EoSs: ► Measured binary mass and NO collapse: as arguably for GW170817 with 2.73 Msun (Margalit & Metzger 2017, Bauswein et. al 2017, Radice et al. 2018, ….)
Current and future multj-messenger constraints ► For GW170817 we obtain R > 10.6 km ► Applicable to any new observatjon with informatjon on the outcome → a lot of potentjal for future – complementary and independent of inspiral fjnite-size efgects arXiv:2010.04461 (cf. R /Λ limits from Bauswein et al. 2017, Radice et. al 2018, Most et al. 2018, Koeppel et al. 2019, Bauswein et al. 2019, Capano et al. 2020, ...)
M max from M thres ► M thres + another NS property (radius or Lambda from other observatjons) → very accurate and robust M max arXiv:2010.04461 see also current estjmates e.g. by Margalit & Metzger 2017, Shibata et al. 2017, Rezzolla et al 2018, Ruiz & Shapiro 2018, Shibata et al. 2019, … (employing GW170817) and Lawrence et al 2015, Fryer et al. 2015, ...
Λ thres and Mthres M tot { Direct collapse M thres { No direct collapse
► Instead of R 1.6 or Λ 1.4 ► Most direct determinatjon via Lambda bda @ M thres es , i.e. combined tjdal deformability of events which determine M thres ► Directly measurable with the same events which determine M thres (with suffjcient SNR) ► Already a single detectjon with informatjon on merger product or poorly constrained parameters can yield interestjng constraint Bauswein et al., PRL 2020 for prompt collapse
► Instead of R 1.6 or Λ 1.4 ► Most direct determinatjon via Lambda bda @ M thres es , i.e. combined tjdal deformability of events which determine M thres ► Directly measurable with the same events which determine M thres (with suffjcient SNR) ► Already a single detectjon with informatjon on merger product or poorly constrained parameters can yield interestjng constraint excluded for prompt collapse
Impact of the binary mass ratio
► Mass ratjo may be well measurable for near-by events / but less accurate in more distant mergers → for both cases we need to understand how Mthres depends on q @~40 Mpc GW170817, Abbotu et al 2019 Similar q range for GW190425 Farr et al. 2016
Mass ratjo efgect on Mthres ► For a selected subset of EoSs determine Mthres(q) ► Typically decrease with binary asymmetry – understandable by Newtonian toy model ► Mthres roughly constant for 0.85 <= q <= 1 ► Higher-order polynomials provide decent descriptjon → power of 3 works well for most (tested) EoSs arXiv:2010.04461 DD2F EoS
Mass ratjo efgect on Mthres: EOS dependent! Mthres for q=1 and q=0.7 ► 40 EoS models – consider difgerence → Reductjon by asymmetry itself EoS dependent Only hadronic models Qualitatjve dependence understandble by semi-analytjc Newtonian toy model !! Bauswein et al., PRL 2020
Generalized formula for Mthres ► We found for fjxed q and for difgerence → suggest to try a combined fjt to the q=1 and q=0.7 data: ► (nearly) as tjght as fjts for fjxed mass ratjo q (average deviatjon 0.017 Msun) ► Useful for applicatjons with a range of q ► Similar relatjons for threshold chirp mass ► Similar relatjons for other R or Lambda (check paper for fjt paramters) ► Valid somewhat below q=0.7
► Impact of EoS on Mthres(q) arXiv:2010.04461 Compatjble with early tentatjve assessments of mass ratjo efgect on stability of remnants, e.g. Bauswein et al. 2013, Bauswein & Stergioulas 2017, Kiuchi et al. 2019, Bernuzzi et al. 2020
Phase diagram of matuer GSI/FAIR High T, low μ: experiments and lattjce QCD Does the phase transitjon to quark-gluon plasma occur (already) in neutron stars or only at higher densitjes? (low T, high rho not accessible by experiments or ab-initjo models)
Does a phase transition have an impact on the collapse behavior ? ► Consider additjonal set of hybrid EoSs (with PT to deconfjned quark matuer) in comparison to purely hadronic EoSs
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