Simulations of neutron star mergers: Status and prospects

Simulations of neutron star mergers: Status and prospects David Radice 1,2 1 Research Associate, Princeton University 2 Taplin Member, Institute for Advanced Study First multi-messenger observations of a neutron star merger and its implications for nuclear physics INT 18-72R March 13, 2018

NS merger: roadmap

Binary NS inspiral

Tidal effects in NS mergers 10 Part of the orbital energy goes into tidal deformation Q ij = 2 E ij Accelerated inspiral Imprinted on the gravitational waves Constrains dimensionless tidal parameter 2 = 2 M 5 R5 M 5

~ 800 700 600 500 400 300 200 100 Inspiral modeling 13 f min = 10Hz, = 50 M c /(1/4) 3/5 = 2.5 M sun, ~ = 0 M c /(1/4) 3/5 = 2.7 M sun, ~ = 0 M c /(1/4) 3/5 = 2.9 M sun, ~ = 0 M c /(1/4) 3/5 = 2.5 M sun, ~ = 1200 M c /(1/4) 3/5 = 2.7 M sun, ~ = 1200 M c /(1/4) 3/5 = 2.9 M sun, ~ = 1200 PRL 114, 161103 (2015) P H Y S I C A 0 400 500 600 700 800 900 1000 f max [Hz] 180 160 140 120 From Kawaguchi, Kiuchi+ (2017) f min = 10Hz, f max = 1000Hz, = 50 From Bernuzzi+ (2015) FIG. 3 (color online). Phasing and amplitude compariso three representative models. Waves are aligned on a timewi the bottom panels indicate the crossing of the TEOB Resum Precision modeling over many orbits, see also Hinderer+ (2016), Dietrich+ (2017), Kiuchi+ (2017) Open issues: spin, last GW cycles before merger

Constraints from GW170817 PRL 119, 161101 (2017) P H Y S I C A L R E V I E W L E T T E R S week ending 20 OCTOBER 2017 " FIG. 5. Probability density for the tidal deformability parameters of the high and low mass components inferred from the detected signals using the R post-newtonian 5 model. Contours enclosing 90% and 50% of the probability density are overlaid (dashed lines). The diagonal dashed line indicates the Λ 1 ¼ Λ 2 boundary. The Λ 1 and Λ 2 parameters characterize the size of the tidally induced mass deformations of M = 16 (M A + 12M B )M 4 (A) A 2 each 5 star and are proportional 13 to k 2 ðr=mþ (M 5 A. Constraints + M B are ) 5 +(A $ B) apple 800 shown for the high-spin scenario jχj 0.89 (left panel) and for the low-spin jχj 0.05 (right panel). As a comparison, we plot predictions for tidal deformability given by a set of representative equations of state [156 160] (shaded filled regions), with labels following [161], all of which support stars of 2.01M. Under the assumption that both components From are LIGO/Virgo neutron stars, we collaboration, apply the function PRL ΛðmÞ 119, prescribed 161101 by that (2017) equation of state to the 90% most #

Prompt-BH formation

Simulation results (1.44 + 1.39) M B1913 + 13 DR, Perego, Zappa, ApJL 852:L29 (2018)

Simulation results (1.44 + 1.39) M B1913 + 13 DR, Perego, Zappa, ApJL 852:L29 (2018)

EOS constraints (I) 3.0 2.5 excluded M [M ] 2.0 1.5 1.0 excluded 0.5 8 10 12 14 16 R [km] From Bauswein, Just+ (2017)

EOS constraints (II) M disk + Mej [M ] 10 1 10 2 10 3 10 4 AT2017gfo tbh [ms] 10 1 10 0 10 2 10 3 L BHBLf DD2 LS220 SFHo See also Bauswein+ 2017 ApJL 850:L34 DR, Perego, Zappa, ApJL 852:L29 (2018)

Hypermassive NSs z

GW-driven phase max [10 15 g cm 3 ] 4 2 LS220-135135 LS220-1365125 LS220-140120 LS220-144139 DD2-135135 DD2-1365125 DD2-140120 DD2-144139 LGW [10 55 erg s 1 ] 0 8 6 4 2 SFHo-135135 SFHo-1365125 SFHo-140120 SFHo-144139 0 5 0 5 10 15 20 25 30 u [ms] Bernuzzi, DR+, PRD 94: 024023 (2016)

Postmerger peak frequency 10 20 f 2 0 f spiral f peak 3.5 2.4 M sun 2.7 M sun h eff,x (20 Mpc) 10 21 Type I adligo f peak [khz] 3 2.5 3.0 M sun 10 22 Type II Type III From Bauswein+ 2015ET 1 2 3 4 f [khz] 2 From Bauswein+ 2016 12 13 14 15 R 1.6 [km] Post-merger signal has a characteristic peak frequency fpeak correlates with the NS radius Small statistical uncertainty, systematics not understood yet See also Takami+ 2014; Rezzolla & Takami 2016; Dietrich+ 2016; Bose+ 2017

Extreme-density physics 2.5 BHB DD2 Neutron stars in binaries have masses clustered around ~1.35 M M [M ] 2.0 1.5 1.0 1.5 M =1.6 M Phase transition at high-density not constrained by the inspiral Can we probe the equation of state of nuclear matter at the highest densities? 0.5 1 2 3 4 5 n max /n nuc 2 Yes, with the postmerger signal See also Bauswein+ 2011, 2013, 2015, Read+ 2013, Hotokezaka+ 2013, Takami+ 2014, Bernuzzi+ 2015, Clark+ 2014, 2016, Bose+ 2017, Chatziioannou 2017, DR, Bernuzzi, Del Pozzo+, ApJL 842:L10 (2017)

Gravitational waveform s] DD2 15 20 10 22 h+ (D = 100 Mpc) f [khz] f [khz] 4 2 0 2 4 3 2 1 0 3 2 1 0 DD2 0 5 10 15 20 t t mrg [ms] 1.35 1.35 BHB BHB DD2 DD2 DD2 32 0 5 10 15 20 5 0 5 10 15 20 t t mrg [ms] t t mrg [ms] 0 4 8 12 16 20 24 28 10 log 10 10 22 h e (f)(d = 100 Mpc) DR, Bernuzzi, Del Pozzo+, ApJL 842:L10 (2017)

End of GW-driven phase EGW/(M ) J/(M 2 ) Zappa, Bernuzzi, DR+, PRL in press (2018)

Viscous evolution to collapse

Angular momentum transport t visc = 1 t visc 15 ms See also: Shibata & Kiuchi 2017; Kiuchi, Kyotoku+ 2017 DR ApJL:838 L2 (2017)

Angular momentum transport t visc = 1 t visc 15 ms See also: Shibata & Kiuchi 2017; Kiuchi, Kyotoku+ 2017 DR ApJL:838 L2 (2017)

Angular momentum transport t visc = 1 t visc 15 ms Delayed collapse! See also: Shibata & Kiuchi 2017; Kiuchi, Kyotoku+ 2017 DR ApJL:838 L2 (2017)

Gravitational waves E GW [M c 2 ] 0.12 0.10 0.08 0.06 0.04 `mix = 0 `mix = 5m `mix = 25 m `mix = 50 m 0.02 5 0 5 10 15 20 25 t t mrg [ms] See also: Shibata & Kiuchi 2017; Kiuchi, Kyotoku+ 2017 DR ApJL:838 L2 (2017)

Gravitational waves E GW [M c 2 ] 0.12 0.10 0.08 0.06 0.04 0.02 `mix = 0 `mix = 5m `mix = 25 m How large is the turbulent viscosity? `mix = 50 m How do hypermassive NS evolve over many viscous timescales? Can we distinguish long- and short-lived hypermassive NSs? 5 0 5 10 15 20 25 t t mrg [ms] See also: Shibata & Kiuchi 2017; Kiuchi, Kyotoku+ 2017 DR ApJL:838 L2 (2017)

Viscous evolution to equilibrium

Long-lived remnants 4.00 3.75 DD2 3.74 3.58 Mb [M ] 3.50 3.25 3.00 3.39 2.95 2.75 M [M ] 2.75 2.50 (1.35 + 1.35)M M0 3 4 5 6 7 8 9 J [Gc 1 M 2 ] 2.54 2.32 DR, Perego, Bernuzzi, Zhang, in prep.

Viscous evolution 3.00 2.95 Mb [M ] 2.90 2.85 2.80 2.75 Disk ejecta Remnant ejecta RNS DD2 (1.35 + 1.35) M M0 2.70 3.5 4.0 4.5 5.0 5.5 6.0 J [Gc 1 M 2 ] See also Fujibayashi, Kiuchi+ (2017) DR, Perego, Bernuzzi, Zhang, in prep.

Excess gravitational mass 0.11 0.10 BHB DD2 LS220 SFHo M [M ] 0.09 0.08 0.07 0.06 0.05 DD2 (1.35 + 1.35)M M0 0.75 0.80 0.85 0.90 0.95 1.00 M b /M RNS DR, Perego, Bernuzzi, Zhang, in prep.

Stable or unstable? From Kaplan, Ott, O Connor+ (2014)

Stable or unstable? ' 0.1 M!!! From Kaplan, Ott, O Connor+ (2014)

The remnant of GW170817 2 Fig. 1. The strength of the red and blue KN signatures of a BNS merger depends on the compact remnant which forms immediately after the merger; the latter in turn depends on the total mass of the original binary or its remnant, Mtot, relative to the maximum NS mass, Mmax. A massive binary (Mtot & 1.3 1.6Mmax ) results in a prompt collapse to a BH; in such cases, the polar shock-heated ejecta is negligible and the accretion disk outflows are weakly irradiated by neutrinos, resulting in a primarily red KN powered by the tidal ejecta (left panel). By contrast, a very low mass binary Mtot. 1.2Mmax creates a long-lived SMNS, which imparts its large rotational energy & 1052 erg to the surrounding ejecta, imparting relativistic expansion speeds to the KN ejecta or producing an abnormally powerful GRB jet (right panel). In the intermediate case, 1.2Mmax. Mtot. 1.3 1.6Mmax a HMNS or short-lived SMNS forms, which produces both blue and red KN ejecta expanding at mildly relativistic velocities, consistent with observations of GW170817. From Margalit & Metzger 2017 Long-lived unlikely the maximum ral (Hinderer et SMNS al. 2010; Damour & Nagar 2010; > Damour limit 2011),on where the proportionality factor NS k 1.3mass 1.6 et al. 2012; Favata 2014; Read et al. 2013; Del Pozzo et al. 2013; Agathos et al. 2015; Lackey & Wade 2015; Chatziioannou et al. 2015) and for quasi-periodic oscillations of the post-merger remnant (e.g. Bauswein & Janka 2012; Bauswein et al. 2012; Clark et al. 2014; Bauswein See etalso Rezzolla+, & Stergioulas 2015; Bauswein al. 2016). Searches on timescales of tens of ms to. 500 s post-merger revealed is greater for smaller values of the NS compactness, Cmax = (GMmax /c2 R1.6 ), where R1.6 is the radius of a 1.6M NS (e.g. Bauswein et al. 2013). For slightly less massive binaries with Mtot. Mth, the merger instead produces a hyper-massive neutron star (HMNS), which Shibata+, (2017) is supportedruiz+ from collapse by di erential rotation (and, potentially, by thermal support). For lower values of

The origin of the elements R-Process Are neutron star mergers the site of the r-process?

Ejection mechanisms [g/cm 3 ] 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 250 150 50 50 150 250 x [km] See also Metzger+2008; Wanajo+2014; Fernandez+2014; Metzger+2014; Perego+2014; Martin+2015; Sekiguchi+2015,2016; Foucart+2016; Siegel+2017 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Ye DR, Galeazzi+ MRAS 460:3255 (2016)

Dynamic ejecta: role of neutrinos Mass fraction 10 1 10 2 10 3 0.4 SFHo: (1.35 + 1.35) M ; cooling only sin 2 ( ) 10 2 Electron fraction 0.3 0.2 0.1 0 20 40 60 80 Polar angle 10 3 10 4 Mass fraction Perego, DR, Bernuzzi, ApJL:850 L37

Dynamic ejecta: role of neutrinos Mass fraction 10 1 10 2 10 3 0.4 SFHo: (1.35 + 1.35) M ; cooling and heating sin 2 ( ) 10 2 Electron fraction 0.3 0.2 0.1 0 20 40 60 80 Polar angle 10 3 10 4 Mass fraction Perego, DR, Bernuzzi, ApJL:850 L37

Conclusions Numerical relativity is essential in the age of multimessenger astronomy Do we really understand the outcome of NS mergers? Neutrinos play a crucial role for nucleosynthesis and EM counterparts

Thank you!