Neutron Star Merger with Tabulated EOS and Spin Wolfgang Kastaun MICRA, Stockholm, Aug. 2015
Topics Part 1: A recent merger simulation ◮ Gauge independent measures ◮ Structure of post-merger fluid flow ◮ Nature of hot spots ◮ Structure of merger remnant ◮ Matter ejection Part 2: Influence of initial NS spin on ◮ Inspiral ◮ GW signal ◮ Matter ejection
Measuring Deformations ◮ Spatial gauge used in evolution bad for analysis of HMNS ◮ Define better coordinates ◮ Consider the equatorial plane ◮ Meaningful coordinate distances g rr = 1 , g φφ,φ = 0 ◮ Prevent spirals � π g r φ d φ = 0 − π ◮ Fix global rotation β φ → 0 for r → ∞ ◮ Choice of origin: use π -symmetry axis
Measuring Deformations ◮ Spatial gauge used in evolution bad for analysis of HMNS ◮ Define better coordinates 20 10 y [km] 0 10 20 20 10 0 10 20 x [km]
Measuring Compactness Problem ◮ Want to quantify density profile and compactness ◮ Compactness should not be sensitive to low density parts ◮ Should not require symmetries or preferred coordinates
Measuring Compactness Problem ◮ Want to quantify density profile and compactness ◮ Compactness should not be sensitive to low density parts ◮ Should not require symmetries or preferred coordinates Solution ◮ Consider shells of constant (rest frame) mass density ◮ Each shell contains proper volume V and baryonic mass M b ⇒ Unambiguous baryonic mass versus proper volume relations ◮ Compute “volumetric” radius R v of Euklidian sphere with same volume ◮ Define compactness C = M b / R v ◮ Define the “bulk” as shell with maximum compactness ⇒ bulk mass, bulk volume, bulk entropy..
Initial data ◮ Irrotational, equal mass ◮ No magnetic field ◮ Zero temperature, β equilibrium ◮ EOS: G. Shen, Horowitz, Teige ◮ Baryonic mass 2 × 1 . 513 M ⊙ ◮ Bulk mass 98% total mass ◮ Grav. mass of single star 1 . 4 M ⊙ ◮ Initial proper separation 57 . 6 km ⇒ 4 Orbits ◮ Maximum TOV baryonic mass 3 . 33 M ⊙ ⇒ Remnant is stable ! ◮ Corner case, probably not realistic
Merger dynamics Computed isodensity surfaces that contain 1 4 of total mass. Cut in xy + t : Ringdown Inspiral Merger
Merger dynamics Computed isodensity surfaces that contain 1 4 of total mass. Cut in xy + t : 1. Bounce Double core phase Fully merged Collision: very compact, rapid rotation
Merger dynamics Computed isodensity surfaces that contain 1 4 of total mass. Cut in xy + t : Pattern velocity decouples from fl uid velocity Angular momentum re-arranges
Merger dynamics ◮ Quantify mass in double core ◮ Total mass of matter with density > central density 3.5 Separate cores 3.0 Bulk 2.5 M b [ M ⊙ ] 2.0 1.5 1.0 0.5 0.0 0 5 10 15 20 25 t [ms]
GW signal 1e 22 3 q h 2 + + h 2 h + 2 × h at 100 MPc 1 0 1 2 3 4.0 3.5 3.0 f [kHz] 2.5 2.0 1.5 1.0 0.5 0.0 0 5 10 15 20 ( t − r ) [ms]
GW signal 1e 24 1.6 1.4 hf at 100 MPc 1.2 1.0 0.8 0.6 ˜ 0.4 0.2 0.0 1e 22 3.0 2.5 | h | at 100 MPc 2.0 1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 f [khz]
Thermal evolution ◮ Bulk entropy produced at merger, then constant ◮ Matter outside bulk hotter, ongoing heating 5 Total S/N Bulk S blk /N blk 4 Disk S d /N d s [ k B / Baryon] 3 2 1 0 0 5 10 15 20 25 30 t [ms]
Thermal evolution Schock heating Concentration into vortices Quadruple hot spots T wo surviving hot spots
Thermal evolution Schock heating Concentration into vortices Quadruple hot spots T wo surviving hot spots
Thermal evolution Schock heating Concentration into vortices Quadruple hot spots T wo surviving hot spots
Thermal evolution Schock heating Concentration into vortices Quadruple hot spots T wo surviving hot spots
Thermal evolution Schock heating Concentration into vortices Quadruple hot spots T wo surviving hot spots
Thermal evolution Hot spots survived >10 ms by now
Thermal evolution Hot spots survived >10 ms by now
Thermal evolution t =6 . 128 ms , φ =3 . 7 π Density 0.50 40 0.45 0.40 20 0.35 0.30 S/V [ k B / fm 3 ] y [km] 0 0.25 0.20 0.15 20 0.10 0.05 40 0.00 40 20 0 20 40 x [km]
Thermal evolution
Thermal evolution
Thermal evolution ◮ Final state convectively stable ◮ Evolve adiabatically during inspiral -0.3 1.25 25 1.00 -3 20 0.75 -2 0.50 log 10 ( s [ k B / baryon]) 15 0.25 -4 t [ms] -5 0.00 10 0.25 -1 0.50 5 0.75 1.00 activate thermal 0 0 10 20 30 40 50 50 × sinh − 1 ( R [ M ⊙ ] / 50)
Rotation profile ◮ Violent rearrangement of rotation profile after merger 25 7.2 6.4 5.6 20 4.8 F rot [kHz] t [ms] 4.0 15 3.2 2.4 10 1.6 0.8 0.0 0 5 10 15 20 25 30 35 40 r c [km]
Rotation profile ◮ Remnant rotation profile has slowly rotating core ◮ Outer layers close to Kepler rate 12 Ω 10 − β φ Ω K 8 Ω [rad ms − 1 ] ˙ φ 22 6 4 2 0 0 5 10 15 20 25 30 35 40 r c [km]
Rotation profile ◮ Final specific angular momentum profile stable ◮ Specific entropy profile adds even more stability 8 6 l φ [ M ⊙ ] 4 2 0 0 5 10 15 20 25 30 35 40 r c [km]
Remnant mass distribution ◮ Central region of remnant very similar to a TOV star Mass inside Volume 3.5 Initial star t =27 . 0 ms (final) 3.0 2.5 2.0 M b [ M ⊙ ] 1.5 1.0 0.5 0.0 0 1 2 3 4 5 6 7 8 1e3 V [ M 3 ⊙ ]
Remnant mass distribution ◮ Central region of remnant very similar to a TOV star ◮ Define TOV core equivalent by matching bulk properties Mass inside Volume 3.5 Initial star t =27 . 0 ms (final) 3.0 TOV, cold TOVs, T =0 2.5 2.0 M b [ M ⊙ ] 1.5 1.0 0.5 0.0 0 1 2 3 4 5 6 7 8 1e3 V [ M 3 ⊙ ]
Remnant mass distribution ◮ Central region of remnant very similar to a TOV star ◮ Define TOV core equivalent by matching bulk properties Mass inside Volume 3.5 Initial star t =27 . 0 ms (final) 3.0 TOV, cold TOVs, T =0 2.5 TOV, s =1 k B TOVs, s =1 k B 2.0 M b [ M ⊙ ] 1.5 1.0 0.5 0.0 0 1 2 3 4 5 6 7 8 1e3 V [ M 3 ⊙ ]
Remnant mass distribution ◮ Bulk baryonic mass 2 . 4 M ⊙ ◮ TOV core equivalent mass 2 . 2 M ⊙ ◮ Mass outside bulk (Envelope+Disk) 0 . 62 M ⊙ ◮ Mass at r > 20 km (Disk) 0 . 3 M ⊙ 10 9 8 50 core 92 % mass s [ k B / Baryon] 7 40 bulk 90 % mass 6 z [km] 30 95 % mass 5 20 4 10 3 2 0 1 60 40 20 0 20 40 60 0 r [km]
Measuring matter ejection Previous estimate for unbound mass ◮ Assume stationary spacetime ◮ Assume fluid moves along geodesics ◮ Compute volume integral of “unbound” mass
Measuring matter ejection Previous estimate for unbound mass ◮ Assume stationary spacetime ◮ Assume fluid moves along geodesics ◮ Compute volume integral of “unbound” mass Problem ◮ Patently wrong close to remnant ◮ Too far from remnant matter diluted below cut-off
Measuring matter ejection Previous estimate for unbound mass ◮ Assume stationary spacetime ◮ Assume fluid moves along geodesics ◮ Compute volume integral of “unbound” mass Problem ◮ Patently wrong close to remnant ◮ Too far from remnant matter diluted below cut-off Solution ◮ Use flux of unbound baryonic mass through spherical shell ◮ Also compute flux of entropy, electron fraction
Matter Ejection ◮ One wave, launched at merger, escape velocity ≈ 0 . 17 c 1e 4 8 r =73 . 84 km 7 6 M [ M ⊙ / ms] 5 4 3 ˙ 2 1 0 0 5 10 15 20 25 t [ms]
Matter Ejection ◮ One wave, launched at merger, escape velocity ≈ 0 . 17 c ◮ Relatively low amount of unbound matter 1e 4 3.0 Surf r =73 . 84 km 2.5 2.0 M [ M ⊙ ] 1.5 1.0 0.5 0.0 0 5 10 15 20 25 t [ms]
Matter Ejection ◮ One wave, launched at merger, escape velocity ≈ 0 . 17 c ◮ Relatively low amount of unbound matter ◮ Average specific entropy ≈ 15 k B / Baryon 80 Surface r =73 . 84 km (flow) 70 Surface r =73 . 84 km (cumulative) 60 s [ k B / Baryon] 50 40 30 20 10 0 12 14 16 18 20 22 24 26 t [ms]
Matter Ejection ◮ One wave, launched at merger, escape velocity ≈ 0 . 17 c ◮ Relatively low amount of unbound matter ◮ Average specific entropy ≈ 15 k B / Baryon ◮ Electron fraction (not accurate without neutrino radiation) 0.5 Surface r =73 . 84 km (flow) Surface r =73 . 84 km (cumulative) 0.4 0.3 Y e 0.2 0.1 0.0 12 14 16 18 20 22 24 26 t [ms]
Spin – Initial data Lattimer-Swesty ( K = 220 MeV ) EOS Equal mass, M B = 3 . 12 M ⊙ = 1 . 10 M Kepler Aligned rotation Irrotational ∆ F R ≈ 160 Hz G. Shen, Horowitz, Teige (NL3) EOS Equal mass, M B = 4 . 01 M ⊙ = 1 . 01 M Kepler Aligned rotation Irrotational ∆ F R ≈ 155 Hz W. Kastaun, F. Galeazzi, Properties of hypermassive neutron stars formed in mergers of spinning binaries , Phys. Rev. D 91, 064027 (2015)
Spin – Inspiral ◮ Inspiral takes longer with spin ◮ Different impact trajectory 40 SHT-M2.0-I LS220-M1.5-S SHT-M2.0-S LS220-M1.7-I Proper distance [ M ∞ ] 35 LS220-M1.5-I LS220-M1.8-I 30 25 20 19 20 18 17 16 15 15 14 10 13 0.0 0.5 1.0 1.5 5 10 8 6 4 2 0 2 Orbits
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