Effects of neutron star dynamic tides on gravitational waveforms within the Effective One-Body approach arXiv:1602.00599 ? Tanja Hinderer (University of Maryland) A. Taracchini F. Foucart K. Hotokezaka A. Buonanno M. Duez K. Kyutoku J. Steinhoff L. E. Kidder M. Shibata H. P . Pfeiffer M. A. Scheel B. Szilagyi C. W. Carpenter Astrophysics seminar Goethe Universität Frankfurt June 14, 2016
Overview Motivation: potential to determine properties of ultra-dense matter using gravitational waves from NS-NS and NS-BH binaries multimessenger studies (sGRBs, afterglows, neutrinos) ? sources of r-process elements Requires robust models Recent improvements: dynamical tides during inspiral Tidal Effective One-Body model Conclusions 1
Neutron stars (NSs) strongest gravitational environment where matter can stably exist other extremes of physics: Debris from a supernova in 1054 spins up to 38000 rpm, huge magnetic fields, superfluidity, superconductivity, solid crust, … 1939: theoretical prediction [Oppenheimer & Volkoff] 1968: discovery of pulsars [Hewish, Bell,+] 1969: pulsars = neutron stars [Gold] > 2000 observed to date (~1/1000 stars) Crab Pulsar masses ≳ Msun, radii ~ 10km matter compressed to several times nuclear density What is the nature of matter in such extreme conditions? 2
Phases of the strong force H 2 O QCD (conjectured) [credit: Garrido] Neutron stars (NSs) [Wambach+2011] 3
NS structure crust : ~ km outer core: ~ few km ? uniform liquid? deep core: ≳ 2 × 𝝇 nuclear exotic states of matter? deconfined quarks? condensates? Theoretical difficulties: many-body problem with strong interactions unknown composition and equation of state (EoS) Experiments: properties of neutron-rich nuclei, phases of the strong force impossible to reproduce conditions in NSs 4
NS global properties from microphysics composition, multi-body forces, etc., reflected in the EoS EoS determines observables (mass, radius, …) Einstein’s pressure vs. density mass vs. radius field equations [ Özel & Freire 2016 ] 5
NS radius measurements Masses: to ~0.0001% from pulsar timing Radii: difficult to determine Quiescent low-mass Thermonuclear X-ray bursts X-ray binaries, isolated cooling NS [image B. Rutledge] Millisecond pulsars: X-ray pulse shape of [image B. Rutledge] rotating hot-spot x-ray intensity vs. time relative to burst start relative flux pulse phase [image: K. Gendreau] [Galloway+2006] 6 other methods,
Results for NS radii Examples of results systematic uncertainties: distance atmosphere size of emitting region surface composition identification of spectral features magnetic field …. potentially more robust EoS measurements with gravitational waves (GWs) asymmetric rotating NSs (crust physics) coalescing binaries [Lattimer & Steiner 2014 ] 7
Gravitational waves (GWs) in brief Matter and energy curve space and warp time That curvature is responsible for gravity Accelerating masses generate ripples in curvature: GWs. Fractional deviation away from flat space: credit: NASA ¨ mv 2 h ∼ G D ∼ G I ∼ 10 − 22 c 4 c 4 D distance to source ≈ 8 × 10 − 45 s 2 kg m Carry enormous power: ≈ 10 51 Watts (c.f. sun radiates ≈ 10 26 Watts) Interact very weakly with matter. Also produced by processes in the early universe, supernova explosions, asymmetric pulsars … 8
Measuring GWs with interferometers X h(t) suspended mirrors beam splitter L+ Δ L laser L photodetector change in intensity due to difference in phase: ∆ φ = 2 π f 2 ∆ L = 4 π f h ( t ) L c c laser frequency extra roundtrip travel time in the arm 9
Worldwide network of GW detectors LIGO Hanford (WA) GEO 600 L=4km KAGRA ~2020 + LIGO Livingston (LA) Advanced Virgo LIGO India major hardware L=4km ~2020 + upgrade almost completed Advanced LIGO first observing run completed ~ 2019 design sensitivity 10
GW signal from black hole (BH) binaries BHs: regions of extreme spacetime curvature, characterized completely by only mass & spin Merger/ringdown Inspiral the orbit shrinks … … until they collide … and merge into 36 M ⦿ a single BH … velocity ~0.6 c, 29 M ⦿ orbital period ~10 ms … 62 M ⦿ waveform 1.0 h(t) 0.5 (x10 -21 ) 0 - 0.5 - 1.0 0.3 0.35 0.4 0.45 time (s) 11
GW signal from BH binaries details of the waveform depend on the parameters (masses, spins, …) equal mass, no spin unequal mass, no spin equal mass, with spins courtesy A. Taracchini extracting the information from the signal requires highly accurate models as templates for data analysis 12
Approaches to the two-body problem Newtonian dynamics orbital separation r/M post-Newtonian theory test timescales: black hole particle ✓ r ◆ 3 / 2 limit perturbation T orbit ∼ M M ◆✓ r ◆ 4 theory ✓ M T inspiral ∼ M µ M Numerical relativity mass ratio M/ 𝞶 13
Approaches to the two-body problem Newtonian dynamics orbital separation r/M post-Newtonian theory path test to timescales: black hole particle ✓ r merger ◆ 3 / 2 limit perturbation T orbit ∼ M M ◆✓ r ◆ 4 theory ✓ M T inspiral ∼ M µ M Numerical relativity LIGO band mass ratio M/ 𝞶 13
Approaches to the two-body problem Newtonian dynamics orbital separation r/M post-Newtonian theory Effective One-Body (EOB) model: path test to timescales: combines all information into a complete waveform model black hole particle ✓ r merger ◆ 3 / 2 limit for LIGO searches perturbation T orbit ∼ M M ◆✓ r ◆ 4 theory ✓ M T inspiral ∼ M [Buonanno, Damour 1999, 2000] µ M Numerical relativity LIGO band mass ratio M/ 𝞶 13
Effective-One-Body (EOB) approach Effective description Binary problem MAP effective particle ν =µ / M effective spacetime lengthy PN description e ff = − A ( M, ν , r )d t 2 + B ( M, ν , r )d r 2 + r 2 d φ 2 d s 2 A = 1 − 2 M + ν δ A PN ( r ; M, ν ) r Hamiltonian for the dynamics: s effective Hamiltonian H eff ✓ H e ff ◆ H EOB ( r, p r , p φ ; M, ν ) = M 1 + 2 ν − 1 µ radiation reaction forces factorized waveforms 14
Complete EOB waveforms waveform GW frequency inspiral ringdown least damped superposition QNM frequ. of QNMs Evolve the two-body dynamics up to the light ring (spherical photon orbit) Smooth transition Ringdown: quasinormal modes (QNM) of final BH 15
Performance of EOB waveforms m 1 =m 2 , S 1 =S 2 =0.98 S max numerical relativity Calibrated 0 EOB 56 57 58 59 60 61 62 6364 no tuning 0 56 57 58 59 60 61 62 6364 60 61 62 64 57 58 59 56 0.3 GW cycles Calibrated tuned 0 56 57 58 59 60 61 62 6364 56 57 58 59 60 61 62 64 GW cycles [courtesy A. Taracchini] recent extension to precessing spins [Taracchini+ 2016] 16
GW150914 detected by LIGO [LSC 2016] 17
The importance of models for GW150914 establish >5 σ detection significance measure source properties 2 σ 3 σ 4 σ 5 . 1 σ > 5 . 1 σ 2 σ 3 σ 4 σ 5 . 1 σ > 5 . 1 σ 10 2 Search Result 10 1 Search Background Background excluding GW150914 10 0 Number of events 10 − 1 10 − 2 GW150914 10 − 3 10 − 4 10 − 5 10 − 6 10 − 7 10 − 8 8 10 12 14 16 18 20 22 24 Detection statistic ˆ ρ c perform tests of general relativity [LSC 2016] 18
Experimental progress LIGO’s visible volume of the universe for GWs from double neutron stars: Advanced LIGO: first observing run initial LIGO design goal: ~ 1 million galaxies credit: atlasoftheuniverse 19
GW signal from NS-NS binaries BH-BH NS-NS NS NS collapse to BH ≈ point-masses tidal effects merger post-merger rich characteristic >10 3 GW cycles last ~ 20 cycles frequency spectrum > kHz [data from T. Dietrich] 20
GW signal from NS-BH binaries BH - BH NS-BH NS BH tidal effects ≈ point-masses tidal disruption or plunge 1 larger modeling uncertainty in small ∼ (1 + q ) 5 point-mass GWs than for NS-NS GW shutoff can be in aLIGO band q = m BH m NS [data from F. Foucart] 21
Tidal effects during inspiral dominant effect: Q NS = − λ E tidal λ = 2 3 k 2 R 5 companion’s induced tidal tidal field quadrupole NS radius deformability Love number λ - mass pressure - density Einstein’s Eqs: linear perturbations to equilibrium sol. [One 2nd order ODE] credit: B. Lackey 22
Influence on the GWs Energy goes into deforming the NS E ∼ E orbit − 1 4 Q NS E tidal Q NS = λ E tidal moving tidal bulges contribute to gravitational radiation i 2 h d 3 ˙ dt 3 ( Q orbit + Q NS ) E GW ∼ ˙ d φ GW d Ω E GW GW phase from energy balance: = 2 Ω , dt = dt dE/d Ω GW ∼ λ ( v/c ) 10 tidal contribution: ∆ φ tidal M 5 [ Flanagan & TH 2008, Vines+ 2011] 23
Influence on the GW phase Tidal phase contribution in the stationary phase approx. : 3 − 39 ✓ − 3115 Λ + 6595 ◆ � Λ x 5 + √ ˜ ˜ 1 − 4 ν δ ˜ x 6 ψ tidal = Λ 128 ν x 5 / 2 2 64 364 x = ( π Mf ) 2 / 3 ν =µ / M most sensitive to the weighted average: 1 + 7 ν − 31 ν 2 � ✓ λ 1 1 + 9 ν − 11 ν 2 � ✓ λ 1 Λ = 8 � + λ 2 ◆ − λ 2 ◆ � √ ˜ � + 1 − 4 ν m 5 m 5 m 5 m 5 13 1 2 1 2 for identical NSs: λ ˜ δ ˜ Λ = Λ = 0 m 5 NS 24
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