How to verify the
Quark-Gluon Plasma
with Gravitational-Wave Detectors
Talk at the Hirschegg Workshop “Neutron Star Mergers:From gravitational waves to nucleosythesis”
Hirschegg (Austria), 16.01.2017

Matthias Hanauske, Kentaro Takami, Luke Bovard, Luciano Rezzolla,
Filippo Galeazzi, José A. Font, and Horst Stöcker
Frankfurt Institute for Advanced Studies
Johann Wolfgang Goethe-University
Institute for Theoretical Physics
Department of Relativistic Astrophysics
Frankfurt am Main, Germany

How to verify theQuark-Gluon Plasma
with Gravitational-Wave Detectors
1. Introduction
2. Numerical General Relativity
3. Equation of Stateand the Hadron-Quark Phase Transition
4. Internal Properties of Hypermassive Neutron andHybrid Stars in the Post-Merger Phase
5. Outlook and Summary

First observation gravitational waves
from binary black hole merger by LIGO
Facts about GW150914
Merger of two black holes of around36 and 29 solar masses
Distance: 410 Mpc (1340 million Ly)

Credit: Les Wade from Kenyon College.

Gravitational Waves
from Binary Neutron Star Mergers
Neutron star merger (Simulation)

Merger oftwo Black Holes

Main Difference:
Neutron star mergers could have apost-merger phase

The Neutron Star Merger ProductRelativistic Hydrodynamics andNumerical General Relativity
The time evolution of a merger scenario of a binary neutron star system requires the (3+1)Split of the Einstein- and hydrodynamic equations.

(3+1)
decompositionof spacetime

All figures and equations from: Luciano Rezzolla, Olindo Zanotti: Relativistic Hydrodynamics, Oxford Univ. Press, Oxford (2013)

The ADM equations
The ADM (Arnowitt, Deser, Misner) equations come from a reformulation of the Einsteinequation using the (3+1) decomposition of spacetime.
Time evolvingpart of ADM
Constraints on each hypersurface

Three dimensional covariant derivative

Spatial and normal
projections of theenergy-momentum
tensor:Extrinsic Curvature:Three dimensional Riemann tensor

All figures and equations from: Luciano Rezzolla, Olindo Zanotti: Relativistic Hydrodynamics, Oxford Univ. Press, Oxford (2013)

General Relativity andQuantum Cromodynamics

The Equation of Stateand the QCD Phase Diagram

Image from http://inspirehep.net/record/823172/files/phd_qgp3D_quarkyonic2.png

The Gibbs Construction
Hadronic and quark matter surface:

Charge neutrality condition is only globally realized

The QCD – Phase Transition and theInterior of a Hybrid Star33 ρρ00SurfaceSurfaceof
ofthetheStarStar

ALF2-EoS
ALF2-EoS

7.8
7.8 ρρ00

CenterCenterof
ofthetheStarStar

The Maxwell Construction
No Mixed Phase Region
Pressure and baryon chemical potential stays constant, while the density and thecharge chemical potential jump discontinuously during the phase transition.
Simple Alford Model

Image from M.G. Alford, S. Han, and M. Prakash, Phys.
Rev. D 88, 083013 (2013)

Hadronic Phase: DD2-Model
Quark Phase: Chiral Quark Meson ModelA.Zacchi, M.Hanauske and Schaffner-Bielich, Phys. Rev. D 93,065011 (2016)

The Compact Star Zoo
Depending on the model used, the compact star zoo consists of different
inhabitants: e.g. neutron stars with and without hyperons, quark stars and strange
quark stars, hybrid stars with color superconducting quark matter, hybrid stars
with Bose-Einstein condensates of antikaons.

Numerical Setup
Several different EOSs : ALF2, APR4,GNH3, H4 and Sly, approximated byBSSNOK conformal traceless formulation
piecewise polytopes. Thermal ideal fluid of the ADM equations. 3+1 Valencia
component (Γ=2) added to the nuclear- formulation and high resolution shock
capturing methods for the hydrodynamic
physics EOSs.
evolution. Full general relativity using theEinstein-Toolkit and theWHISKY/WhiskyTHC code for thegeneral-relativistic hydrodynamicequations.

LS220: Temperature dependent
EOS-table (Lattimer-Swesty)

Grid Structure:
Adaptive mesh refinement (six ref. levels)
Grid resolution: (from 221 m to 7.1 km)
Outer Boundary: 759 km
Initial separation of stellar cores: 45 km

HMNS Evolution for different EoSs
High mass simulations (M=1.35)

Central value of the lapse function αc (upper panel) and maximum of the rest mass density ρmax inunits of ρ0 (lower panel) versus time for the high mass simulations.

HMNS Evolution for different EoSs
Low mass simulations (M=1.25)

Central value of the lapse function αc (upper panel) and maximum of the rest mass density ρmax inunits of ρ0 (lower panel) versus time for the low mass simulations .

Evolution of therest-mass density distribution
ALF2, High mass model: Mixed phase region starts at 3ρ0Initial NS mass: 1.35 Msolar

Gravitational wave amplitude
at a distance of 50 Mpc

Rest mass density distribution ρ(x,y)
in the equatorial planein units of the nuclear matter density ρ0

The Angular Velocity in the (3+1)-Split
The angular velocity Ω in the (3+1)-Split is a combination of the lapse function α , theφ-component of the shift vector βφ and the 3-velocity vφ of the fluid (spatial projectionof the 4-velocity u):(3+1)-decompositionof spacetime:

AngularAngularvelocity
velocity ΩΩΦ-component
LapseLapse function
function Φ-componentφofααof 3-velocity
3-velocity vvφFocus:
Focus:Inner
Innercore
coreofofthe
thedifferentiallydifferentiallyrotatingrotatingHMNS
HMNS
M. Shibata, K. Taniguchi, and K. Uryu, Phys. Rev. D 71, 084021 (2005)
M. Shibata, K. Taniguchi, and K. Uryu, Phys. Rev. D 71, 084021 (2005)
M. Shibata and K. Taniguchi, Phys. Rev. D 73, 064027 (2006)
M. Shibata and K. Taniguchi, Phys. Rev. D 73, 064027 (2006)
F. Galeazzi, S. Yoshida and Y. Eriguchi, A&A 541, p. A156 (2012)
F. Galeazzi, S. Yoshida and Y. Eriguchi, A&A 541, p. A156 (2012)
W. Kastaun and F. Galeazzi, Phys. Rev. D 91, p. 064027 (2015)
W. Kastaun and F. Galeazzi, Phys. Rev. D 91, p. 064027 (2015)

Frame-dragging
Frame-dragging
ββφφ

EoS: ALF2, M=1.35 Post-Merger Phase
Gravitational
Gravitationalwave
wave
amplitude
amplitudehh++and
and|h||h|atataa
distance
distanceof
of738
738km
km
forforthe
theALF2-M135
ALF2-M135
modelmodelRotation Profiles (ALF2-1.35 Model)

Rotation Profiles (ALF2-1.25 Model)LS220 M=1.32
Rest mass density, rotationprofile, Shift vector and TemperatureLS220 M=1.32
Co-rotating frame and fluid tracersLS220 M=1.32
Co-rotating frame and fluid tracersTemperature profiles in the (x,y)-plane
LS220-M132 binary at t = 6.7 ms (left panel) and t = 23.8 ms (rightpanel). The trajectories of several tracer-cells are additionally visualized.

LS220 M=1.32
Co-rotating frame and fluid tracersLS220 M=1.32
Co-rotating frame and fluid tracers

Averaging Procedure for ΩIn order to compare the structure of the rotation profiles between the different
EOSs, a certain time averaging procedure has been used:Time-averaged Rotation Profiles( R* , Ω* )SoftSoft EoSs:
EoSs:
SlySly
APR4
APR4

Stiff
Stiff EoSs:
EoSs:
GNH3
GNH3
H4
H4

Time-averaged rotation profiles for different EoS
Low mass runs (solid curves), high mass runs (dashed curves).

GW-Spectrum for different EoSs
See:
Kentaro Takami, LucianoRezzolla, and Luca Baiotti,
Physical Review D 91, 064001(2015)
Hotokezaka, K., Kiuchi, K.,
Kyutoku, K., Muranushi, T.,
Sekiguchi, Y. I., Shibata, M., &Taniguchi, K. (2013). PhysicalReview D, 88(4), 044026.
Bauswein, A., & Janka, H. T.
(2012). Physical review letters,108(1), 011101.
Clark, J. A., Bauswein, A.,
Stergioulas, N., & Shoemaker,D. (2015). arXiv:1509.08522.
Bernuzzi, S., Dietrich, T., &Nagar, A. (2015). Physicalreview letters, 115(9), 091101.

Time Evolution of the GW-Spectrum
The power spectral density profile of the post-merger emission is characterized byseveral distinct frequencies fmax , f1 , f2 , f3 and f2−0 . After approximately 5 ms aftermerger, the only remaining dominant frequency is the f 2-frequency.
See L.Rezzolla and K.Takami, arXiv:1604.00246

Stiff EoS

Soft EoS

Evolution of the frequency spectrum of the emitted gravitational waves for the stiff GNH3 (left) and soft APR4 (right) EOS.

Gravitational Waves andthe maximum of the Rotation Curve

How to observe the QGP
with gravitational waves from NS mergers?

Outlook

Maximum of the rest mass density ρmaxin units of ρ0 versus timefor the high mass simulations.

The power spectral density profile ofthe post-merger emission ischaracterized by several distinct
frequencies fmax , f1 , f2 , …, f2-PT

Summary

1. With the first observation of gravitational waves from binary
black hole merger by LIGO, the whole branch ofobservational astronomy will enter a new era - the so called
gravitational-wave astronomy.
2. GWs emitted from merging neutron star binaries are on theverge of their first detection.
3. The spectrum of the emitted GWs (within the merger and postmerger phase) depend strongly on the high density regime ofthe EOS.
4. With the knowledge of the f1- and f2-frequency peak and thetotal mass the system, the GW signal can set tight constraints
on the EOS.
5. The phasetransition to the Quark-Gluon-Plasma might beobservable with Gravitational Wave Detektors (f2-PT- peak)Universal Behavior of f1 and fmax

Values of the low-frequency peaks f 1
shown as a function of the tidal
deformability parameter κT2.

Mass-weighted frequencies at amplitude
maximum fmax shown as a function of thetidal deformability parameter κT2.

Universal behavior of the f2-peak

Values of the low-frequency peaks f 2 shown
as a function of the tidal deformability parameter κT2.

Gravitational Waves

Equation of StateThe detection of GWs from merging neutron star binaries can be used to determine
the high density regime of the EOS. With the knowledge of f 1, f2 and the total mass thesystem, the GW signal can set tight constraints on the EOS.

L.Rezzolla and K.Takami, arXiv:1604.00246
K.Takami, L.Rezzolla, and L.Baiotti, Physical Review D 91, 064001 (also PRL 113, 091104)

Gravitational Waves andthe maximum of the Rotation CurveTime-averaged Rotation Profiles( R* , Ω* )SoftSoft EoSs:
EoSs:
Sly
Sly
APR4
APR4

Stiff
Stiff EoSs:
EoSs:
GNH3
GNH3
H4
H4

Time-averaged rotation profiles for different EoS
Low mass runs (solid curves), high mass runs (dashed curves).

Frame-Dragging
and Gravitomagnetism
The dragging of local inertial frames is quite large in the interior of the HMNS andtherefore an additional gravitomagnetic force is present. Like the Lorentz-force inelectromagnetism, it acts orthogonal to the fluids velocity and the frame dragging.
(strong time andIngredients of the angular velocity:φ-dependence !)Maximum Value of Ω and its
Radial Position (high mass run)t < 5 ms
Violent early phase

5 ms < t < 13 ms
Gravitomagnetism

Collapse to a black holeMaximum Value of Ω and its
Radial Position (low mass run)

5 ms < t < 15 ms
t < 5 ms
Violent early phase Gravitomagnetismt > 15 ms:
Quasi equilibrated and φ-symmetric HMNS

Einstein inside Ausstellung
in Frankfurt am Main

Values of the low-frequency peaks f 2 shown
as a function of the tidal deformability parameter κT2.

Vorlesung: ART mit dem Computer

Values of the low-frequency peaks f 2 shownwww.fias.uni-frankfurt/~hanauske/VARTC/

Warum (noch) keine Gravitationswellen
von kollidierenden Neutronensternen?
Wissenschaftliche Datenaufnahme in 2015

Zukünftige Updates

Erste Datenaufnahme

Nächste Datenaufnahme (Herbst 2016)

The ballroom dance of NS-mergers

WienerWalzer(Solo dance)

DiscoFox

Merengue
Tango