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Rotation law emerging from GR numerical simulation of merging neutron stars

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Rotation law emerging from GR numerical

simulation of merging neutron stars

Andrzej Odrzywołek

Dept. of General Relativity & Astrophysics, IF UJ

25 Sept 2018, Tue, 19:00

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Stationary configurations

Configuration of interest is a Kerr black hole + massive, stationary, axisymmetric torus (see also talks by P. Mach, E. Malec, W.

Kulczycki, M. Piróg).

Object is fully specified by:

1 Black Hole and torus masses & angular momenta

2 Equation of State

last but not least: rotation law

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General remarks on rotating fluids

so-called rotation law connecting angular velocity Ω “ uϕ{ut or angular momentum j “ uϕut with „distance” from rotation axis is a free function j pΩq, e.g. j “ const, j “ Ωδ, . . .

above reflect freedom of how are you stirring sugar in a glass of tea (neglecting viscosity & meridional currents)

Keplerian rotation law of a test particle around point mass/black hole (m “ 1) play a special role in astrophysics

1 Newton (3rd Kepler law):

1 j 9 Ω1{3

2 Schwarzschild:

1

j 9 Ω1{3´ 3Ω

3 and finally Kerr:

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Conjecture of „attractor” in rotating GR systems

Postulate: all generic/realistic GR disks should rotate according to

„Keplerian” rotation law:

j pΩq “ ´1 2

d d Ωln

1 ´ pa22` 3w4323p1 ´ aΩq43q ı

, w “ f pmq where m, a are now free parameters unrelated to those of central Kerr black hole.

How to verify above statement?

Compare computed toroid structure with:

astronomical observations

toroid emerging in GR simulation of NS-NS merger (binary neutron star merger, kilonova, e.g. GW170817 )

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Numerical GR data used for comparison

Data used later is from article: Roberto De Pietri, Alessandra Feo, Francesco Maione, Frank L¨offler, Modeling equal and unequal mass binary neutron star mergers using public codes, Physical Review D, Volume 93, Issue 6, id.064047.

Technically, we used:

1 equatorial plane „XY” slices of full 3D data

2 all 400 timesteps covering from late NS-NS inspiral to toroid stabilization

3 Carpet-HDF5 BSSN fixed mesh-refinemet files for α, gXX, gXY, gYY, βX, βY, VX, VY, ρ

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Neutron star mergers (kilonova)

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Neutron star mergers (kilonova)

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Neutron star mergers (kilonova)

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Neutron star mergers (kilonova)

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Neutron star mergers (kilonova)

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Angular velocity and momentum in isotropic coordinates

Lorentz factor:

W “ 1

b

1 ´ gxxVx2´ gyyVy2´ 2gxyVxVy Transversal velocity component:

Vϕ“ ´y pgxxVx` gxyVyq ` x pgyyVy` gxyVxq Angular velocity:

Ω “ x pαVy´ βyq ´ y pαVx´ βxq x2` y2

Angular momentum:

W2V

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Expected j pΩq

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Raw j pΩq data from simulation

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Raw j pΩq data from simulation

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Raw j pΩq data from simulation

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Raw j pΩq data fits

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Fit j pΩq after cut

10´9 ă ρ ă ρmax “ 2.76 ˆ 10´9

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Conclusions

1 data extracted from GR simulation

2 j pΩq curve formed quickly after black hole formation

3 naive raw data fit seems poorly related to Mach-Malec formula

4 fit weighted with matter density gives rotation law with Kerr parameter a » 1.50

5 above result is surprising but not forbidden

6 more investigation required

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References

1 Self-gravitating axially symmetric disks in general-relativistic rotation, Janusz Karkowski, Wojciech Kulczycki, Patryk Mach, Edward Malec, Andrzej Odrzywołek, and Michał Piróg Phys. Rev. D 97, 104017 – Published 15 May 2018

2 General-relativistic rotation: Self-gravitating fluid tori in motion around black holes, Janusz Karkowski, Wojciech Kulczycki, Patryk Mach, Edward Malec, Andrzej Odrzywołek, and Michał Piróg Phys. Rev. D 97, 104034 – Published 21 May 2018

3 Modeling equal and unequal mass binary neutron star mergers using public codes Roberto De Pietri, Alessandra Feo,

Francesco Maione, and Frank L¨offler Phys. Rev. D 93, 064047 – Published 21 March 2016

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