Entropy Profiles

1. Initial Orbits
2. No B-Field
3. Aligned B-Field
4. Tilted B-Field 45^o
5. Tilted B-Field 90^o
6. Comparison

Initial Orbits

Fig. 1-1: Initial Configuration of Black Hole and Neutron Star

Here, we plot the entropy profile in the matter as measured by K/K₀, where K = P/ρ ^Γ and K₀ = K at t = 0 Shock heating causes the ratio K/K₀ to increase above unity. Here we show the first four orbits.

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No B-Field

In the clip, the entropy of the star K/K₀ is plotted on a logarithmic scale. The remaining evolution is shown here. No magnetic field is present in this case.

Fig. 2-1: Entropy profile at time t/M = 633	Fig. 2-2: Entropy profile at time t/M = 882
Fig. 2-3: Entropy profile at time t/M = 974	Fig. 2-4: Entropy profile at time t/M = 2072

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Aligned B-Field

In the clip, the entropy of the star K/K₀ is plotted on a logarithmic scale.After four orbits, the unmagnetized interior of the unmagnetized neutron star is seeded with a purely poloidal magnetic field parallel to the spin axis of the black hole . With an average magnetic-to-gas pressure of 0.5%, the magnetic fields are dynamically unimportant to the neutron star.

Fig. 3-1: Entropy profile at time t/M = 633	Fig. 3-2: Entropy profile at time t/M = 882
Fig. 3-3: Entropy profile at time t/M = 974	Fig. 3-4: Entropy profile at time t/M = 2072

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Tilted B-Field 45^o

In the clip, the entropy of the star K/K₀ is plotted on a logarithmic scale. After four orbits, the unmagnetized interior of the unmagnetized neutron star is seeded with a purely poloidal magnetic field tilted 45^o with respect to the spin axis of the black hole. With an average magnetic-to-gas pressure of 0.5%, the magnetic fields are dynamically unimportant to the neutron star.

Fig. 4-1: Entropy profile at time t/M = 633	Fig. 4-2: Entropy profile at time t/M = 882
Fig. 4-3: Entropy profile at time t/M = 974	Fig. 4-4: Entropy profile at time t/M = 2072

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Tilted B-Field 90^o

In the clip, the entropy of the star K/K₀ is plotted on a logarithmic scale. After four orbits, the unmagnetized interior of the unmagnetized neutron star is seeded with a purely poloidal magnetic field tilted perpendicular with respect to the spin axis of the black hole. With an average magnetic-to-gas pressure of 0.5%, the magnetic fields are dynamically unimportant to the neutron star.

Fig. 5-1: Entropy profile at time t/M = 633	Fig. 5-2: Entropy profile at time t/M = 882
Fig. 5-3: Entropy profile at time t/M = 974	Fig. 5-4: Entropy profile at time t/M = 2072

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Comparison

In the clip, the entropy of the star K/K₀ is plotted on a logarithmic scale. After four orbits, the unmagnetized interior of the unmagnetized neutron star is seeded with a magnetic field parallel (top right), tilted 45^o (bottom left), and perpendicular (bottom right) to their orbital axis. The top left star is left unmagnetized. With an average magnetic-to-gas pressure of 0.5%, these magnetic fields are dynamically unimportant to the neutron star.

Fig. 6-1: Entropy profiles at time t/M = 633	Fig. 6-2: Entropy profiles at time t/M = 882
Fig. 6-3: Entropys profile at time t/M = 974	Fig. 6-4: Entropy profiles at time t/M = 2072

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Given the weakness of the initial magnetic field in all the cases, there is very little difference in the entropy evolution between the four cases. Approximately 14% of the neutron star rest-mass remains outside the remnant black hole in all cases.