Calculation of realistic electrostatic potentials in star crusts

Transcription

1 Calculation of realistic electrostatic potentials in star crusts Claudio Ebel 1 2 November 3, Strong electric fields induced on a sharp stellar boundary I.N.Mishustin, C.Ebel, and W.Greiner, J.Phys.G 37, 7521 (21) 2 Calculation of realistic electrostatic potentials in star crusts C.Ebel, I. N. Mishustin, W. Greiner and T. Buervenich, in preparation 1/2

2 Table of content 1 Start 2 Motivation 3 The model 4 Results 5 Conclusions 2/2

3 The life and death of a star Figure: From sparse gas to supernova 3/2

4 A first look inside a neutron star Figure: Cross section of a neutron star 4/2

5 Pasta phases 5/2

6 Calculations in Wigner-Seitz cells Different geometries Figure: Sphere Figure: Rod Figure: Plate The number of the protons (red) is equal to the number of electrons (green) in the cell. The total charge of the cell vanishes (Q cell = ). 6/2

7 Boundary conditions, T = ρ ρ p ρ e ρ n R R c z The three constraints fixed cell size, Woods-Saxon density distribution ρ p (z) = charge neutrality ρ p dv = Z = ρ e dv and ρ p 1+e z R a chemical potential µ not depending on coordinates overdetermine the system. 7/2

8 Thomas-Fermi approximation The energy of an electron with momentum k at point z is: ǫ(k F (z),z) = kf 2(z)+m2 eφ(z). All states up to µ are occupied, so ǫ(k F,z) = µ. The local Fermi momentum is k F (z) = (eφ+µ) 2 m 2 with the local electron density ρ e (z) = k3 F (z) [ (eφ+µ) 2 m 2] 3/2 3π 2 = 3π 2. 8/2

9 Simple example The Electrostatic potential φ(z): e d2 dx 2φ(z) = e2 (ρ p ρ e ) The boundary conditions for the potential: e d φ(z = ) = dx eφ(z = R) = 9/2

10 Wigner-Seitz cell, spherical case ρ p = ρ, Y e =.2 ρp/fm 3 ρe/fm 3 eφ/mev.3.15 E/ MV fm z/fm 1/2

11 Chemical potential 2 15 µ/mev 1 5 Spheres Cylinders Slaps Tubes Bubbles ρ B ρ 11/2

12 Electric energy + surface energy /MeV W+Eσ NB Spheres Cylinders Slaps Tubes -.8 Bubbles ρ B ρ 12/2

13 Ratio of constant to realistic Coulomb energy /% Wconst WTF Wconst ρ ρ Droplets Rods Slaps 13/2

14 Realistic calculations within the Hartree-Fock formulation ρp/fm 3 ρe/fm eφ/mev E/ MV fm z/fm work in progress: Ebel, Heinzmann, Mishustin, Schramm 14/ 2

15 Star crusts Hadron to Quark matter phase transition in neutron (hybrid) stars discontinuity in baryon and charge density (e.g. MIT bag equation of state Stars made of Strange Quark Matter (SQM) (Witten, Farhi & Jaffe, Alcock et al.) Nuclei embedded in an electron gas in supernova matter (Buervenich, Mishustin, Greiner, 27) Strong electric fields induced on a sharp boundary (Mishustin, Ebel, Greiner) 15/2

16 Strong electric fields, E c = 2.6 kv/fm 16/2

17 Fermi and Dirac seas 17/2

18 Future work: nuclear chart 18/2

19 Conclusions Exact calculation of the electrostatic energy is important for nuclear stability calculations In the future these calculations will be implemented into the relativistic mean-field models for cold and hot nuclear matter We are planning to perform the following studies: nuclear structure in neutron star crusts nuclei in supernova environments (finite T) mixed phase in deconfinement hadronisation transition 19/2

20 Thank you for your attention! Special thanks to my collaborators: I. Mishustin W. Greiner S. Schramm T. Buervenich U. Heinzmann And of course: To you! 2/2