Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches

Size: px

Start display at page:

Download "Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches"

Madlyn Kelley
5 years ago
Views:

INT Program INT-16-2b The Phases of Dense Matter July

Vortex-Nucleus Interaction for Neutron Star Glitches

M. Forbes 2,3 Faculty of Physics, Warsaw University

1 INT Program INT-16-2b The Phases of Dense Matter July 11 - August 12, 2016 Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Kazuyuki Sekizawa 1 in collaboration with G. Wlazłowski 1,2 P. Magierski 1,2 A. Bulgac 2 M.M. Forbes 2,3 Faculty of Physics, Warsaw University of Technology 1 Department of Physics, University of Washington 2 Department of Physics & Astronomy, Washington State University 3

2 Goal: To clarify the mechanism of glitches Need to describe pinning/unpinning dynamics of a huge number of vortices Superfluid neutrons Vortex tension Effective mass We can extract these ingredients from microscopic, dynamical simulations

3 1. Introduction

Pulsar: a rotating neutron star Period (sec) year 1970 1975 1980 0.8925 0.8924 0.8923 0.

8920 Time Sudden decrease of the period = Sudden increase of the frequency V.B.

4 What is the glitch? Glitch: a sudden increase of the rotational frequency p Glitches in the Vela pulsar Ø Pulsar: a rotating neutron star Period (sec) year Time Sudden decrease of the period = Sudden increase of the frequency V.B. Bhatia, A Textbook of Astronomy and Astrophysics with Elements of Cosmology, Alpha Science, K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

5 Vortices and glitches In rotating superfluid, an array of quantum vortices is generated p Observation in ultra-cold atomic gases W. Ketterle, MIT Physics Annual K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

6 Vortices and glitches In rotating superfluid, an array of quantum vortices is generated p Observation in ultra-cold atomic gases Vortex-number density Low Rotation speed High W. Ketterle, MIT Physics Annual K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

Vortices and glitches In rotating superfluid, an array of quantum vortices is generated p Observation in ultra-cold atomic gases Vortex-number density Low

7 Vortices and glitches In rotating superfluid, an array of quantum vortices is generated p Observation in ultra-cold atomic gases Vortex-number density Low Rotation speed High W. Ketterle, MIT Physics Annual K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

8 Studies of the pinning force Representative studies of the pinning force p Hartree-Fock-Bogoliubov theory P. Avogadro, F. Barranco, R.A. Broglia, and E. Vigezzi, PRC75(2007)012805(R); NPA788(2007)130; NPA811(2008)378 p Thomas-Fermi + LDA P.M. Pizzochero, L. Viverit, and R. A. Broglia, PRL79(1997)3347 P. Donati and P.M. Pizzochero, PRL90(2003)211101; NPA742(2004)363; PLB640(2006)74 S. Seveso, P.M. Pizzochero, F. Grill, and B. Haskell, MNRAS455(2016)3952 p Hydrodynamics + Ginzburg-Landau (for pairing) M.A. Alpar et al. Astrophys. J. 213(1977)527; 276(1984)325 R.I. Epstein, G. Baym, Astrophys. J. 328(1988)680 R.K. Link, R.I. Epstein, Astrophys. J. 373(1991)592 K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

Superfluid hydrodynamics Density dependence and asymptotic behavior of the force are predicted Interaction energy between a vortex line and an impurity : attraction :

9 Superfluid hydrodynamics Density dependence and asymptotic behavior of the force are predicted Interaction energy between a vortex line and an impurity : attraction : repulsion *ρ in/out : superfluid density inside/outside a nucleus vortex K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

10 What was the state-of-the-art? Microscopic, static HFB calculations were performed assuming axial symmetry Energy to create a vortex line on a nuclear impurity Energy to create a vortex line in a uniform matter E.g.) fm -3 (SLy4) 6.19 MeV P. Avogadro, F. Barranco, R.A. Broglia, and E. Vigezzi, PRC75(2007)012805(R); NPA788(2007)130; NPA811(2008)378 K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

What was the state-of-the-art? Property of the pinning force is still unclear HFB (Avogadro et al.) Interstitial pinning TF+LDA (Donati & Pizzochero) Nuclear pinning P. Avogadro, F.

11 What was the state-of-the-art? Property of the pinning force is still unclear HFB (Avogadro et al.) Interstitial pinning TF+LDA (Donati & Pizzochero) Nuclear pinning P. Avogadro, F. Barranco, R.A. Broglia, and E. Vigezzi, PRC75(2007)012805(R); NPA811(2008)378 K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

12 2. Methods

13 What we have performed We performed 3D, dynamical simulations by TDDFT with superfluidity p TDSLDA equations (or TDHFB, TD-BdG) PNM SNM p Energy density functional (EDF) : Fayans EDF (FaNDF 0 ) w/o LS S.A. Fayans and D. Zawischa, arxiv:nucl-th/ K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

14 What we have performed We performed 3D, dynamical simulations by TDDFT with superfluidity p TDSLDA equations (or TDHFB, TD-BdG) PNM SNM p Energy density functional (EDF) : Fayans EDF (FaNDF 0 ) w/o LS S.A. Fayans and D. Zawischa, arxiv:nucl-th/ K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

What we have performed We performed 3D, dynamical simulations by TDDFT with superfluidity p TDSLDA equations (or TDHFB, TD-BdG) a vortex line exists here p

15 What we have performed We performed 3D, dynamical simulations by TDDFT with superfluidity p TDSLDA equations (or TDHFB, TD-BdG) a vortex line exists here p Computational details Nuclear impurity: # of quasi-particle w.f. E.g. K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

equations (or TDHFB, TD-BdG) TITAN, Oak Ridge p

Nuclear impurity: MPI+GPU 48h w/ 200GPUs for

Sekizawa Microscopic Calculation of Vortex-Nucleus

16 What we have performed We performed 3D, dynamical simulations by TDDFT with superfluidity p TDSLDA equations (or TDHFB, TD-BdG) TITAN, Oak Ridge p Computational details NERSC Edison, Berkeley Nuclear impurity: MPI+GPU 48h w/ 200GPUs for 10,000 fm/c # of quasi-particle w.f. HA-PACS, Tsukuba K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

17 3. Results Superfluid neutrons Vortex tension Effective mass

18 How to extract the force We directly measure the force in dynamical simulation p Newton s law if p We keep a nuclear motion in a constant velocity Superfluid neutrons vortex K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

19 Results of TDSLDA calculation: Blue line: vortex-core Red dot: c.m. of protons v 0 : along x-axis Force exerts on the nucleus will be shown by a black arrow or? K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

20 Results of TDSLDA calculation: Repulsive!! K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

Measured force The force is essentially central, not a simple function of R F t is negligibly small Measured force 0.0-0.5-1.0-1.5-2.

21 Measured force The force is essentially central, not a simple function of R F t is negligibly small Measured force R F t F c : negative for repulsive F t : positive for anti-clockwise -F c Long-ranged for higher density (smaller Δ, larger ξ) K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

22 Force per unit length We can predict the force for any vortex-nucleus configuration Ø Force per unit length Padé approximant (n=2 was used) K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

23 Results of TDSLDA calculation: Pinned configuration is dynamically unstable K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

24 Superfluid neutrons Vortex tension Effective mass

25 Vortex tension We can evaluate the vortex tension from the dynamical simulations Work done by F ext cf. hydrodynamic approx.: K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

26 Superfluid neutrons Vortex tension Effective mass

How to extract the effective mass Dragging by a constant force provides the effective mass p Newton s law p We accelerate a nuclear impurity by a

27 How to extract the effective mass Dragging by a constant force provides the effective mass p Newton s law p We accelerate a nuclear impurity by a constant force Superfluid neutrons v(t) Time K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

28 Effective mass Dynamical effects may reduce the effective mass Preliminary ρ(x) x K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

29 Effective mass: future work We are going to calculate M* and v c through out the inner crust ü We have prepared initial states for dynamical simulations K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

30 4. Conclusion

31 Conclusion We can compute various ingredients of the inner crust by microscopic, dynamical simulations! Superfluid neutrons : critical velocity Vortex tension Effective mass K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Wed., July 27, 2016

32 Kazuyuki Sekizawa Research Assistant Professor Faculty of Physics, Warsaw University of Technology ulica Koszykowa 75, Warsaw, Poland if.pw.edu.pl

33 Backup

34 Initial states K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Thu., June 23, 2016

35 Vortex detection K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Thu., June 23, 2016

36 K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Thu., June 23, 2016

Pulsar: a rotating neutron star Pulsar is one of the

(Crab pulsar) p More than 2000 pulsars have been found p

at most a few tens of ms per year Irregularities in

38 Pulsar: a rotating neutron star Pulsar is one of the most accurate atomic clock p First observation in 1968 (Crab pulsar) p More than 2000 pulsars have been found p Rotation period: a few ms - several seconds p Spin-down: at most a few tens of ms per year Irregularities in their rotational frequency have been observed: the glitches 3/22

39 What is the glitch? Glitch is a sudden spin-up of the rotational frequency Ex.) The Vela pulsar (PSR B ) Cumulative angular momentum MJD (year) p One of the most active glitching pulsars p Period of pulsation: 89 ms p Time between glitches: a few years p ΔΩ/Ω~10-6 p It repeats regularly *MJD: Modified Julian Date Something must happen inside the neutron star! K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

Where are glitches originated from? The inner crust of a neutron star is relevant to the glitches Outer crust Nuclei (Fe), electrons 0.3-0.

16 fm -3 ; Nuclear saturation density Uniform nuclear matter: n, p, e -, μ - Inner crust 0.5-0.

40 Where are glitches originated from? The inner crust of a neutron star is relevant to the glitches Outer crust Nuclei (Fe), electrons km ρ < ρ drip ρ drip ~ ρ 0 ; Above ρ drip unbound neutrons exist outside nuclei ρ 0 =2.8x10 14 g/cm 3 =0.16 fm -3 ; Nuclear saturation density Uniform nuclear matter: n, p, e -, μ - Inner crust km Nuclei, electrons, dripped neutrons ρ drip ρ 0.6ρ 0 Hyperons? Meson condensates? Outer/inner core 9-12 km 0.6ρ 0 < ρ 3-5ρ 0 Quark matter? K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

41 Structure of the inner crust A lattice of neutron-rich nuclei are immersed in a neutron superfluid Quantum vortices can exist! Pressure ionization Neutronization Neutron drip Nuclear pasta Fig.4 in N. Chamel and P. Haensel, Living Rev. Relativity 11, 10 (2008) K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

42 Scenario of the glitch K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

43 Scenario of the glitch ü Superfluid component is decoupled from normal one Neutron superfluid Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

44 Scenario of the glitch ü Core must spin down due to the radiation processes γ, e ± Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

45 Scenario of the glitch ü Neutron superfluid follows the spin-down by expelling vortices outward γ, e ± Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

46 Scenario of the glitch γ, e ± ü The vortices are trapped by the lattice of nuclei vortex nucleus Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

47 Scenario of the glitch ü Since v super > v core, the Magnus force exerts on the pinned vortices γ, e ± v core Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

48 Scenario of the glitch γ, e ± ü Since v super > v core, the Magnus force exerts on the pinned vortices v super v core Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

49 Scenario of the glitch γ, e ± ü Since v super > v core, the Magnus force exerts on the pinned vortices v super v core F Magnus Core K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

50 What happens in a glitch event? P.W. Anderson and N. Itoh, Nature 256, 25 (1975) Pinning and unpinning of vortices may cause the glitches p Vortex-mediated glitch Inner crust Superfluid neutrons v core v super K. Sekizawa Microscopic Calculation of Vortex-Nucleus Interaction for Neutron Star Glitches Thu., June 23, 2016

51 State-of-the-art study Binding energy was evaluated by axially symmetric HFB calculation E pair (MeV) ΔE (MeV) - Cylinder: R=30 fm, h=40 fm - Mesh: 0.25 fm - Skyrme SLy4 & SkM* - Pairing: DDDI (Ec=60 MeV) P. Avogadro, F. Barranco, R.A. Broglia, and E. Vigezzi, PRC75(2007)012805(R); NPA811(2008)378 K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22 E kin (MeV) k F (fm -1 )

52 TDSLDA: Time-Dependent Superfluid Local Density Approximation We assume a local form of the Kohn-Sham EDF in TDDFT p TDSLDA equations: u i (r), v i (r): quasi-particle wave functions h(r): single-particle Hamiltonian µ: chemical potential p Local energy density functional: Fayans EDF (FaNDF 0 ) w/o LS S.A. Fayans and D. Zawischa, arxiv:nucl-th/ Δ(r): local pairing field ν(r): anomalous density K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

53 Regularization for zero-range pairing interaction We can efficiently work with the local pairing field pproblem: ν(r 1, r 2 ) and thus Δ(r 1, r 2 ) diverge when r 1 =r 2 pprescription: (l c k F k c ) E c : a cutoff energy pexample: 110 Sn, Woods-Saxon Homogeneous neutron matter Δ n [MeV] r [fm] E c =45, 50 MeV E c =40 MeV E c =35 MeV E c =30 MeV E c =20 MeV Δ n [MeV] g eff [MeV fm 3 ] E c [MeV] w/ k c & l c w/ k c Vacuum regularization See A. Bulgac and Y. Yu, PRL88(2002)042504; PRC65(2002)051305(R); arxiv:nucl-th/ , and references therein K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

54 Computational settings We use our own 3D TDSLDA code written in CUDA C with MPI p Some details - EDF: Fayans EDF (FaNDF 0 ) w/o LS - 3D uniform lattice: 50x50x40 - Mesh spacing: 1.5 fm - dt~0.054 fm/c - E c =75 MeV (Nwf_n: 32,665, Nwf_p: 13,967) - Time-evolution: split-operator w/ predictor corrector - Derivatives: Fourier transformation - Periodic boundary condition - Each CUDA core is responsible for each grid point Confining tube by V ext 60 fm 75 fm 30 fm 75 fm p Physical situation - N: Z: 50 (Sn) p Performance ρ n ~0.016 fm -3, k F ~0.78 fm -1 Ex: 48 nodes (192 GPUs) on HA-PACS -> 28 hours for 10,000 fm/c time-evolution Δ [MeV] PNM k F [fm -1 ] K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

55 Initial state generation We dynamically generate an initial configuration starting from a uniform system p Adiabatic switching s(t): a smooth switch function [0, 1] p Quantum friction 0 p What we do in practice: *U qf removes any irrotational currents Uniform system +Tube +HO +Coulomb -HO Put it to a static solver w/o Coulomb A. Bulgac, M.M. Forbes, K.J. Roche, and G. Wlazłowski, arxiv: [nucl-th] K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

56 Initial state generation: Impurity at the center Neutron density Proton density 14/22

57 The prepared initial states I. separated configuration II. pinned configuration K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Nov. 20, /22

58 Vortex-nucleus dynamics I: from separated configuration 17/22

59 The extracted force We find repulsive nature of the vortex-nucleus interaction Force and R vs. time impurity vortex core F t R F c dragging along x-axis F c : positive for repulsive F t : positive for anti-clockwise *Green line: averaged over 50 measurements (540 fm/c) K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

60 Vortex-nucleus dynamics II: from pinned configuration 19/22

61 The extracted force We find repulsive nature of the vortex-nucleus interaction Force and R vs. time impurity vortex core unpinning! F t R F c dragging along x-axis F c : positive for repulsive F t : positive for anti-clockwise *Green line: averaged over 50 measurements (540 fm/c) K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

62 Remaining tasks p To determine the force per unit length when the vortex line bends dl r f The total force may take a form: p To examine density dependence of the interaction K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

63 Summary and Conclusion Our simulation will provide significant impact on glitch studies! Summary ü The vortex-nucleus interaction is the essential quantity to understand the glitches. ü We are conducting microscopic, dynamical simulations with TDSLDA. ü Our simulation is providing qualitatively new things: Ø The first, three-dimensional, microscopic, dynamical simulation for the vortex-nucleus interaction with a new force extraction technique Ø The bending mode of the vortex line Ø The repulsive nature of the interaction (at least for ρ~0.1ρ 0 ) K. Sekizawa TDSLDA calculations for vortex-nucleus interaction Fri., Jan. 8, /22

66 Initial state generation: Impurity at the center Summary Cooling w/ tube & Coulomb, w/o HO Real-time evolution w/ tube & Coulomb, w/o HO turning on w/ Coulomb turning on HO turning off Cooling K. Sekizawa Product run on HA-PACS - Initial states Fri., Nov. 20, 2015

67 LEFT: PRC84(2011) RIGHT: arxiv: [astro-ph]

THE NEUTRON STAR CRUST AND SURFACE WORKSHOP. Quantum calculation of nucleus-vortex interaction in the inner crust of neutron stars

THE NEUTRON STAR CRUST AND SURFACE WORKSHOP Seattle 25-29 June 2007 Quantum calculation of nucleus-vortex interaction in the inner crust of neutron stars P. Avogadro, F.Barranco, R.A.Broglia, E.Vigezzi