Thesis

Strong magnetic fields and the crust

• Call:

  IDPASC Portugal - PHD Programme 2016

• Academic Year:

  2016 / 2017

• Domain:

  Astrophysics

• Supervisor:

  Constança Providência

• Co-Supervisor:

• Institution:

  Universidade de Coimbra

• Host Institution:

• Abstract:

  Recent investigations show that soft ?-ray repeaters and some anomalous X-ray pulsars are neutron stars with surface magnetic fields larger that 10 14 - 10 15 G, Duncan1992, the so called magnetars. The strongest estimated magnetic field is B = 2 × 10 15 G and was detected in a quite young star, SGR 1806-20. It is unknown the intensity of the field in the magnetar interior, but fields as large as 10 18 G are estimated using the virial theorem. Recently, the time evolution of the magnetic field of isolated X-ray pulsars has been studied by Pons et al. (Pon2013) The authors have shown that a fast decay of the magnetic field could explain the non observation of stars with periods above 12 s. The decay of the magnetic field was obtained including a high electrical resistivity in the inner crust, attributed to the possible existence of an amorphous and heterogeneous layer at the bottom of the inner crust. The lack of isolated X-ray pulsars with a period higher than 12s, could, therefore, be a direct indication of the existence of an amorphous inner crust, possibly in the form of pasta phases. A strong magnetic field can affect neutron stars in two ways: it affects the Equation of State (EoS) due to Landau quantization of the constituent particles (Chakrabarty1997) and it breaks the spherical symmetry of the star (Oertel2014). Observational quantities, such as the maximum mass may, therefore, be affected by strong magnetic fields. We have investigated the effect of the magnetic field on the EOS of stellar matter, namely in the hadron-quark phase transition, Rabhi2009, in warm stellar matter with trapped neutrinos, and in quark matter in the framework of the Nambu-Jona-Lasinio (NJL) and Polyakov NJL models, Menezes2009, Costa2015. Only fields above 10 18 G affect the EoS in a non negligible way. However, non- negligible effects of fields below 10 18 G are expected at low densities, and therefore in the neutron star crust. The effect of a static strong magnetic on the pasta structure within a TF approach was studied in Lima2013, however, no anomalous magnetic moment was included and the lowest field considered was still qutie high, 2 × 10 17 G. Results indicate that if the local magnetic field suffers fluctuations, large stresses will appear in the pasta phase. Recently, we have shown that the effect of strong magnetic fields, of the order of 10 15 ? 10 17 G, on the extension of the crust of magnetized neutron stars is non-negiglible, Fang2016. The dynamical instability region of neutron-proton-electron (npe) matter at subsaturation densities and the mode with the largest growth rate were determined and it was shown that the effect of a strong magnetic field on the instability region originates an increase of the extension of the crust and of the charge content of clusters and that it is very sensitive to the density dependence of the symmetry energy. To confirm these results it is important to calculate the structures of the inner-crust, in particular, the pasta-phases and the associated impurity coefficient. An increase of the inner crust may also have important consequences on the explanation of the pulsar glitch mechanism, Archibald2013. The objective of the present projetct is to study the inner-crust composition of a magne- tized star. The crust is composed by non-uniform matter and a realistic calculation shouldtake this into account. We have performed an exploratory calculation of the pasta phase in the presence of a strong magnetic field, Lima2013, however in this first approach the anoma- lous magnetic moment (AMM) of neutrons and protons was not included and not low enough fields have been considered. The inclusion of AMM, a necessary generalization will be perfor- med. Both a Thomas Fermi approach and a compressible liquid drop model approach will be developed. Other methods, such as the Molecular Dynamics approach may be necessary, Ho- rowitz2004,Sonoda2008. We expect from the compressible liquid drop model qualitative results that will help the calculation of more quantitative results using the other methods. Archibald2013 R. F. Archibald et al, Nature 497, 591 (2013). Costa2015 Pedro Costa, M ?arcio Ferreira, D ?ebora P. Menezes, Jo ?ao Moreira, Constan ?ca Pro- vidˆencia, Phys. Rev. D 92, 036012 (2015) Chakrabarty1997 Somenath Chakrabarty, Debades Bandyopadhyay, Subrata Pal, Phys. Rev. Lett. 78, 2898 (1997). Duncan1992 R. C. Duncan and C. Thompson, Astrophys. J. 392, L9 (1992); C. Thompson and R. C. Duncan, Mon. Not. R. Astron. Soc. 275, 255 (1995). Fang2016 J. Fang, H. Pais, S. S. Avancini and C. Providˆencia, arXiv:1603.05000 [nucl-th]. Horowitz2004 C. J. Horowitz, M. A. P ?erez-Garc ??a, and J. Piekarewicz, Phys. Rev. C 69, 045804(2004) Lima2013 R. C. R. de Lima, S. S. Avancini, and C. Providˆencia, Phys. Rev. C 88, 035804 (2013). Menezes2009 D.P.Menezes, M. Benghi Pinto, S.S. Avancini, A. Perez Martinez, C. Provi- dencia, Phys. Rev. C79, 035807 (2009) Oertel2014 Debarati Chatterjee, Thomas Elghozi, Jerome Novak, Micaela Oertel, MNRAS 447 (2015) 3785, Pons2013 J. A. Pons, D. Vigan`o, N. Rea, Nature Phys. 9, 431 (2013). Rabhi2009 A. Rabhi, C. Providˆencia, J. Da Providˆencia, Phys. Rev. C 79, 015804 (2009). Sonoda2008 Hidetaka Sonoda, Gentaro Watanabe, Katsuhiko Sato, Kenji Yasuoka, and Toshi- kazu Ebisuzaki, Phys. Rev. C 77, 035806 (2008)