Neutron Stars (NSs) are the compact remnants left behind the evolutionary history of massive stars. Characterized by strong-gravity, supranuclear densities, fast rotation and super strong magnetic fields, NSs are among the most exotic and fascinating objects in the Universe. They represent a unique environment where our knowledge of nature and its fundamental laws can be tested under extreme conditions not achievable on Earth. Nevertheless, their astronomical manifestation is extremely diverse and still today it is difficult to draw a unifying picture of NSs phenomenology, necessary to properly investigate their physical properties. It is however largely believed that the magnetic field dramatically affects the way a NS manifests. This holds particularly true for magnetars, a particular class of NSs characterized by magnetic fields as strong as ∼ 10^15−16 G. Their extraordinary emission properties are usually explained in terms of the rearrangement and the dissipation of the magnetic field hidden in the interior. Unfortunately, astronomical observations provide us only direct indications about the exterior magnetic field, or at most, about the field residing in the crust. The study and the modelization of the morphology of the internal magnetic field is thus of primary interest in order to gain new insights in the physics and phenomenology of magnetars or NSs in general. Previous studies of magnetized equilibrium models have mainly focused on understanding the effects of the magnetic field on the structure of the star. Strong magnetic fields are indeed able to induce high quadrupolar deformations that, in conjunction with rapid rotation, can lead to the emission of Gravitational Waves (GWs). Other works, instead, analyzed the evolutionary and stability properties of different magnetic field geometries in order to assess the possible structure of the field in the interior of the star. In general, due to the complexity of the problem, models have been obtained or in the Newtonian regime or in General Relativity (GR), adopting a perturbative regime or considering a restricted set of equilibria or magnetic field morphologies. Moreover, a detailed modelization of the interior field and the magnetosphere of NSs, have been always obtained separately without considering the relations between the two. Only very recent works have attempted to obtain global models able to unveil possible relations between the exterior and the interior magnetic field. This thesis focuses on the development of a comprehensive numerical study of magnetized configurations, derived in the full GR regime, taking into account different magnetic field geometries as well as the effects of rapid rotation. Numerical solutions have been obtained through the XNS code, which has been updated and improved during this Ph.D. project. The main difficulties and limitations in solving for equilibrium models in GR are due to the complexity of Einstein’s equation. While in some specific cases it is possible to simplify the metric of the spacetime, exploiting its symmetry properties, this is not possible for general configurations of the magnetic field. Here, instead of solving the exact equations, we approximate the spacetime metric to be conformally flat. This allows us to substantially simplify the equations involved and recast them in a numerically stable form without spoiling the accuracy of the obtained solutions. Indeed, we have verified that the conformal flatness approximation provides results that are indistinguishable, within the typical accuracy of numerical solutions, from those obtained under the exact formulations. Our approach has allowed us to sample a wide and general class of current distributions performing a vast parameter study of magnetized equilibrium configurations (up to the fully non-linear regime), necessary to establish general trends and expectations regarding how different current distributions affects the structure of the star and the morphology of the associated magnetic field, considering also the coupling with centrifugal and compactness effects. The analysis of this large parameter space has provided us the opportunity to extend previous result present in literature (assessing their robustness and generality) but also to derive new quantitative and qualitative relations between different stellar quantities such as the induced deformations, the gravitational mass, the stellar radius, the energy content of the system, together with the multipolar structure of the magnetic field. In particular, in this work we have analyzed purely toroidal, purely poloidal and mixed magnetic field configurations. In general we have verified that the effects of the magnetic field are more pronounced in less compact stars and that, at fixed gravitational mass, changes in the internal structure of the NS are able to limit the strength of the magnetic field contained inside the star. We have provided a general parametrization of the induced deformation in terms of magnetic field strength or in terms of the associated energetics. We find that, in general, the deformation of the star is mainly explainable in terms of the energy redistribution between the magnetic energy, the rotational energy and the gravitational binding energy. This nice behaviour, however, fails in presence of highly non-linear currents that, depending on their location, are able to accentuate or reduce the effects of the associated magnetic field. This may suggest that in order to establish if newly born rapidly rotating magnetars are able to trigger observable GW emission, one needs to know the current distribution arising from the amplification of the magnetic field during core collapse. The magnetic field left behind the formation of the NS is expected to be energetically dominated by its toroidal component, due to differential rotation that develops during the infall. This kind of configurations is also favourite in terms of stability criteria. However, our analysis has shown that toroidally dominated configurations can not be easily achieved assuming a barotropic equilibrium unless one considers some very ad hoc prescriptions discussed in literature. Our results are indicative of the fact that the magnetic energy ratio between the toroidal and poloidal components is more related to the non-barotropicity and the stratification of the star rather than the current distribution. Investigating how the system reacts to different current distributions, we have also shown how the structure of the surface magnetic field can significantly differ from a simple dipolar one. This may have important effects on those physical processes that occur near the surface of the star and control the observational properties of the NS. In particular we have modeled NSs endowed with twisted magnetosphere (usually invoked to explain the spectral features of magnetars emission), showing that there is always a maximum twist that can be stored in the magnetosphere before magnetic reconnection phenomena set in. Fast rotating newly born magnetars have been also suggested as possible central engine for GRBs. Hence, as an applications of the results and the numerical tools developed during this Ph.D. research, we have explored the possible implications of quark deconfinement on the phenomenology of long GRBs within the proto-magnetar scenario. Modeling the quasi-stationary spindown evolution of both NSs and Quark Stars (QSs) we have assessed the conditions, in terms of timescales and energetics, for which the transition from a NS to a QS can in principle occurs giving rise to peculiar observable features in the light-curve of GRBs. We also show how our results can be applied to the specific case of the double burst GRB 110709B.

`http://hdl.handle.net/2158/1088219`

Titolo: | Modeling magnetized neutron stars in general relativity |

Autori di Ateneo: | |

Autori: | PILI, ANTONIO GRAZIANO |

Tutor: | Niccolò Bucciantini, Luca Del Zanna |

Nazionalità autore: | ITALIA |

Data di discussione: | 2017 |

Abstract: | Neutron Stars (NSs) are the compact remnants left behind the evolutionary history of massive stars. Characterized by strong-gravity, supranuclear densities, fast rotation and super strong magnetic fields, NSs are among the most exotic and fascinating objects in the Universe. They represent a unique environment where our knowledge of nature and its fundamental laws can be tested under extreme conditions not achievable on Earth. Nevertheless, their astronomical manifestation is extremely diverse and still today it is difficult to draw a unifying picture of NSs phenomenology, necessary to properly investigate their physical properties. It is however largely believed that the magnetic field dramatically affects the way a NS manifests. This holds particularly true for magnetars, a particular class of NSs characterized by magnetic fields as strong as ∼ 10^15−16 G. Their extraordinary emission properties are usually explained in terms of the rearrangement and the dissipation of the magnetic field hidden in the interior. Unfortunately, astronomical observations provide us only direct indications about the exterior magnetic field, or at most, about the field residing in the crust. The study and the modelization of the morphology of the internal magnetic field is thus of primary interest in order to gain new insights in the physics and phenomenology of magnetars or NSs in general. Previous studies of magnetized equilibrium models have mainly focused on understanding the effects of the magnetic field on the structure of the star. Strong magnetic fields are indeed able to induce high quadrupolar deformations that, in conjunction with rapid rotation, can lead to the emission of Gravitational Waves (GWs). Other works, instead, analyzed the evolutionary and stability properties of different magnetic field geometries in order to assess the possible structure of the field in the interior of the star. In general, due to the complexity of the problem, models have been obtained or in the Newtonian regime or in General Relativity (GR), adopting a perturbative regime or considering a restricted set of equilibria or magnetic field morphologies. Moreover, a detailed modelization of the interior field and the magnetosphere of NSs, have been always obtained separately without considering the relations between the two. Only very recent works have attempted to obtain global models able to unveil possible relations between the exterior and the interior magnetic field. This thesis focuses on the development of a comprehensive numerical study of magnetized configurations, derived in the full GR regime, taking into account different magnetic field geometries as well as the effects of rapid rotation. Numerical solutions have been obtained through the XNS code, which has been updated and improved during this Ph.D. project. The main difficulties and limitations in solving for equilibrium models in GR are due to the complexity of Einstein’s equation. While in some specific cases it is possible to simplify the metric of the spacetime, exploiting its symmetry properties, this is not possible for general configurations of the magnetic field. Here, instead of solving the exact equations, we approximate the spacetime metric to be conformally flat. This allows us to substantially simplify the equations involved and recast them in a numerically stable form without spoiling the accuracy of the obtained solutions. Indeed, we have verified that the conformal flatness approximation provides results that are indistinguishable, within the typical accuracy of numerical solutions, from those obtained under the exact formulations. Our approach has allowed us to sample a wide and general class of current distributions performing a vast parameter study of magnetized equilibrium configurations (up to the fully non-linear regime), necessary to establish general trends and expectations regarding how different current distributions affects the structure of the star and the morphology of the associated magnetic field, considering also the coupling with centrifugal and compactness effects. The analysis of this large parameter space has provided us the opportunity to extend previous result present in literature (assessing their robustness and generality) but also to derive new quantitative and qualitative relations between different stellar quantities such as the induced deformations, the gravitational mass, the stellar radius, the energy content of the system, together with the multipolar structure of the magnetic field. In particular, in this work we have analyzed purely toroidal, purely poloidal and mixed magnetic field configurations. In general we have verified that the effects of the magnetic field are more pronounced in less compact stars and that, at fixed gravitational mass, changes in the internal structure of the NS are able to limit the strength of the magnetic field contained inside the star. We have provided a general parametrization of the induced deformation in terms of magnetic field strength or in terms of the associated energetics. We find that, in general, the deformation of the star is mainly explainable in terms of the energy redistribution between the magnetic energy, the rotational energy and the gravitational binding energy. This nice behaviour, however, fails in presence of highly non-linear currents that, depending on their location, are able to accentuate or reduce the effects of the associated magnetic field. This may suggest that in order to establish if newly born rapidly rotating magnetars are able to trigger observable GW emission, one needs to know the current distribution arising from the amplification of the magnetic field during core collapse. The magnetic field left behind the formation of the NS is expected to be energetically dominated by its toroidal component, due to differential rotation that develops during the infall. This kind of configurations is also favourite in terms of stability criteria. However, our analysis has shown that toroidally dominated configurations can not be easily achieved assuming a barotropic equilibrium unless one considers some very ad hoc prescriptions discussed in literature. Our results are indicative of the fact that the magnetic energy ratio between the toroidal and poloidal components is more related to the non-barotropicity and the stratification of the star rather than the current distribution. Investigating how the system reacts to different current distributions, we have also shown how the structure of the surface magnetic field can significantly differ from a simple dipolar one. This may have important effects on those physical processes that occur near the surface of the star and control the observational properties of the NS. In particular we have modeled NSs endowed with twisted magnetosphere (usually invoked to explain the spectral features of magnetars emission), showing that there is always a maximum twist that can be stored in the magnetosphere before magnetic reconnection phenomena set in. Fast rotating newly born magnetars have been also suggested as possible central engine for GRBs. Hence, as an applications of the results and the numerical tools developed during this Ph.D. research, we have explored the possible implications of quark deconfinement on the phenomenology of long GRBs within the proto-magnetar scenario. Modeling the quasi-stationary spindown evolution of both NSs and Quark Stars (QSs) we have assessed the conditions, in terms of timescales and energetics, for which the transition from a NS to a QS can in principle occurs giving rise to peculiar observable features in the light-curve of GRBs. We also show how our results can be applied to the specific case of the double burst GRB 110709B. |

Appare nelle tipologie: | 8a - Tesi di dottorato |

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