Supernovae

GENERAL RELATIVISTIC COLLAPSE OF ROTATING STELLAR CORES

Author: Cerdá Durán Pablo.
Year: 2005.
University: VALENCIA.
Place of defense: Dpto. Astronomía y Astrofísica. Facultad de física.
Place of preparation: Facultad de Física.

Summary: *** *** * Introduction The gravitational wave astronomy In the early twentieth century, Einstein's theory of general relativity revolutionized the way we understand the physical world with a new paradigm that not only described gravitation but spacetime itself. Now this theory is deeply rooted, and is the basis of the models more realistic in cosmology and astrophysics. However, all of their predictions have not been able yet to be confirmed by the observations. One of these predictions is the existence of gravity waves. At the dawn of a new century is emerging a new branch of astronomy, astronomy of gravitational waves, dedicated to the study of astrophysical and cosmological objects by detecting gravitational waves emitted by them. For an astrophysical object emits gravitational waves observable from Earth, it must be a compact object with strong gravity fields also have temporal variations. The study of gravity waves emitted is an excellent tool for observing the most remote parts of these astrophysical objects. For example, you can see the collapse of stellar nucleus in the formation of supernovae or neighborhood surrounded by black hole accretion disks. These regions are invisible to any other observation of the electromagnetic spectrum. It also can detect the perturbations of space-time caused by the collision of two black holes, which would otherwise remain invisible. In addition it will be possible to make further observations of known sources of electromagnetic radiation, as scenarios involving neutron stars or white dwarfs. These observations will help us to better constrain the parameters of these systems (mass, angular momentum, size, the equation of state of nuclear, etc.). To boost growth of this new branch of astronomy is a vital development in parallel detectors and modeling sources. Over the last two decades have been designed a large number of gravitational wave detectors. We have built huge facilities with laser interferometric detectors based in Europe (VIRGO, EGO), USA (LIGO) and Japan (TAMA), to detect gravitational waves in the kHz range, and extensions of these interferometers are already planned (Advanced LIGO in the United States, LCGT in Japan and in Europe EURO). Also in space interferometers (collaboration ESA / NASA called LISA) to observe sources emitting in the range of mHz. Moreover, the source modeling is needed to establish which objects astrophysical and cosmological be detectable in terms of signal amplitude and frequency range, and reperrcute in the design of current and future detectors. But the theoretical models are not only useful for the design of the detector, but are also an essential part of the discovery process. The low signal / noise detectors detection becomes a challenge, which can only be overcome if we use specific techniques such as filtering by pattern recognition (matched filtering). In these techniques, templates for gravity waves provided by the modeling sources are crucial to assist in data analysis. Furthermore, theoretical models are needed to interpret these waves and extract its contents physical, which is in the end the ultimate goal of the gravitational wave astronomy. One of the most interesting scenarios astrophysicists look where gravity waves is the gravitational collapse of the cores of massive stars in iron (M> 8 M_sol). The resulting object, a proto-estrella neutron (PNS) or a black hole surrounded po 8 r a dis 1ff8 co-accretion, is the basis of the models of some of the most energetic phenomena observable universe: type Ib supernova / Ic / II eruptions gamma (GRBs) and training jets. These are promising sources of gravitational waves, and its theoretical research is of great interest to understand the implications of his remarks. The main objective of this thesis is the study of gravitational radiation produced in a scenario in particular, the gravitational collapse of stellar rotating nuclei and the subsequent evolution of the PNS that form. * Waves of gravitational collapse of stellar cores Electromagnetic radiation and neutrinos are not the only emissions from a supernova explosion. The global movement of the collapsing star, bouncing around densities to those of the nuclear, and asymmetries in the nucleus, producing a flash (burst) for gravity waves. According to the star turn as a parent and as appropriate the collapse, the gravity waves are emitted from a different type [Zwerger 1997]. Although amplitudes realistic estimates for parents outside our galaxy are small to be detected with current detectors of gravitational waves [Mueller 2004], other processes can produce gravity waves more intense after the collapse. In particular, the convective movements after the shock wave produced by the deposition of the energy of neutrinos emitted in the PNS, may lead to even higher amplitudes for slowly rotating nuclei [Mueller 2004]. In addition, the proto-estrella neutron is in itself a promising source of gravitational waves detectable. For rhythms of degrees of rotation and differential rotation sufficiently high instabilities develop not axisimétricas on time scales dynamic (These figures, however, may not be realistic, since it was not known evolutionary path leading to the creation of the PNS rhythms of rotation required.) as the call rate volatility bar [Tohline 1985, Shibata 2002], which produces strong signals of gravity waves. When the neutron star has cooled to around 10E10 K may be subject to the so-called instability of Chandrasekhar-Friedman-Schutz [Chandrasekhar 1970; Friedman & Schutz 1978] and becomes an important source of gravitational waves [see Stergioulas 2003 for more information]. As a result, a modeling in detail the transformation of the PNS hot to cold NS is essential to be able to make predictions in the emission of gravitational waves of neutron stars. Special attention should be devoted to the rhythms of rotation, the distribution of angular momentum and the structure and intensity of the magnetic field. * Physical involved in the collapse order to properly study the gravitational collapse of iron nuclei and the gravity waves emitted by it, you should include a certain amount of physical ingredients. Here we summarize the most important to consider:-General Relativity: The mass involved in the collapse is of the order of 1 M_sol. In the final stage of collapse, this mass is locked in the PNS, with a radius of a few tens of kilometers. For these settings so compact, the effects of general relativity are beginning to appear, and the severity Newtoniana is not sufficient to describe the balance and dynamics of the system [see for example Chapter. ~ 29 of Misner, Thorne & Wheeler, 1973] . Equation of state-of the nuclear field: It takes a description of the thermodynamics nuclear power to properly estimate the dynamics of the entire process, how it is produced rebound and the final configuration of the PNS [see Glendenning 1997, Prakash 2001 for more information ]. - Transport of neutrinos: it is a crucial aspect in modeling to be able to describe the mechanism of the delayed explosion, as well as cooling of the newly formed PNS leading to the final NS [see Janka 2005y references cited therein]. - Magnetic fields: Some observations suggest the presence of magnetic fields on the stage of collapse and the resulting objects. The discovery of anomalous X-ray pulsars and Soft Gamma-Ray Repeaters, interpreted as neutron stars heavily magnetizadas (magnetares) [Duncan 1992, Thompson 1996, Kou 1999], makes the study of the collapse magnetized be of great interest. - Other energy transport mechanisms: Probably there are other mechanisms of energy transport within the nucleus that play an important role in the dynamics of collapse, and should not be despised. Some of these are convection, turbulence, transport and diffusion by radiative viscosity. It should be emphasized that the inclusion of all of these effects in a numeric code could not be undertaken today, mainly because the computational cost prohibitive both in memory and in time of calculation. Therefore must be some simplifications in the simulations required to describe the highly non-linear dynamics involving the collapse of stellar cores. Theoretical Framework *** *** The overall framework used in this thesis is that of general relativity in the formalism 3 +1 [Lichnerowicz 1944, Foures 1952]. This formalism, as described in Chapter 2, allows us to leaf spacetime in a series of hipersuperficies space without intersection, parameterized by the same time. Thus, each containing hypersurface dimensional space full for a certain value of time itself. This type of foliation of space allows us to treat the problem of changing the equations of Einstein as a problem of initial conditions, which from the content of energy and matter hypersurface in a given system can evolve over time . This decomposition still leaves some parameters set free. We will specify how the coordinates describing hipersuperficies space, and the particular way in which folia spacetime (slicing). To do so we must impose four conditions gauge. The choice of these is crucial to the proper resolution of the problem, especially if it involves the resolution numerical equations of Einstein. Moreover, the resolution of the complete system of equations of Einstein is generally a problem of great difficulty. Therefore it may be desirable, at least in some scenarios, perform some approximation to facilitate the resolution of equations without eliminating any element essential. In Chapter 3 describes the equations that govern fluid dynamics and magnetic fields in the formalism 3 +1 of general relativity. These equations are expressed adequately for their numerical resolution. We assume that the fluid modelamos is both a perfect fluid (without viscosity) as a perfect conductor (status of magnetohidrodinámica ideal). Under these conditions, the equations are simplified considerably. In Chapter 5 we present a new approach to the equations of Einstein's gravitational field, which we call CFCs +. This approach is based on a second-order correction in the development post-Newtoniano of metrics in line with flat, ie CFCs + represents an extension of the approximation CFCs (or Isenberg -- Wilson -- Mathews), as described in chapter 4. The derivation of the extended system of equations is done in great detail, as well as boundary conditions it is necessary to apply the system to solve numerically. All equations CFC + are elliptical, as a second order post-Newtoniano the hyperbolic nature of the equations of Einstein disappears. Also note that the failure to solve equations elliptical ensures the stability of the numerical solution and avoids some numerical problems that can appear in evol 8 uciones 1ff8 long-term systems with intense gravity (black holes) when using the formulation 3 +1 of the general relativity. On the other hand, the price to be paid for using the approximation CFCs + is the lack of reaction of the gravitational radiation in the dynamic, responsible for the extraction of energy and angular momentum of the system carried by the gravity waves. But in the scenarios we use this approach, this effect can be considered negligible since the energy losses are negligible in time scales dynamic. Removal of gravity waves is described in Chapter 6, and is performed by the formula cuadrupolar of Einstein-Landau-Lifshitz. This formula incorporates the key word in the approximation of slow speed, and there is conducting a multi-polar development of the metric in the future infinite void, as well as a development post-Newtoniano of sources to first order (Newtonian). It also gives a relationship between the gravitational wave given by the formula cuadrupolar and the asymptotic behavior of the metric in the approximation CFCs +. Numerical methods *** *** Chapter 7 is devoted to the description of the numerical methods employed in solving the equations of hydrodynamics (magneto-) in general relativity. Solving these equations must be conducted in a manner that respects the laws of conservation representing (energy, time and number of baryons). To use this method of high resolution capture shocks (HRSC its acronym in English) [see for example Leveque 1990, Toro 1999, Marti 2002, Font 2003], which allow solving systems of Hyperbolic conservation laws, using a method that correctly described the formation and propagation of shock waves. The case of the equations of magneto-hidrodinámica ideal is separate and additional to the equation is introduced (induction equation) also needs special treatment. For the divergence of the magnetic field is maintained zero during evolution, namely retaining the magnetic flux, we use the method flux-CT [Evans 1988]. In particular, we use the scheme [Anton 2006], which makes use of a linear reconstruction of the primitive variables and patterns focusing for calculating the numerical flow [Kurganov et al. 2000]. Chapter 8 is devoted to the numerical methods used to solve the equations of the metric, either approximate or CFCs in its extension CFCs +. All equations with which we are kind of elliptical, and can be expressed as pseudo-ecuaciones Poisson. The different methods used depend on the different stages of calculating the metric CFCs +. It first calculates the Newtonian potential through an expansion of the angular part of the equation in axial symmetry in polinómios Legendre [Mueller et al. 1995, Zwerger et al. 1995]. The second step is to calculate the cross without trace and the 3-métrica. This calculation is reduced to solving linear systems of equations Poisson, which is done through direct investment system discretizado expressed in matrix form. The investment system is done through the LU decomposition, which increases the efficiency of the numerical scheme used in these equations. Finally resolves system CFCs amended by the corrections 2PN CFC +, which consists of five elliptical nonlinear coupled equations. For each equation we use the same resolvedor Poisson in the case of Newtonian potential, doing a fixed-point iteration to obtain convergence. *** *** * Conclusions CFCs +: dynamics of radiation and gravitational collapse improved. In chapter 9 of this theory are conducted tests and simulations of the collapse of rotating stellar cores using the new approach CFCs +, presented in chapter 5. Tests were conducted to check its applicability to the simulation of space for rotating neutron stars, either in balance or configurations resulting from the gravitational collapse of stellar cores. We also compare the new approach CFCs + with the approximation used by CFCs [Dimmelmeier et al. 2002 a, b] in two different scenarios, oscillations of neutron stars and stellar cores collapse to NS. In the case of pulsed NS, we have not found any difference in the calculation of the frequencies of the modes cuasi-normales of those objects, even in the most extreme situations (ie with rotation Kepleriana, near the limit of mass loss by rotation ). We have also been able to compare our results directly with simulations in general relativity without approximations, getting back excellent agreement. Our simulations of the collapse of rotating nuclei cover the various types of collapse studied by [Dimmelmeier et al.2002b], including also an extreme case of a core with high turnover differential and an almost toroidal structure. Again, there has been no significant differences between the two approaches used. Therefore, we can conclude that the corrections to second order post-Newtoniano of CFCs metrics do not improve significantly the results of the dynamics of the collapse of a stellar cores of neutron stars, or the dynamics of the neutron star itself. As for the extraction of gravitational radiation have not seen substantial differences between CFCs and CFC +. The comparison has been made using the formula cuadrupolar of Einstein-Landau-Lifshitz, commonly used in the literature to draw waveforms. We have also calculated the gravity waves directly from the components of the metric CFCs +. While calculating waveforms latter mode can not be considered an independent method for calculating the airwaves, provides a test of consistency of approach CFCs + used to validate the numerical scheme used in calculating the metric. The main conclusion of Chapter 9 is to confirm the approximate CFCs as a useful alternative to the equations of Einstein complete scenarios axisimétricos involving neutron stars rotating in balance and final state of collapse. These findings are based on two facts: First, we have demonstrated that the correction second order post-Newtoniano do not play an important role either in the dynamics either in the form of gravity waves emitted in the collapse. This suggests that higher-order corrections are completely negligible, at least in time scales dynamic. Secondly, the direct comparison of approximate CFC simulations in general relativity has recently been done by [Shibata et al. 2004] in the context of simulations of stellar collapse of nuclei in axial symmetry. Again, the differences found in the dynamics and in the form of waves are not significant, which highlights the applicability of CFCs (and CFC +) to perform accurate simulation of these scenarios without the need to solve the complete system of equations Einstein. * Collapse magnetized in Chapter 10 presents simulations of the collapse of stellar magnetizados rotating nuclei, as well as tests that validate the numerical approximation used to solve the equations of magneto-hidrodiámica ideal in general relativity. It has designed a method to calculate configurations stationary stars weakly magnetizadas in general relativity, either with toroidal component or poloidal (or both) of the magnetic field. Used approximate field passive (or field test) for the initial models, in which the magnetic pressure is several orders of magnitude lower than the pressure of the fluid (thermal). Tests have also been conducted to verify the pr 8 ecisión 13e2 and convergence properties of the extension `` magnetizada "our numerical code. The result is an order of a greater convergence in the magnetic field in all tests. When stationary order of convergence is obtained is more than two. These results are consistent with the second order, spatial and temporal pattern of numerical used only reduced to first order in the clashes. It provides the necessary resolution to the magnetic field evolution properly in a simulation of the collapse of stellar cores. errors in all cases in which the theoretical solution is known are below 0.1%, except in the clashes, which are correctly captured in a couple of numerical cells using HRSC schemes. Regarding simulations of the collapse of nuclei magnetizados on aligning CFCs, have been seen cases with magnetic field purely poloidal at baseline (range D3M0) and purely toroidal (series T3M0), in the approximate area passive. models D3M0 are an extension to general relativity some of the models considered by [Obergaulinger et al. 2005] gravity Newtoniana and magneto-hidrodinámica ideal. Our intention is to compare the dynamics and gravitational waves with these previous results. No. they are qualitative differences in the models studied, although the magnitude of the magnetic field in the rebound and thereafter is if CFCs consistently lower (50-80%) than in the Newtonian case. each set of models, the gain the magnetic field comes from a different way. Whereas in the models D3M0 the winding lines of the field poloidales in toroidal lines due to the differential rotation (dínamo-Omega), is the main mechanism of amplification in the collapse, in models T3M0 the magnetic field is amplified only because of the radial compression, since the component poloidal field is absent in evolution. found that because the models studied, dínamo-Omega is much more efficient amplifying the magnetic field compression radio . Therefore, the toroidal component of the magnetic field at the end of the trend is weaker in models T3M0 that models D3M0, where there was no such component initially. At the end of our simulations of fluid variables reach a state of cuasi-equilibrio. order models D3M0, proto-estrella neutron formed has a core structure / wrapper.'s core, where the nuclear density has been achieved, the dominant component of the magnetic field is the poloidal, and the rotation profiles are virtually flat, ie the core of the PNS tour rigidly. Moreover, the sheath that surrounds it turns differentially, and therefore the toroidal magnetic field component dominates in this region due to the mechanism of dínamo- Omega. This effect produces a linear growth sustained component of the toroidal after the rebound. Without other processes, the magnetic field is saturaria in ~ 1 s in values B_phi ~ 10E15 G. In models T3M0 the dínamo-Omega is not since there is no active component poloidal magnetic field. Therefore, reaching a PNS state cuasi-equilibrio, the magnetic field remains stationary. mechanisms Other amplification of the field can act if it is not considered approximate field passive or removes the condition axisimetría. It has been estimated the effect of amplification mechanism probably dominant, ie instability magneto-rotacional (MRI). found that during the collapse, the time scale typical of the way that grows faster in the MRI is approximately 1 s, and therefore not affect the stage of collapse. however, after the rebound, there are two regions that could develop MRI: the region after the shock and the region surrounding the convecting PNS . In both regions the estimated time scale of the MRI, ~ 1 ms, is the order of the time scale dynamics. simulations without approximate field liabilities and resolutely big enough, it is expected that the MRI is developed in these its dynamic regions and fluent in a few milliseconds.

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