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ÖgeInteraction between magnetized stars and disks(Lisansüstü Eğitim Enstitüsü, 2021)Xray binary systems consist of a compact object, such as a neutron star, white dwarf or black hole, and a normal star that transfers mass to this compact object. Xray binary systems are split into two groups depending on the mass of the donor star. If the mass of the donor star is Md ≤ 1M⊙, these kinds of systems are called LMXB and if the donor star mass is Md > 10M⊙, these systems are known as HMXB. The other component of the Xray binary systems are compact stars: white dwarfs, neutron stars or black holes. The observed Xray power of these systems originate from the gravitational potential energy released by the accretion of matter onto the compact star and depends on the compactness, M∗/R. In LMXB, matter from the outer envelope of the donor star may may be transferred to the compact star by Roche lobe overflow. In HMXB, matter from the outer envelope of the donor star may be transferred to compact star by stellar wind. In both cases because the matter transferred from the donor star has angular momentum, the matter can not accrete on to the compact object directly; instead an accretion disk forms. The physical parameters that define the interaction between a neutron star and a surrounding disk are the magnetic field and angular velocity of the of the compact star, and the mass flow rate in the disk. The interactions occur in three different stages: i) Mass accretion stage: If the inner radius of the disk, Rm, is smaller than the corotation radius, Rco, the matter follows the magnetic field lines and flow to the polar caps of the neutron stars. ii) Propeller stage: In this stage, Rm > Rco, the matter at the inner region of the disk meets with more rapidly rotating field lines attached to the star. A decline may occur in the observed Xray flux because the mass accretion is centrifugally inhibited. iii) Radio pulsar stage: If the inner radius of the disk is larger than the light cylinder radius, RL, an interaction can not occur between the neutron star and the disk. In this stage, the cause of the observed Xray flux is the slowing down of the rotation of the neutron star. The QPO are thought to be generated in regions close to the neutron star and the inner part of the disk. Therefore, special types of QPOs provide direct evidence for diskmagnetosphere interaction. In this study, models were created by using both observational physical parameters (period, period derivative, luminosity, etc) and QPOs. The observation that the Xray luminosity does not change significantly during transitions to the spindown stage led to MTD of Ghosh & Lamb in 1979. In this model, magnetic field can thread the disk by instabilities between disk and magnetosphere and the presence of turbulence in the disk. The magnetic field lines slip around the disk due to the differential rotation between disk and the neutron star. According to the Ghosh & Lamb model, there is a stable region in which the twisted magnetic field balances the spread magnetic field around the disk. In this way a toroidal magnetic field is generated. However, as long as the magnetic field gets twisted around the disk, arbitrarily strong toroidal magnetic field is generated and such strong magnetic fields can destroy the disk. Because of the problems mentioned above, Ghosh & Lamb model have important inadequacies. The magnetic field lines that penetrate the disk beyond the corotation radius slow down the neutron star. The net torque acting on the neutron star is the sum of the material torque which spins up the star and the magnetic torque which slows down the star. Toroidal magnetic field is an important factor that determines the net torque. In order to understand the longterm evolution of the neutron star, it is important to specify how the torque depends on the fastness parameter, ω∗. As LMXB have weak magnetic fields, it is hard to observe the spin change of the system. Also HMXB have stellar winds that affect the torque and observed luminosity, the relation between the fastness and the torque can not be specified, sensitively. For these reasons, we choose 4U–1626 67 which has high magnetic field and accretes from a low mass donor star. 4U–1626 67 underwent two torque reversals in June 1990 and February 2008. We used the torque reversal data and explored the coherence between observational data and some torque models in the literature. It is discovered that each nearby galaxy host one or two "ultraluminous Xray sources" (ULXs) whose luminosity exceed the Eddington limit for a solar mass object. It was initially assumed that the ULX host IMBH but later with the discovery of Xray pulsations from some of these objects (e.g M82 X2, ULX NGC 5907, ULX NGC 7793 P13, NGC 300 ULX1, M51 ULX7, NGC 1313 X2 and Swift J0243.6+6124) showed that they at least some of them are neutron stars. Population studies indicate that the accreting neutron stars are common sources in the ULX population. In this thesis, we investigate the surface magnetic field dipole strength, beaming fraction and fastness parameter of the, PULX, taking into account the accretion flow in the supercritical regime, beaming of Xray emission and the reduction of the scattering cross section in the presence of a strong magnetic field. We used three different methods for determining the magnetic fields of the PULX: i) We assume the system to be near torque equilibrium. ii) We rely on the spinup rate and solve the torque equation. iii) We assume the systems to be accreting at the critical rate. This critical rate depends on the electron scattering crosssection determined by the supercritical magnetic fields. The plan of the thesis is as follows: In Chapter 1, the main ideas of the stardisk interactions are given. In Chapter 2, the flux, the period and the period derivative data of 4U1626 67 embracing the torque reversal events in June 1990 and February 2008 are analysed and compared with GhoshLamb model and some other models in the literature. In Chapter 3, the magnetic fields of the pulsating Xray sources are calculated using three different assumptions. Also, as the beaming fraction depends on the inner radius of the disc which in turn depends on the mass accretion rate, we find that the isotropicequivalent luminosity of the source does not depend linearly on the mass accretion rate. In Chapter 4 all of the results are discussed

ÖgeNonrelativistic gravity in threedimensions(Lisansüstü Eğitim Enstitüsü, 2021)In this thesis, we examined the nonrelativistic threedimensional $\mathcal{N}=2$ supergravity theories. These gravity theories are based on a symmetry algebra in which Lie algebra admits nondegenerate, invariant, and symmetric Killing form. We considered a supersymmetric extension of nonrelativistic symmetry algebras from which we constructed ChernSimons actions, and as a result, we have obtained their gauge transformations and field equations, and the matter couplings. In addition, we developed a framework to construct Lie algebra expansion to obtain extended Schrödinger algebra for the first time in the literature, and this result will be used for our future plan for constructing matter multiplets that transform under supersymmetric extended Schrödinger symmetries. The first chapter of the thesis presents a sufficient groundwork for the following sections. Our purpose is to elaborate on NewtonCartan geometry, NewtonCartan gravity, threedimensional Einstein gravity, ChernSimons formalism, and finally basics of spinors in three dimensions. Having collected these tools, we apply the corresponding formalism into threedimensional nonrelativistic symmetries. With the term nonrelativistic symmetry we imply that all the algebras that we will consider next sections are an extension of Galilei algebra, since we designate the symmetry algebras as nonrelativistic. In Ch. 2, we establish the supersymmetric extension of the extended NewtonHooke, Lifshitz and Schrödinger algebras and construct the corresponding ChernSimons supergravity models. The extended NewtonHooke superalgebra admits two distinct nondegenerate invariant bilinear forms that gives rise to two different supergravity models with the same equations of motion. These two models are particularly different in terms of the parity of the bosonic actions. In particular, we showed that there is an exotic nonrelativistic model such that parityeven field equations arise from a parityodd Lagrangian. We then showed that it is possible to improve the extended Bargmann superalgebra with dilatations (without including nonrelativistic special conformal symmetry) which we called the extended Lifshitz superalgebra and also established the ChernSimons extended Lifshitz supergravity action. In the final step, we include the nonrelativistic special conformal symmetry and establish the extended Schrödinger superalgebra and the corresponding ChernSimons extended Schrödinger supergravity action. We consider our result as a first step to construct an offshell formulation for the extended Bargmann supergravity and its matter couplings. In Ch. 3, we present a threedimensional nonrelativistic model of gravity that is invariant under the central extension of the symmetry group that leaves the recently constructed Newtonian gravity action invariant. In particular, we show that the threedimensional model is the contraction of a bimetric model that is the sum of the Einstein gravity in Lorentzian and the Euclidean signatures. Moreover, the model is distinct from the Newtonian gravity both at the level of action and the matter coupling. By choosing fields appropriately, we show that this action can be obtained by a contraction procedure. Our model is of the ChernSimons type, which allowes us to establish the supersymmetric completion by extending the algebra with five supersymmetry generators. The supersymmetric completion of this action provides one of the very few examples of action for nonrelativistic supergravity. In Ch 4, we present a Lie algebra expansion method to generate higherorder threedimensional Schrödinger algebras. Our construction relies on a recent novel threedimensional nonrelativistic conformal Galilei algebra that we used as a core algebra. By employing the Lie algebra expansions, we first recovered the extended Schrödinger algebra and obtained a new higherorder Schrödinger algebra which we refer to as the enhanced Schrödinger algebra. We, next, truncate the nonrelativistic conformal symmetry generators and find a new algebra that goes beyond the threedimensional extended Bargmann algebra. In particular, we show that the symmetry algebra that was proposed as the symmetry algebra of action for Newtonian gravity is not uniquely defined but can be closed with three parameters. We also show that for a particular choice of these parameters the Bargmann algebra becomes a subalgebra of the extended algebra and one can introduce a mass current in a Bargmanninvariant sense to the extended theory.

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