LEE- Fizik Mühendisliği Lisansüstü Programı

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http://hdl.handle.net/11527/19275

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Yazar "Bakır, İrem" ile LEE- Fizik Mühendisliği Lisansüstü Programı'a göz atma
  • Öge
    Dynamo generation of neutron star magnetic fields
    (ITU Graduate School, 2025-06-25) Bakır, İrem ; Ekşi, Kazım Yavuz ; 509221114 ; Physics Engineering
    Neutron stars are very dense objects with a radius of 10-12 km, and a mass of a few solar masses. Like most of the celestial bodies, they are magnetized with dipole (poloidal) field strength of $B_{\rm p} \sim 10^{12}$ G, and toroidal field strength of $B_\phi \sim 10^{14}$~G. Magnetars, on the other hand, are known as the most magnetized objects in the Universe with field strengths of $B_{\rm p} \sim 10^{14}$ G and $B_\phi \gtrsim 10^{15}$ G. Thus, the origin of neutron stars' magnetic fields became a discussion with the identification of magnetars. Two ideas are considered as the possible origin of the magnetic fields of neutron stars. One of them is the fossil-field hypothesis, which states that neutron stars inherit their magnetic fields from their progenitors, since the magnetic flux is conserved during the core collapse. In this scenario, there is no new field generation; the seed field grows as the radius shrinks, with $B \propto R^{-2}$. The other idea that is considered as the source of the magnetic fields of neutron stars is a dynamo process, which states that the magnetic fields of neutron stars are generated inside the proto-neutron star by the fluid motions. However, studies show that the number of progenitors with strong magnetic fields is much lower than the number of known magnetars (30). Let us consider a collapsing core with a radius of 3000 km where the magnetic field strength is approximately $5\times10^5$ G in the surrounding medium. After the collapse, only a magnetic field of $3\times 10^9$ G will be inherited by a proto-neutron star with a radius of 40 km, by only the magnetic flux conservation. When this proto-neutron star shrinks to a neutron star with a radius of 12 km, the neutron star will inherit a magnetic field of $\sim10^{10}$~G by flux conservation. This field strength is approximately 2 orders of magnitude smaller than the magnetic fields of standard neutron stars. However, this field strength is of the order of the dipole magnetic fields of central compact objects. Therefore, although the flux conservation is widely accepted as the source of the magnetic fields in some populations, it is not enough to explain the magnetic fields of neutron stars, especially the field strengths at magnetar levels. Thus, it became clear that there must be another mechanism that generates magnetic fields at those levels. A dynamo process operating inside the proto-neutron star is now the most promising scenario for the generation of neutron star magnetic fields. Two main types of dynamo mechanisms are the $\alpha^2$ and $\alpha-\Omega$ dynamos. Just after the core collapse, hydrodynamic instabilities operate inside the star, and these instabilities create convective motions. In an $\alpha^2$ dynamo, toroidal and poloidal fields generate each other by only convective motions, which is called the $\alpha$-effect. On the other hand, different parts inside the star rotate with different angular velocities, which is the well-known differential rotation. This differential rotation plays a key role in generating strong magnetic fields in an $\alpha-\Omega$ dynamo. In this type of dynamo, when convective motions generate poloidal field by lifting and twisting the toroidal field lines (the $\alpha$-effect), differential rotation generates toroidal field shearing the poloidal field lines, which is known as the $\Omega$-effect. Due to the absence of strong effect of the differential rotation, $\alpha^2$ dynamos generate relatively weak fields compared to $\alpha-\Omega$ dynamos. Thus, an $\alpha-\Omega$ dynamo is the most accepted mechanism for the generation of magnetar fields. Studies demonstrate that magnetic field strengths of even $\gtrsim 10^{15}$ G can be achieved by an $\alpha-\Omega$ dynamo. Therefore, in this study, the field generation at neutron star levels is investigated by an $\alpha-\Omega$ dynamo. In this study, a 1-dimensional $\alpha-\Omega$ dynamo model, which is first proposed for white dwarf fields is adopted to proto-neutron stars, adding the shrinkage of the radius, accordingly, loss of mass, and the flux conservation. Moreover, two viscous processes are involved in the model. One of them is the viscosity due to magneto-rotational instability. Magneto-rotational instability is a dynamical instability that arises from the electrically conducting and differentially rotating fluids in the presence of a weak magnetic field. This instability generates turbulence, which creates this type of viscosity. The other viscous process is the convective viscosity, which is created by convective motions. Dynamo processes are studied with several 2 and 3-dimensional models. However, these models can not be studied with realistic parameters. With this 1-dimensional model, a dynamo process is examined with realistic parameters. In the study, the model equations are solved with Runge-Kutta method, and it is seen that the field components grow in time and get saturated at the end of the dynamo process (approximately 50 s), as expected. Both of the saturation values of the fields are at the magnetar levels. Thus, this study demonstrates that the magnetar fields can be generated by an $\alpha-\Omega$ dynamo which operates inside a proto-neutron star. On the other hand, examinations for proto-neutron stars with relatively long rotational periods are conducted, and results demonstrate that magnetic fields at levels of standard pulsars, high-field pulsars and low-field magnetars can be achieved for slow rotations. With this result, it is evident that the fast rotation of the proto-neutron star plays a key role in the generation of magnetic fields of magnetars in dynamo processes. This is consistent with the studies which indicate that relatively slower rotations generate weaker fields. Moreover, results show that as the poloidal fields of central compact objects ($B_{\rm p}\sim 10^{10}$~G) are inherited from the progenitor star by flux conservation, their toroidal fields are amplified by the $\Omega$-effect. This is an interesting result which indicates that central compact objects can experience a dynamo process in which the $\alpha$-effect is ineffective. Additionally, with this 1-dimensional model, the impacts of the parameters on the results are also investigated, which is not possible with 2 or 3-dimensional models.