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Register a new userModified virial theorem for highly magnetized white dwarfs
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Added by
Banibrata Mukhopadhyay
Publication date
2020
fields
Physics
and research's language is
English
Authors
Banibrata Mukhopadhyay
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Generally the virial theorem provides a relation between various components of energy integrated over a system. This helps us to understand the underlying equilibrium. Based on the virial theorem we can estimate, for example, the maximum allowed magnetic field in a star. Recent studies have proposed the existence of highly magnetized white dwarfs, with masses significantly higher than the Chandrasekhar limit. Surface magnetic fields of such white dwarfs could be more than 10^9 G with the central magnitude several orders higher. These white dwarfs could be significantly smaller in size than their ordinary counterparts (with surface fields restricted to about 10^9 G). In this paper we reformulate the virial theorem for non-rotating, highly magnetized white dwarfs (B-WDs) in which, unlike in previous formulations, the contribution of the magnetic pressure to the magnetohydrostatic balance cannot be neglected. Along with the new equation of magnetohydrostatic equilibrium, we approach the problem by invoking magnetic flux conservation and by varying the internal magnetic field with the matter density as a power law. Either of these choices are supported by previous independent work and neither violates any important physics. They are useful while there is no prior knowledge of field profile within a white dwarf. We then compute the modified gravitational, thermal and magnetic energies and examine how the magnetic pressure influences the properties of such white dwarfs. Based on our results we predict important properties of these B-WDs, which turn out to be independent of our chosen field profiles.
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We explore the luminosity L of magnetized white dwarfs and its effect on the mass-radius relation. We self-consistently obtain the interface between the electron degenerate gas dominated inner core and the outer ideal gas surface layer or envelope by incorporating both the components of gas throughout the model white dwarf. This is obtained by solving the set of magnetostatic equilibrium, photon diffusion and mass conservation equations in the Newtonian framework, for different sets of luminosity and magnetic field. We appropriately use magnetic opacity, instead of Kramers opacity, wherever required. We show that the Chandrasekhar-limit is retained, even at high luminosity upto about 10^{-2} solar luminosity but without magnetic field, if the temperature is set constant inside the interface. However there is an increased mass for large-radius white dwarfs, an effect of photon diffusion. Nevertheless, in the presence of strong magnetic fields, with central strength of about 10^{14} G, super-Chandrasekhar white dwarfs, with masses of about 1.9 solar mass, are obtained even when the temperature inside the interface is kept constant. Most interestingly, small-radius magnetic white dwarfs remain super-Chandrasekhar even if their luminosity decreases to as low as about 10^{-20} solar luminosity. However, their large-radius counterparts in the same mass-radius relation merge with Chandrasekhars result at low L. Hence, we argue for the possibility of highly magnetized, low luminous super-Chandrasekhar mass white dwarfs which, owing to their faintness, can be practically hidden.
We sketch a possible evolutionary scenario by which a highly magnetized super-Chandrasekhar white dwarf could be formed by accretion on to a commonly observed magnetized white dwarf. This is an exploratory study, when the physics in cataclysmic variables (CVs) is very rich and complex. Based on this, we also explore the possibility that the white dwarf pulsar AR Sco acquired its high spin and magnetic field due to repeated episodes of accretion and spin-down. We show that strong magnetic field dramatically decreases luminosity of highly magnetized white dwarf (B-WD), letting them below the current detection limit. The repetition of this cycle can eventually lead to a B-WD, recently postulated to be the reason for over-luminous type Ia supernovae. A spinning B-WD could also be an ideal source for continuous gravitational radiation and soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs). SGRs/AXPs are generally believed to be highly magnetized, but observationally not confirmed yet, neutron stars. Invoking B-WDs does not require the magnetic field to be as high as for neutron star based model, however reproducing other observed properties intact.
The purpose of this thesis is to obtain more realistic equations of state to describe the matter forming magnetized white dwarfs, and use them to solve its structure equations. The equations of state are determined by considering the weak magnetic field approximation $B<B_c$ ($B_c=4.41times10^{13}text{ G}$) for the electron gas of the star. The magnetic field introduces anisotropic pressures, even for the moderate values present in white dwarfs. Also, we consider the energy and pressure correction due to the Coulomb interaction of the electron gas with the ions located in a crystal lattice. Moreover, spherically symmetric Tolman-Oppenheimer-Volkoff structure equations are solved independently for the perpendicular and parallel pressures, confirming the necessity of using axisymmetric structure equations, more adequate to describe the anisotropic system. Therefore, we study the solutions in cylindrical coordinates. In this case, the mass per longitude unit is obtained instead of the total mass of the white dwarf.
Since their initial discovery, the origin of isolated white dwarfs (WDs) with magnetic fields in excess of $sim$1 MG has remained a mystery. Recently, the formation of these high-field magnetic WDs has been observationally linked to strong binary interactions incurred during post-main-sequence evolution. Planetary, brown dwarf or stellar companions located within a few AU of main-sequence stars may become engulfed during the primarys expansion off the main sequence. Sufficiently low-mass companions in-spiral inside a common envelope until they are tidally shredded near the natal white dwarf. Formation of an accretion disk from the disrupted companion provides a source of turbulence and shear which act to amplify magnetic fields and transport them to the WD surface. We show that these disk-generated fields explain the observed range of magnetic field strengths for isolated, high-field magnetic WDs. Additionally, we discuss a high-mass binary analogue which generates a strongly-magnetized WD core inside a pre-collapse, massive star. Subsequent core-collapse to a neutron star may produce a magnetar.
Over the past couple of decades, researchers have predicted more than a dozen super-Chandrasekhar white dwarfs from the detections of over-luminous type Ia supernovae. It turns out that magnetic fields and rotation can explain such massive white dwarfs. If these rotating magnetized white dwarfs follow specific conditions, they can efficiently emit continuous gravitational waves and various futuristic detectors, viz. LISA, BBO, DECIGO, and ALIA can detect such gravitational waves with a significant signal-to-noise ratio. Moreover, we discuss various timescales over which these white dwarfs can emit dipole and quadrupole radiations and show that in the future, the gravitational wave detectors can directly detect the super-Chandrasekhar white dwarfs depending on the magnetic field geometry and its strength.
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