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We revisit in this work the problem of the maximum masses of magnetized White Dwarfs (WD). The impact of a strong magnetic field onto the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into a parallel and perpendicular components. We first construct stable solutions of TOV equations for the parallel pressures, and found that physical solutions vanish for the perpendicular pressure when $B gtrsim 10^{13}$ G. This fact establishes an upper bound for a magnetic field and the stability of the configurations in the (quasi) spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WD with super Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we derived structure equations appropriated for a cylindrical metric with anisotropic pressures. From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for $B sim 10^{13} $ G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WD, with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.
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In this paper we review the current status of research on the observational and theoretical characteristics of isolated and binary magnetic white dwarfs (MWDs). Magnetic fields of isolated MWDs are observed to lie in the range 10^3-10^9G. While the upper limit cutoff appears to be real, the lower limit is more difficult to investigate. The incidence of magnetism below a few 10^3G still needs to be established by sensitive spectropolarimetric surveys conducted on 8m class telescopes. Highly magnetic WDs tend to exhibit a complex and non-dipolar field structure with some objects showing the presence of higher order multipoles. There is no evidence that fields of highly magnetic WDs decay over time, which is consistent with the estimated Ohmic decay times scales of ~10^11 yrs. MWDs, as a class, also appear to be more massive than their weakly or non-magnetic counterparts. MWDs are also found in binary systems where they accrete matter from a low-mass donor star. These binaries, called magnetic Cataclysmic Variables (MCVs) and comprise about 20-25% of all known CVs. Zeeman and cyclotron spectroscopy of MCVs have revealed the presence of fields in the range $sim 7-230$,MG. Complex field geometries have been inferred in the high field MCVs (the polars) whilst magnetic field strength and structure in the lower field group (intermediate polars, IPs) are much harder to establish. The origin of fields in MWDs is still being debated. While the fossil field hypothesis remains an attractive possibility, field generation within the common envelope of a binary system has been gaining momentum, since it would explain the absence of MWDs paired with non-degenerate companions and also the lack of relatively wide pre-MCVs.
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.
There are no known examples of magnetic white dwarfs with fields larger than about 3MG paired with a non-degenerate companion in detached binary systems. The suggestion is that highly magnetic, isolated white dwarfs may originate from stars that coalesce during common envelope evolution while those stars that emerge from a common envelope on a close orbit may evolve into double degenerate systems consisting of two white dwarfs, one or both magnetic. The presence of planets or planetary debris around white dwarfs is also a new and exciting area of research that may give us important clues on the formation of first and second generation planetary systems, since these place unique signatures in the spectra of white dwarfs.
The hard X-ray spectrum of magnetic cataclysmic variables can be modelled to provide a measurement of white dwarf mass. This method is complementary to radial velocity measurements, which depend on the (typically rather uncertain) binary inclination. Here we present results from a Legacy Survey of 19 magnetic cataclysmic variables with NuSTAR. We fit accretion column models to their 20-78 keV spectra and derive the white dwarf masses, finding a weighted average $bar{M}_{rm WD}=0.77pm0.02$ $M_{odot}$, with a standard deviation $sigma=0.10$ $M_{odot}$, when we include the masses derived from previous NuSTAR observations of seven additional magnetic cataclysmic variables. We find that the mass distribution of accreting magnetic white dwarfs is consistent with that of white dwarfs in non-magnetic cataclysmic variables. Both peak at a higher mass than the distributions of isolated white dwarfs and post-common-envelope binaries. We speculate as to why this might be the case, proposing that consequential angular momentum losses may play a role in accreting magnetic white dwarfs and/or that our knowledge of how the white dwarf mass changes over accretion-nova cycles may also be incomplete.
We present the first radiation magnetohydrodynamics simulations of the atmosphere of white dwarf stars. We demonstrate that convective energy transfer is seriously impeded by magnetic fields when the plasma-beta parameter, the thermal to magnetic pressure ratio, becomes smaller than unity. The critical field strength that inhibits convection in the photosphere of white dwarfs is in the range B = 1-50 kG, which is much smaller than the typical 1-1000 MG field strengths observed in magnetic white dwarfs, implying that these objects have radiative atmospheres. We have then employed evolutionary models to study the cooling process of high-field magnetic white dwarfs, where convection is entirely suppressed during the full evolution (B > 10 MG). We find that the inhibition of convection has no effect on cooling rates until the effective temperature (Teff) reaches a value of around 5500 K. In this regime, the standard convective sequences start to deviate from the ones without convection owing to the convective coupling between the outer layers and the degenerate reservoir of thermal energy. Since no magnetic white dwarfs are currently known at the low temperatures where this coupling significantly changes the evolution, effects of magnetism on cooling rates are not expected to be observed. This result contrasts with a recent suggestion that magnetic white dwarfs with Teff < 10,000 K cool significantly slower than non-magnetic degenerates.
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