Magnetic confinement of accreted plasma is a common mechanism for compact objects, but so far it has been studied in detail almost exclusively on neutron stars. White dwarfs in close binary systems, such as polars and intermediate polars, also channel matter onto their magnetic poles, creating localized accretion columns. Recent observations of micronovae on strongly magnetized white dwarfs confirmed that thermonuclear burning can occur in confined regions near the poles. However, the question of whether white dwarfs can support large magnetically confined structures remained open. This work transfers the formalism developed for neutron stars to the physical conditions of white dwarfs.
The authors solve the Grad–Shafranov equation for an axisymmetric equilibrium configuration with an isothermal equation of state. They apply an iterative self-consistent scheme in which the source function is determined from the condition of flux freezing: mass does not cross magnetic surfaces. A 256×256 grid with logarithmic refinement near the surface is used. Unlike the traditional successive over-relaxation method, the equation is solved with the direct sparse solver UMFPACK. To find the maximum supported mass, a binary search is used with convergence checks based on the residual and mass error. Parameters vary over the ranges: magnetic field from $10^5$ to 3×$10^8$ G, temperature from 2×$10^4$ to $10^7$ K.
For typical parameters (M=0.8 M⊙, R=7×$10^8$ cm, B=5×$10^7$ G, T=1.59×$10^5$ K), a mountain with mass $10^{-3}$ M⊙ has a characteristic height of about $10^5$ cm. The maximum density at the base reaches 2.48×$10^7$ g/cm^3. The magnetic field lines are noticeably deformed and shifted toward the equator, but equilibrium is maintained. The maximum mass that can be supported follows a power law: $M_{max}$ = 4.07×$10^{-3}$ M⊙ (T/$10^5$ K)^-2 (B/5×$10^7$ G)^2. This amounts to about 3% of the critical mass previously obtained analytically for small accretions. Magnetic burial reduces the dipole moment to 10% of its initial value, and the relative reduction is independent of the field strength. The field remains predominantly dipolar, but odd multipole moments (l=3,5,7,9) are excited.
This work provides, for the first time, a quantitative estimate of magnetically confined mountains on white dwarfs, filling the gap between neutron star theory and observations of cataclysmic variables. Unlike previous estimates based on simple spherical or cylindrical models, here the full equilibrium equation is solved with self-consistent flux freezing. This allows a reliable determination of the maximum mass and the degree of magnetic burial. The results show that magnetic burial on white dwarfs is weaker than on neutron stars: the field is reduced by only 10%, not by orders of magnitude. This approach can serve as a basis for interpreting observational data on magnetic fields and accretion in polars and intermediate polars.
The model can be extended by abandoning the isothermal equation of state and including realistic temperature profiles. Accounting for the mountain's sinking into the stellar atmosphere and mixing of material, as done for neutron stars, will refine the structure. Introducing finite conductivity and non-ideal effects will open the way to studying dissipation and reconnection. Dynamical simulations based on the obtained equilibria will help assess the stability of mountains and their evolution. Of particular interest is the inclusion of rotation and the propeller regime, which may limit mass accumulation in asynchronous systems.
The results are applicable to interpreting observations of magnetic cataclysmic variables, including polars and intermediate polars. They also provide a basis for estimating the ellipticity of white dwarfs and the possible emission of continuous gravitational waves detectable by future space interferometers.
The next step will be to include a realistic equation of state and account for the sinking of accreted material into the stellar atmosphere. Hydrodynamic simulations are also needed to test the stability of the found equilibria and to study the development of instabilities.
This work connects the theory of magnetic confinement with observational manifestations of accretion on white dwarfs, such as micronovae and changes in magnetic fields. The question of the long-term evolution of the magnetic field during prolonged accretion and the role of instabilities in destroying mountains remains open.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
In this work, the Grad-Shafranov equation is solved numerically for magnetically confined mountains on white dwarfs, taking into account flux freezing. A formula is derived for the maximum mass as a function of field and temperature, and it is shown that accretion reduces the dipole moment to 10% while the structure remains predominantly dipolar.
Where its strength is
This is the first quantitative assessment of magnetically confined mountains on white dwarfs using a fully self-consistent solution, which bridges the gap between neutron star theory and observations of cataclysmic variables.
Where it could go next
Worth trying
Why this may matter
Such mountains could affect the observational signatures of accreting white dwarfs, from the shape of X-ray pulsations to the evolution of the magnetic moment, which is important for interpreting data from missions like XMM-Newton and future surveys.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.58, against a usual 0.64. It looks like few have drilled nearby.
White dwarfs can have magnetic fields from $10^3$ to $10^9$ G, which is a range spanning a factor of a million. At a field of $10^8$ G, the maximum supported mass reaches 0.067 solar masses, comparable to the mass of an entire giant planet.