Stellar remnants like white dwarfs and neutron stars are the endpoints of ordinary stellar evolution. Ordinary white dwarfs—Chandrasekhar's domain—are supported solely by the pressure of degenerate electrons. But the hypothesis that strange quark matter might be more stable than nuclear matter opens the door to exotic objects: strange dwarfs. At their center lies a self-gravitating quark core, with many kilometers of ordinary matter on top. It's the crust, not the core, that determines the observed radius, so any disturbance—say, a strong magnetic field—can shift the whole star on the mass–radius diagram. If such objects exist, they are hard to distinguish from ordinary white dwarfs, but anomalously small radii could be the key to discovery.
In this work, equilibrium sequences of strange dwarfs are constructed using the anisotropic Tolman–Oppenheimer–Volkoff equation, generalized for different radial and tangential pressures. The core is described by the MIT bag model—strange quark matter is considered isotropic. The crust consists of ions and degenerate electrons; Coulomb corrections from the crystal lattice are included. The magnetic field is introduced via Landau quantization of electrons: the radial pressure is obtained from the standard sum over Landau levels, while the tangential pressure comes from subtracting the magnetization contribution. Anisotropy is switched on only in the crust using a step function; scalar branches (P=$P_r$ or P=$P_t$) serve as control calculations. Crust sequences are traced from pure C, O, Ne, Mg up to the threshold of inverse beta-decay and further to neutron drip; 50/50 mixtures are also considered. In all cases, core and crust are joined at pressure $P_{join}$, which physically corresponds either to the beta-instability threshold or to neutron drip. For comparison, ordinary white dwarfs and compact objects from the Montreal White Dwarf Database are used (numerical integration was performed for parameter families).
The magnetic field compresses the strange dwarf. At a fixed mass (1 M⊙), increasing the dimensionless field from B⋆ = 0.01 to 1 shrinks the radius by about 20–30% for all crust compositions. For example, for the carbon sequence, truncated at the beta-decay threshold, the radius drops from 5118 km to 3783 km; extended to neutron drip, from 4851 km to 3653 km. Heavier elements (O, Ne, Mg) and mixtures show the same trend. The advanced crust (down to drip) itself provides additional compaction: its equation of state is softer, the pressure at the core boundary is higher, and the core becomes more massive. The anisotropic term 2(Pt-Pr)/r is always negative in the studied density range and acts as an extra squeeze; it doesn't just renormalize the pressure but changes the balance of forces. The maximum mass of the strange dwarf changes only slightly—about 1.37 M⊙ for carbon—while radii at low masses shrink more noticeably. Observational data from the MWDD catalog indicate that the most compact white dwarf candidates lie precisely in the region where magnetic anisotropy shifts the theoretical branches.
The result underlines that the strange dwarf's crust is no passive shell. Even if the quark core does not feel the magnetic field directly, the response of ordinary matter in the crust can alter the star's global parameters. This shifts the problem of identifying strange dwarfs to the observational plane: rather than exotic core signatures, one should look for anomalously compact white dwarfs with known spectra and magnetic field estimates. Moreover, localizing the anisotropy only in the crust is a step toward more physical models where different stellar components interact differently with the magnetic field. The traditional replacement of the whole star with a single scalar pressure may mask real effects, especially when the radius is largely determined by the outer layers.
The model assumes spherical symmetry and effective anisotropy, but real magnetic fields break this. The next step is two-dimensional calculations with a specific field geometry, which will allow explicit computation of stellar deformation and clarify the role of anisotropy. Another direction is analyzing the radial stability of the obtained configurations with proper boundary conditions at the core–crust interface. Finally, more detailed comparisons with observed white dwarfs, especially those with measured magnetic fields and determined atmospheric chemical compositions, could provide the first constraints on the existence of strange dwarfs.
Astrophysics of compact objects and the physics of strong magnetic fields are the immediate beneficiaries. Interpreting massive white dwarfs with anomalous radii, especially in GAIA and MWDD catalogs, may require accounting for such effects, even if the quark core remains hypothetical.
It is necessary to compute radial modes to check the dynamical stability of the selected branches. Also, the crust composition tables should be extended to full mixtures with neutron drip, and a wider range of magnetic fields should be explored.
The paper touches on several open questions: the equation of state of dense matter at high densities and in strong magnetic fields, the stability of hybrid stars, and the observational identification of exotic compact objects. The anisotropic structure of the crust could be a link between microphysics and astrophysical observations.
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What the work does
The paper constructs equilibrium configurations of strange dwarfs with a quark core and a crust made of ions and degenerate electrons. The effect of a strong magnetic field is included via Landau quantization and pressure anisotropy in the crust. It is shown that the magnetic field and crust composition significantly reduce the stellar radius at a fixed mass, which may help distinguish such objects among ordinary white dwarfs.
Where its strength is
The strength of the work lies in the detailed treatment of the anisotropy arising from the magnetic field in the crust and in tracing its influence on the mass–radius relation for different chemical compositions. This provides a concrete observational signature—anomalously small radii—for searching for strange dwarfs.
Where it could go next
Worth trying
Why this may matter
If crust anisotropy indeed strongly compresses strange dwarfs, this offers a direct way to search for candidates among known white dwarfs by their anomalously small radii. Such a discovery would be the first observational evidence for the existence of stable strange quark matter, which is of fundamental importance for the physics of strong interactions.
Nearby works in our archive
The closest work in the archive sits at 0.65 by meaning — the usual level for our corpus.
Strange quark matter gets its name from the flavor of the s-quark (strange). If a droplet of such matter fell to Earth, it would convert ordinary matter into strange matter, releasing energy — a scenario known as a 'strangelet.' Fortunately, there is no experimental evidence for this.