Laplace transform analysis of a multiplicative asset transfer model

We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, solving it analytically and numerically for the steady-state distribution, and exploring the solutions for various values of $f\in(0,1)$. The Laplace transform analysis is superior to agent-based simulations as it does not depend on the number of agents, enabling us to study entropy and inequality in regimes that are costly to address with simulations. We demonstrate that Boltzmann entropy is not a suitable (e.g. non-monotonic) measure of disorder in a multiplicative asset transfer system and suggest an asymmetric stochastic process that is equivalent to the asset transfer model

Cyclotron line signatures of thermal and magnetic mountains from accreting neutron stars

Cyclotron resonance scattering features (CRSFs) in the X-ray spectrum of an accreting neutron star are modified differently by accretion mounds sustained by magnetic and thermocompositional gradients. It is shown that one can discriminate, in principle, between mounds of different physical origins by studying how the line energy, width, and depth of a CRSF depend on the orientation of the neutron star, accreted mass, surface temperature distribution, and equation of state. CRSF signatures including gravitational light bending are computed for both phase-resolved and phase-averaged spectra on the basis of self-consistent Grad-Shafranov mound equilibria satisfying a global flux-freezing constraint. The prospects of multimessenger X-ray and gravitational-wave observations with future instruments are canvassed briefly.Comment: 17 pages, 12 figures, accepted for publication in MNRA

Neutron star deformation due to poloidal-toroidal magnetic fields of arbitrary multipole order: a new analytic approach

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar.Comment: 14 pages, 6 figures, 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Societ