Magnetic protection of potentially habitable planets plays a central role in determining their actual habitability and/or the chances of detecting atmospheric biosignatures. We develop here a thermal evolution model of potentially habitable Earth-like planets and super-Earths. Using up-to-date dynamo scaling laws we predict the properties of core dynamo magnetic fields and study the influence of thermal evolution on their properties. The level of magnetic protection of tidally locked and unlocked planets is estimated by combining simplified models of the planetary magnetosphere and a phenomenological description of the stellar wind. Thermal evolution introduces a strong dependence of magnetic protection on planetary mass and rotation rate. Tidally locked terrestrial planets with an Earth-like composition would have early dayside magnetospause distances between 1.5 and 4.0 R p , larger than previously estimated. Unlocked planets with periods of rotation ∼ 1 day are protected by magnetospheres extending between 3 and 8 R p . Our results are robust against variations in planetary bulk composition and uncertainties in other critical model parameters. For illustration purposes the thermal evolution and magnetic protection of the potentially habitable super-Earths GL 581d, GJ 667Cc and HD 40307g were also studied. Assuming an Earth-like composition we found that the dynamos of these planets are already extinct or close to being shut down. While GL 581d is the best protected, the protection of HD 40307g cannot be reliably estimated. GJ 667Cc, even under optimistic conditions, seems to be severely exposed to the stellar wind and, under the conditions of our model, has probably suffered massive atmospheric losses.

Aims. This paper is the first in a series that aims to understand the long-term evolution of neutron star magnetic fields. Methods. We model the stellar matter as an electrically neutral and lightly-ionized plasma composed of three moving particle species: neutrons, protons, and electrons; these species can be converted into each other by weak interactions (beta decays), suffer binary collisions, and be affected by each other's macroscopic electromagnetic fields. Since the evolution of the magnetic field occurs over thousands of years or more, compared to dynamical timescales (sound and Alfvén) of milliseconds to seconds, we use a slow-motion approximation in which we neglect the inertial terms in the equations of motion for the particles. This approximation leads to three nonlinear partial-differential equations describing the evolution of the magnetic field, as well as the movement of two fluids: the charged particles (protons and electrons) and the neutrons. These equations are first rather than second order in time (involving the velocities of the three species but not their accelerations). Results. In this paper, we restrict ourselves to a one-dimensional geometry in which the magnetic field points in one Cartesian direction, but varies only along an orthogonal direction. We study the evolution of the system in three different ways: (i) estimating timescales directly from the equations, guided by physical intuition; (ii) a normal-mode analysis in the limit of a nearly uniform system; and (iii) a finite-difference numerical integration of the full set of nonlinear partial-differential equations. We find good agreement between our analytical normal-mode solutions and the numerical simulations. We show that the magnetic field and the particles evolve through successive quasi-equilibrium states, on timescales that can be understood by physical arguments. Depending on parameter values, the magnetic field can evolve by ohmic diffusion or by ambipolar diffusion, the latter being limited either by interparticle collisions or by relaxation to chemical quasi-equilibrium through beta decays. The numerical simulations are further validated by verifying that they satisfy the known conservation laws in highly nonlinear situations.

We review the effect of finite amplitude circularly polarized waves on the behavior of linear ion-beam plasma instabilities. It has been shown that left-hand polarized waves can stabilize linear right-handed instabilities [1]. It has also been shown that for beam velocities capable of destabilizing left-handed waves, left-hand polarized large amplitude waves can also stabilize these waves. On the other hand, when the large amplitude wave is right-hand polarized, they can either stabilize or destabilize right-handed instabilities depending on the wave frequency and beam speed [2]. Finally, we show that the presence of large amplitude left-hand polarized waves can also trigger electrostatic ion-acoustic instabilities by forcing the phase velocities of two ion acoutic waves to become equal, above a threshold amplitude value.

In the solid crusts of neutron stars, the advection of the magnetic field by the current-carrying electrons, an effect known as Hall drift, should play a very important role as the ions remain essentially fixed (as long as the solid does not break). Although Hall drift preserves the magnetic field energy, it has been argued that it may drive a turbulent cascade to scales at which Ohmic dissipation becomes effective, allowing a much faster decay in objects with very strong fields. On the other hand, it has been found that there are "Hall equilibria", i.e., field configurations that are unaffected by Hall drift. Here, we address the crucial question of the stability of these equilibria through axially symmetric (2D) numerical simulations of Hall drift and Ohmic diffusion, with the simplifying assumption of uniform electron density and conductivity. We demonstrate the 2D-stability of a purely poloidal equilibrium, for which Ohmic dissipation makes the field evolve towards an attractor state through adjacent stable configurations, around which damped oscillations occur. For this field, the decay scales with the Ohmic timescale. We also study the case of an unstable equilibrium consisting of both poloidal and toroidal field components that are confined within the crust. This field evolves into a stable configuration, which undergoes damped oscillations superimposed on a slow evolution towards an attractor, just as the purely poloidal one.

[1] In a previous paper, sufficiently large-amplitude and left-handed ''pump waves'' propagating parallel to the background magnetic field were shown to stabilize a moderately dense beam in a proton plasma against the generation of waves drawing their energy from the differential streaming motion of the beam [Gomberoff, 2003]. We now examine the general case of both left-hand and right-hand pump waves and their effects on beam instability as a function of pump wave amplitude and frequency, beam speed, and plasma component temperatures. We find that the left-hand pump wave always gives beam stability above a threshold amplitude. Larger threshold trend with increasing beam speed and lower ones with increasing temperature. It is also shown that they can stabilize left-hand polarized instabilities in the case of large drift velocities. The right-hand pump similarly suppresses beam instabilities when its pump frequency is below the linearly unstable range of frequencies. However, when its pump frequency is within the range of instability, that part of the range below the pump frequency is stabilized beyond a threshold amplitude, but the part above becomes even more unstable in the presence of a right-hand pump.