Ohmic Decay Research Articles

Ohmic decay of crustal neutron star magnetic fields

Calculations of ohmic decay of dipolar magnetic fields which are created so that they are initially confined to the crust are presented for the first time. It is shown that the field does not decay exponentially as has been assumed in most analyses of pulsar observations and that, if the field occupies the entire crust, it decays by less than a factor of order 100 in the Hubble time. Fields that are confined to the outer crust (rho less than or equal to 10 to the 11th g/cu cm) decay too quickly, and again nonexponentially, in conflict with observations. Thus it is difficult to justify, at present, any of the models for field decay which have been proposed. The results, therefore, suggest that neutron star magnetic fields may not decay significantly. 28 references.

Evolution of emerging force-free flux tube to be a flare loop

Evolution of a filamentary magnetic flux tube emerging from the photosphere is investigated in the assumption that the magnetic field is force-free and unchanged during the evolution. If a characteristic radius of the flux tube is 3 km or less setting the field to 1000G, the temperature increases at first due to Joule heating up to about one million degree keeping the plasma density almost constant, and then the density decreases down to a critical value at which a current instability may occur. Thus, a.strong field-aligned electric field of 200 million volts or more is expected to be produced during the following anomalous Ohmic decay of the magnetic field as already shown by a numerical simulation.

A Molecular Weight Gradient Battery Mechanism for Stellar Magnetic Fields

Dolginov (1977) pointed out that a non spherical distribution of molecular weight μ can drive a Biermann type “battery” mechanism in a star and so generate a toroidal magnetic field. We consider uniformly rotating axisymmetric models of this type, containing a ‘primeval’ poloidal field, in which the currents maintaining the toroidal field flow along poloidal field lines, thus ensuring that the configuration is torque free. When the molecular weight distribution is chosen so as to produce a meridional circulation which exactly cancels the Eddington-Sweet circulation, then battery fields of order 1000 gauss can be maintained against ohmic decay in models appropriate to Ap stars near the main sequence with period of order 5 days.

On the role of rotation in the generation of magnetic fields by fluid motions

It is generally accepted that the magnetic fields of planets and stars are produced by the self-exciting dynamo process (first proposed by Larmor) and that observed near-alignments of magnetic dipole axes with rotation axes are due to the influence of Coriolis forces on underlying fluid motions. The detailed role of rotation in the generation of cosmical magnetic fields has yet to be elucidated but useful insight can be obtained from general considerations of the governing magnetohydrodynamic equations. A magnetic field B cannot be maintained or amplified by fluid motion u against the effects of ohmic decay unless (a) the magnetic Reynolds number R = ULno is sufficiently large, and (b) the patterns of B and u are sufficiently complicated (where U is a characteristic flow speed, a characteristic length and J and o are typical values of the magnetic permeability and electrical conductivity respectively). Axisymmetric magnetic fields will always decay (a result that suggests that palaeomagnetic and archaeomagnetic data might show evidence that departures from axial symmetry in the geomagnetic field are systematically less during the decay phase of a polarity ‘ reversal ’ or * excursion ’ than during the recovery phase). Dynamo action is stimulated by Coriolis forces, which promote departures from axial symmetry in the pattern of uwhen B is weak, and is opposed by Lorentz forces, which increase in influence as B grows in strength. If equilibrium is attained when Coriolis and Lorentz forces are roughly equal in magnitude then the system becomes ‘ magnetostrophic' and the strengths of the internal and external parts of the field, and respectively, satisfy B i < B 8 R 1/2 and B e < B 8 R -1/2 if B 8 = UL~1 *X)/c f)i » (p being the mean density of the fluid and Q the angular speed of rotation). The slow and dispersive ‘magnetohydrodynamic inertial wave’ with a frequency that depends on the square of the Alfven speed [B]/(up) 1/2 and inversely on Q exemplifies magnetostrophic flow. Such waves probably occur in the electrically conducting fluid interiors of planets and stars, where they play an important role in the generation of magnetic fields as well as in other processes, such as the topographic coupling between the Earth’s liquid core and solid mantle.

Pair production and pulsar cutoff in magnetized neutron stars with nondipolar magnetic geometry

We construct models of the open field zone in pulsars in which we assume space-charge limited, time independent, electron flow from the surface of a conducting magnetized neutron star with dipolar and quadrupolar components to the magnetic field. We find that the radius of curvature of the field can be much less than in a pure dipole field and can be sufficient to account quantitatively for the cutoff line in the P-P diagram if systematic departures from our basic assumptions about the outer magnetosphere occur (such as decreasing the maximum radius of the last closed field line at small P). We further investigate the effects on the cutoff line of three simple models of torque decay: ohmic decay of the dipolar magnetic field, magnetic field complication due to an MHD-secular instability suggested by Flowers and Ruderman, and alignment of the magnetic dipole result (e.g., that potential drops at low altitude in the nondipolar field might result in self consistent particle acceleration even in the aligned rotator). We suggest possible observational consequences to the existence of higher order components to the field (e.g., differences in the polarization angle versus pulse longitude relation).

The magnetic flux linkage of a moving medium: A theorem and geophysical applications

The time of change N (S;t) of the ‘number of intersections’ N (S;t) of the lines of force of a magnetic field with a closed surface S satisfies a certain theorem. This leads directly to a necessary and sufficient condition for self‐exciting hydromagnetic dynamo action (involving inductive interactions between and fluid motions) in the electrically conducting fluid ‘core’ of a ‘planet,’ in terms of the structure of at the core surface S0. The condition shows the crucial importance of representing that structure with great accuracy in numerical or analytical models of dynamos, and it suggests that dynamo action might be associated with certain topological properties of the pattern of the normal component of on S0. The condition also indicates that axisymmetric (but not necessarily steady) magnetic fields cannot be maintained by fluid motions; such fields must ultimately decay away, even in a compressible fluid (contrary to a recent claim in the literature to the contrary). The condition has to be modified when thermoelectric emf's are present, but when these emf's are proportional to , they cannot prevent the decay of axisymmetric magnetic fields. This result refutes a recent claim that such fields can be maintained by Nernst‐Ettinghausen effects. The theorem for N (S;t) also shows that while fluctuations in can take place on time scales down to that (τa ) associated with core motions (decades to centuries in the case of the earth), the quantity N (S0;t) cannot change on time scales shorter than the Ohmic decay time τd, (≥ 104 years). This result provides the basis of a method for solving the inverse problem of determining the radius of the core of the planet from observations of secular changes in near the surface of the planet. The method has been applied to the earth and Jupiter with encouraging results.

Self-exciting dynamos and geomagnetic polarity changes

Cosmical magnetic fields are produced and maintained against the effects of ohmic decay by inductive interactions with fluid motions. But neither a steady nor a non-steady magnetic field can be supported by this so-called ‘self-exciting homogeneous dynamo’ process if the field possesses an axis of symmetry. This suggests that palaeomagnetic and archaeomagnetic data might be expected to show evidence that departures from axial symmetry are systematically less during the decay phase of a geomagnetic polarity ‘reversal’ or ‘excursion’ than during the growth or recovery phase. The recent proof that neither fluid compressibility nor thermoelectric effects of the Nernst–Ettinghausen type can prevent the ohmic decay of axisymmetric magnetic fields is also discussed here.

Magnetic Fields and Highly Condensed Objects

IT has become conventional in astrophysics to accept the widespread presence of magnetic fields, but not to worry much about their origin. Because of the very long time scales for ohmic decay in most objects it is usual to ascribe the present magnetic field to a field that existed at earlier epochs. By repetition of this process one can trace the fields back to the beginning of a big-bang universe—for example, one attributes the magnetic fields of stars to that which existed in the gas cloud from which the stars condensed, the fields in such clouds to the galaxy containing them, the field of the galaxy to the universe, and the latter to the first moment of time. Then one need no longer trouble oneself with the problem, which is convenient because the problem is otherwise awkward: a voltage ∼1014 V would have to be applied across the galaxy for 1010 yr in order to build a galactic field of ∼10−5 G.