Primordial magnetic fields in the post-recombination era and early reionization

We explore the ways in which primordial magnetic fields influence the thermal and ionization history of the post-recombination Universe. After recombination, the Universe becomes mostly neutral, resulting also in a sharp drop in the radiative viscosity. Primordial magnetic fields can then dissipate their energy into the intergalactic medium via ambipolar diffusion and, for small enough scales, by generating decaying magnetohydrodynamics turbulence. These processes can significantly modify the thermal and ionization history of the post-recombination Universe. We show that the dissipation effects of magnetic fields, which redshifts to a present value   B ₀= 3 × 10⁻⁹ G  smoothed on the magnetic Jeans scale and below, can give rise to Thomson scattering optical depths  τ≳ 0.1  , although not in the range of redshifts needed to explain the recent Wilkinson Microwave Anisotropy Probe ( WMAP ) polarization observations. We also study the possibility that primordial fields could induce the formation of subgalactic structures for   z ≳ 15  . We show that early structure formation induced by nanoGauss magnetic fields is potentially capable of producing the early reionization implied by the WMAP data. Future cosmic microwave background observations will be very useful to probe the modified ionization histories produced by primordial magnetic field evolution and constrain their strength.     

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal magnetohydrodynamics. The collapse of the cloud is computed for global mass-to-flux ratios of  ∞, 20, 10, 5  and 3, i.e. using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma  β < 1  the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density striations aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetized runs, leading to up to a 75 per cent reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetized runs due to a reduction in the importance of protostellar ejections.     

Non-axisymmetric solar magnetic fields

A simple non-linear, non-axisymmetric mean field dynamo model is applied to a differentially rotating spherical shell. Two approximations are used for the angular velocity, to represent what is now believed to be the solar rotation law. In each case, stable solutions are found which possess a small non-axisymmetric field component. Although the model has a number of obvious shortcomings, it may be relevant to the problem of the solar active longitudes.     

Large-scale magnetic fields: galaxy two-point correlation function

We study the effect of large-scale tangled magnetic fields on the galaxy two-point correlation function in the redshift space. We show that (i) the magnetic field effects can be comparable to the gravity-induced clustering for present magnetic field strength   B ₀≃ 5 × 10⁻⁸ G  , (ii) the absence of this signal from the present data gives an upper bound   B ₀≲ 3 × 10⁻⁸ G  and (iii) the future data can probe the magnetic fields of  ≃10⁻⁸ G  . A comparison with other constraints on the present magnetic field shows that they are marginally compatible. However, if the magnetic fields corresponding to   B ₀≃ 10⁻⁸ G  existed at the last scattering surface, they will cause unacceptably large cosmic microwave background radiation anisotropies.     

Primordial magnetic fields in the f2FF model in large field inflation under de Sitter and power law expansion

We use the f²FF model to study the generation of primordial magnetic fields (PMF) in the context of large field inflation (LFI), described by the potential, V ∼ Mϕ^p. We compute the magnetic and electric spectra for all possible values of the model parameters under de Sitter and power law expansion. We show that scale invariant PMF are not obtained in LFI to first order in the slow roll approximation, if we impose the constraint V (ϕ = 0) ∼ 0. Alternatively, if these constraints are relaxed, the scale invariant PMF can be generated. The associated electric field energy can fall below the energy density of inflation, ρ_Inf for the ranges of comoving wavenumbers, k > 8 × 10^–7 Mpc^–1 and k > 4 × 10^–6 Mpc^–1 in de Sitter and power law (PL) expansion. Further, it can drop below ρ_Inf on the ranges, e‐foldings N > 51, p < 1.66, p > 2.03, l₀ > 3 × 10⁵ M_Pl^–1(H_i < 3.3 × 10^–6 M_Pl), and M > 2.8 × 10^–3 M_Pl. All of the above ranges fit with the observational constraints. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seed magnetic Fields Generated by Primordial Supernova Explosions

The origin of the magnetic field in galaxies is an open question in astrophysics. Several mechanisms have been proposed related, in general, to the generation of small seed fields amplified by a dynamo mechanism. In general, these mechanisms have difficulty in satisfying both the requirements of a sufficiently high strength for the magnetic field and the necessary large coherent scales. We show that the formation of dense and turbulent shells of matter, in the multiple explosion scenario of Miranda &38; Opher for the formation of the large-scale structures of the Universe, can naturally act as a seed for the generation of a magnetic field. During the collapse and explosion of Population III objects, a temperature gradient not parallel to a density gradient can naturally be established, producing a seed magnetic field through the Biermann battery mechanism. We show that seed magnetic fields ∼ 10⁻¹²–10⁻¹⁴ G can be produced in this multiple explosion scenario on scales of the order of clusters of galaxies (with coherence length L  ∼ 1.8 Mpc) and up to ∼ 4.5 × 10⁻¹⁰ G on scales of galaxies ( L  ∼ 100 kpc).     

A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Helical fields and filamentary molecular clouds – I

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first apply the virial theorem to filamentary molecular clouds, including the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds.
We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We examine the effects of the equation of state by comparing 'isothermal' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state.
Our theoretical models involve three parameters: two to describe the mass loading of the toroidal and poloidal fields, and a third that describes the radial concentration of the filament. We thoroughly explore our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r ^−1.8 to r ⁻², while logatropes have density profiles that range from r ⁻¹ to r ^−1.8. We find that purely poloidal fields produce filaments with steep radial density gradients that are not allowed by the observations.     

Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields

We consider the effect of toroidal magnetic fields on hydrodynamically stable Taylor–Couette differential rotation flows. For current-free magnetic fields a non-axisymmetric   m = 1  magnetorotational instability arises when the magnetic Reynolds number exceeds   O (100)  . We then consider how this 'azimuthal magnetorotational instability' (AMRI) is modified if the magnetic field is not current-free, but also has an associated electric current throughout the fluid. This gives rise to current-driven Tayler instabilities (TIs) that exist even without any differential rotation at all. The interaction of the AMRI and the TI is then considered when both electric currents and differential rotation are present simultaneously. The magnetic Prandtl number Pm turns out to be crucial in this case. Large Pm have a destabilizing influence, and lead to a smooth transition between the AMRI and the TI. In contrast, small Pm have a stabilizing influence, with a broad stable zone separating the AMRI and the TI. In this region the differential rotation is acting to stabilize the TIs, with possible astrophysical applications (Ap stars). The growth rates of both the AMRI and the TI are largely independent of Pm , with the TI acting on the time-scale of a single rotation period, and the AMRI slightly slower, but still on the basic rotational time-scale. The azimuthal drift time-scale is ∼20 rotations, and may thus be a (flip-flop) time-scale of stellar activity between the rotation period and the diffusion time.     

Three-dimensional simulations of molecular cloud fragmentation regulated by magnetic fields and ambipolar diffusion

We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion–neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infalling speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (≳0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (ρ) and the strength of the magnetic field ( B ) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both the relations tend to   B ∝ρ^0.5  .     

A magnetic scaleheight: the effect of toroidal magnetic fields on the thickness of accretion discs

We consider accreting systems in which the central object interacts, via the agency of its magnetic field, with the disc that surrounds it. The disc is turbulent and, so, has a finite effective conductivity. The field sweeps across the face of the disc, thereby forming a current that is directed radially within the disc. In turn, this disc current creates a toroidal field, where the interaction between the disc current and the toroidal field produces a Lorentz force that compresses the disc. We investigate this compression, which creates a magnetic scaleheight of the disc that can be much smaller than the conventional scaleheight. We derive an analytic expression for the magnetic scaleheight and apply it to fully ionized discs.     

Stability of toroidal magnetic fields in the solar tachocline and beneath

Stability of toroidal magnetic field in a stellar radiation zone is considered for the cases of uniform and differential rotation. In the rigidly rotating radiative core shortly below the tachocline, the critical magnetic field for instability is about 600 G. The unstable disturbances for slightly supercritical fields have short radial scales ∼1 Mm. Radial mixing produced by the instability is estimated to conclude that the internal field of the sun can exceed the critical value of 600 G only marginally. Otherwise, the mixing is too strong and not compatible with the observed lithium abundance. Analysis of joint instability of differential rotation and toroidal field leads to the conclusion that axisymmetric models of the laminar solar tachocline are stable to nonaxisymmetric disturbances. The question of whether sun-like stars can posses tachoclines is addressed with positive answer for stars with rotation periods shorter than about two months. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)