Primordial magnetic fields and formation of molecular hydrogen

We study the implications of primordial magnetic fields for the thermal and ionization history of the post-recombination era. In particular, we compute the effects of dissipation of primordial magnetic fields owing to ambipolar diffusion and decaying turbulence in the intergalactic medium (IGM) and the collapsing haloes, and compute the effects of the altered thermal and ionization history on the formation of molecular hydrogen. We show that, for magnetic field strengths in the range  2 × 10⁻¹⁰≲ B ₀≲ 2 × 10⁻⁹ G  , the molecular hydrogen fraction in IGM and collapsing halo can increase by a factor of 5 to 1000 over the case with no magnetic fields. We discuss the implication of the increased molecular hydrogen fraction on the radiative transfer of ultraviolet photons and the formation of first structures in the universe.     

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.     

Primordial magnetic field,inflation and cosmic strings

The possibility of a primordial magnetic field is discussed. The formation of closed, superconducting cosmic strings before the end of inflation is pointed out as a mechanism able to preserve a magnetic field inside the loops which could provide seeds for galactic magnetic fields.     

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).     

The stability of force-free magnetic fields with cylindrical symmetry in the context of solar flares

The problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of the chromosphere and corona. The consequences of a large ratio of magnetic pressure to gas pressure are investigated. In this case the field must be approximately force-free. The only suitable force-free fields which allow an analytical treatment are those of cylindrical symmetry. The stability of these fields is studied with the energy principle. It is shown that they are always unstable due to kink type instabilities. The shape of the unstable perturbations is described in detail and an upper limit for their amplitude is estimated. The consequences for the proposed mechanism of energy storage are briefly discussed.     

Solar magnetic fields

Since the structuring and variability of the Sun and other stars are governed by magnetic fields, much of present-day stellar physics centers around the measurement and understanding of the magnetic fields and their interactions. The Sun, being a prototypical star, plays a unique role in astrophysics, since its proximity allows the fundamental processes to be explored in detail. The PRL anniversary gives us an opportunity to look back at past milestones and try to identify the main unsolved issues that will be addressed in the future.     

Coronal magnetic fields

The observational evidence on the strength of the coronal magnetic field above active regions is reviewed. Recent advances in observations and plasma theory are used to determine which data are the more reliable and to revise some earlier estimates of field strength. The results from the different techniques are found to be in general agreement, and the relation 279-01, 1.02 R/R 10 is consistent with all the data to within a factor of about 3.The National Center for Atmospheric Research is supported by the National Science Foundation.     

Cluster-scale magnetic fields

The search for non thermal radio emission from clusters of galaxies is a powerful tool to investigate the existence of magnetic fields on such large scale. Unfortunately, such observations are scarce thus far, mainly because of the very faint large scale radio emission expected in clusters of galaxies. In the present contribution we will first review the status of the radio observations of clusters of galaxies, carried out with the aim of detecting large scale radio emission.We will then focus on the large scale radio emission detected at 327 MHz and 610 MHz in the Coma cluster of galaxies. The features of the detected radio emission suggest that a magnetic field with an intensity of the order of ~ 10^–7 Gauss must be present on a scale of about 2 Mpc (forH _o = 100km s ^–1 Mpc ^–1). The morphology of the radio emission is similar to that of the most recent X-ray images derived with ROSAT, and follows the distribution of the galaxies in the cluster. All these pieces of information will be taken into account in the discussion on the possible origin of this large scale magnetic field.     

Solar magnetic fields and convection

The solar magnetic fields observed in active regions and their residues are thought to be parts of toroidal field systems renewed every 11-yr cycle from a poloidal field. The latter may be either a reversing (dynamo) field or a non-reversing, primordial field. The latter view was held for some 70 yr, but the apparent reversals of the polar-cap fields in 1957–8 and the development of dynamo theory brought wide acceptance of the former. Here we consider evidence for and against each model, with these conclusions. (i) Several errors combine so that the non-spot measurements of gross magnetic fluxes are too low by factors of 10 or more. A permanent field of 2 G or more might remain unobserved. (ii) Measurements of average magnetic field strength are subject to various large errors. In particular, the reported reversals of the polar-cap fields are better explained in terms of tilts of toroidal field residues. (iii) Observations of new-cycle magnetic fields among old-cycle fields, of the gradual fading away of large unipolar regions, and the ubiquitous jumble of very small magnetic loop structures appear explicable only in terms of a primordial field. (iv) More positive evidence of a primordial field is found in the extreme order, symmetry and long-term stability of the polar cap streamers or rays. During one eclipse (1954) the primordial field was seen in the absence of all toroidal field residues. (v) A form of reversal of the interplanetary magnetic field is re-interpreted and shown to be consistent with a primordial, but not a dynamo, field. (vi) A test for a primordial field is that the fields below coronal holes should tend to be positive (outwards) in the northern hemisphere and negative in the southern hemisphere. (vii) Further evidence may be available by studying various plasma structures below coronal holes. An urgent requirement is a study of fibrils, faculae, macrospicules and rays in these regions.     

Solar magnetic fields and convection

Recent developments in solar dynamo and other theories of magnetic fields and convection are discussed and extended. A basic requirement of these theories, that surplus fields are eliminated by turbulent or eddy diffusion, is shown to be invalid. A second basic requirement, that strong surface fields are created by granule or supergranule motions, is shown to be improbable. Parker's new thin-filament dynamo, based on the Petschek mechanism, is shown to provide the alternative possibilities: either the magnetic fields halt all convection or a steady state is reached in which the fields are a tangle of long, thin filaments. From the above and other considerations it is concluded that the dynamo and related diffuse-field theories are unacceptable, that solar magnetic fields are not dominated by convection, and that all the fields emerge as strong, concentrated fields (flux ropes) which were wound and twisted from a permanent, primordial field. The discussion may, incidentally, provide the physical elements of a deductive theory of hydromagnetic convection.     

Filaments and large-scale magnetic fields

We have used Stanford magnetic field maps to construct distributions of longitudinal magnetic field gradients in the neighbourhood of polarity inversion lines. The distributions were constructed with proper account of the type of the polarity inversion lines and of the existence or absence of dark filaments above them. It is shown that for polarity inversion lines that pass inside active regions or on their boundary, grad B_II distributions for portions of the lines with persisting filament are shifted toward lower values of gradient as compared with grad B_II distributions for portions of the lines without filaments. The influence of the spatial resolution of the magnetograms upon polarity inversion line characteristics is discussed.     

Photospheric and heliospheric magnetic fields

The magnetic field in the heliosphere evolves in response to the photospheric field at its base. This evolution, together with the rotation of the Sun, drives space weather through the continually changing conditions of the solar wind and the magnetic field embedded within it. We combine observations and simulations to investigate the sources of the heliospheric field from 1996 to 2001. Our algorithms assimilate SOHO/MDI magnetograms into a flux-dispersal model, showing the evolving field on the full sphere with an unprecedented duration of 5.5 yr and temporal resolution of 6 hr. We demonstrate that acoustic far-side imaging can be successfully used to estimate the location and magnitude of large active regions well before they become visible on the solar disk. The results from our assimilation model, complemented with a potential-field source-surface model for the coronal and inner-heliospheric magnetic fields, match Yohkoh/SXT and KPNO/He?10830 Å coronal hole boundaries quite well. Even subject to the simplification of a uniform, steady solar wind from the source surface outward, our model matches the polarity of the interplanetary magnetic field (IMF) at Earth ～3% of the time during the period 1997–2001 (independent of whether far-side acoustic data are incorporated into the simulation). We find that around cycle maximum, the IMF originates typically in a dozen disjoint regions. Whereas active regions are often ignored as a source for the IMF, the fraction of the IMF that connects to magnetic plage with absolute flux densities exceeding 50 Mx cm^?2 increases from ?10% at cycle minimum up to 30–50% at cycle maximum, with even direct connections between sunspots and the heliosphere. For the overall heliospheric field, these fractions are ?1% to 20–30%, respectively. Two case studies based on high-resolution TRACE observations support the direct connection of the IMF to magnetic plage, and even to sunspots. Parallel to the data assimilation, we run a pure simulation in which active regions are injected based on random selection from parent distribution functions derived from solar data. The global properties inferred for the photospheric and heliospheric fields for these two models are in remarkable agreement, confirming earlier studies that no subtle flux-emergence patterns or field-dispersal properties are required of the solar dynamo beyond those that are included in the model in order to understand the large-scale solar and heliospheric fields.

     

Solar magnetic fields and convection

Solar meridional drift motions are vitally important in connection with the origin of magnetic fields, the source of differential rotation, and perhaps convection. A large body of observational evidence is collated with the following conclusions. (i) Sunspot motions reveal latitudinal drifts (Figures 2 and 3) of a few metres per second which vary with latitude and have a strong 11-yr periodicity. There may also be a 22-yr component polewards during even cycles and equatorwards during odd. (ii) Various other tracers, all basically magnetic structures, show the 11-yr drifts at mid- and high latitudes up to the polar caps, motion being polewards during the three years starting just before minimum activity (Figure 4). (iii) The earlier evidence for giant cells or Rossby-type waves is shown to be merely misinterpretation of the hydromagnetic motions of tracers. Evidence against such giant eddies is found in the great stability of other tracer structures. (iv) From the various tracer motions a four cell axisymmetric meridional drift system is determined (Figure 5 (b)) with an 11-yr period of oscillation and amplitude a few metres per second. (v) These meridional oscillations must be a basic component of the activity cycle. They add to the difficulties of the dynamo theory, but may explain the emergence of stitches of flux ropes to form relatively small bipolar magnetic regions. (vi) The two cells also throw light on thetwo sunspot zones in each hemisphere, discussed earlier by Becker and by Antalová and Gnevyshev.     

Solar magnetic fields and convection

The flux-rope-fibre model of solar magnetic fields is developed further to cover post-spot evolution of the fields, faculae, and the influence of magnetic fields on some convective motions. (i) Unipolar magnetic regions of a strongly dominant polarity are explained, as are some fields outside the network, and some tiny reversed polarity fields. (ii) The migration of magnetic regions is explained: the following regions to the poles where most of the flux just vanishes and the preceding towards the equator. (iii) The model explains the rotation of the gross pattern of background fields with a period of 27 days. It explains the puzzling features of active longitudes and of magnetic longitudes extending across the equator. (iv) The magnetic model provides a framework for the various chromospheric fine structures, the rosettes, bushes, double chains, mottles and spicules. It provides qualitative models of these features and points the way to a very complicated quantitative model of the network. (v) Several new convective patterns are described and explained in terms of magnetic stresses. The first is the moat around sunspots, which replaces the supergranule motions there. The second is the long-lived (4–7 days) supergranule cell enclosed by strong fields. The third is a small-scale () convective motion, and the fourth is aligned or long granules, both caused by small-scale magnetic fields. (vi) Photospheric line faculae and photospheric continuum faculae are different phenomena. The former, like the chromospheric faculae, are caused by Alfvén-wave heating. The latter are caused by a new small-scale convective motion. (vii) A model of the 3-min oscillation is described.     

Flares and changing magnetic fields

An observational study of maps of the longitudinal component of the photospheric fields in flaring active regions leads to the following conclusions:

1. The broad-wing Hα kernels characteristic of the impulsive phase of flares occur within 10″ of neutral lines encircling features of isolated magnetic polarity (‘satellite sunspots’).
2. Photospheric field changes intimately associated with several importance 1 flares and one importance 2B flare are confined to satellite sunspots, which are small (10″ diam). They often correspond to spot pores in white-light photographs.
3. The field at these features appears to strengthen in the half hour just before the flares. During the flares the growth is reversed, the field drops and then recovers to its previous level.
4. The magnetic flux through flare-associated features changes by about 4 × 10¹⁹ Mx in a day. The features are the same as the ‘Structures Magnétiques Evolutives’ of Martres et al. (1968a).
5. An upper limit of 10²¹ Mx is set for the total flux change through McMath Regions 10381 and 10385 as the result of the 2B flare of 24 October, 1969.
6. Large spots in the regions investigated did not evince flux changes or large proper motions at flare time.
7. The results are taken to imply that the initial instability of a flare occurs at a neutral point, but the magnetic energy lost cannot yet be related to the total energy of the subsequent flare.
8. No unusual velocities are observed in the photosphere at flare time.

     

Solar magnetic fields and convection

The traditional model of solar magnetic fields is based on convection which dominates generally weak, diffuse fields and so tends to create increasingly tangled fields. Surplus fields must be eliminated by merging of opposite polarities; for example a solar dynamo of period≈10 yr requires fields to be reduced to a scale of<100 km or diffusivity to be increased by a factor of≈10⁷ over molecular diffusivity. It is now shown that the true requirements of any diffuse-field theory are far more stringent, and that surplus fields must be eliminated within a single eddy period of 1 day (10 min) for the supergranules (granules). The reason is that during that period fresh fields are created with flux and energy comparable with those of the old fields. The numerical models of Weiss and Moss are used to confirm this result which is fatal to all diffuse-field theories. The basic error in these theories is found in the assumption that because heat and other passive properties of a fluid diffuse much faster in the presence of turbulence, passive magnetic fields should do likewise. The error is that the heat content of an eddy is not increased by the motion while the magnetic flux and energy are increased rapidly. It is shown that the observed concentrations of surface fields into strengths of?100 G cannot be accounted for by observed surface motions. Nor are they accounted for by the numerical models of turbulence of Weiss or Moss whatever values of the magnetic Reynolds number are assumed. A detailed comparison is made between both small-scale and large-scale surface magnetic features and the predictions of the diffuse-field theory. The differences appear irreconcilable and the features only explicable in terms of the twisted flux-rope model.     

Active region magnetic fields

The tilt angles of sunspot groups are defined, using the Mount Wilson data set. It is shown that groups with tilt angles greater than or less than the average value (&amp;#x2248; 5 deg) show different latitude dependences. This effect is also seen in synoptic magnetic field data defining plages. The fraction of the total sunspot group area that is found in the leading spots is discussed as a parameter that can be useful in studying the dynamics of sunspot groups. This parameter is larger for low tilt angles, and small for extreme tilt angles in either direction. The daily variations of sunspot group tilt angles are discussed. The result that sunspot tilt angles tend to rotate toward the average value is reviewed. It is suggested that at some depth, perhaps 50 Mm, there is a flow relative to the surface that results from a rotation rate faster than the surface rate by about 60 m/sec and a meridional drift that is slower than the surface rate by about 5 m/sec. This results in a slanted relative flow at that depth that is in the direction of the average tilt angle and may be responsible for the tendency for sunspot groups (and plages) to rotate their magnetic axes in the direction of the average tilt angle.     

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.     

Modelling coronal magnetic fields

The hairy ball model of coronal magnetic fields has a spherical source surface separating potential and radial magnetic fields. In the present model the source surface is chosen such that the wind speed equals the Alfvénic speed at selected points on the source surface. Results have been obtained for a dipole base field and an isothermal corona.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.