Relaxing the bounds on primordial magnetic seed fields

Abstract

We point out that the lower bound on the primordial magnetic field required to seed the galactic dynamo is significantly relaxed in an open universe or in a universe with a positive cosmological constant. It is shown that, for reasonable cosmological parameters, primordial seed fields of strength 10 −30 Gauss or less at the time of galaxy formation could explain observed galactic magnetic fields. As a consequence, mechanisms of primordial magnetic seed-field generation that have previously been ruled out could well be viable. We also comment on the implications of the observation of micro-Gauss magnetic fields in galaxies at high redshift.PACS numbers: 98.35.Eq, 98.62.En, 98.80.Es Magnetic fields pervade most astrophysical systems [1], but their origin is unknown. Spiral galaxies are observed to possess large-scale magnetic fields with strength of the order of 10 −6 G and direction aligned with the rotational motion. A plausible explanation is that galactic magnetic fields result from the exponential amplification of an initially weak seed field by a mean-field dynamo [2,3]. Many proposals have been put forward regarding the origin of such a seed field. One suggestion is that it might arise spontaneously from non-parallel gradients of pressure and charge-density during galaxy formation [4]. A wider range of possibilities is offered if the seed field is of primordial origin. This category includes cosmological magnetic fields [5] as well as magnetic fields created by any of a number of early-universe particle-physics mechanisms [6] such as collisions of bubbles in a first-order phase transition [7] or false-vacuum inflation [8,9].The seed-field strength required at the time of completed galaxy formation (t gf ) for a galactic dynamo to produce the present magnetic field strength B 0 ∼ 10 −6 G is usually quoted in the range ∼ 10 −23 -10 −19 G. Such lower bounds are obtained by considering the dynamo amplification in a flat universe with zero cosmological constant for "typical" values of the parameters of the αω-dynamo. The seed field must also be coherent on a scale at least as large as the size of the largest turbulent eddy, ∼ 100 pc [2]. Most proposed models of primordial seed-field generation fail to meet these requirements as formulated above.In this paper we address the issue in the light of recent developments in cosmology. Observations of distant type-IA supernovae [10] and of anisotropies in the cosmic microwave background (CMB) [11] in combination have made it increasingly likely that the universe is less dense than the critical density and has a positive cosmological constant Λ. Most previous studies of magnetic fields have assumed a Λ = 0 universe with critical matter density. We shall recalculate the constraints on primordial seed fields for general Friedmann universes with matter density parameter Ω 0 and vacuum energy density parameter λ 0 ≡ Λ/(3H 2 0 ) such that Ω 0 + λ 0 ≤ 1 (the subscript 0 here indicates quantities at present time and H 0 is the Hubble parameter). In addition to finding revis...

TeV gamma rays from blazars beyondz=1?

“…Rectilinear propagation of protons is possible along a line of sight which does not cross any galaxies, clusters of galaxies, because their magnetic fields would cause a significant deflection. In addition, IGMFs can cause deflections in the voids, where the fields can be as low as 10 −30 G [30,31], but the analysis of blazar spectra including cosmic rays and secondary photons points to a range from 0.01 to 30 femtogauss [25]. As long as IGMFs are smaller than a femtogauss, they do not affect the point images of blazars.…”

N-flationary Magnetic Fields

“…However, the dynamo is only a means of amplification, and a seed field of primordial origin is still required. Due to the current evidences in favor of an accelerated expansion of the Universe, this seed field can be as small as 10 −30 G on a length of ∼ 10 kpc, significantly weaker than previously thought [11] (for comprehensive reviews of magnetic fields in the early Universe see for instance [12]). …”

Cosmological magnetic fields

“…In general qualitative terms, the seed field will be much less than that required for purely adiabatic compression. In terms of the r-factor in equation (11), a seed without dynamo amplification requires r ∼ 10 −14 , whereas a seed with dynamo amplification could have r as low as ∼ 10 −34 (this may be further reduced in the presence of a cosmological constant [8]). …”

“…The kinematic quantities are Θ (the volume expansion of u µ -flowlines), ω µ (vorticity),u µ (four-acceleration), and σ µν (shear). The key equation is (8), which is the induction equation in covariant form. When contracted with B µ , it leads to the conservation equation for magnetic energy density:…”