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Register a new userWhat can we say about seed fields for galactic dynamos?
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We demonstrate that a quasi-uniform cosmological seed field is a much less suitable seed for a galactic dynamo than has often been believed. The age of the Universe is insufficient for a conventional galactic dynamo to generate a contemporary galactic magnetic field starting from such a seed, accepting conventional estimates for physical quantities. We discuss modifications to the scenario for the evolution of galactic magnetic fields implied by this result. We also consider briefly the implications of a dynamo number that is significantly larger than that given by conventional estimates.
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In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian inference offers an increasingly-popular strategy to overcome the inherent ill-posedness of this signal reconstruction challenge. However, there remains a great deal of confusion within the astronomical community regarding the appropriate mathematical devices for framing such analyses and the diversity of available computational procedures for recovering posterior functionals. In this brief research note I will attempt to clarify both these issues from an applied statistics perpective, with insights garnered from my post-astronomy experiences as a computational Bayesian / epidemiological geostatistician.
Magnetic fields in galaxies and galaxy clusters are amplified from a very weak seed value to the observed $mu{rm G}$ strengths by the turbulent dynamo. The seed magnetic field can be of primordial or astrophysical origin. The strength and structure of the seed field, on the galaxy or galaxy cluster scale, can be very different, depending on the seed-field generation mechanism. The seed field first encounters the small-scale dynamo, thus we investigate the effects of the strength and structure of the seed field on the small-scale dynamo action. Using numerical simulations of driven turbulence and considering three different seed-field configurations: 1) uniform field, 2) random field with a power-law spectrum, and 3) random field with a parabolic spectrum, we show that the strength and statistical properties of the dynamo-generated magnetic fields are independent of the details of the seed field. We demonstrate that, even when the small-scale dynamo is not active, small-scale magnetic fields can be generated and amplified linearly due to the tangling of the large-scale field. In the presence of the small-scale dynamo action, we find that any memory of the seed field for the non-linear small-scale dynamo generated magnetic fields is lost and thus, it is not possible to trace back seed-field information from the evolved magnetic fields in a turbulent medium.
We construct a simple and robust approach for deriving constraints on magnetic fields in galaxy clusters from rotation measure (RM) maps. Relaxing the commonly used assumptions of a correlation between the magnetic field strength and the plasma density and of a power-law (in wave number) magnetic field power spectrum, and using an efficient numerical analysis method, we test the consistency of a wide range of magnetic field models with RM maps of 11 extended sources in 5 clusters, for which the data were made available to us. We show that the data reveal no indication for a radial dependence of the average magnetic field strength, and in particular no indication for a correlation between the gas density and the field strength. The RM maps of a considerable fraction of the sources either require or are consistent with the presence of a spatially uniform magnetic field of a relatively small strength, 0.02-0.3 muG, which contributes significantly to the RM. The RM maps of all but one source do not require a power-law magnetic field power spectrum, and most are consistent with a power spectrum dominated by a single wave length. The uncertainties in the magnetic field strengths (and spatial correlation lengths) derived from RM maps exceed an order of magnitude (and often more). These uncertainties imply, in particular, that there is no indication in current RM data for a systematic difference between the magnetic field strengths in radio-halo clusters and in radio-quiet clusters. With the improvement expected in the near future of the quality and quantity of RM data, our analysis method will enable one to derive more accurate constraints on magnetic fields in galaxy clusters.
The effect of magnetic fields on the frequencies of toroidal oscillations of neutron stars is derived to lowest order. Interpreting the fine structure in the QPO power spectrum of magnetars following giant flares reported by Strohmayer and Watts (2006) to be Zeeman splitting of degenerate toroidal modes, we estimate a crustal magnetic field of order 10^{15} Gauss or more. We suggest that residual m, -m symmetry following such splitting might allow beating of individual frequency components that is slow enough to be observed.
In the present paper, we investigate the cosmographic problem using the bias-variance trade-off. We find that both the z-redshift and the $y=z/(1+z)$-redshift can present a small bias estimation. It means that the cosmography can describe the supernova data more accurately. Minimizing risk, it suggests that cosmography up to the second order is the best approximation. Forecasting the constraint from future measurements, we find that future supernova and redshift drift can significantly improve the constraint, thus having the potential to solve the cosmographic problem. We also exploit the values of cosmography on the deceleration parameter and equation of state of dark energy $w(z)$. We find that supernova cosmography cannot give stable estimations on them. However, much useful information was obtained, such as that the cosmography favors a complicated dark energy with varying $w(z)$, and the derivative $dw/dz<0$ for low redshift. The cosmography is helpful to model the dark energy.
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