scholarly journals CMB anisotropies and linear matter power spectrum in models with non-thermal neutrinos and primordial magnetic fields

2021 ◽  
Vol 2021 (11) ◽  
pp. 044
Author(s):  
Kerstin E. Kunze
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Thermal Model ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Power Spectra ◽  
Space Distribution ◽  
Thermal Phase ◽  
Primordial Magnetic Fields ◽  
Stochastic Magnetic Field

Abstract Angular power spectra of temperature anisotropies and polarization of the cosmic microwave background (CMB) as well as the linear matter power spectra are calculated for models with three light neutrinos with non-thermal phase-space distributions in the presence of a primordial stochastic magnetic field. The non-thermal phase-space distribution function is assumed to be the sum of a Fermi-Dirac and a gaussian distribution. It is found that the known effective description of the non-thermal model in terms of a twin thermal model with extra relativistic degrees of freedom can also be extended to models including a stochastic magnetic field. Numerical solutions are obtained for a range of magnetic field parameters.

Von Neumann lattices of Wannier functions for Bloch electrons in a magnetic field

1986 ◽  
Vol 403 (1824) ◽  
pp. 135-166 ◽  
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Periodic Function ◽  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Effective Hamiltonian ◽  
Hall Conductance ◽  
Von Neumann ◽  
Wannier Functions ◽  
Bloch Electrons

The problem of Bloch electrons in a magnetic field in two dimensions can be reduced to a one-dimensional problem with a Hamiltonian Ĥ that is a periodic function of x ^ and p ^ . Wannier functions can be defined for the sub-bands of the spectrum of this effective Hamiltonian. When the Chern class (quantized Hall conductance integer) of the sub-band is zero, the Weyl-Wigner formalism can be used to represent these Wannier functions by a von Neumann lattice. It is shown how this von Neumann lattice of Wannier functions can be defined for irrational as well as rational magnetic fields. An important benefit from using the Weyl-Wigner formalism is that symmetries of the periodic potential are reflected by symmetries of the effective Hamiltonian in phase space. It is shown how the Wannier functions can be defined so that their Wigner functions have the point symmetries of the effective Hamiltonian. An example of how these results can prove useful is given: if we take matrix elements of the Hamiltonian between the Wannier states of a sub-band, we derive a new effective Hamiltonian describing this sub-band, which is again a periodic function of coordinate and momentum operators. Since, by projecting onto a sub-band, we have also reduced the number of degrees of freedom, this operation is a renormalization group transformation. It is shown that the symmetry of the new effective Hamil­tonian in phase space is the same as that of the original one. This preservation of symmetry helps to explain some unusual properties of the spectrum when the Hamiltonian has fourfold symmetry.

scholarly journals Turbulent power distribution in the local interstellar medium

2019 ◽  
Vol 627 ◽  
pp. A112 ◽  
Author(s):  
P. M. W. Kalberla ◽  
U. Haud
Keyword(s):  
Phase Transitions ◽  
Phase Space ◽  
Interstellar Medium ◽  
Power Distribution ◽  
Single Channel ◽  
Power Spectra ◽  
Hierarchical Structures ◽  
Space Distribution ◽  
Neutral Medium ◽  
Highly Correlated

Context. The interstellar medium (ISM) on all scales is full of structures that can be used as tracers of processes that feed turbulence. Aims. We used H I survey data to derive global properties of the angular power distribution of the local ISM. Methods. HI4PI observations on an nside = 1024 HEALPix grid and Gaussian components representing three phases, the cold, warm, and unstable lukewarm neutral medium (CNM, WNM, and LNM), were used for velocities |vLSR|≤ 25 km s−1. For high latitudes |b| > 20° we generated apodized maps. After beam deconvolution we fitted angular power spectra. Results. Power spectra for observed column densities are exceptionally well defined and straight in log-log presentation with 3D power law indices γ ≥−3 for the local gas. For intermediate velocity clouds (IVCs) we derive γ = −2.6 and for high velocity clouds (HVCs) γ = −2.0. Single-phase power distributions for the CNM, LNM, and WNM are highly correlated and shallow with γ ~−2.5 for multipoles l ≤ 100. Excess power from cold filamentary structures is observed at larger multipoles. The steepest single-channel power spectra for the CNM are found at velocities with large CNM and low WNM phase fractions. Conclusions. The phase space distribution in the local ISM is configured by phase transitions and needs to be described with three distinct different phases, being highly correlated but having distributions with different properties. Phase transitions cause locally hierarchical structures in phase space. The CNM is structured on small scales and is restricted in position-velocity space. The LNM as an interface to the WNM envelops the CNM. It extends to larger scales than the CNM and covers a wider range of velocities. Correlations between the phases are self-similar in velocity.

scholarly journals Tracing Primordial Magnetic Fields with 21 cm Line Observations

Galaxies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 37 ◽  
Author(s):  
Kerstin Kunze
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Cosmic Microwave Background ◽  
Large Scale ◽  
Numerical Solutions ◽  
Gaussian Random Field ◽  
Microwave Background ◽  
Matter Power Spectrum ◽  
Primordial Magnetic Fields ◽  
The Universe

Magnetic fields are observed on a large range of scales in the universe. Up until recently, the evidence always pointed to magnetic fields associated with some kind of structure, from planets to clusters of galaxies. Blazar observations have been used to posit the first evidence of truly cosmological magnetic fields or void magnetic fields. A cosmological magnetic field generated in the very early universe before recombination has implications for the cosmic microwave background (CMB), large scale structure as well as the 21 cm line signal. In particular, the Lorentz term causes a change in the linear matter power spectrum. Its implication on the 21 cm line signal was the focus of our recent simulations which will be summarised here. Modelling the cosmological magnetic field as a gaussian random field numerical solutions were found for magnetic fields with present day amplitudes of 5 nG and negative spectral indices which are within the range of observational constraints imposed by the cosmic microwave background (CMB).

Stochastic magnetic field generation in MHD resistive instabilities: validity limits of linear stability analysis

1988 ◽  
Vol 40 (3) ◽  
pp. 419-440 ◽  
Author(s):  
Marco Pettini ◽  
Guidetta Torricelli-Ciamponi
Keyword(s):  
Magnetic Field ◽  
Explicit Expression ◽  
Degrees Of Freedom ◽  
Analytical Form ◽  
Magnetic Field Generation ◽  
Stochasticity Threshold ◽  
Field Lines ◽  
Spatial Stochasticity ◽  
Stochastic Magnetic Field ◽  
The Magnetic Field

This paper aims at determining the validity limits of a linear analysis for a resistive instability. To this purpose, the effects of mode-coupling on the magnetic field structure are investigated in the reconnecting layer. Given an equilibrium magnetic field and a perturbation field, the conditions are found under which the equations for the magnetic field lines of force can be expressed in Hamiltonian form. These conditions can be fulfilled by a resistive instability. Consequently, in a simple equilibrium magnetic field the resistive eigenmodes have been analytically derived. This result is used to give an explicit expression of the Hamiltonian for field-line equations when two resistive eigenmodes are taken into account. The analytical form of the resulting Hamiltonian coincides with the so-called paradigm Hamiltonian (1·5 degrees of freedom) for which the Escande–Doveil renormalization procedure leads to an explicit expression for the global stochasticity threshold. Thus it can be shown that any pair of modes – in a suitable range of parameters – yields spatial stochasticity of magnetic field lines when the perturbation amplitude is still very low. Hence a limit of validity of the linear theory can be found. The linear phase of the resistive instability turns out to be relevant only to describe the onset of the instability itself.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Stochastic magnetic field lines diffusion in a toroidal configuration (Tokamak)

2000 ◽  
Vol 12 (2) ◽  
pp. 145-153 ◽  
Author(s):  
R. Tabet ◽  
H. Imrane ◽  
D. Saifaoui ◽  
A. Dezairi ◽  
F. Miskane
Keyword(s):  
Magnetic Field ◽  
Field Lines ◽  
Stochastic Magnetic Field

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

scholarly journals The halo model as a versatile tool to predict intrinsic alignments

2020 ◽  
Author(s):  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Benjamin Joachimi ◽  
Harry Johnston ◽  
Nora Elisa Chisari ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Power Spectra ◽  
Stage Iv ◽  
Stage Iii ◽  
Radial Dependence ◽  
Additional Parameter ◽  
Small Scales ◽  
Cosmic Shear ◽  
Galaxy Populations ◽  
The Impact

Abstract Intrinsic alignments (IAs) of galaxies are an important contaminant for cosmic shear studies, but the modelling is complicated by the dependence of the signal on the source galaxy sample. In this paper, we use the halo model formalism to capture this diversity and examine its implications for Stage-III and Stage-IV cosmic shear surveys. We account for the different IA signatures at large and small scales, as well for the different contributions from central/satellite and red/blue galaxies, and we use realistic mocks to account for the characteristics of the galaxy populations as a function of redshift. We inform our model using the most recent observational findings: we include a luminosity dependence at both large and small scales and a radial dependence of the signal within the halo. We predict the impact of the total IA signal on the lensing angular power spectra, including the current uncertainties from the IA best-fits to illustrate the range of possible impact on the lensing signal: the lack of constraints for fainter galaxies is the main source of uncertainty for our predictions of the IA signal. We investigate how well effective models with limited degrees of freedom can account for the complexity of the IA signal. Although these lead to negligible biases for Stage-III surveys, we find that, for Stage-IV surveys, it is essential to at least include an additional parameter to capture the redshift dependence.

Sign in / Sign up

Export Citation Format

Share Document