Large-scale magnetic fields from density perturbations

To investigate the relationship between solar activity and the large-scale axisymmetric magnetic field of the Sun, we inferred from sunspot data over the period 1964–1985 a latitude–time distribution of magnetic field associated with active regions. This has been done allowing for both bipolar structure of the active regions and inclination of their axes to parallels of latitude, so the inferred magnetic field characterizes latitudinal separation of magnetic polarities which might be related to the large-scale magnetic field of the Sun according to the Babcock–Leighton model. The inferred magnetic field, Az, is compared with the longitude-averaged (zonal) magnetic field of the Sun, Bz, derived from series of magnetograms obtained at Mount Wilson Observatory in the years 1964–1976, and at Kitt Peak National Observatory during the period from 1976 to 1985. The inferred magnetic field, Az, exhibits a complex structure distribution of magnetic polarities with respect to latitude and time. Apart from concentration of the different polarity magnetic fields inside the high- and low-latitude portions of the sunspot belts, bipolar active regions produce an intensive, shorter-scale component of the magnetic field which varies on the time scale of about 2 years. Such a short-term variation of Az reveals substantial correlation with the short-term component of Bz which has the form of the poleward-drifting streams of magnetic field. Most significant correlation takes place between the short-term variations of Az occurring at latitudes below 20° and those of the large-scale magnetic fields occurring at middle latitudes of 40–50°. Moreover we analyze harmonic coefficients al and bl obtained by expanding Az and Bz into series in terms of the spherical harmonics. Power spectra of the time-dependent harmonic coefficients indicate that both Az and Bz reveal a number of resonant modes which oscillate either with the 22-year period in the case of the anti-symmetric (odd-l) modes or with periods of about 2 years in the case of the symmetric (even-l) modes, but the resonant modes of Az have significantly larger values of the spherical harmonic degree l (and, hence, smaller spatial scales) as compared to those of Bz. It is found that there is a close relationship between the harmonic coefficients bl and am for which either m−l≈16 (even l=4,...,10) or m−l=4 (odd l=5,...,15).

Context. The Parker Solar Probe (PSP) is operational since 2018 and has provided invaluable new data that measure the solar vicinity in situ at smaller heliocentric distances than ever before. These data can be used to shed new light on the turbulent dynamics in the solar atmosphere and solar wind, which in turn are thought to be important to explain long-standing problems of the heating and acceleration in these regions. In recent years, it was realized that background inhomogeneities in magnetohydrodynamics could influence the development of turbulence and might enable other cascade channels, such as the self-cascade of waves, in addition to the well-known Alfvén collisional cascade. This phenomenon has been called uniturbulence. However, the precise influence of the background inhomogeneity on turbulent spectra has not been not studied so far. Aims. In this work, we study the influence of background roughness on the turbulent magnetic field spectrum in PSP data, including data from encounter 1 up to and including encounter 14. Methods. The magnetic spectral index αB receives our highest attention. Motivated by the presumably different turbulent dynamics in the presence of large-scale inhomogeneities, we searched for correlations between the magnetic power spectra and a measure for the degree of inhomogeneity. The latter was probed by taking the standard deviation (STD) of the total magnetic field magnitude after applying an appropriate averaging. The data of each PSP encounter were split into many short time windows, of which we subsequently calculated both αB and background STD. Results. We find a significant impact of the background STD on αB. As the variations in the background become stronger, αB becomes more negative, indicating a steepening of the magnetic power spectrum. We show that this effect is consistent in all investigated PSP encounters, and it is unaffected by heliocentric distance up to 50 R⊙. By making use of artificial magnetic field data in the form of synthetic colored noise, we show that this effect is not simply due to the fluctuations imposed on the total magnetic field, but must have another as yet unidentified cause. Conclusions. There is a strong indication that the background inhomogeneity affects the turbulent dynamics, possibly through uniturbulence. This leads to a different power spectrum in the presence of large-scale total magnetic field variations. The fact that it is present in all investigated encounters and at all radial distances up to 50 R⊙ suggests that it represents a general and ubiquitous feature of solar wind dynamics. The analysis with the synthetic colored noise indicates that the observed steepening effect is not to be attributed simply to the small-scale fluctuations superposed on the total magnetic field. This conclusion is confirmed by the fact that no similar consistent steepening trend is observed for the magnetic compressibility Cb instead of background STD. The steepening trend is instead a real physical effect induced by the large-scale variations in the background magnetic field.

We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field's effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, $\lambda_B$, and damped oscillations for scales smaller than $\lambda_B$. For small wavenumbers $k$ (large length scales), we find the magnetic field-induced density power spectrum generally scales as $k^4$. We derive the magnetic Jeans length explicitly by including the back--reaction of the velocity field onto the magnetic field by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present {\it rms} magnetic field of $10^{-10}$ G on intergalactic scales, we find that perturbations on galactic scales could have gone non--linear at $z \simeq 6$. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with non--baryonic dark matter.

We present a statistical study of the orientation of outflows with respect to large-scale filaments and magnetic fields. Although filaments are widely observed toward Galactic star-forming regions, the exact role of filaments in star formation is unclear. Studies toward low-mass star-forming regions revealed both preferred and random orientations of outflows with respect to the filament long axes, while outflows in massive star-forming regions are mostly oriented perpendicular to the host filaments and parallel to the magnetic fields at similar physical scales. Here, we explore outflows in a sample of 11 protoclusters in H ii regions, a more evolved stage compared to infared dark clouds, using Atacama Large Millimeter/submillimeter Array CO (3–2) line observations. We identify a total of 105 outflow lobes in these protoclusters. Among the 11 targets, 7 are embedded within parsec-scale filamentary structures detected in 13CO line and 870 μm continuum emissions. The angles between outflow axes and corresponding filaments (γ Fil) do not show any hint of preferred orientations (i.e., orthogonal or parallel as inferred in numerical models) with respect to the position angle of the filaments. Identified outflow lobes are also not correlated with the magnetic fields and Galactic plane position angles. Outflows associated with filaments aligned along the large-scale magnetic fields are also randomly oriented. Our study presents the first statistical results of outflow orientation with respect to large-scale filaments and magnetic fields in evolved massive star-forming regions. The random distribution suggests a lack of alignment of outflows with filaments, which may be a result of the evolutionary stage of the clusters.

Magnetic fields are an energetically important component of star formation galaxies, but it is often difficult to measure their properties from observations. One of the complexities stems from the fact that the magnetic fields, especially in spiral galaxies, have a two-scale nature: a large-scale field, coherent over kpc scales, and a small-scale random field, with a scale of ${\lesssim} 100 \, {\rm pc}$. Moreover, it is known that the strength of small- and large-scale fields is comparable and this makes it even harder to find their imprints in radio polarization observations such as the Faraday rotation measure (RM), which is the integral over the path-length of the product of the thermal electron density and the parallel component of the magnetic field to the line of sight. Here, we propose and demonstrate the use of second-order structure functions of RM computed with multiple higher-order stencils as a powerful analysis to separate the small- and large-scale magnetic field components. In particular, we provide new methods and calibrations to compute the scale and the strength of the large-scale magnetic field in the presence of small-scale magnetic fluctuations. We then apply the method to find the scale of large-scale magnetic fields in the nearby galaxies M51 and NGC 6946, using archival data, and further discuss the need for computing the RM structure functions with higher-order stencils. With multiple modern radio polarization observatories and eventually the Square Kilometre Array, RM observations will significantly improve in quantity and quality, and the higher-order stencil structure function techniques developed here can be used to extract information about multiscale magnetic fields in galaxies.

Context. Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. Aims. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Methods. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. Results. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50–350 MHz and 950–1760 MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARray 2.0 and the MeerKAT+ telescope. Conclusions. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediatefrequency radio telescopes make them the favourite instruments for the study of these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.

Aims. The goal of this study is to investigate the small-scale magnetic fields of the two spectroscopic binary T Tauri stars V1878 Ori and V4046 Sgr. This is done to complete the observational characterisation of the surface magnetic fields of these stars because only their large-scale magnetic fields have been studied with Zeeman Doppler imaging (ZDI) so far. Methods. To investigate the small-scale magnetic fields, the differential Zeeman intensification of near-infrared Ti I lines was investigated using high-resolution archival spectra obtained with the ESPaDOnS spectrograph at the CFHT. In order to study the binary components separately, the spectra were disentangled by considering observations taken at different orbital phases. The Zeeman-intensification analysis was performed based on detailed polarised radiative transfer calculations aided by the Markov chain Monte Carlo inference, treating magnetic field filling factors and other stellar parameters that could affect the spectra as free parameters. Results. The obtained average magnetic field strengths of the components of V1878 Ori are 1.33 ± 0.08 and 1.57 ± 0.09 kG, respectively. Previous ZDI studies of V1878 Ori recovered about 14 and 20% of this total magnetic field strength. For V4046 Sgr, the magnetic field strengths are 1.96 ± 0.18 and 1.83 ± 0.18 kG, respectively. In this case, about 12 and 9% of the total magnetic field strength was detected by ZDI. Conclusions. The small-scale magnetic field strengths obtained from Zeeman intensification are similar for the two components of each binary. This is in contrast to the large-scale magnetic fields obtained from ZDI investigations, performed using the same observations, which found that magnetic field strengths and topologies vary significantly in the components of the two binaries. While the large-scale field might look significantly different, the overall magnetic energy, primarily carried by the small-scale magnetic fields, appears to be quite similar. This indicates that the efficiency of the magnetic dynamo is comparable for the components of the two binaries.

Large-scale magnetic fields and anomalies of chemical composition of stellar coronae

We study the production of large-scale (\ensuremath{\sim}Mpc) magnetic fields in inflationary Universe models. The magnetic fields produced are uninterestingly small unless the conformal invariance of the electromagnetic field is broken. Once the conformal invariance is broken, a mechanism akin to ``superadiabatic amplification'' can operate and lead to sizable primeval magnetic fields. We consider three ways of breaking the conformal invariance: through gravitational couplings of the photon; through the coupling of the photon to a charged massless, nonconformally invariant scalar field; and through the anomalous coupling of the photon to axions. The primeval magnetic fields which result can have astrophysically interesting strengths, but are very model dependent.

Energetic astrophysical jets have always been associated with relatively strong large-scale magnetic fields that extract energy from the rotation of a central black hole and its surrounding accretion disk. This natural association does not answer the fundamental question what is the origin of the large-scale magnetic field. When the disk is non-diffusive, standard MHD advection can bring the field in from large distances, as attested by the multitude of ideal MHD simulations of magnetized astrophysical accretion disks. When this is not the case, however, the large-scale dipolar magnetic field expected at the origin of astrophysical jets is generated naturally by the anisotropic radiation pressure around the central black hole. In this Chapter, we discuss the scenario where the innermost part of the accretion disk generates and holds one polarity of the magnetic field, while the return polarity diffuses outward through the outer diffusive part of the disk. This is the Cosmic Battery first proposed by Contopoulos and Kazanas in 1998.

We use direct numerical simulations to investigate the energy pathways between the velocity and the magnetic fields in a rotating plane layer dynamo driven by Rayleigh–Bénard convection. The kinetic and magnetic energies are divided into mean and turbulent components to study the production, transport and dissipation in large- and small-scale dynamos. This energy balance-based characterisation reveals distinct mechanisms for large- and small-scale magnetic field generation in dynamos, depending on the nature of the velocity field and the conditions imposed at the boundaries. The efficiency of a dynamo in converting the kinetic energy to magnetic energy, apart from the energy redistribution inside the domain, is found to depend on the kinematic and magnetic boundary conditions. In a small-scale dynamo with a turbulent velocity field, the turbulent kinetic energy converts to turbulent magnetic energy via small-scale magnetic field stretching. This term also represents the amplification of the turbulent magnetic energy due to work done by stretching the small-scale magnetic field lines owing to fluctuating velocity gradients. The stretching of the large-scale magnetic field plays a significant role in this energy conversion in a large-scale turbulent dynamo, leading to a broad range of energetic scales in the magnetic field compared with a small-scale dynamo. This large-scale magnetic field stretching becomes the dominant mechanism of magnetic energy generation in a weakly nonlinear dynamo. We also find that, in the weakly nonlinear dynamo, an upscale energy transfer from the small-scale magnetic field to the large-scale magnetic field occurs owing to the presence of a gradient of the mean magnetic field.

The growth of density contrasts of collisionless particles and nucleonic matter is pursued from the decoupling era up to the present in the Newtonian mechanics. The negative density perturbation of collisionles particles grows quickly to the void and surrounding ridge. Meanwhile, the shell-crossing occurs. The nucleonic matter, which is set uniformly at the decoupling epoch, is enforced to concentrate into the ridge by the gravitational force at this shell-crossing epoch. At the same time, the temperature of nucleonic matter increases rapidly due to the dissipation of kinetic energy by the pressure force. The dependence of results upon the amplitude of the initial density perturbation is made clear. If the galaxies were formed after the shell-crossing, the initial amplitude of density perturbation of collisionless particles must be higher than 0.03 in the Einstein-de Sitter universe. Through the analysis of gravitational instability of ridges, a possible scenario for the formation of the large-scale structure of the universe within the adiabatic theory is presented.

Magnetic fields play a crucial role throughout stellar evolution in regulating angular momentum, channelling accretion, and launching jets and outflows. While the magnetic properties of classical T Tauri stars (CTTSs) have been extensively characterised, those of their progenitors, Class I and flat-spectrum (FS) protostars, remain poorly constrained due to their embedded nature, which provides an observational challenge. Our aim was to detect and characterise the large-scale magnetic fields in a sample of Class I and FS protostars. These young stars are expected to host strong magnetic fields generated by dynamo processes in their largely convective interiors. We have used SPIRou, a high-resolution spectropolarimeter working in the near-infrared domain, to analyse the polarised light of Class I and FS protostars. We used the least-squares deconvolution (LSD) technique to perform the magnetic analysis and measure the longitudinal magnetic fields from circularly polarised Stokes V profiles. We report new large-scale magnetic field detections in five FS protostars. Including the previous detection of the large-scale magnetic-field in the V347 Aur FS-protostar, 40% of our final sample of 15 protostars is confirmed to be magnetic. These magnetic stars show clear Zeeman signatures, with longitudinal field strengths ranging from ∼80 to ∼200 G in absolute value. The remaining stars exhibit no detectable Stokes V signature, but the estimated upper limits on a hidden dipolar field range from 500 G to more than 5 kG. For stars in which no magnetic fields are detected, it is still conceivable that a magnetic field exists, but is intrinsically weak, highly complex and dominated by small-scale structures, or cancelled out in integrated spectropolarimetric signals due to opposing polarities. We show that Class I and FS protostars can host large-scale magnetic fields with strengths that may be weaker than in more evolved CTTSs. This supports the idea that magnetic processes are already active during the main accretion phase and may influence star--disk interactions from the earliest stages.