We introduced our preliminary results of chromospheric activity of late-type stars based on the stellar spectrum of the pilot survey of the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST, also called Guo Shou Jing telescope). We have found 1151 active M stars from 17471 M samples using the chromospheric active indicator of the Hα line.

Magnetic fields in our Galaxy and nearby galaxies have been revealed by starlight polarization, polarized emission from dust grains and clouds at millimeter and submillimeter wavelength, the Zeeman effect of spectral lines or maser lines from clouds or clumps, diffuse radio synchrotron emission from relativistic electrons in interstellar magnetic fields, and the Faraday rotation of background radio sources as well as pulsars for our Milky Way. It is easy to get a global structure for magnetic fields in nearby galaxies, while we have observed many details of magnetic fields in our Milky Way, especially by using pulsar rotation measure data. In general, magnetic fields in spiral galaxies probably have a large-scale structure. The fields follow the spiral arms with or without the field direction reversals. In the halo of spiral galaxies magnetic fields exist and probably also have a large-scale structure as toroidal and poloidal fields, but seem to be slightly weaker than those in the disk. In the central region of some galaxies, poloidal fields have been detected as vertical components. Magnetic field directions in galaxies seem to have been preserved during cloud formation and star formation, from large-scale diffuse interstellar medium to molecular clouds and then to the cloud cores in star formation regions or clumps for the maser spots. Magnetic fields in galaxies are passive to dynamics.

We review recent developments of amplification models of galactic and intergalactic magnetic field. The most popular scenarios involve variety of physical mechanisms, including turbulence generation on a wide range of physical scales, effects of supernovae, buoyancy as well as the magnetorotational instability. Other models rely on galaxy interaction, which generate galactic and intergalactic magnetic fields during galaxy mergers. We present also global galactic-scale numerical models of the Cosmic Ray (CR) driven dynamo, which was originally proposed by Parker (1992). We conduct a series of direct CR+MHD numerical simulations of the dynamics of the interstellar medium (ISM), composed of gas, magnetic fields and CR components. We take into account CRs accelerated in randomly distributed supernova (SN) remnants, and assume that SNe deposit small-scale, randomly oriented, dipolar magnetic fields into the ISM. The amplification timescale of the large-scale magnetic field resulting from the CR-driven dynamo is comparable to the galactic rotation period. The process efficiently converts small-scale magnetic fields of SN-remnants into galactic-scale magnetic fields. The resulting magnetic field structure resembles the X-shaped magnetic fields observed in edge-on galaxies.

The first galaxies form due to gravitational collapse of primordial halos. During this collapse, weak magnetic seed fields get amplified exponentially by the small-scale dynamo - a process converting kinetic energy from turbulence into magnetic energy. We use the Kazantsev theory, which describes the small-scale dynamo analytically, to study magnetic field amplification for different turbulent velocity correlation functions. For incompressible turbulence (Kolmogorov turbulence), we find that the growth rate is proportional to the square root of the hydrodynamic Reynolds number, Re1/2. In the case of highly compressible turbulence (Burgers turbulence) the growth rate increases proportional to Re1/3. With a detailed chemical network we are able to follow the chemical evolution and determine the kinetic and magnetic viscosities (due to Ohmic and ambipolar diffusion) during the collapse of the halo. This way, we can calculate the growth rate of the small-scale dynamo quantitatively and predict the evolution of the small-scale magnetic field. As the magnetic energy is transported to larger scales on the local eddy-timescale, we obtain an estimate for the magnetic field on the Jeans scale. Even there, we find that equipartition with the kinetic energy is reached on small timescales. Dynamically relevant field structures can thus be expected already during the formation of the first objects in the Universe.

The theory of mean-field galactic dynamos is generalized by allowing for a finite response time of the mean electromotive force (emf) to variations in the mean magnetic field and small-scale turbulence. A non-axisymmetric forcing of the dynamo by a spiral pattern (either stationary or transient) is invoked. The resulting magnetic spiral arms are phase-shifted from the spiral arms of the pattern by an angle 15°–40°, opposite to the sense of galactic rotation. Our findings may help to explain the phase shift between material and magnetic arms observed in NGC 6946 and other galaxies.

During an active star formation phase, it is conceivable that the turbulent level of a galaxy increases and consequently an increase in magnetic field by turbulent dynamo process. We point out that the thickness of the dynamo region is sensitive to the turbulent level. We examine the linear growth rate of three different dynamos, namely, αω, α2ω and α2 dynamos. We find that the dependence of the growth rate on turbulent level is quite different for different dynamos. Moreover, the growth rate is not necessary monotonic to turbulence level even in the linear regime.

H-band (1.6 μm) starlight polarimetry was used to test predictions of the large-scale symmetry of the Galactic magnetic field and to measure the Galactic magnetic pitch angle. Polarimetry was obtained with the Mimir instrument on the 1.8m Perkins Telescope outside of Flagstaff, AZ USA along a line of constant Galactic longitude for a range of Galactic latitudes. Comparison with all-sky predictions of starlight polarimetry allows significant rejection of disk anti-symmetric Galactic magnetic field geometries and favored disk symmetric geometries. The Galactic magnetic field pitch angle was also constrained to be p=–6±2° towards this direction.

I review the currently available techniques for the starspots detection including the one-dimensional spot modelling of photometric light curves. Special attention will be paid to the modelling of photospheric activity based on the high-precision light curves obtained with space missions MOST, CoRoT, and Kepler. Physical spot parameters (temperature, sizes and variability time scales including short-term activity cycles) are discussed.

Spontaneous formation of self-organized magnetic structures, such as sunspots and pores, is one of intriguing and oldest problems, which represents a complicated interaction of convection and magnetic fields on different scales. Observations of sunspots and pores formation reveal a fast process of accumulation of emerging magnetic field into stable long-living magnetic structures. However, the physical mechanisms of the flux accumulation into the compact magnetic structures with high field strength and their stability are not clear. Development of observational capabilities, theory, and realistic-type MHD numerical simulations open a new level of our understanding of the turbulent processes of the magnetic field accumulation. I discuss the recent progress in observations and radiative MHD simulations that provide important clues for possible mechanisms of formation and stability of sunspots and pores, and their links to the dynamo process.

We present preliminary results from high resolution magneto-convection simulations where we find the formation of flux concentrations from an initially uniform magnetic field. The structures appear in roughly ten convective turnover times and live close to a turbulent diffusion time. The time scales are compatible with the negative effective magnetic pressure instability (NEMPI), although structure formation is not restricted to regions where the effective magnetic pressure is negative.

An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this talk, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.

Magnetic helicity (volume integral of the product of the magnetic field vector B and the vector potential A), or its proxy, the current helicity at the surface (surface integral of B·J or BzJz), is an important quantity which characterizes the helical nature of solar magnetic fields. The current helicity on the Sun shows a tendency, though with large dispersion, that it is positive in the southern hemisphere and negative in the northern hemisphere (the helicity sign rule). However, there are indications that the helicity sign rule may be reversed at activity minimum periods. We will discuss the significance of this property by focusing on the statistical distributions of helicity whether its dispersion follows Gaussian distribution or not.

We present results of convective turbulent dynamo simulations including a coronal layer in a spherical wedge. We find an equatorward migration of the radial and azimuthal fields similar to the behavior of sunspots during the solar cycle. The migration of the field coexist with a spoke-like differential rotation and anti-solar (clockwise) meridional circulation. Even though the migration extends over the whole convection zone, the mechanism causing this is not yet fully understood.

We investigate to what extent the current helicity distribution observed in solar active regions is compatible with solar dynamo models. We use an advanced 2D mean-field dynamo model with dynamo action largely concentrated near the bottom of the convective zone, and dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtain butterfly diagrams for both the small-scale current helicity and the large-scale magnetic helicity, and compare them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by −A·B evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here B and A are respectively the dynamo generated mean magnetic field and its vector potential.

Magnetic helicity can be transported from sub-photosphere into corona by the emergence of helical magnetic field lines and the shuffling motions of foot-points of pre-existing coronal field lines. Active region NOAA 10930 was observed by SP and NFI of SOT on board Hinode when it pass through the solar meridian. Based on these observations, we calculate magnetic helicity flow of both terms, by regarding Doppler velocity as normal velocity. The results are compared with which calculated by method proposed by Zhang et. al. (2012). Our results show that helicity injection maps calculated by both methods have similar distribution and the integration values have the same magnitude.

Movement and coalescence of magnetic elements could explain the evolution and growth of pores. There have been numerous studies focusing on flow fields in and around individual pores. We have undertaken a systematic study of the statistical properties of such flows. Data of the Hinode Solar Optical Telescope offer an opportunity for this type of research, because of the uniform data quality and absence of seeing so that pores can directly be compared in different environments and at various stages of their evolution. We analyzed about 220 time-series of G-band images using local correlation tracking. The thus computed flow maps make up a database, which covers various scenes on the solar surface. We use an isolated pore to illustrate the statistical parameters collected for further statistical analyses, which include information about morphology, horizontal flows, evolutionary stage (young, mature, or decaying), complexity of the surrounding magnetic field, and proximity to sunspots or cluster of G-band bright points.

Magnetohydrodynamic (MHD) turbulence is a critical component of the current paradigms of star formation, dynamo theory, particle transport, magnetic reconnection and evolution of the ISM. In order to gain understanding of how MHD turbulence regulates processes in the Galaxy, a confluence of numerics, observations and theory must be imployed. In these proceedings we review recent progress that has been made on the connections between theoretical, numerical, and observational understanding of MHD turbulence as it applies to both the neutral and ionized interstellar medium.

The role of turbulence in astrophysical environments and its interplay with magnetic fields is still highly debated. In this lecture, we will discuss this issue in the framework of dynamo processes. We will first present a very brief summary of turbulent dynamo theories, then will focus on small scale turbulent dynamos and their particular relevance on the origin and maintenance of magnetic fields in the intra-cluster media (ICM) of galaxies. In these environments, the very low density of the flow requires a collisionless-MHD treatment. We will show the implications of this approach in the turbulent amplification of the magnetic fields in these environments. To finalize, we will also briefly address the connection between MHD turbulence and fast magnetic reconnection and its possible implications in the diffusion of magnetic flux in the dynamo process.

The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations and suggests that the detailed structure of turbulent MHD boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.

Magnetic field relaxation is determined by both the field's geometry and its topology. For relaxation processes, however, it turns out that its topology is a much more stringent constraint. As quantifier for the topology we use magnetic helicity and test whether it is a stronger condition than the linking of field lines. Further, we search for evidence of other topological invariants, which give rise to further restrictions in the field's relaxation. We find that magnetic helicity is the sole determinant in most cases. Nevertheless, we see evidence for restrictions not captured through magnetic helicity.