S. S. Hasan

Dynamics of the Solar Magnetic Network. II. Heating the Magnetized Chromosphere

We consider recent observations of the chromospheric network and argue that the bright network grains observed in the Ca II H and K lines are heated by an as-yet-unidentified quasi-steady process. We propose that the heating is caused by dissipation of short-period magnetoacoustic waves in magnetic flux tubes (periods less than 100 s). Magnetohydrodynamic (MHD) models of such waves are presented. We consider wave generation in the network due to two separate processes: (1) transverse motions at the base of the flux tube and (2) the absorption of acoustic waves generated in the ambient medium. We find that the former mechanism leads to efficient heating of the chromosphere by slow magnetoacoustic waves propagating along magnetic field lines. This heating is produced by shock waves with a horizontal size of a few hundred kilometers. In contrast, acoustic waves excited in the ambient medium are converted into transverse fast modes that travel rapidly through the flux tube and do not form shocks, unless the acoustic sources are located within 100 km from the tube axis. We conclude that the magnetic network may be heated by magnetoacoustic waves that are generated in or near the flux tubes.

Dynamics of the Solar Magnetic Network: Two-dimensional MHD Simulations

The aim of this work is to identify the physical processes that occur in the network and contribute to its dynamics and heating. We model the network as consisting of individual flux tubes, each with a nonpotential field structure, that are located in intergranular lanes. With a typical horizontal size of about 150 km at the base of the photosphere, they expand upward and merge with their neighbors at a height of about 600 km. Above a height of approximately 1000 km the magnetic field starts to become uniform. Waves are excited in this medium by means of motions at the lower boundary. We focus on transverse driving, which generates both fast and slow waves within a flux tube and acoustic waves at the interface of the tube and the ambient medium. The acoustic waves at the interface are due to compression of the gas on one side of the flux tube and expansion on the other. These longitudinal waves are guided upward along field lines at the two sides of the flux tube, and their amplitude increases with height due to the density stratification. Being acoustic in nature, they produce a compression and significant shock heating of the plasma in the chromospheric part of the flux tube. For impulsive excitation with a time constant of 120 s, we find that a dominant feature of our simulations is the creation of vortical motions that propagate upward. We have identified an efficient mechanism for the generation of acoustic waves at the tube edge, which is a consequence of the sharp interface of the flux concentration. We examine some broad implications of our results.

KINK AND LONGITUDINAL OSCILLATIONS IN THE MAGNETIC NETWORK ON THE SUN: NONLINEAR EFFECTS AND MODE TRANSFORMATION

We examine the propagation of kink and longitudinal waves in the solar magnetic network. Previously, we investigated the excitation of network oscillations in vertical magnetic flux tubes through buffeting by granules and found that footpoint motions of the tubes can generate sufficient wave energy for chromospheric heating. We assumed that the kink and longitudinal waves are decoupled and linear. We overcome these limitations by treating the nonlinear MHD equations for coupled kink and longitudinal waves in a thin flux tube. For the parameters we have chosen, the thin tube approximation is valid up to the layers of formation of the emission features in the H and K lines of Ca II, at a height of about 1 Mm. By solving the nonlinear, time-dependent MHD equations we are able to study the onset of wave coupling, which occurs when the Mach number of the kink waves is of the order of 0.3. We also investigate the transfer of energy from the kink to the longitudinal waves, which is important for the dissipation of the wave energy in shocks. We find that kink waves excited by footpoint motions of a flux tube generate longitudinal modes by mode coupling. For subsonic velocities, the amplitude of a longitudinal wave increases as the square of the amplitude of the transverse wave, and for amplitudes near Mach number unity, the coupling saturates and becomes linear when the energy is nearly evenly divided between the two modes.

Three-dimensional Simulations of Magnetohydrodynamic Waves in Magnetized Solar Atmosphere

We present results of three-dimensional numerical simulations of magnetohydrodynamic (MHD) wave propagation in a solar magnetic flux tube. Our study aims at understanding the properties of a range of MHD wave modes generated by different photospheric motions. We consider two scenarios observed in the lower solar photosphere, namely, granular buffeting and vortex-like motion, among the simplest mechanism for the generation of waves within a strong, localized magnetic flux concentration. We show that granular buffeting is likely to generate stronger slow and fast magnetoacoustic waves as compared to swirly motions. Correspondingly, the energy flux transported differs as a result of the driving motions. We also demonstrate that the waves generated by granular buffeting are likely to manifest in stronger emission in the chromospheric network. We argue that different mechanisms of wave generation are active during the evolution of a magnetic element in the intergranular lane, resulting in temporally varying emission at chromospheric heights.

Wave propagation and energy transport in the magnetic network of the Sun

Aims. We investigate wave propagation and energy transport in magnetic elements, which are representatives of small scale magnetic flux concentrations in the magnetic network on the Sun. This is a continuation of earlier work by Hasan et al. (2005, ApJ, 631, 1270). The new features in the present investigation include a quantitative evaluation of the energy transport in the various modes and for different field strengths, as well as the effect of the boundary-layer thickness on wave propagation. Methods. We carry out 2D MHD numerical simulations of magnetic flux concentrations for strong and moderate magnetic fields for which β (the ratio of gas to magnetic pressure) on the tube axis at the photospheric base is 0.4 and 1.7, respectively. Waves are excited in the tube and ambient medium by a transverse impulsive motion of the lower boundary. Results. The nature of the modes excited depends on the value of β. Mode conversion occurs in the moderate field case when the fast mode crosses the β = 1 contour. In the strong field case the fast mode undergoes conversion from predominantly magnetic to predominantly acoustic when waves are leaking from the interior of the flux concentration to the ambient medium. We also estimate the energy fluxes in the acoustic and magnetic modes and find that in the strong field case, the vertically directed acoustic wave fluxes reach spatially averaged, temporal maximum values of a few times 10 6 erg cm −2 s −1 at chromospheric height levels. Conclusions. The main conclusions of our work are twofold: firstly, for transverse, impulsive excitation, flux tubes/sheets with strong fields are more efficient than those with weak fields in providing acoustic flux to the chromosphere. However, there is insufficient energy in the acoustic flux to balance the chromospheric radiative losses in the network, even for the strong field case. Secondly, the acoustic emission from the interface between the flux concentration and the ambient medium decreases with the width of the boundary layer.

Probing the internal magnetic field of slowly pulsating B-stars through g modes

modes often occur in multiplets with closely spaced periods (with a typical separation of 1%). In some cases this separation can clearly not be due to rotational splitting, which would yield much larger spacings, as was pointed out by De Cat and Aerts (2002). In this letter we propose that such frequency splitt ings are due to the presence of a magnetic field. If this hypothesis is correct, then the splitting of frequencies can be used to e stimate the field strength in the interior of SPB stars.

Dynamics and heating of the magnetic network on the Sun - Efficiency of mode transformation

We aim to identify the physical processes which occur in the magnetic network of the chromosphere and which contribute to its dynamics and heating. Specifically, we study the propagation of transverse (kink) MHD waves which are impulsively excited in flux tubes through footpoint motions. When these waves travel upwards, they get partially converted to longitudinal waves through nonlinear effects (mode coupling). By solving the nonlinear, time-dependent MHD equations we find that significant longitudinal wave generation occurs in the photosphere typically for Mach numbers as low as 0.2 and that the onset of shock formation occurs at heights of about 600 km above the photospheric base. We also investigate the compressional heating due to longitudinal waves and the efficiency of mode coupling for various values of the plasma β ,t hat parameterises the magnetic field strength in the network. We find that this efficiency is maximum for field strengths correspond- ing to β ≈ 0.2, when the kink and tube wave speeds are almost identical. This can have interesting observational implications. Furthermore, we find that even when the two speeds are different, once shock formation occurs, the longitudinal and transverse shocks exhibit strong mode coupling.

OBSERVATIONS AND MODELING OF THE EMERGING EXTREME-ULTRAVIOLET LOOPS IN THE QUIET SUN AS SEEN WITH THE SOLAR DYNAMICS OBSERVATORY

We used data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) to study coronal loops at small scales, emerging in the quiet Sun. With HMI line-of-sight magnetograms, we derive the integrated and unsigned photospheric magnetic flux at the loop footpoints in the photosphere. These loops are bright in the EUV channels of AIA. Using the six AIA EUV filters, we construct the differential emission measure (DEM) in the temperature range 5.7-6.5 in log T (K) for several hours of observations. The observed DEMs have a peak distribution around log T ≈ 6.3, falling rapidly at higher temperatures. For log T < 6.3, DEMs are comparable to their peak values within an order of magnitude. The emission-weighted temperature is calculated, and its time variations are compared with those of magnetic flux. We present two possibilities for explaining the observed DEMs and temperatures variations. (1) Assuming that the observed loops are composed of a hundred thin strands with certain radius and length, we tested three time-dependent heating models and compared the resulting DEMs and temperatures with the observed quantities. This modeling used enthalpy-based thermal evolution of loops (EBTEL), a zero-dimensional (0D) hydrodynamic code. The comparisons suggest that a medium-frequency heating model with a population of different heating amplitudes can roughly reproduce the observations. (2) We also consider a loop model with steady heating and non-uniform cross-section of the loop along its length, and find that this model can also reproduce the observed DEMs, provided the loop expansion factor γ ~ 5-10. More observational constraints are required to better understand the nature of coronal heating in the short emerging loops on the quiet Sun.

Modulation in the solar irradiance due to surface magnetism during cycles 21, 22 and 23

Magnetic field indices derived from synoptic magnetograms of the Mt. Wilson Observatory, i.e. Magnetic Plage Strength Index (MPSI) and Mt. Wilson Sunspot Index (MWSI), are used to study the effects of surface magnetism on total solar irradiance variability during solar cycles 21, 22 and 23. We find that most of the solar cycle variation in the total solar irradiance can be accounted for by the absolute magnetic field strength on the solar disk, if fields associated with dark and bright regions are considered separately. However, there is a large scatter in the calculated and observed values of TSI during solar cycle 21. On the other hand, the multiple correlation coefficients obtained for solar cycles 22 and 23 are 0.88 and 0.91 respectively. Furthermore, separate regression analyses for solar cycles 22 and 23 do not show any significant differences in the total solar irradiance during these cycles. Our study further strengthens the view that surface magnetism indeed plays a dominant role in modulating solar irradiance.

Convective Intensification of Magnetic Flux Tubes in Stellar Photospheres

The convective collapse of thin magnetic flux tubes in the photospheres of Sun-like stars is investigated using realistic models of the superadiabatic upper convection zone layers of these stars. The strengths of convectively stable flux tubes are computed as a function of surface gravity and effective temperature. We find that while stars with Teff ≥ 5500 K and log g ≥ 4.0 show flux tubes highly evacuated of gas, and hence strong field strengths due to convective collapse, cooler stars exhibit flux tubes with lower field strengths. Observations reveal the existence of field strengths close to thermal equipartition limits even in cooler stars, implying highly evacuated tubes, for which we suggest possible reasons.