Nonlinear Force-Free Field Modeling of the Solar Magnetic Carpet and Comparison with SDO/HMI and Sunrise/IMaX Observations

In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet, which continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager (HMI) on the textit{Solar Dynamics Observatory} (textit{SDO}), and the Imaging Magnetograph eXperiment (IMaX) instrument on the textit{Sunrise} balloon-borne observatory, as time dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce time series of three-dimensional (3D) nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate, and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.

Observations and modeling of the emerging EUV loops in the quiet Sun as seen with the Solar Dynamics Observatory

We used data from the Helioseismic and Magnetic Imager (HMI), and Atmospheric Imaging Assembly (AIA) on the textit{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 $T approx$ 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. (a) Assuming the observed loops are comprised of 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. (b) 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 $gamma sim$ 5 - 10. More observational constraints are required to better understand the nature of coronal heating in the short emerging loops on the quiet Sun.

Dynamics of the solar magnetic bright points derived from their horizontal motions

The sub-arcsec bright points (BP) associated with the small scale magnetic fields in the lower solar atmosphere are advected by the evolution of the photospheric granules. We measure various quantities related to the horizontal motions of the BPs observed in two wavelengths, including the velocity auto-correlation function. A 1 hr time sequence of wideband H$alpha$ observations conducted at the textit{Swedish 1-m Solar Telescope} (textit{SST}), and a 4 hr textit{Hinode} textit{G}-band time sequence observed with the Solar Optical telescope are used in this work. We follow 97 textit{SST} and 212 textit{Hinode} BPs with 3800 and 1950 individual velocity measurements respectively. For its high cadence of 5 s as compared to 30 s for textit{Hinode} data, we emphasize more on the results from textit{SST} data. The BP positional uncertainty achieved by textit{SST} is as low as 3 km. The position errors contribute 0.75 km$^2$ s$^{-2}$ to the variance of the observed velocities. The textit{raw} and textit{corrected} velocity measurements in both directions, i.e., $(v_x,v_y)$, have Gaussian distributions with standard deviations of $(1.32,1.22)$ and $(1.00, 0.86)$ km s$^{-1}$ respectively. The BP motions have correlation times of about $22 - 30$ s. We construct the power spectrum of the horizontal motions as a function of frequency, a quantity that is useful and relevant to the studies of generation of Alfven waves. Photospheric turbulent diffusion at time scales less than 200 s is found to satisfy a power law with an index of 1.59.