The physics of twisted magnetic tubes rising in a stratified medium: two dimensional results

The physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical MHD code. The problem considered is fully compressible (no Boussinesq approximation), includes ohmic resistivity, and is two dimensional, i.e., there is no variation of the variables in the direction of the tube axis. We study a high plasma beta case with small ratio of radius to external pressure scaleheight. The results obtained can therefore be of relevance to understand the transport of magnetic flux across the solar convection zone.Comment: To be published in ApJ, Vol. 492, Jan 10th, 1998; 25 pages, 16 figures. NEW VERSION: THE PREVIOUS ONE DIDN'T PRINT CORRECTLY. The style file overrulehere.sty is include

Turbulent Erosion of Magnetic Flux Tubes

Results from a numerical and analytical investigation of the solution of a nonlinear axially symmetric diffusion equation for the magnetic field are presented for the case when the nonlinear dependence of the diffusivity nu(B) on the magnetic field satisfies basic physical requirements. We find that for sufficiently strong nonlinearity (i.e. for sufficiently strong reduction of nu inside the tube) a current sheet is spontaneously formed around the tube within one diffusion timescale. This sheet propagates inwards with a velocity inversely proportional to the ratio of the field strength just inside the current sheet to the equipartition field strength B0/Be, so the lifetime of a tube with constant internal flux density is increased approximately by a factor not exceeding B0/Be, even for infinitely effective inhibition of turbulence inside the tube. Among the applications of these results we point out that toroidal flux tubes in the solar convective zone are subject to significant flux loss owing to turbulent erosion on a timescale of about 1 month, and that turbulent erosion may be responsible for the formation of a current sheet around a sunspot. It is further proposed that, despite the simplifying assumptions involved, our solutions correctly reflect the essential features of the sunspot decay process.Comment: 17 pages, 11 figure

The power spectrum of solar convection flows from high-resolution observations and 3D simulations

We compare Fourier spectra of photospheric velocity fields from very high resolution IMaX observations to those from recent 3D numerical magnetoconvection models. We carry out a proper comparison by synthesizing spectral lines from the numerical models and then applying to them the adequate residual instrumental degradation that affects the observational data. Also, the validity of the usual observational proxies is tested by obtaining synthetic observations from the numerical boxes and comparing the velocity proxies to the actual velocity values from the numerical grid. For the observations, data from the SUNRISE/IMaX instrument with about 120 km spatial resolution are used, thus allowing the calculation of observational Fourier spectra well into the subgranular range. For the simulations, we use four series of runs obtained with the STAGGER code and synthesize the IMaX spectral line (FeI 5250.2 A) from them. Proxies for the velocity field are obtained via Dopplergrams (vertical component) and local correlation tracking (horizontal component). A very good match between observational and simulated Fourier power spectra is obtained for the vertical velocity data for scales between 200 km and 6 Mm. Instead, a clear vertical shift is obtained when the synthetic observations are not degraded. The match for the horizontal velocity data is much less impressive because of the inaccuracies of the LCT procedure. Concerning the internal comparison of the direct velocity values of the numerical boxes with those from the synthetic observations, a high correlation (0.96) is obtained for the vertical component when using the velocity values on the log($tau_{500}$) = -1 surface in the box. The corresponding Fourier spectra are near each other. A lower maximum correlation (0.5) is reached (at $tau_{500}$ = 1) for the horizontal velocities as a result of the coarseness of the LCT procedure.Comment: 12 pages, 9 figures, accepted in A&

Solar Fe abundance and magnetic fields - Towards a consistent reference metallicity

We investigate the impact on Fe abundance determination of including magnetic flux in series of 3D radiation-MHD simulations of solar convection which we used to synthesize spectral intensity profiles corresponding to disc centre. A differential approach is used to quantify the changes in theoretical equivalent width of a set of 28 iron spectral lines spanning a wide range in lambda, excitation potential, oscillator strength, Land\'e factor, and formation height. The lines were computed in LTE using the spectral synthesis code LILIA. We used input magnetoconvection snapshots covering 50 minutes of solar evolution and belonging to series having an average vertical magnetic flux density of 0, 50, 100 and 200 G. For the relevant calculations we used the Copenhagen Stagger code. The presence of magnetic fields causes both a direct (Zeeman-broadening) effect on spectral lines with non-zero Land\'e factor and an indirect effect on temperature-sensitive lines via a change in the photospheric T-tau stratification. The corresponding correction in the estimated atomic abundance ranges from a few hundredths of a dex up to |Delta log(Fe)| ~ 0.15 dex, depending on the spectral line and on the amount of average magnetic flux within the range of values we considered. The Zeeman-broadening effect gains relatively more importance in the IR. The largest modification to previous solar abundance determinations based on visible spectral lines is instead due to the indirect effect, i.e., the line-weakening caused by a warmer stratification on an optical depth scale. Our results indicate that the average solar iron abundance obtained when using magnetoconvection models can be 0.03-0.11 dex higher than when using the simpler HD convection approach. We demonstrate that accounting for magnetic flux is important in state-of-the-art solar photospheric abundance determinations based on 3D simulations.Comment: 12 pages, 7 figures, A&A in pres

Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree (l≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jiménez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic fiel

Thermodynamic fluctuations in solar photospheric three-dimensional convection simulations and observations

Numerical 3D radiative (M)HD simulations of solar convection are used to understand the physical properties of the solar photosphere. To validate this approach, it is important to check that no excessive thermodynamic fluctuations arise as a consequence of the partially incomplete treatment of radiative transfer. We investigate the realism of 3D convection simulations carried out with the Stagger code. We compared the characteristic properties of several spectral lines in solar disc centre observations with spectra synthesized from the simulations. We degraded the synthetic spectra to the spatial resolution of the observations using the continuum intensity distribution. We estimated the necessary spectral degradation by comparing atlas spectra with averaged observed spectra. In addition to deriving a set of line parameters directly, we used the SIR code to invert the spectra. Most of the line parameters from the observational data are matched well by the degraded simulation spectra. The inversions predict a macroturbulent velocity below 10 m/s for the simulation at full spatial resolution, whereas they yield ~< 1000 m/s at a spatial resolution of 0.3". The temperature fluctuations in the inversion of the degraded simulation do not exceed those from the observational data (of the order of 100-200 K rms for -2<log tau<-0.5). The comparison of line parameters in spatially averaged profiles with the averaged values of line parameters in spatially resolved profiles indicates a significant change of (average) line properties at a spatial scale between 0.13" and 0.3". Up to a spatial resolution of 0.3", we find no indications of the presence of excessive thermodynamic fluctuations in the 3D HD simulation. To definitely confirm that simulations without spatial degradation contain fully realistic thermodynamic fluctuations requires observations at even better spatial resolution.Comment: 21 pages, 15 figures + 2 pages Appendix, accepted for publication in A&A; v2 version: corrected for an error in the calculation of stray-light estimates, for details see the Corrigendum to A&A, 2013, 557, 109 (DOI: 10.1051/0004-6361/201321596). Corrected text and numbers are in bold font. Apart from the stray-light estimates, nothing in the rest of the paper was affected by the erro

Surges and Si IV bursts in the solar atmosphere. Understanding IRIS and SST observations through RMHD experiments

Surges often appear as a result of the emergence of magnetized plasma from the solar interior. Traditionally, they are observed in chromospheric lines such as H$\alpha$ 6563 \AA and Ca II 8542 \AA. However, whether there is a response to the surge appearance and evolution in the Si IV lines or, in fact, in many other transition region lines has not been studied. In this paper we analyze a simultaneous episode of an H$\alpha$ surge and a Si IV burst that occurred on 2016 September 03 in active region AR12585. To that end, we use coordinated observations from the Interface Region Imaging Spectrograph (IRIS) and the Swedish 1-m Solar Telescope (SST). For the first time, we report emission of Si IV within the surge, finding profiles that are brighter and broader than the average. Furthermore, the brightest Si IV patches within the domain of the surge are located mainly near its footpoints. To understand the relation between the surges and the emission in transition region lines like Si IV, we have carried out 2.5D radiative MHD (RMHD) experiments of magnetic flux emergence episodes using the Bifrost code and including the non-equilibrium ionization of silicon. Through spectral synthesis we explain several features of the observations. We show that the presence of Si IV emission patches within the surge, their location near the surge footpoints and various observed spectral features are a natural consequence of the emergence of magnetized plasma from the interior to the atmosphere and the ensuing reconnection processes.Comment: 13 pages, 8 figures. The Astrophysical Journal (Accepted