The Helioseismic and Magnetic Imager (HMI) has just started producing data that will help determine what the sources and mechanisms of variability in the Sun's interior are. The instrument measures the Doppler shift and the polarization of the Fe I 6173 A line, on the entire solar disk at a relatively-high cadence, in order to study the oscillations and the evolution of the full vector magnetic field of the solar Photosphere. After the data are properly calibrated, they are given to a Milne-Eddington inversion code (VFISV, Borrero et al. 2010) whose purpose is to infer certain aspects of the physical conditions in the Sun's Photosphere, such as the full 3-D topology of the magnetic field and the line-of-sight velocity at the solar surface. We will briefly describe the characteristics of the inversion code, its advantages and limitations --both in the context of the model atmosphere and the actual nature of the data--, and other aspects of its performance on such a remarkable data load. Also, a cross-comparison with near-simultaneous maps from the Spectro-Polarimeter (SP) onboard Hinode will be made.
The Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) instruments onboard the Solar Dynamics Observatory satellite produce Doppler velocity and continuum intensity at 6173 A as well as intensity maps at 1600 A and 1700 A, which can be used for helioseismic studies at different heights in the solar photosphere. We perform a Hankel-Fourier analysis in an annulus centered around sunspots or quiet-Sun regions, to estimate the change in power of waves crossing these regions of interest. We find that there is a dependence of power-reduction coefficients on measurement…
The solar mean magnetic field (SMMF) provided by the Wilcox Solar Observatory (WSO) is compared with the SMMF acquired by the \textit{Helioseismic and Magnetic Imager} (HMI) onboard the \textit{Solar Dynamic Observatory} (SDO). We found that despite the different spectral lines and measurement techniques used in both instruments the Pearson correlation coefficient between these two datasets equals 0.86 while the conversion factor is very close to unity: B(HMI) = 0.99(2)B(WSO). We also discuss artifacts of the SDO/HMI magnetic field measurements, namely the 12 and 24-hour oscillations in SMMF a…
The meridional circulation at high latitudes is crucial to the build-up and reversal of the Sun's polar magnetic fields. Here we characterize the axisymmetric flows by applying a magnetic feature cross-correlation procedure to high resolution magnetograms obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We focus on Carrington Rotations 2096-2107 (April 2010 to March 2011) - the overlap interval between HMI and the Michelson Doppler Investigation (MDI). HMI magnetograms averaged over 720 seconds are first mapped into heliographic coordinates. …
This document provides some technical notes on the polar field correction scheme for the HMI synoptic maps and daily updated synchronic frames. It is intended as a reference for the new data products and for some minor updates on our previous scheme for MDI (Sun et al. 2011).
We analysed line-of-sight magnetic fields and magnetic power spectra of an undisturbed photosphere using magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamic Observatory (SDO) and the Near InfraRed Imaging Spectrapolarimeter (NIRIS) operating at the Goode Solar Telescope (GST) of the Big Bear Solar Observatory. In the NIRIS data revealed the presence of thin flux tubes of 200-400~km in diameter and of field strength of 1000-2000~G. The HMI power spectra determined for a coronal hole, a quiet sun and a plage areas exhibit the same spectral index of -1 o…
A specific type of artifacts, that originate due to displacement of the image of a moving object along the digital (pixel) matrix of receiver are analyzed in detail. The criteria of appearance and the influence of these artifacts on the study of long-term oscillations of sunspots are deduced. The obtained criteria suggest us methods for reduction or even elimination of these artifacts. It is shown that the use of integral parameters can be very effective against the artifact distortions. The simultaneous observations of sunspot magnetic field and ultraviolet intensity of the umbra have given t…
Following Couvidat (2013), we analyze data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) instruments onboard the Solar Dynamics Observatory: Doppler velocity and continuum intensity at 6173 A as well as intensity maps at 1600 A and 1700 A. Datasets of 14 active regions and four quiet-Sun regions are studied at four heights in the solar photosphere. An Hankel-Fourier analysis is performed around these regions of interest. Outgoing-ingoing scattering phase shifts at a given atmospheric height are computed, as well as ingoing-ingoing and outgoing-outgo…
The \textit{Sun Watcher using Active Pixel system detector and Image Processing}(SWAP) on board the \textit{PRoject for OnBoard Autonomy\todash 2} (PROBA\todash 2) spacecraft provides images of the solar corona in EUV channel centered at 174 Å. These data, together with \textit{Atmospheric Imaging Assembly} (AIA) and the \textit{Helioseismic and Magnetic Imager} (HMI) on board \textit{Solar Dynamics Observatory} (SDO), are used to study the dynamics of coronal bright points. The evolution of the magnetic polarities and associated changes in morphology are studied using magnetograms and multi-w…
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 evolu…
Using data from the Helioseismic Magnetic Imager, we report on the amplitudes and phase relations of oscillations in quiet-Sun, plage, umbra and the polarity inversion line (PIL) of an active region NOAA$\#$11158. We employ Fourier, wavelet and cross correlation spectra analysis. Waves with 5-minute periods are observed in umbra, PIL and plage with common phase values of $ϕ(v,I)=\fracπ{2}$, $ϕ(v,B_{los})=-\fracπ{2}$. In addition, $ϕ(I,B_{los})=π$ in plage are observed. These phase values are consistent with slow standing or fast standing surface sausage wave modes. The line width variations, a…
Solar flares with a broadband emission in the white-light range of the electromagnetic spectrum belong to most enigmatic phenomena on the Sun. The origin of the white-light emission is not entirely understood. We aim to systematically study the visible-light emission connected to solar flares in SDO/HMI observations. We developed a code for automatic detection of kernels of flares with HMI intensity brightenings and study properties of detected candidates. The code was tuned and tested and with a little effort, it could be applied to any suitable data set. By studying a few flare examples, we …
We study the role of rotating sunspots in relation to the evolution of various physical parameters characterizing the non-potentiality of the active region NOAA 11158 and its eruptive events using the magnetic field data from the Helioseismic and Magnetic Imager (HMI) and multi-wavelength observations from the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO). From the evolutionary study of HMI intensity and AIA channels, it is observed that the AR consists of two major rotating sunspots one connected to flare-prone region and another with CME. The constructed space-…
We quantify the emergence and decay rates of preceder (p) and follower (f) sunspots within ten active regions from 2010-2014 using Space-weather Helioseismic Magnetic Imager Active Region Patch data. The sunspots are small- to mid-sized regions and contain a signed flux within a single polarity sunspot of $(1.1-6.5)\times 10^{21}$ Mx. The net unsigned flux within the regions, including plage, ranges from $(5.1-20)\times 10^{21}$ Mx. Rates are calculated with and without intensity contours to differentiate between sunspot formation and flux emergence. Signed flux emergence rates, calculated wit…
The measurement of the Sun's surface motions with a high spatial and temporal resolution is still a challenge. We wish to validate horizontal velocity measurements all over the visible disk of the Sun from Solar Dynamics Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) data. Horizontal velocity fields are measured by following the proper motions of solar granules using a newly developed version of the Coherent Structure Tracking (CST) code. The comparison of the surface flows measured at high spatial resolution (Hinode, 0.1 arcsec) and low resolution (SDO/HMI, 0.5 arcsec) allows us to d…
We present a PSF for SDO/HMI and discuss the effects of its removal on the apparent properties of solar surface phenomena in HMI data. The PSF was retrieved from observations of Venus in transit by matching it to the convolution of a model of the venusian disc and solar background with a guess PSF. Observations recorded near in time to the transit of Venus were corrected for instrumental scattered light by the deconvolution with the PSF. Granulation contrast in restored HMI data is greatly enhanced relative to the original data and exhibit reasonable agreement with numerical simulations. Image…
The Sun is the only star where the superficial turbulent convection can be observed at very high spatial resolution. The Solar Dynamics Observatory (SDO) has continuously observed the full Sun from space with multi-wavelength filters since July 2010. In particular, the Helioseismic and Magnetic Imager (HMI) instrument takes high-cadence frames (45 seconds) of continuum intensity in which solar granulation is visible. We aimed to follow the evolution of the solar granules over an activity cycle and look for changes in their spatial properties. We investigated the density of granules and their m…
The primary task of the Debrecen Heliophysical Observatory (DHO) has been the most detailed, reliable, and precise documentation of the solar photospheric activity since 1958. This long-term effort resulted in various solar catalogs based on ground-based and space-borne observations. A series of sunspot databases and on-line tools were compiled at DHO: the Debrecen Photoheliographic Data (DPD, 1974--), the dataset based on the Michelson Doppler Imager (MDI) of the Solar and Heliospheric Observatory (SOHO) called SOHO/MDI--Debrecen Data (SDD, 1996--2010), and the dataset based on the Helioseism…
Solar magnetic activity produces extreme solar flares and coronal mass ejections, which pose grave threats to electronic infrastructure and can significantly disrupt economic activity. It is therefore important to appreciate the triggers of explosive solar activity and develop reliable space-weather forecasting. Photospheric vector-magnetic-field data capture sunspot magnetic-field complexity and can therefore improve the quality of space-weather prediction. However, state-of-the-art vector-field observations are consistently only available from Solar Dynamics Observatory/Helioseismic and Magn…
The solar atmosphere is extremely dynamic, and many important phenomena develop on small scales that are unresolved in observations with the Helioseismic and Magnetic Imager (HMI) instrument on the Solar Dynamics Observatory (SDO). For correct calibration and interpretation of the observations, it is very important to investigate the effects of small-scale structures and dynamics on the HMI observables, such as Doppler shift, continuum intensity, spectral line depth, and width. We use 3D radiative hydrodynamics simulations of the upper turbulent convective layer and the atmosphere of the Sun, …
Solar magnetic fields are generated in the solar interior and pop up at the solar surface to form active regions. As the magnetic field appears on the surface, it forms various structures like small magnetic elements, pores, and sunspots. The nature of these formation processes is largely unknown. In this contribution we elaborate on the formation of sunspots and particularly on the formation of penumbrae. We report on observations that we obtained at the German VTT on July 4, 2009 on the formation of the spot in AR 11024. This data set is accomplished with data from SOHO/MDI which offers an e…
The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chos…
Solar photospheric velocities measured in space: a comparison between SO/PHI-HRT and SDO/HMI
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；Universitat de València（瓦伦西亚大学）；Advanced Research Center for Space Science and Technology, Institute of Science and Engineering, Kanazawa University（金泽大学理工学研究科宇宙科学技术研究高级研究中心）
We analyse observations of the X9.3 solar flare (SOL2017-09-06T11:53) observed by SDO/HMI and Hinode/SOT. Our aim is to learn about the nature of the HMI pseudocontinuum Ic used as a proxy for the white-light continuum. From model atmospheres retrieved by an inversion code applied to the Stokes profiles observed by the Hinode satellite we synthesise profiles of the FeI 617.3 nm line and compare them to HMI observations. Based on a pixel-by-pixel comparison we show that the value of Ic represents the continuum level well in quiet-Sun regions only. In magnetised regions it suffers from a simplis…
The Sun's axisymmetric flows, differential rotation and meridional flow, govern the dynamics of the solar magnetic cycle and variety of methods are used to measure these flows, each with its own strengths and weaknesses. Flow measurements based on cross-correlating images of the surface magnetic field have been made since the 1970s which require advanced numerical techniques that are capable of detecting movements of less than the pixel size in images of the Sun. We have identified several systematic errors in addition to the center-to-limb effect that influence previous measurements of these …
We compare measurements of horizontal flows on the surface of the Sun using helioseismic time--distance inversions and coherent structure tracking of solar granules. Tracking provides 2D horizontal flows on the solar surface, whereas the time--distance inversions estimate the full 3-D velocity flows in the shallow near-surface layers. Both techniques use HMI observations as an input. We find good correlations between the various measurements resulting from the two techniques. Further, we find a good agreement between these measurements and the time-averaged Doppler line-of-sight velocity, and …
Helioseismology has provided unprecedented information about the internal rotation of the Sun. One of the important achievements was the discovery of two radial shear layers: one near the bottom of the convection zone (the tachocline) and one near the surface. These shear layers may be important ingredients for explaining the magnetic cycle of the Sun. We measure the logarithmic radial gradient of the rotation rate ($\rm d\lnΩ/\rm d\ln r$) near the surface of the Sun using 15 years of f mode rotational frequency splittings from the Michelson Doppler Imager (MDI) and four years of data from the…
We present the {\it Solar Dynamics Observatory} (SDO) Atmospheric Imaging Assembly (AIA) observations of EUV cyclones in the quiet Sun. These cyclones are rooted in the Rotating Network magnetic Fields (RNFs). Such cyclones can last several to more than ten hours, and, at the later phase, they are found to be associated with EUV brightenings (microflares) and even EUV waves. SDO Helioseismic and Magnetic Imager (HMI) observations show an ubiquitous presence of the RNFs. Using HMI line-of-sight magnetograms on 2010 July 8, we find 388 RNFs in an area of 800$\times$980 square arcseconds near the…
Large scale flows in the Sun play an important role in the dynamo process linked to the solar cycle. The important large scale flows are the differential rotation and the meridional circulation with an amplitude of km/s and few m/s , respectively. These flows also have a cycle related components, namely the torsional oscillations. Our attempt is to determine large-scale plasma flows on the solar surface by deriving horizontal flow velocities using the techniques of solar granule tracking, dopplergrams, and time distance helioseismology. Coherent structure tracking (CST) and time distance helio…
We use high-resolution images of the sun obtained by the SDO/AIA instrument to study the evolution of the coronal loops in a flaring solar active region. During 15 February 2011 a X-2.2 class flare occurred in NOAA 11158, a $βγδ$ sunspot complex. We identify three distinct phases of the coronal loop dynamics during this event: (i) {\it Slow rise phase}: slow rising motion of the loop-tops prior to the flare in response to slow rise of the underlying flux rope, (ii) {\it Collapse phase}: sudden contraction of the loop-tops with lower loops collapsing earlier than the higher loops, and (iii) {\i…
Downflows on the solar surface are suspected to play a major role in the dynamics of the convection zone. We investigate the existence of the long-lasting downflows whose effects influence the interior of the Sun and the outer layers. We study the sets of Dopplergrams and magnetograms observed with SDO and Hinode spacecrafts and a MHD simulation. All of the aligned sequences, which were corrected from the satellite motions and tracked with the differential rotation, were used to detect the long-lasting downflows in the quiet-Sun at the disc centre. To learn about the structure of the flows bel…
The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. We develop a data-analysis pipeline based on the time-distance helioseismology method to measure acoustic travel times using HMI Doppler-shift observations, and infer solar interior properties by inverting these measurements. The pipeline is used for routine production of near-real-time full-disk maps of subsurface wave-speed perturbations and horizontal flow velocities for depths ranging from 0 to 20 Mm, every eight hours. In addition, Carring…
NASA's Solar Dynamics Observatory is delivering vector field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geostationary orbit. The relative spacecraft-Sun velocity varies by $\pm3$~km/s over a day which introduces major orbital artifacts in the Helioseismic Magnetic Imager data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly-developed three stage procedure for mitigating these artifacts in the Doppler data derived from the Milne-Eddin…
Context. Local correlation tracking of granulation (LCT) is an important method for measuring horizontal flows in the photosphere. This method exhibits a systematic error that looks like a flow converging towards disk center, also known as the shrinking-Sun effect. Aims. We aim at studying the nature of the shrinking-Sun effect for continuum intensity data and at deriving a simple model that can explain its origin. Methods. We derived LCT flow maps by running the local correlation tracking code FLCT on tracked and remapped continuum intensity maps provided by the Helioseismic and Magnetic Imag…
Extrapolation codes in Cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) on board solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). We use Helioseismic and Magnetic Imager and Vector Sp…
In this work we seek evidence for global torsional oscillations in alpha sunspots. We have used long time series of continuum intensity and magnetic field vector maps from the Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) spacecraft. The time series analysed here span the total disk passage of 25 isolated sunspots. We found no evidence of global long-term periodic oscillations in the azimuthal angle of the sunspot magnetic field within $\sim$ 1 degree. This study could help us to understand the sunspot dynamics and its internal structure.
The average unsigned magnetic flux density in magnetograms of the quiet Sun is generally dominated by instrumental noise. Due to the entirely different scaling behavior of the noise and the solar magnetic pattern it has been possible to determine the standard deviation of the Gaussian noise distribution and remove the noise contribution from the average unsigned flux density for the whole 15-yr SOHO/MDI data set and for a selection of SDO/HMI magnetograms. There is a very close correlation between the MDI disk-averaged unsigned vertical flux density and the sunspot number, and regression analy…
The Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO) observes the Sun at the Fe I 6173 Å line and returns full-disk maps of line-of-sight (LOS) observables including the magnetic flux density, velocities, Fe I line width, line depth, and continuum intensity. These data are estimated through an algorithm (the MDI-like algorithm, hereafter), which combines observables obtained at six wavelength positions within the Fe I 6173 Å line. To properly interpret such data it is important to understand any effects of the instrument and the pipeline that generates these d…
The X2.2-class solar flare of February 15, 2011, produced a powerful `sunquake' event, representing a seismic response to the flare impact. The impulsively excited seismic waves formed a compact wavepacket traveling through the solar interior and appeared on the surface as expanding wave ripples. The Helioseismic and Magnetic Imager (HMI), instrument on SDO, observes variations of intensity, magnetic field and plasma velocity (Dopplergrams) on the surface of Sun almost uninterruptedly with high resolution (0.5 arcsec/pixel) and high cadence (45 sec). The flare impact on the solar surface was o…
Active region NOAA 12673 was extremely volatile in 2017 September, producing many solar flares, including the largest of solar cycle 24, an X9.3 flare of 06 September 2017. It has been reported that this flare produced a number of sunquakes along the flare ribbon (Sharykin & Kosovichev 2018; Zhao & Chen 2018). We have used co-temporal and co-spatial Helioseismic and Magnetic Imager (HMI) line-of-sight (LOS) and Swedish 1-m Solar Telescope observations to show evidence of the chromospheric response to these sunquakes. Analysis of the Ca II 8542 Å\space line profiles of the wavefronts revealed t…
As the global magnetic field of the Sun has an activity cycle, one expects to observe some variation of the dynamical properties of the flows visible in the photosphere. We investigate the flow field during the solar cycle by analysing SDO/HMI observations of continuum intensity, Doppler velocity and longitudinal magnetic field. We first picked data at disk center during 6 years along the solar cycle with a 48-hour time step in order to study the overall evolution of the continuum intensity and magnetic field. Then we focused on thirty 6-hour sequences of quiet regions without any remnant of m…
In this paper, we try to improve the magnetogram calibration method of the Solar Magnetic Field Telescope (SMFT). The improved calibration process fits the observed full Stokes information, using six points on the profile of Fe ı 5324.18 Å line, and the analytical Stokes profiles under the Milne-Eddington atmosphere model, adopting the Levenberg-Marquardt least-square fitting algorithm. In Comparison with the linear calibration methods, which employs one point, there is large difference in the strength of longitudinal field $B_l$ and tranverse field $B_t$, caused by the non-linear relationship…
Since May 1, 2010, we have been able to study (almost) continuously the vector magnetic field in the Sun, thanks to two space-based observatories: the Solar Dynamics Observatory (SDO) and Hinode. Both are equipped with instruments able to measure the Stokes parameters of Zeeman-induced polarization of photospheric line radiation. But the observation modes, the spectral lines, the spatial, spectral and temporal sampling, and even the inversion codes used to recover magnetic and thermodynamic information from the Stokes profiles are different. We compare the vector magnetic fields derived from o…
We derive horizontal fluid motions on the solar surface over large areas covering the quiet-Sun magnetic network from local correlation tracking of convective granules imaged in continuum intensity and Doppler velocity by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). From these we calculate horizontal divergence, vertical component of vorticity, and kinetic helicity of fluid motions. We study the correlations between fluid divergence and vorticity, and that between vorticity (kinetic helicity) and magnetic field. We find that the vorticity (kinetic he…
Dating back to the first observations of the on-disk corona, there has been a qualitative link between the photosphere's magnetic network and enhanced transition-temperature plasma emission. These observations led to the development of a general model that describes emission structures through the partitioning of the atmospheric volume with different magnetic loop geometries that exhibit different energetic equilibria. Does the internetwork produce transition-temperature emission? What fraction of network flux connects to the corona? How does quiet sun emission compare with low-activity Sun-li…
Temporal variations of solar inertial mode parameters from GONG (2002-2024) and HMI (2010-2024): Rossby modes ($3 \leq m \leq 16 $) and $m=1$ high-latitude mode
Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系统研究所）；National Solar Observatory（美国国家太阳天文台）；Institut für Astrophysik und Geophysik, Georg-August-Universität Göttingen（哥廷根大学天体物理与地球物理研究所）；Center for Astrophysics and Space Science, NYUAD Institute, New York University Abu Dhabi（纽约大学阿布扎比分校天体物理学与空间科学中心）；LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台拉伊尔实验室（隶属于巴黎文理研究大学、索邦大学、巴黎西岱大学、塞吉-蓬图瓦兹大学及法国国家科学研究中心））
A process of diffusion of small-scale magnetic elements inside four active regions (ARs) was analyzed. Line-of-sight magnetograms acquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO) during a two-day time interval around the AR culmination time were utilized. Small magnetic elements of size of 3-100 squared HMI pixels with the field strength above the detection threshold of 30 Mx cm$^{-2}$ were detected and tracked. The turbulent diffusion coefficient was retrieved using the pair-separation technique. Comparison with the previously reported quiet-s…
The global oscillations of the Sun are investigated on the base of three independent sets of data: 1. Records of Total Solar Irradiance (TSI). 2. The average brightness of the photosphere in MDI (SOHO) and HMI (SDO) images. 3. Records of the time variations of sunlight reflected from the planets during their passage in the field of view of the LASCO C3 coronagraph. It is found that in the low-frequency spectrum of solar oscillations as a star there are modes of 8-10, 36-38 hours and the main stable 9-day mode. The last mode can be regarded as a reflection of oscillatory processes near the fast…
The second law of thermodynamics imposes an increase of macroscopic entropy with time in an isolated system. Microscopically, however, the entropy production can be negative for a single, microscopic realization of a thermodynamic process. The so-called fluctuation theorems provide exact relations between the stochastic entropy consumption and generation. Here, we analyse pixel-to-pixel fluctuations in time of small-scale magnetic fields (SSMF) in the quiet Sun observed with the SDO/HMI instrument. We demonstrate that entropy generated by SSMF obeys the fluctuation theorems. In particular, the…
