Modelling amplitudes of stochastically excited oscillations in stars is a powerful tool for understanding the properties of the convective zones. For instance, it gives us information on the way turbulent eddies are temporally correlated in a very large Reynolds number regime. We discuss the way the time correlation between eddies is modelled and we present recent theoretical developments as well as observational results. Eventually, we discuss the physical underlying meaning of the results by introducing the Ornstein-Uhlenbeck process, which is a sub-class of a Gaussian Markov process.
Turbulent eddy-time-correlation in the solar convective zone
类太阳振荡驱动过程的理论模拟是理解太阳型恒星对流区性质的一个有力途径。在这个框架中，湍流涡旋之间的时间相关性的描述是模式振幅的一个重要组成部分。然而，在涡旋时间关联函数的高斯或洛伦兹描述之间存在争论（Samadi et al. 2003，Chaplin et al. 2005）。事实上，高斯描述再现了太阳模式振幅的低频形状，但从理论角度来看并不令人满意（Houdek，2009），并导致与观测结果的其他分歧（Samadi等人，2007年）。这些都是通过使用洛伦兹描述解决的，但是太阳观测的低频形状没有正确地再现。我们调和这两种描述，通过采用扫描近似，其中包括在假设的涡时间关联函数是由平流的涡，在惯性范围内，由能量轴承涡为主。使用洛伦兹函数以及从扫描假设导出的截止频率，使我们能够再现观测的低频形状。这一结果也证实了太阳情况下高度湍流的扫掠假设。
Simulating deep solar convection and its coupled mean-field motions is a formidable challenge where few observational results constrain models that suffer from the non-physical influence of the grid resolution. We present hydrodynamic global Implicit Large-Eddy simulations (ILES) of deep solar convection performed with the EULAG-MHD code, and explore the effects of grid resolution on the properties of rotating and non-rotating convection. The results, based on low-order moments and turbulent spectra reveal that convergence could be achieved in non-rotating simulations provided sufficient resol…
Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations (DNS) of turbulent flows at high Reynolds numbers (Re). However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between $64^2$ and $2048^2$ grid points, along with the estimation of their effective viscosities, resulting in effective …
Generation and annihilation of three dimensional magnetic nulls in extrapolated solar coronal magnetic field: Data-based Implicit Large Eddy Simulation
Since the first observations of solar oscillations in 1962, helioseismology has probably been one of the most successful fields of astrophysics. Besides the improvement of observational data, solar seismologists developed sophisticated techniques to infer the internal structure of the Sun. Back in 1990s these comparisons showed a very high agreement between solar models and the Sun. However, the downward revision of the CNO surface abundances in the Sun in 2005, confirmed in 2009, induced a drastic reduction of this agreement leading to the so-called solar modelling problem. More than ten year…
Solar flares are explosive events in the solar corona, representing fast conversion of magnetic energy into thermal and kinetic energy, and hence radiation, due to magnetic reconnection. Modelling is essential for understanding and predicting these events. However, self-consistent modelling is extremely difficult due to the vast spatial and temporal scale separation between processes involving thermal plasma (normally considered using magnetohydrodynamic (MHD) approach) and non-thermal plasma (requiring a kinetic approach). In this mini-review we consider different approaches aimed at bridging…
Extensions have been made recently to the coronal approximation for the purpose of modelling line emission from carbon and oxygen in the lower solar atmosphere. The same modelling is used here for other elements routinely observed in the solar transition region: N, Ne, Mg, Si and S. The modelling includes the effects of higher densities suppressing dielectronic recombination and populating long-lived, metastable levels; the presence of metastable levels typically causes effective ionisation rates to increase and recombination rates to decrease. Processes induced by the radiation field, namely …
The aim of this work is to improve the modelling of ion populations in higher density, lower temperature astrophysical plasmas, of the type commonly found in lower solar and stellar atmospheres. Ion population models for these regions frequently employ the coronal approximation, which assumes conditions more suitable to the upper solar atmosphere, where high temperatures and lower densities prevail. Using the coronal approximation for modelling the solar transition region gives theoretical lines intensities for the Li-like and Na-like isoelectronic sequences which can be factors of 2-5 times l…
Since the first observations of solar oscillations, helioseismology has been one of the most successful fields of astrophysics. Data of high quality were obtained through the implementation of networks of ground-based observatories such as the GONG project or the BiSON network, coupled with space-based telescopes such as SOHO and SDO missions. Besides the improvement of observational data, solar seismologists developed sophisticated techniques to infer the internal structure of the Sun. These methods, then already extensively used in the field of Geophysics, are called inversion techniques. Th…
Time-evolving coronal modelling of the solar maximum around the solar storms in May 2024 by COCONUT
KU Leuven（荷语鲁汶大学）；University of Maria Curie-Skłodowska（玛丽亚·居里-斯可夫多夫斯卡大学）；Von Karman Institute For Fluid Dynamics（冯·卡门流体力学研究所）；University of Oslo（奥斯陆大学）
The Sun is the most studied of stars and a laboratory of fundamental physics. However, the understanding of our star is stained by the solar modelling problem which can stem from various causes. We combine inversions of sound speed, an entropy proxy and the Ledoux discriminant with the position of the base of the convective zone and the photospheric helium abundance to test combinations of ingredients such as equation of state, abundance and opacity tables. We study the potential of the inversions to constrain ad-hoc opacity modifications and additional mixing in the Sun. We show that they pro…
The magnetic network extending from the photosphere (solar radius $\simeq R_\odot$) to lower corona ($R_\odot + 10$ Mm) plays an important role in the heating mechanisms of the solar atmosphere. Here we further develop the models with realistic open magnetic flux tubes of the authors in order to model more complicated configurations. Closed magnetic loops, and combinations of closed and open magnetic flux tubes are modelled. These are embedded within a stratified atmosphere, derived from observationally motivated semi-empirical and data-driven models subject to solar gravity and capable of spa…
The capability to predict the parameters of an SEP event such as its onset, peak flux, and duration is critical to assessing any potential space weather impact. We present a new flexible modelling system simulating the propagation of Solar Energetic Particles (SEPs) from locations near the Sun to any given location in the heliosphere to forecast the SEP flux profiles. SPARX uses an innovative methodology, that allows implementation within an operational framework, to overcome the time constraints of test particle modelling of SEP profiles, allowing the production of near real time SEP nowcasts…
Our ability to model the shapes and strengths of iron lines in the solar spectrum is a critical test of the accuracy of the solar iron abundance, which sets the absolute zero-point of all stellar metallicities. We use an extensive 463-level Fe atom with new photoionisation cross-sections for FeI as well as quantum mechanical calculations of collisional excitation and charge transfer with neutral hydrogen; the latter effectively remove a free parameter that has hampered all previous line formation studies of Fe in non-local thermodynamic equilibrium (NLTE). For the first time, we use realistic …
A parametric model of granulation employing a small number of parameters was developed. Synthetic spectra calculated using this model closely match observed spectra and, in particular, reproduce the asymmetries observed in spectral lines. Both the microturbulent motions and the large-scale flow velocity decrease exponentially with a scale height of 368 km as the height within the photosphere increases. The model agrees with observations of the solar granulation (from which it was derived). The horizontal motions associated with granulation were found and used to calculate spectra emergent away…
The aim of this study is to generate maps of the hard X-ray emission produced by energetic electrons in a solar flare and compare them with observations. The ultimate goal is to test the viability of the combined MHD/test-particle approach for data-driven modelling of active events in the solar corona and their impact on the heliosphere. Based on an MHD model of X-class solar flare observed on the 8th of September 2017, we calculate trajectories of a large number of electrons and protons using the relativistic guiding-centre approach. Using the obtained particle trajectories, we deduce the spa…
Solar carbon abundance from 3D non-LTE modelling of the diagnostic lines of the CH molecule
Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Ruprecht-Karls Universität（鲁普雷希特-卡尔大学）；Institut für Astrophysik und Geophysik（天体物理学与地球物理学研究所）；Lowell Observatory（洛厄尔天文台）；Northern Arizona University（北亚利桑那大学）；University of Copenhagen（哥本哈根大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；Stockholm University（斯德哥尔摩大学）；Laboratoire Univers et Particules de Montpellier（蒙彼利埃宇宙与粒子实验室）；Univ Montpellier（蒙彼利埃大学）；CNRS（法国国家科学研究中心）；Institute of Space Sciences (ICE-CSIC)（空间科学研究所（ICE-CSIC））
We present a technique to construct a spectropolarimetrically accurate magneto-hydrostatic model of a large-scale solar magnetic field concentration, mimicking a sunspot. Using the constructed model we perform a simulation of acoustic wave propagation, conversion and absorption in the solar interior and photosphere with the sunspot embedded into it. With the $6173\mathrmÅ$ magnetically sensitive photospheric absorption line of neutral iron, we calculate observable quantities such as continuum intensities, Doppler velocities, as well as full Stokes vector for the simulation at various positions…
Solar flare emission is detected in all EM bands and variations in flux density of solar energetic particles. Often the EM radiation generated in solar and stellar flares shows a pronounced oscillatory pattern, with characteristic periods ranging from a fraction of a second to several minutes. These oscillations are referred to as quasi-periodic pulsations (QPPs), to emphasise that they often contain apparent amplitude and period modulation. We review the current understanding of quasi-periodic pulsations in solar and stellar flares. In particular, we focus on the possible physical mechanisms,…
Recent hydrodynamical simulations of convection in a solar-like model suggest that penetrative convective flows at the boundary of the convective envelope modify the thermal background in the overshooting layer. Based on these results, we implement in one-dimensional stellar evolution codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model. This simple prescription qualitatively reproduces the behaviour found in the hydrodynamical simulations, namely a local heating and smoothing of the temperature gradient below the convective boundary. We…
The flux transport dynamo, in which the poloidal magnetic field is generated by the Babcock--Leighton mechanism and the meridional circulation plays a crucial role, has emerged as an attractive model for the solar cycle. Based on theoretical calculations done with this model, we argue that the fluctuations in the Babcock--Leighton mechanism and the fluctuations in the meridional circulation are the most likely causes of the irregularities of the solar cycle. With our increased theoretical understanding of how these irregularities arise, it can be possible to predict a future solar cycle by fee…
Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near $20^\circ$-$30^\circ$, and decrease at higher latitudes. We search for an explanation that takes into account solar latitudinal differential rotation. In the equatorial $β$ plane, we study the propagation of linear Rossby waves (phase speed $c <0$) in a parabolic zonal shear flow, $U = - \ov…
Solar twins are objects of great interest in that they allow us to understand better how stellar evolution and structure are affected by variations of the stellar mass, age and chemical composition in the vicinity of the commonly accepted solar values. We aim to use the existing spectrophotometric, interferometric and asteroseismic data for the solar twin 18 Sco to constrain stellar evolution models. 18 Sco is the brightest solar twin and is a good benchmark for the study of solar twins. The goal is to obtain realistic estimates of its physical characteristics (mass, age, initial chemical comp…
We aim to gain insight into the effect of network and faculae on solar irradiance from their apparent intensity. Taking full-disc observations from the Solar Dynamics Observatory, we examined the intensity contrast of network and faculae in the continuum and core of the Fe I 6173 Å line and 1700 Å, including the variation with magnetic flux density, distance from disc centre, nearby magnetic fields, and time. The brightness of network and faculae is believed to be suppressed by nearby magnetic fields from its effect on convection. The difference in intensity contrast between the quiet-Sun netw…
We explore the response of the He II 304 Å and He I 584 Å line intensities to electron beam heating in solar flares using radiative hydrodynamic simulations. Comparing different electron beams parameters, we found that the intensities of both He lines are very sensitive to the energy flux deposited in the chromosphere, or more specifically to the heating rate, with He II 304 Å being more sensitive to the heating than He I 584 Å. Therefore, the He line ratio increases for larger heating rates in the chromosphere. A similar trend is found in observations, using SDO/EVE He irradiance ratios and e…
Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be force-free (the Lorentz-force vanishes), this is not the case in the mixed plasma $β$ environment in …
The hydrogen Lyman lines ( 91.2 nm < lambda < 121.6 nm) are significant contributors to the radiative losses of the solar chromosphere, and are enhanced during flares. We have shown previously that the Lyman lines observed by the Extreme Ultraviolet Variability instrument onboard the Solar Dynamics Observatory exhibit Doppler motions equivalent to speeds on the order of 30 km/s. But contrary to expectation, no dominant flow direction was observed, with both redshifts and blueshifts present. To understand the formation of the Lyman lines, particularly their Doppler motions, we have used the rad…
Observations and modelling of stars with near-solar masses in their early phases of evolution is critical for a better understanding of how dynamos of solar-type stars evolve. We examine the chemical composition and the spot distribution of the pre-main-sequence solar analogue EK Dra. Using spectra from the HERMES Spectrograph (La Palma), we obtain the abundances of 23 elements with respect to the solar ones, which lead to a $[{\rm Fe/H}]=0.03$, with significant overabundance of Li and Ba. The s-process elements Sr, Y, and Ce are marginally overabundant, while Co, Ni, Cu, Zn are marginally def…
The peculiar behaviour of the solar cycle 23 and its prolonged minima has been one of the most studied problems over the last few years. In the present paper, we study the asymmetries in active region magnetic flux in the northern and southern hemispheres during complete solar cycle 23 and rising phase of solar cycle 24. During the declining phase of solar cycle 23, we find that the magnetic flux in the southern hemisphere is about 10 times stronger than that in the northern hemisphere during the declining phase of the solar cycle 23 and during the rising phase of cycle 24, however, this trend…
Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, th…
We examine the production of energetic neutral atoms (ENAs) in solar flares and CME-driven shocks and their subsequent propagation to 1 au. Time profiles and fluence spectra of solar ENAs at 1 au are computed for two scenarios: 1) ENAs are produced downstream at CME-driven shocks, and 2) ENAs are produced at large-scale post-flare loops in solar flares. Both the time profiles and fluence spectra for these two scenarios are vastly different. Our calculations indicate that we can use solar ENAs as a new probe to examine the underlying acceleration process of solar energetic particles (SEPs) and …
The Sun is the most studied of all stars. It is a reference for all other observed stars and a laboratory of fundamental physics helping us understand processes occuring in conditions irreproducible on Earth. However, our understanding of the Sun is currently stained by the solar modelling problem which can stem from various causes, such as the opacities, the equation of state and the mixing of chemical elements. We combine inversions of sound speed, an entropy proxy and the Ledoux discriminant with constraints such as the position of the base of the convective zone and the photospheric helium…
Our aim is to test potential solar prominence plasma diagnostics as obtained with the new solar capability of the Atacama Large Millimeter / submillimeter Array (ALMA). We investigate the thermal and plasma diagnostic potential of ALMA for solar prominences through the computation of brightness temperatures at ALMA wavelengths. The brightness temperature, for a chosen line of sight, is calculated using densities of hydrogen and helium obtained from a radiative transfer code under non local thermodynamic equilibrium (NLTE) conditions, as well as the input internal parameters of the prominence m…
Asteroseismic forward modelling techniques are being used to determine fundamental properties (e.g. mass, radius, and age) of solar-type stars. The need to take into account all possible sources of error is of paramount importance towards a robust determination of stellar properties. We present a study of 34 solar-type stars for which high signal-to-noise asteroseismic data is available from multi-year Kepler photometry. We explore the internal systematics on the stellar properties, that is, associated with the uncertainty in the input physics used to construct the stellar models. In particula…
Context. Solar activity cycles vary in amplitude and duration. The variations can be at least partly explained by fluctuations in dynamo parameters. Aims. We want to restrict uncertainty in fluctuating dynamo parameters and find out which properties of the fluctuations control the amplitudes of the magnetic field and energy in variable dynamo cycles. Methods. A flux-transport model for the solar dynamo with fluctuations of the Babcock-Leighton type $α$-effect was applied to generate statistics of magnetic cycles for our purposes. The statistics were compared with data on solar cycle periods to…
Solar flares are 3D phenomenon but modelling a flare in 3D, including many of the important processes in the chromosphere, is a computational challenge. Accurately modelling the chromosphere is important, even if the transition region and corona are the areas of interest, due to the flow of energy, mass, and radiation through the interconnected layers. We present a solar flare arcade model, that aims to bridge the gap between 1D and 3D modelling. Our approach is limited to the synthesis of optically thin emission. Using observed active region loop structures in a 3D domain we graft simulated 1…
Geometric modelling of Coronal Mass Ejections (CMEs) is a widely used tool for assessing their kinematic evolution. Furthermore, techniques based on geometric modelling, such as ELEvoHI, are being developed into forecast tools for space weather prediction. These models assume that solar wind structure does not affect the evolution of the CME, which is an unquantified source of uncertainty. We use a large number of Cone CME simulations with the HUXt solar wind model to quantify the scale of uncertainty introduced into geometric modelling and the ELEvoHI CME arrival times by solar wind structure…
We present the implementation of coupling the EUropean Heliospheric FORcasting Information Asset (EUHFORIA) and the improved Particle Acceleration and Transport in the Heliosphere (iPATH) model and simulate the widespread solar energetic particle (SEP) event of 2020 November 29. We compare the simulated time intensity profiles with measurements at Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A, SOlar and Heliospheric Observatory (SOHO) and Solar Orbiter (SolO). We focus on the influence of the history of shock acceleration on the varying SEP time intensity pro…
To predict line emission in the solar atmosphere requires models which are fundamentally different depending on whether the emission is from the chromosphere or the corona. At some point between the two regions, there must be a change between the two modelling regimes. Recent extensions to the coronal modelling for carbon and oxygen lines in the solar transition region have shown improvements in the emission of singly- and doubly-charged ions, along with Li-like ions. However, discrepancies still remain, particularly for singly-charged ions and intercombination lines. The aim of this work is t…
Solar flares stem from the reconnection of twisted magnetic field lines in the solar photosphere. The energy and waiting time distributions of these events follow complex patterns that have been carefully considered in the past and that bear some resemblance with earthquakes and stockmarkets. Here we explore in detail the tangling motion of interacting flux tubes anchored in the plasma and the energy ejections resulting when they recombine. The mechanism for energy accumulation and release in the flow is reminiscent of self-organized criticality. From this model we suggest the origin for two i…
