Solar Convection Research Articles

MODELING THE ROSSITER–MCLAUGHLIN EFFECT: IMPACT OF THE CONVECTIVE CENTER-TO-LIMB VARIATIONS IN THE STELLAR PHOTOSPHERE

ABSTRACT Observations of the Rossiter–McLaughlin (RM) effect provide information on star–planet alignments, which can inform planetary migration and evolution theories. Here, we go beyond the classical RM modeling and explore the impact of a convective blueshift that varies across the stellar disk and non-Gaussian stellar photospheric profiles. We simulated an aligned hot Jupiter with a four-day orbit about a Sun-like star and injected center-to-limb velocity (and profile shape) variations based on radiative 3D magnetohydrodynamic simulations of solar surface convection. The residuals between our modeling and classical RM modeling were dependent on the intrinsic profile width and v sin i; the amplitude of the residuals increased with increasing v sin i and with decreasing intrinsic profile width. For slowly rotating stars the center-to-limb convective variation dominated the residuals (with amplitudes of 10 s of cm s−1 to ∼1 m s−1); however, for faster rotating stars the dominant residual signature was due a non-Gaussian intrinsic profile (with amplitudes from 0.5 to 9 m s−1). When the impact factor was 0, neglecting to account for the convective center-to-limb variation led to an uncertainty in the obliquity of ∼10°–20°, even though the true v sin i was known. Additionally, neglecting to properly model an asymmetric intrinsic profile had a greater impact for more rapidly rotating stars (e.g., v sin i = 6 km s−1) and caused systematic errors on the order of ∼20° in the measured obliquities. Hence, neglecting the impact of stellar surface convection may bias star–planet alignment measurements and consequently theories on planetary migration and evolution.

NON-GREY RADIATIVE TRANSFER IN THE PHOTOSPHERIC CONVECTION : VALIDITY OF THE EDDINGTON APPROXIMATION

The aim of this study is to describe the physical processes taking place in the solar photosphere. Based on 3D hydrodynamic simulations including a detailed radiation transfer scheme, we investigate thermodynamic structures and radiation fields in solar surface convection. As a starting model, the initial stratification in the outer envelope calculated using the solar calibrations in the context of the standard stellar theory. When the numerical fluid becomes thermally relaxed, the thermodynamic structure of the steady-state turbulent flow was explicitly collected. Particularly, a non-grey radiative transfer incorporating the opacity distribution function was considered in our calculations. In addition, we evaluate the classical approximations that are usually adopted in the onedimensional stellar structure models. We numerically reconfirm that radiation fields are well represented by the asymptotic characteristics of the Eddington approximation (the diffusion limit and the streaming limit). However, this classical approximation underestimates radiation energy in the shallow layers near the surface, which implies that a reliable treatment of the non-grey line opacities is crucial for the accurate description of the photospheric convection phenomenon.

THE SPECTRAL AMPLITUDE OF STELLAR CONVECTION AND ITS SCALING IN THE HIGH-RAYLEIGH-NUMBER REGIME

ABSTRACT Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owing to this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star’s interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

Identification and morphology analysis of granules using the New Vacuum Solar Telephone Observations

Solar granulation is a plasma convective phenomenon from the solar convection zone to the photosphere, which appears as a cellular pattern on the solar surface. Morphological characteristics and evolution process of granules can help us to better understand the mechanism of the convective motion and the relationship to solar magnetic field. Therefore, an accurate identification method is crucial to study the mechanism and relationship. However, the traditional identification methods based on intensity- and gradient-threshold are very difficult to identify granules because the intensity distribution of granules is non-uniform and their boundaries appear to be blurred. In this paper, we proposed a new method based on phase congruency to identify granules and analyzed their morphological characteristics. The identification procedure includes three steps: (1) obtaining phase congruency feature from an original image; (2) obtaining binary image of phase congruency feature; (3) morphological filter to extract granule shapes. We selected two high-resolution image sequences taken from the New Vacuum Solar Telescope (NVST) at Fuxian Solar Observatory (FSO) to illustrate the identification procedure. For evaluating the accuracy of the proposed method, two traditional methods based on intensity threshold and marked watershed were compare to our method. Furthermore, we also selected three different thresholds to inspect the influence. The experiment result demonstrates that our proposed method is effective and accurate, and insensitive to those selected threshold. This demonstrates that our proposed method can be used to study granules evolution and their physical mechanism.

Seismic Sounding of Convection in the Sun

Thermal convection is the dominant mechanism of energy transport in the outer envelope of the Sun (one-third by radius). It drives global fluid circulations and magnetic fields observed on the solar surface. Vigorous surface convection excites a broadband spectrum of acoustic waves that propagate within the interior and set up modal resonances. These acoustic waves, also called seismic waves in this context, are observed at the surface of the Sun by space- and ground-based telescopes. Seismic sounding, the study of these seismic waves to infer the internal properties of the Sun, constitutes helioseismology. Here we review our knowledge of solar convection, especially that obtained through seismic inference. Several characteristics of solar convection, such as differential rotation, anisotropic Reynolds stresses, the influence of rotation on convection, and supergranulation, are considered. On larger scales, several inferences suggest that convective velocities are substantially smaller than those predicted by theory and simulations. This discrepancy challenges the models of internal differential rotation that rely on convective stresses as a driving mechanism and provide an important benchmark for numerical simulations.

Predictions of Solar Cycle 24: How are we doing?

AbstractPredictions of solar activity are an essential part of our Space Weather forecast capability. Users are requiring usable predictions of an upcoming solar cycle to be delivered several years before solar minimum. A set of predictions of the amplitude of Solar Cycle 24 accumulated in 2008 ranged from zero to unprecedented levels of solar activity. The predictions formed an almost normal distribution, centered on the average amplitude of all preceding solar cycles. The average of the current compilation of 105 predictions of the annual‐average sunspot number is 106 ± 31, slightly lower than earlier compilations but still with a wide distribution. Solar Cycle 24 is on track to have a below‐average amplitude, peaking at an annual sunspot number of about 80. Our need for solar activity predictions and our desire for those predictions to be made ever earlier in the preceding solar cycle will be discussed. Solar Cycle 24 has been a below‐average sunspot cycle. There were peaks in the daily and monthly averaged sunspot number in the Northern Hemisphere in 2011 and in the Southern Hemisphere in 2014. With the rapid increase in solar data and capability of numerical models of the solar convection zone we are developing the ability to forecast the level of the next sunspot cycle. But predictions based only on the statistics of the sunspot number are not adequate for predicting the next solar maximum. I will describe how we did in predicting the amplitude of Solar Cycle 24 and describe how solar polar field predictions could be made more accurate in the future.

Comparison between IEEE and CIGRE Thermal Behaviour Standards and Measured Temperature on a 132-kV Overhead Power Line

This paper presents the steady and dynamic thermal balances of an overhead power line proposed by CIGRE (Technical Brochure 601, 2014) and IEEE (Std.738, 2012) standards. The estimated temperatures calculated by the standards are compared with the averaged conductor temperature obtained every 8 min during a year. The conductor is a LA 280 Hawk type, used in a 132-kV overhead line. The steady and dynamic state comparison shows that the number of cases with deviations to conductor temperatures higher than 5 ∘ C decreases from around 20% to 15% when the dynamic analysis is used. As some of the most critical variables are magnitude and direction of the wind speed, ambient temperature and solar radiation, their influence on the conductor temperature is studied. Both standards give similar results with slight differences due to the different way to calculate the solar radiation and convection. Considering the wind, both standards provide better results for the estimated conductor temperature as the wind speed increases and the angle with the line is closer to 90 ∘ . In addition, if the theoretical radiation is replaced by that measured with the pyranometer, the number of samples with deviations higher than 5 ∘ C is reduced from around 15% to 5%.

Strong plume fluxes at Mars observed by MAVEN: An important planetary ion escape channel

AbstractWe present observations by the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission of a substantial plume‐like distribution of escaping ions from the Martian atmosphere, organized by the upstream solar wind convection electric field. From a case study of MAVEN particle‐and‐field data during one spacecraft orbit, we identified three escaping planetary ion populations: plume fluxes mainly along the upstream electric field over the north pole region of the Mars‐Sun‐Electric field (MSE) coordinate system, antisunward ion fluxes in the tail region, and much weaker upstream pickup ion fluxes. A statistical study of O+ fluxes using 3 month MAVEN data shows that the plume is a constant structure with strong fluxes widely distributed in the MSE northern hemisphere, which constitutes an important planetary ion escape channel. The escape rate through the plume is estimated to be ~30% of the tailward escape and ~23% of the total escape for > 25 eV O+ ions.

The spatial distribution of planetary ion fluxes near Mars observed by MAVEN

AbstractWe present the results of an initial effort to statistically map the fluxes of planetary ions on a closed surface around Mars. Choosing a spherical shell ~1000 km above the planet, we map both outgoing and incoming ion fluxes (with energies >25 eV) over a 4 month period. The results show net escape of planetary ions behind Mars and strong fluxes of escaping ions from the northern hemisphere with respect to the solar wind convection electric field. Planetary ions also travel toward the planet, and return fluxes are particularly strong in the southern electric field hemisphere. We obtain a lower bound estimate for planetary ion escape of ~3 × 1024 s−1, accounting for the ~10% of ions that return toward the planet and assuming that the ~70% of the surface covered so far is representative of the regions not yet visited by Mars Atmosphere and Volatile EvolutioN (MAVEN).

MERIDIONAL CIRCULATION IN THE SOLAR CONVECTION ZONE: TIME–DISTANCE HELIOSEISMIC INFERENCES FROM FOUR YEARS OF HMI/SDOOBSERVATIONS

We present and discuss results from time-distance helioseismic measurements of meridional circulation in the solar convection zone using 4 years of Doppler velocity observations by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Using an in-built mass conservation constraint in terms of the stream function we invert helioseismic travel times to infer meridional circulation in the solar convection zone. We find that the return flow that closes the meridional circulation is possibly beneath the depth of $0.77 R_{\odot}$. We discuss the significance of this result in relation to other helioseismic inferences published recently and possible reasons for the differences in the results. Our results show clearly the pitfalls involved in the measurements of material flows in the deep solar interior given the current limits on signal-to-noise and our limited understanding of systematics in the data. We also discuss the implications of our results for the dynamics of solar interior and popular solar dynamo models.

EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION

We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD "millenium simulation" of Passos & Charbonneau (2014). This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally-oriented bands of strong magnetic field accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly subadiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of subadiabaticity in the stable fluid layers underlying the convection zone.

Erratum to “Solar radiation assisted mixed convection MHD flow of nanofluids over an inclined transparent plate embedded in a porous medium”

Erratum to “Solar radiation assisted mixed convection MHD flow of nanofluids over an inclined transparent plate embedded in a porous medium”

Dynamics of planetary ions in the induced magnetospheres of Venus and Mars

We compare dynamics of planetary ions in the induced magnetospheres of Venus and Mars in a global hybrid simulation to study factors controlling the ion escape at unmagnetized planets. In the simulation we find that the finite Larmor radius (FLR) effects of escaping heavy ions are stronger at Mars than Venus under nominal solar wind conditions. But, varying upstream conditions, especially the IMF, affects the strength of the FLR effects. We classify three basic types of planetary ion dynamics in an induced magnetosphere. First, light ions such as hydrogen follow the E×B drift, and escape in the wake in the hemisphere where the solar wind convection electric field is pointing towards the planet. Second, heavy ions like oxygen undergo FLR effects, and escape mainly outside of the wake in the hemisphere where the solar wind convection electric field is pointing away from the planet. Third, ion species between light and heavy ions can have both the E×B and FLR type dynamics in the same time.

Persistent Near-Surface Flow Structures from Local Helioseismology

Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the {\em Global Oscillation Network Group} (GONG) and the {\em Helioseismic and Magnetic Imager} (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latitudes of 60$^{\circ}$ and above the HMI flow data reveal a strong signature of a two-sided zonal flow structure. This signature may be related to recent reports of "giant cells" in solar convection.

Solar-Cycle Variation of Subsurface Meridional Flow Derived with Ring-Diagram Analysis

We study the solar-cycle variation of the meridional flow in the near-surface layers of the solar convection zone from the surface to a depth of 16 Mm. We have analyzed Global Oscillation Network Group (GONG) Dopplergrams with a ring-diagram analysis covering about 13 years (July 2001 – October 2014), from the maximum of Cycle 23 through the rising phase of Cycle 24, and Helioseismic and Magnetic Imager (HMI) Dopplergrams covering more than four years (May 2010 – January 2015). GONG and HMI lead to similar meridional flows during common epochs and latitudes. The meridional flow averaged over a Carrington rotation is poleward up to about $70^{\circ}$ in both hemispheres at all depths after correcting for systematic effects. The flow amplitude peaks at about $40^{\circ}$ latitude with an amplitude of about 16 to $20~\mbox{m}\,\mbox{s}^{-1}$ depending on depth. The meridional flow varies with the solar cycle; the flow amplitudes are larger during cycle minimum than during maximum at low- and mid-latitudes. The flows are mainly faster or more-poleward-than-average on the equatorward side of the mean latitude of activity and slower or less-poleward-than-average on its poleward side. The residual meridional flow converges near the mean latitude of activity. A comparison with the corresponding zonal flow derived from GONG and HMI data shows that the bands of more-poleward-than-average meridional flow coincide with the bands of faster-than-average zonal flow and that the bands of less-poleward-than-average meridional flow coincide with the bands of slower-than-average zonal flow. This implies that the residual flows are cyclonic. The bands of fast meridional flow appear at mid-latitudes about three years before magnetic activity of Cycle 24 is present in synoptic maps.

Relativistic opacities for astrophysical applications

We report on the use of the Los Alamos suite of relativistic atomic physics codes to generate radiative opacities for the modeling of astrophysically relevant plasmas under local thermodynamic equilibrium (LTE) conditions. The atomic structure calculations are carried out in fine-structure detail, including full configuration interaction. Three example applications are considered: iron opacities at conditions relevant to the base of the solar convection zone, nickel opacities for the modeling of stellar envelopes, and samarium opacities for the modeling of light curves produced by neutron star mergers. In the first two examples, comparisons are made between opacities that are generated with the fully and semi-relativistic capabilities in the Los Alamos suite of codes. As expected for these highly charged, iron-peak ions, the two methods produce reasonably similar results, providing confidence that the numerical methods have been correctly implemented. However, discrepancies greater than 10% are observed for nickel and investigated in detail. In the final application, the relativistic capability is used in a preliminary investigation of the complicated absorption spectrum associated with cold lanthanide elements.

Equation of state for solar near-surface convection

Abstract. Numerical 3-D radiative hydrodynamical simulations are the main tool for the analysis of the interface between the solar convection zone and the photosphere. The equation of state is one of the necessary ingredients of these simulations. We compare two equations of state that are commonly used, one ideal and one nonideal, and quantify their differences. Using a numerical code we explore how these differences propagate with time in a 2-D convection simulation. We show that the runs with different equations of state (EOSs) and everything else identical relax to statistically steady states in which the mean temperature (in the range of the continuum optical depths typical for the solar photosphere) differs by less than 0.2%. For most applications this difference may be considered insignificant.

EFFECTS OF SOLAR SURFACE MAGNETIC FIELDS ON THE TIME–DISTANCE ANALYSIS OF SOLAR SUBSURFACE MERIDIONAL FLOWS

The solar meridional flow in the deep convection zone can be measured with time?distance analysis. The difference between northward and southward acoustic wave travel times relates to the speed of meridional flow in the solar convection zone. We study the effects of surface magnetic field on the measured travel time difference in time?distance analysis by comparing the results using data with and without removing surface magnetic regions. Two results are significantly different if the field strength threshold used to remove magnetic regions is small enough, such as 50 G. The difference represents the surface magnetic effects. This difference strongly correlates with the sunspot number. The range of travel distance in this study is 7??75?, corresponding to a depth range of . The difference depends on the travel time distance, and is greatest for the travel distance of The study with different field strength thresholds indicates that a threshold of about 50 G can remove most surface magnetic effects. The measured surface magnetic effects can be explained by an effective downflow inside magnetic regions. These signals are not related to the large-scale meridional flow; they need to be considered in the measured travel time difference even when activity is low, if the travel time difference is used to infer meridional flow signals.

MERIDIONAL FLOW IN THE SOLAR CONVECTION ZONE. II. HELIOSEISMIC INVERSIONS OF GONG DATA

Meridional flow is thought to play a very important role in the dynamics of the solar convection zone; however, because of its relatively small amplitude, precisely measuring it poses a significant challenge. Here we present a complete time-distance helioseismic analysis of about two years of ground-based GONG Doppler data to retrieve the meridional circulation profile for modest latitudes, in an attempt to corroborate results from other studies. We use an empirical correction to the travel times due to an unknown center-to-limb systematic effect. The helioseismic inversion procedure is first tested and reasonably validated on artificial data from a large-scale numerical simulation, followed by a test to broadly recover the solar differential rotation found from global seismology. From GONG data, we measure poleward photospheric flows at all latitudes with properties that are comparable with earlier studies, and a shallow equatorward flow about $65$\,Mm beneath the surface, in agreement with recent findings from HMI data. No strong evidence of multiple circulation cells in depth nor latitude is found, yet the whole phase space has not yet been explored. Tests of mass flux conservation are then carried out on the inferred GONG and HMI flows and compared to a fiducial numerical baseline from models, and we find that the continuity equation is poorly satisfied. While the two disparate data sets do give similar results for about the outer $15\%$ of the interior radius, the total inverted circulation pattern appears to be unphysical in terms of mass conservation when interpreted over modest time scales. We can likely attribute this to both the influence of realization noise and subtle effects in the data and measurement procedure.

ANELASTIC VERSUS FULLY COMPRESSIBLE TURBULENT RAYLEIGH–BÉNARD CONVECTION

Numerical simulations of turbulent Rayleigh-B\'enard convection in an ideal gas, using either the anelastic approximation or the fully compressible equations, are compared. Theoretically, the anelastic approximation is expected to hold in weakly superadiabatic systems with $\epsilon = \Delta T / T_r \ll 1$, where $\Delta T$ denotes the superadiabatic temperature drop over the convective layer and $T_r$ the bottom temperature. Using direct numerical simulations, a systematic comparison of anelastic and fully compressible convection is carried out. With decreasing superadiabaticity $\epsilon$, the fully compressible results are found to converge linearly to the anelastic solution with larger density contrasts generally improving the match. We conclude that in many solar and planetary applications, where the superadiabaticity is expected to be vanishingly small, results obtained with the anelastic approximation are in fact more accurate than fully compressible computations, which typically fail to reach small $\epsilon$ for numerical reasons. On the other hand, if the astrophysical system studied contains $\epsilon\sim O(1)$ regions, such as the solar photosphere, fully compressible simulations have the advantage of capturing the full physics. Interestingly, even in weakly superadiabatic regions, like the bulk of the solar convection zone, the errors introduced by using artificially large values for $\epsilon$ for efficiency reasons remain moderate. If quantitative errors of the order of $10\%$ are acceptable in such low $\epsilon$ regions, our work suggests that fully compressible simulations can indeed be computationally more efficient than their anelastic counterparts.