Figure 5 - uploaded by Mark S. Miesch
Content may be subject to copyright.
Schematic diagram illustrating the energy flow in an anelastic model. The thermal energy incorporates both the internal energy of the plasma and the gravitational potential energy as described in the text. The buoyancy force and compression can transfer energy among the thermal and kinetic energy reservoirs while the Lorentz force can transfer energy among the kinetic and magnetic energy reservoirs. Viscous and Ohmic heating can also convert kinetic and magnetic energy to thermal energy.
Source publication
The past few decades have seen dramatic progress in our understanding of solar interior dynamics, prompted by the relatively new science of helioseismology and increasingly sophisticated numerical models. As the ultimate driver of solar variability and space weather, global-scale convective motions are of particular interest from a practical as wel...
Contexts in source publication
Context 1
... boundary conditions may lead to energy transport into or out of the domain. Figure 5 summarizes the exchange of energy between the different reservoirs of the system. Energy is supplied from below via a radiative energy flux which ultimately originates from nuclear burning in the solar core. ...
Context 2
... in the most turbulent parameter regimes, a persistent feature of global-scale simulations of rotating convection has been the presence of extended downflow lanes at low latitudes aligned in a north-south orientation (see Section 6.2). Such flow structures naturally give rise to prograde equatorial differential rotation as demonstrated in panel a of Figure 15. The Coriolis force tends to divert eastward (prograde) flows toward the equator and westward (retrograde) flows toward the poles, leading to positive < v θ v φ > correlations which transport angular momentum toward the equator via the Reynolds stress [see Equation (70)]. ...
Context 3
... additional complication to the problem of polar spin-up occurs when the convection is allowed to penetrate into an underlying stable region, as demonstrated in panel b of Figure 15. In turbulent parameter regimes, the convection is dominated by downflow plumes and lanes which acquire cyclonic vorticity in the upper convection zone due to the tendency for converging horizontal flows to conserve their angular momentum (see Section 6.2). ...
Context 4
... 17, panel d). This can be attributed to the turbulent alignment of downflow plumes as illustrated in panel b of Figure 15 and as discussed in Section 4.3. In turbulent parameter regimes, convective overshoot is dominated by helical downflow plumes which are tilted toward the rotation axis with respect to the vertical. ...
Context 5
... rates for the m = 1 and m = 2 SW modes of a toroidal band are shown in Figure 25 for parameter values characteristic of the overshoot region and lower tachocline (G is the reduced gravity and s is the fractional angular velocity contrast between the equator and pole). In the overshoot region, weak bands (≤ 10 4 G) are unstable at all latitudes. ...
Similar publications
Sunspots are of basic interest in the study of the Sun. Their relevance ranges from them being an activity indicator of magnetic fields to being the place where coronal mass ejections and flares erupt. They are therefore also an important ingredient of space weather. Their formation, however, is still an unresolved problem in solar physics. Observa...
Citations
... Energy is generated in the Sun's core by nuclear fusion and transported to the surface primarily through radiative and convective mechanisms. Convection is thought to dominate in the outer 30% of the Sun (by radius R ⊙ ), especially in the near-surface layers, due to the high opacity of the plasma 1 . The details of these convective flows matter since they are thought to govern thermal transport, maintain differential rotation and meridional circulation, influence the solar dynamo and play a role in the emergence of magnetic fields 2 . ...
Supergranules, which are solar flow features with a lateral scale of 30,000–40,000 km and a lifetime of ~24 h, form a prominent component of the Sun’s convective spectrum. However, their internal flows, which can be probed only by helioseismology, are not well understood. We analyse dopplergrams recorded by the Solar Dynamics Observatory satellite to identify and characterize ~23,000 supergranules. We find that the vertical flows peak at a depth of ~10,000 km, and remain invariant over the full range of lateral supergranular scales, contrary to numerical predictions. We also infer that, within the local seismic resolution (≳5,000 km), downflows are ~40% weaker than upflows, indicating an apparent mass-flux imbalance. This may imply that the descending flows also comprise plumes, which maintain the mass balance but are simply too small to be detected by seismic waves. These results challenge the widely used mixing-length description of solar convection.
... In addition, the solar MC redistributes the an-gular momentum (AM) inside the convective zone (e.g. Miesch 2005). In a statistically steady state, the AM profile is determined by a balance between the amount of AM transported by MC and that transported by turbulent Reynolds stresses (c.f. ...
We have carried out inversions of travel times as measured by Gizon et al. (2020) to infer the internal profile of the solar meridional circulation (MC). A linear inverse problem has been solved by the regularized least-squares method with a constraint that the angular momentum (AM) transport by MC should be equatorward (HK21-type constraint). Our motivation for using this constraint is based on the result by Hotta and Kusano (2021) where the solar equator-fast rotation was reproduced successfully without any manipulation. The inversion result indicates that the MC profile is a double-cell structure if the so-called HK21 regime, in which AM transported by MC sustains the equator-fast rotation, correctly describes the physics inside the solar convective zone. The sum of the squared residuals computed with the inferred double-cell MC profile is comparable to that computed with the single-cell MC profile obtained when we exclude the HK21-type constraint, showing that both profiles can explain the data more or less at the same level. However, we also find that adding the HK21-type constraint degrades the resolution of the averaging kernels. Although it is difficult for us to determine the large-scale morphology of the solar MC at the moment, our attempt highlights the relevance of investigating the solar MC profile from both theoretical and observational perspectives.
... Because of mass conservation, the flow submerges into the interior, switches direction, and returns toward the equator at some depth. This flow is of great relevance to the global dynamics of the Sun and to its magnetism because it may play an important role in modulating the amplitude and duration of sunspot cycles (e.g., Jiang et al. 2010;Upton & Hathaway 2014a, 2014b and at transporting angular momentum and magnetic flux (e.g., Wang et al. 1989;Miesch 2005;Featherstone & Miesch 2015). Yet, characterizing the structure of the meridional circulation has been a challenge. ...
Meridional circulation regulates the Sun’s interior dynamics and magnetism. While it is well accepted that meridional flows are poleward at the Sun’s surface, helioseismic observations have yet to provide a definitive answer for the depth at which those flows return to the equator, or the number of circulation cells in depth. Here, we explore the observability of multiple circulation cells stacked in radius. Specifically, we examine the seismic signature of several meridional flow profiles by convolving time–distance averaging kernels with mean flows obtained from a suite of 3D hydrodynamic simulations. At mid and high latitudes, we find that weak flow structures in the deep convection zone can be obscured by signals from the much stronger surface flows. This contamination of 1–2 m s ⁻¹ is caused by extended side lobes in the averaging kernels, which produce a spurious equatorward signal with flow speeds that are 1 order of magnitude stronger than the original flow speeds in the simulations. At low latitudes, the flows in the deep layers of the simulations are stronger (>2 m s ⁻¹ ) and multiple cells across the convection zone can produce a sufficiently strong signal to survive the convolution process. Now that meridional flows can be measured over two decades of data, the uncertainties arising from convective noise have fallen to a level where they are comparable in magnitude to the systematic biases caused by nonlocal features in the averaging kernels. Hence, these systematic errors are beginning to influence current helioseismic deductions and need broader consideration.
... A general introduction to this topic can be found in Sect. 8.2 of Miesch (2005). ...
The solar tachocline is an internal region of the Sun possessing strong radial and latitudinal shears straddling the base of the convective envelope. Based on helioseismic inversions, the tachocline is known to be thin (less than 5% of the solar radius). Since the first theory of the solar tachocline in 1992, this thinness has not ceased to puzzle solar physicists. In this review, we lay out the grounds of our understanding of this fascinating region of the solar interior. We detail the various physical mechanisms at stake in the solar tachocline, and put a particular focus on the mechanisms that have been proposed to explain its thinness. We also examine the full range of MHD processes including waves and instabilities that are likely to occur in the tachocline, as well as their possible connection with active region patterns observed at the surface. We reflect on the most recent findings for each of them, and highlight the physical understanding that is still missing and that would allow the research community to understand, in a generic sense, how the solar tachocline and stellar tachocline are formed, are sustained, and evolve on secular timescales.
... Solar magnetic phenomena originate in the dynamic processes of thermal convection of electrically conducting plasma deep within the solar interior. High-resolution numerical simulations of thermal convection and magnetic field generation in rotating spherical shells based on fundamental physical laws have emerged as useful tools for understanding the complexities of solar dynamics [1,2]. Global simulations are increasingly compared to observational data and used to aid in observational interpretation. ...
... An evolution equation for the differential rotation generated by thermal convection in a rotating spherical shell can be obtained by averaging the zonal component of the momentum Equation (2b) over longitude. The result reveals that differential rotation is driven and maintained by a balance of Reynolds and Maxwell stresses modulated by stresses due to meridional circulation, magnetic tension and viscous dissipation [1,30]. Naturally, parameter values affect all of these stresses. ...
... There is a clear distinction between the uniform cases ( Figure 5A,C,E) and the nonuniform cases ( Figure 5B,D,F), with a break in positive S ϕ,t from mid to high/low latitudes. This result is significant because deviations of differential rotations form geostrophy (cylindrical profiles) are known to also be enhanced by the presence of non-vanishing latitudinal entropy gradients [1,30,38]. Indeed, when pressure gradients and Coriolis and buoyancy forces are in a dominant balance, as occured in our simulations and may indeed occur in the bulk of the solar convection zone, it can be shown that the zonal component of the curl of the momentum Equation (2b) reduces to the so-called thermal wind balancê ...
Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.
... The STABLE dynamo model solves the kinematic MHD induction equation as first reported in Miesch and Dikpati (2014) and later in more detail by Miesch and Teweldebirhan (2016), Hazra, Choudhuri and Miesch (2016) and Karak and Miesch (2017). The Anelastic Spherical Harmonic (ASH) code (Brun, Miesch and Toomre, 2004;Miesch, 2005;Miesch and Toomre, 2009;Brun, 2010) serves as the dynamical core for the STABLE model. STABLE is a 3D Babcock-Leighton/Flux Transport dynamo model in which the source of the poloidal field is determined from the explicit emergence, distortion, and dispersal of BMRs by differential rotation, meridional circulation and now inflow into the BMRs (see Figure 1). ...
The changing magnetic fields of the Sun are generated and maintained by a solar dynamo, the exact nature of which remains an unsolved fundamental problem in solar physics. Our objective in this paper is to investigate the role and impact of converging flows toward Bipolar Magnetic Regions (BMR inflows) on the Sun's global solar dynamo. These flows are large-scale physical phenomena that have been observed and so should be included in any comprehensive solar dynamo model. We have augmented the Surface flux Transport And Babcock–LEighton (STABLE) dynamo model to study the nonlinear feedback effect of BMR inflows with magnitudes varying with surface magnetic fields. This fully-3D realistic dynamo model produces the sunspot butterfly diagram and allows a study of the relative roles of dynamo saturation mechanisms such as tilt-angle quenching and BMR inflows. The results of our STABLE simulations show that BMR inflows significantly affect the evolution of the BMRs themselves and result in a reduced buildup of the global poloidal field due to local flux cancellation within the BMRs, to an extent that is sufficient to saturate the dynamo. As a consequence, for the first time, we have achieved fully 3D solar dynamo solutions in which BMR inflows alone regulate the amplitudes and periods of the magnetic cycles.
... This makes our estimated value of δ TW a lower bound. It has been proposed that the tachocline is substantially thinner than the inversion kernels (e.g., Elliott 1997 ), but the true thickness is still unknown and would have important consequences for the global solar dynamo and the tachocline confinement problem (e.g., Miesch 2005 ;Matilsky et al. 2022 ). If we accept thermal wind balance a priori, then a precisely measured δ in the tachocline (after subtracting the δ cent and δ quad given here) should yield the true value of δ TW , and hence . ...
In many rotating fluids, the lowest-order force balance is between gravity, pressure, and rotational acceleration (‘GPR’ balance). Terrestrial GPR balance takes the form of geostrophy and hydrostasy, which together yield the terrestrial thermal wind equation. By contrast, stellar GPR balance is an oblateness equation, which determines the departures of the thermal variables from spherical symmetry; its curl yields the ‘stellar thermal wind equation.’ In this sense, the stellar thermal wind should be viewed not as a consequence of geostrophy, but of baroclinicity in the oblateness. Here we treat the full stellar oblateness, including the thermal wind, using pressure coordinates. We derive the generalised stellar thermal wind equation and identify the parameter regime for which it holds. In the case of the Sun, not considering the full oblateness has resulted in conflicting calculations of the theoretical aspherical temperature anomaly. We provide new calculation here and find that the baroclinic anomaly is ∼3–60 times smaller than the barotropic anomaly. Thus, the anomaly from the thermal wind may not be measurable helioseismically; but if measurement were possible, this would potentially yield a new way to bracket the depth of the solar tachocline.
... In the cases of interest, the centrifugal force is very small compared MNRAS 525, 508-526 (2023) to the gravitational force, into which it can be subsumed. F or e xample, in the Sun, the centrifugal force is about 10 5 times smaller than the gravitational force (Miesch 2005 ). For this reason, it is neglected here. ...
... MNRAS 525, 508-526 (2023) both in the Sun (Miesch 2005 ) and in Jupiter (Guillot et al. 2004 ). In the bulk of the conv ectiv e zone, the energy contained in the large scale eddies is transported towards the surface mostly by the enthalpy flux, with comparatively very little dissipation due to viscous stresses acting on the smaller scales. ...
This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective timescale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} /t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv}/ \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta \left( r \right) \sim r \omega_{\rm osc}/ \left( g \left( r \right) t_{\rm conv} \left( r \right)\right)$, where $g$ is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g / r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta \left( r \right) $ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta}$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta}$ is shown to be equal to the standard tidal dissipation factor.
... Substantial progress has been made in helioseismology [1] in the last few decades, particularly after the availability of continuous observations by ground-based Global Oscillation Networks Group (GONG; [2]), space-based Solar and Heliospheric Observatory / Michelson Doppler Imager (SOHO/MDI; [3]), and Solar Dynamics Observatory / Helioseismic and Magnetic Imager (SDO/HMI; [4,5]). Analyzing the Sun's photospheric oscillation signals, helioseismologists have derived the solar interior structure [6] and differential rotations [7,8,9] with unprecedented precision, which helped to advance our understanding of solar dynamo [10] and global-scale convection [11,12]. Below we will give a brief overview of the current status on the topics of interior rotation, meridional circulation, and helioseismology of sunspots and active regions. ...
... The Sun's meridional circulation plays an important role in transporting magnetic flux and angular momentum across different latitudes [12], thus is another important component in the Sun's global-scale dynamics and solar dynamo [15]. However, the detailed structure of the interior meridional circulation is still not well agreed upon among helioseismologists. ...
... Solar magnetic patches have been observed over decades by various land-based and space-based instruments (see e.g., Miesch, 2005; Bellot Rubio and Orozco Suárez, 2019, and the references therein). The Solar Dynamics Observatory (SDO) mis- sion, launched in 2010, is a well-equipped spacecraft that has provided high-quality data in recent years. ...
Solar and stellar magnetic patches (i.e., magnetic fluxes that reach the surface from the interior) are believed to be the primary sources of a star's atmospheric conditions. Hence, detecting and identifying these features (also known as magnetic elements) are among the essential topics in the community. Here, we apply the complex network approach to recognize the solar magnetic patches. For this purpose, we use the line-of-sight magnetograms provided by the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. We construct the magnetic network following a specific visibility graph condition between pairs of pixels with opposite polarities and search for possible links between these regions. The complex network approach also provides the ability to rank the patches based on their connectivity (i.e., degree of nodes) and importance (i.e., PageRank). The use of the developed algorithm in the identification of magnetic patches is examined by tracking the features in consecutive frames, as well as making a comparison with the other approaches to identification. We find that this method could conveniently identify features regardless of their sizes. For small-scale (one or two pixels) features, we estimate the average of 8% false-positive and 1% false-negative errors.
