Simulations of magnetic-flux transport in solar active regions

We simulate the evolution of several observed solar active regions by solving a transport equation for magnetic flux at the photosphere. The rates of rotation, meridional flow, and diffusion of the flux are determined self-consistently in the calculations. Our findings are in good quantitative agreement with previous measures of the rotation rate and diffusion constant associated with photospheric magnetic fields. Although our meridional velocities are consistent in direction and magnitude with recently reported poleward flows, relatively large uncertainties in our velocity determinations make this result inconclusive.Laboratory for Computational Physics.E. O. Hulburt Center for Space Research.     

An Evolving Synoptic Magnetic Flux map and Implications for the Distribution of Photospheric Magnetic Flux

We describe a procedure intended to produce accurate daily estimates of the magnetic flux distribution on the entire solar surface. Models of differential rotation, meridional flow, supergranulation, and the random emergence of background flux elements are used to regularly update unobserved or poorly observed portions of an initial traditional magnetic synoptic map that acts as a seed. Fresh observations replace model estimates when available. Application of these surface magnetic transport models gives us new insight into the distribution and evolution of magnetic flux on the Sun, especially at the poles where canopy effects, limited spatial resolution, and foreshortening result in poor measurements. We find that meridional circulation has a considerable effect on the distribution of polar magnetic fields. We present a modeled polar field distribution as well as time series of the difference between the northern and southern polar magnetic flux; this flux imbalance is related to the heliospheric current sheet tilt. We also estimate that the amount of new background magnetic flux needed to sustain the `quiet-Sun' magnetic field is about 1.1×10²³ Mx d^–1 (equivalent to several large active regions) at the spatial resolution and epoch of our maps. We comment on the diffusive properties of supergranules, ephemeral regions, and intranetwork flux. The maps are available on the NSO World Wide Web page.     

An Exploration of Non-kinematic Effects in Flux Transport Dynamos

Recent global magnetohydrodynamical simulations of solar convection producing a large-scale magnetic field undergoing regular, solar-like polarity reversals also present related cyclic modulations of large-scale flows developing in the convecting layers. Examination of these simulations reveal that the meridional flow, a crucial element in flux transport dynamos, is driven at least in part by the Lorentz force associated with the cycling large-scale magnetic field. This suggests that the backreaction of the field onto the flow may have a pronounced influence on the long-term evolution of the dynamo. We explore some of the associated dynamics using a low-order dynamo model that includes this Lorentz force feedback. We identify several characteristic solutions which include single period cycles, period doubling and chaos. To emulate the role of turbulence in the backreaction process we subject the model to stochastic fluctuations in the parameter that controls the Lorentz force amplitude. We find that short term fluctuations produce long-term modulations of the solar cycle and, in some cases, grand minima episodes where the amplitude of the magnetic field decays to near zero. The chain of events that triggers these quiescent phases is identified. A subsequent analysis of the energy transfer between large-scale fields and flows in the global magnetohydrodynamical simulation of solar convection shows that the magnetic field extracts energy from the solar differential rotation and deposits part of that energy into the meridional flow. The potential consequences of this marked departure from the kinematic regime are discussed in the context of current solar cycle modeling efforts based on flux transport dynamos.     

Solar shear flows deduced from helioseismic dense-pack samplings of ring diagrams

We report on large-scale horizontal flows in the solar convection zone and their variability in time and space using a local-helioseismology technique known as ring-diagram analysis. By performing this analysis on a dense mosaic of individual regions on the solar disk, i.e., a `Dense-Pack' sampling, and repeating the analysis periodically on several time scales, we are able to assess the variation of horizontal flows from day-to-day, week-to-week, and year-to-year. We find that although there are changes in the flows on all these time scales, there are also basic patterns that persist. On a daily time scale we observe that the flow is reduced in those areas which are occupied by large active regions. On somewhat longer time-scales we see bands of persistent fast and slow zonal flow that are identifiable as torsional oscillations. As we examine these bands during a series of years, we find that these bands migrate toward the equator as solar activity increases. Similarly, the latitudes at which the meridional flow reaches maximum follow these regions of fast zonal flow as they migrate equatorwards. These Dense-Pack samplings also reveal substantial differences in the zonal and meridional flow patterns in the northern and southern hemispheres.     

Magnetic Fields and Solar Activities

We discuss the study of solar magnetic fields based on the photospheric vector magnetograms of solar active regions which were obtained at Huairou Solar Observing Station near Beijing in the period of 22nd and 23th solar cycles. The measurements of the chromospheric magnetic field and the spatial configuration of the field at the lower solar atmosphere inferred by the distribution of the solar photospheric and chromospheric magnetic field. After the analysis on the formation process of delta configuration in some super active regions based on the photospheric vector magnetogram observations, some results are obtained: (1) The analysis of magnetic writhe of whole active regions cannot be limited in the strong field of sunspots, because the contribution of the fraction of decayed magnetic field is non-negligible. (2) The magnetic model of kink magnetic ropes, proposed to be generated in the subatmosphere, is not consistent with the evolution of large-scale twisted photospheric transverse magnetic field and the relationship with magnetic shear in some delta active regions completely. (3) The proposition is that the large-scale delta active regions are formed from contribution by highly sheared non-potential magnetic flux bundles generated in the subatmosphere. We present some results of a study of the magnetic helicity. We also compare these results with other data sets obtained by magnetographs (or Stokes polarimeters) at different observatories, and analyze the basic chirality of the magnetic field in the solar atmosphere.     

Comparison of Large-Scale Flows on the Sun Measured by Time-Distance Helioseismology and Local Correlation Tracking

We present a direct comparison between two different techniques: time-distance helioseismology and a local correlation tracking method for measuring mass flows in the solar photosphere and in a near-surface layer. We applied both methods to the same dataset (MDI high-cadence Dopplergrams covering almost the entire Carrington rotation 1974) and compared the results. We found that, after necessary corrections, the vector flow fields obtained by these techniques are very similar. The median difference between directions of corresponding vectors is 24°, and the correlation coefficients of the results for mean zonal and meridional flows are 0.98 and 0.88, respectively. The largest discrepancies are found in areas of small velocities where the inaccuracies of the computed vectors play a significant role. The good agreement of these two methods increases confidence in the reliability of large-scale synoptic maps obtained by them.     

Some recent developments in solar dynamo theory

We discuss the current status of solar dynamo theory and describe the dynamo model developed by our group. The toroidal magnetic field is generated in the tachocline by the strong differential rotation and rises to the solar surface due to magnetic buoyancy to create active regions. The decay of these active regions at the surface gives rise to the poloidal magnetic field by the Babcock-Leighton mechanism. This poloidal field is advected by the meridional circulation first to high latitudes and then down below to the tachocline. Dynamo models based on these ideas match different aspects of observational data reasonably well.     

Helioseismology of Time-Varying Flows Through The Solar Cycle

Flows in the upper convection zone are measured by helioseismology on a wide variety of scales. These include differential rotation and meridional circulation, local flows around complexes of magnetic activity and sunspots, and convective flows. The temporal evolution of flows through cycle 23 reveals connections between mass motions in the solar interior and the large-scale characteristics of the magnetic cycle. Here I summarize the latest observations and their implications. Observations from local helioseismology suggest that subsurface flows around active regions introduce a solar-cycle variation in the meridional circulation.     

Meridional Motion and Reynolds Stress from Debrecen Photoheliographic Data

The Debrecen Photoheliographic Data catalogue is a continuation of the Greenwich Photoheliographic Results providing daily positions of sunspots and sunspot groups. We analyse the data for sunspot groups focussing on meridional motions and transfer of angular momentum towards the solar equator. Velocities are calculated with a daily shift method including an automatic iterative process of removing the outliers. Apart from the standard differential rotation profile, we find meridional motion directed towards the zone of solar activity. The difference in measured meridional flow in comparison to Doppler measurements and some other tracer measurements is interpreted as a consequence of different flow patterns inside and outside of active regions. We also find a statistically significant dependence of meridional motion on rotation velocity residuals confirming the transfer of angular momentum towards the equator. Analysis of horizontal Reynolds stress reveals that the transfer of angular momentum is stronger with increasing latitude up to about \(40^{\circ}\), where there is a possible maximum in absolute value.     

Horizontal Flows in the Photosphere and Subphotosphere of Two Active Regions

We compare horizontal flow fields in the photosphere and in the subphotosphere (a layer 0.5 Mm below the photosphere) in two solar active regions: AR?11084 and AR?11158. AR?11084 is a mature, simple active region without significant flaring activity, and AR?11158 is a multipolar, complex active region with magnetic flux emerging during the period studied. Flows in the photosphere are derived by applying the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) on HMI-observed vector magnetic fields, and the subphotospheric flows are inferred by time–distance helioseismology using HMI-observed Dopplergrams. Similar flow patterns are found for both layers for AR?11084: inward flows in the sunspot umbra and outward flows surrounding the sunspot. The boundary between the inward and outward flows, which is slightly different in the photosphere and the subphotosphere, is within the sunspot penumbra. The area having inward flows in the subphotosphere is larger than that in the photosphere. For AR?11158, flows in these two layers show great similarities in some areas and significant differences in other areas. Both layers exhibit consistent outward flows in the areas surrounding sunspots. On the other hand, most well-documented flux-emergence-related flow features seen in the photosphere do not have counterparts in the subphotosphere. This implies that the horizontal flows caused by flux emergence do not extend deeply into the subsurface.     

Vorticity of Subsurface Flows of Emerging and Decaying Active Regions

We study the temporal variation of the vorticity of subsurface flows of 828 active regions and 977 quiet regions. The vorticity of these flows is derived from measured subsurface velocities. The horizontal flows are determined by analyzing high-resolution Global Oscillation Network Group Doppler data with ring-diagram analysis covering a range of depths from the surface to about 16 Mm. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. We determine the change in unsigned magnetic flux density during the disk passage of each active region using Michelson Doppler Imager (MDI) magnetograms binned to the ring-diagram grid with centers spaced by 7.5° ranging ± 52.5° in latitude and central meridian distance with an effective diameter of 15° after apodization. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that the vorticity of subsurface flows increases during flux emergence and decreases when active regions decay. For flux emergence, the absolute values of the zonal and meridional vorticity components show the most coherent variation with activity, while for flux decrease the strongest signature is in the absolute values of the meridional and vertical vorticity components. The temporal variation of the enstrophy (residual vorticity squared) is thus a good indicator for either flux increase or decrease. There are some indications that the increase in vorticity during flux emergence happens about a day later at depths below about 8 Mm compared to layers shallower than about 4 Mm. This timing difference might imply that the vorticity signal analyzed here is caused by the interaction between magnetic flux and turbulent flows near the solar surface. There are also hints that the vorticity decrease during flux decay begins about a day earlier at layers deeper than about 8 Mm compared to shallower ones. However, the timing difference between the change at different depths is comparable to the time step of the analysis.     

Subsurface Velocity of Emerging and Decaying Active Regions

We study the temporal variation of subsurface flows of 828 active regions and 977 quiet regions. The horizontal flows cover a range of depths from the surface to about 16 Mm and are determined by analyzing Global Oscillation Network Group high-resolution Doppler data with ring-diagram analyses. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. For comparison, we analyze Michelson Doppler Imager (MDI) Dynamics Run data covering 68 active regions common to both data sets. We determine the change in unsigned magnetic flux during the disk passage of each active region using MDI magnetograms binned to the ring-diagram grid. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that emerging flux has a faster rotation than the ambient fluid and pushes it up, as indicated by enhanced vertical velocity and faster-than-average zonal flow. After active regions are formed, downflows are established within two days of emergence in shallow layers between about 4 and 10 Mm. Emerging flux in existing active regions shows a similar scenario, where the upflows at depths greater than about 10 Mm are enhanced and the already established downflows at shallower depths are weakened. When active regions decay, the corresponding flow pattern disappears as well; the zonal flow slows down to values comparable to that of quiet regions and the upflows become weaker at deeper layers. The residual meridional velocity is mainly poleward and shows no obvious variation. The magnitude of the residual velocity, defined as the sum of the squares of the residual velocity components, increases with increasing magnetic flux and decreases with decreasing flux.     

The impact of meridional circulation on stellar butterfly diagrams and polar caps

Observations of rapidly rotating solar-like stars show a significant mixture of opposite-polarity magnetic fields within their polar regions. To explain these observations, models describing the surface transport of magnetic flux demand the presence of fast meridional flows. Here, we link subsurface and surface magnetic flux transport simulations to investigate (i) the impact of meridional circulations with peak velocities of  ≤125 m s⁻¹  on the latitudinal eruption pattern of magnetic flux tubes and (ii) the influence of the resulting butterfly diagrams on polar magnetic field properties. Prior to their eruption, magnetic flux tubes with low field strengths and initial cross-sections below  ∼300 km  experience an enhanced poleward deflection through meridional flows (assumed to be polewards at the top of the convection zone and equatorwards at the bottom). In particular, flux tubes which originate between low and intermediate latitudes within the convective overshoot region are strongly affected. This latitude-dependent poleward deflection of erupting magnetic flux renders the wings of stellar butterfly diagrams distinctively convex. The subsequent evolution of the surface magnetic field shows that the increased number of newly emerging bipoles at higher latitudes promotes the intermingling of opposite polarities of polar magnetic fields. The associated magnetic flux densities are about 20 per cent higher than in the case disregarding the pre-eruptive deflection, which eases the necessity for fast meridional flows predicted by previous investigations. In order to reproduce the observed polar field properties, the rate of the meridional circulation has to be of the order of 100 m s⁻¹, and the latitudinal range from which magnetic flux tubes originate at the base of the convective zone (≲50°) must be larger than in the solar case (≲35°).     

The Evolution of the Sun's Open Magnetic Flux – II. Full Solar Cycle Simulations

In this paper the origin and evolution of the Sun's open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun's open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.     

Surface magnetic fields during the solar activity cycle

We examine magnetic field measurements from Mount Wilson that cover the solar surface over a 13 1/2 year interval, from 1967 to mid-1980. Seen in long-term averages, the sunspot latitudes are characterized by fields of preceding polarity, while the polar fields are built up by a few discrete flows of following polarity fields. These drift speeds average about 10 m s^-1 in latitude - slower early in the cycle and faster later in the cycle - and result from a large-scale poleward displacement of field lines, not diffusion. Weak field plots show essentially the same pattern as the stronger fields, and both data indicate that the large-scale field patterns result only from fields emerging at active region latitudes. The total magnetic flux over the solar surface varies only by a factor of about 3 from minimum to a very strong maximum (1979). Magnetic flux is highly concentrated toward the solar equator; only about 1% of the flux is at the poles. Magnetic flux appears at the solar surface at a rate which is sufficient to create all the flux that is seen at the solar surface within a period of only 10 days. Flux can spread relatively rapidly over the solar surface from outbreaks of activity. This is presumably caused by diffusion. In general, magnetic field lines at the photospheric level are nearly radial.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow

We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range ±?45°. We show that the time-varying components of the meridional flow at these two depths have opposite sign, whereas the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle-dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model.     

Time-Distance Helioseismology with f Modes as a Method for Measurement of Near-Surface Flows

Travel times measured for the f mode have been used to study flows near the solar surface in conjunction with simultaneous measurements of the magnetic field. Previous flow measurements of Doppler surface rotation, small magnetic feature rotation, supergranular pattern rotation, and surface meridional circulation have been confirmed. In addition, the flow in supergranules due to Coriolis forces has been measured. The spatial and temporal power spectra for a six-day observing sequence have been measured.     

The Sun’s Large-Scale Magnetic Field and Its Long-Term Evolution

The Sun’s large-scale external field is formed through the emergence of magnetic flux in active regions and its subsequent dispersal over the solar surface by differential rotation, supergranular convection, and meridional flow. The observed evolution of the polar fields and open flux (or interplanetary field) during recent solar cycles can be reproduced by assuming a supergranular diffusion rate of 500 – 600 km² s⁻¹ and a poleward flow speed of 10 –20 m s⁻¹. The nonaxisymmetric component of the large-scale field decays on the flow timescale of ∼1 yr and must be continually regenerated by new sunspot activity. Stochastic fluctuations in the longitudinal distribution of active regions can produce large peaks in the Sun’s equatorial dipole moment and in the interplanetary field strength during the declining phase of the cycle; by the same token, they can lead to sudden weakenings of the large-scale field near sunspot maximum (Gnevyshev gaps). Flux transport simulations over many solar cycles suggest that the meridional flow speed is correlated with cycle amplitude, with the flow being slower during less active cycles.     

Imaging bright-spots in the accretion flow near the black hole horizon of Sgr A*

Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.     

太阳表面磁场的分布与演化研究进展

太阳磁场、较差自转和内部对流使得日面磁场与磁活动在很大的时间尺度和空间尺度范围均表现得相当复杂.其中最有名的是太阳活动的11年周期,或22年磁周期.在较小时间尺度上,从几秒到几小时,有时太阳大气中会发生一些壮观的爆发事件,如耀斑、日珥爆发、日冕物质抛射等.所有这些形式的事件都与太阳磁场紧密关联.简单评述了太阳磁场起源与观测方法,重点论述了不同尺度太阳磁场的空间分布与演化,介绍了从太阳磁活动现象统计得到的有关太阳磁场的几个典型特征,同时讨论了进一步研究的方向.