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Formation of solar bipolar regions: Magnetic flux concentrations from suction of the negative effective magnetic pressure instability
Stockholm University, Faculty of Science, Department of Astronomy. (Astrophysics)
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Sunspots stand out on the visible solar surface. They appear as dark structures evolving and changing over time. They host energetic and violent events, like coronal mass ejections and flares, and concentrate strong magnetic fields. Hundreds of years of studies provide a record of sunspot cycles, as reported by the well-known butterfly diagram, as well as some of their general observational properties, such as size, maximum field strength, and lifetime. However, we lack a general theory that explains how the magnetic field cluster in the spots and how it evolves over time.

This thesis studies the negative effective magnetic pressure instability (NEMPI) as a mechanism able to form such magnetic flux concentrations and thus magnetic spots. A weak magnetic field suppresses the turbulence locally and reduces the turbulent pressure. The resulting contraction concentrates the field further, which reduces the turbulent pressure even more, and so on. We study the conditions where NEMPI is excited, trying to reproduce some of the complexities of the solar environment. We focus on the effects of rotation, the change of stratification, and the influence of a simplified corona. We solve the magnetohydrodynamic equations using both direct numerical simulations and mean-field simulations of strongly stratified turbulence in a weak magnetic field.

Even slow rotation with a Coriolis number of 0.01 can suppress the instability. Higher values of rotation lead to dynamo action, increasing the magnetic field in a new coupled dynamo-NEMPI system. In the solar case, the dependence of NEMPI on rotation constrains the depth where the instability can operate: since the Coriolis number is very small in the uppermost layers of the Sun, NEMPI can only be a shallow phenomenon. Changing the type of stratification from isothermal to polytropic pushes the instability further to the upper parts of the computational domain. Unlike the isothermal case, in the polytropic cases the density scale height is no longer constant, but the stratification decreases deeper down, making it increasingly difficult for NEMPI to operate.

A corona changes dramatically the semblance of flux concentrations. A bipolar region is formed, instead of a single spot. It develops at the interface between the turbulent and the non-turbulent layers, forming a loop-like structure in the coronal layer. The bipoles move apart and finally decay and disappear. We study the structure in a wide range of parameters and test the physical conditions of its appearance. Higher stratification and imposed field strength intensify the magnetic structures, which reach even equipartition values, until a plateau and subsequent decrease occur. The increase of the domain size strengthens the maximum magnetic field and gives more coherence to the spots, keeping their sizes. We measure a strong large-scale downward and converging flows associated with the concentration of flux. Finally, we also include rotation in the two-layer model, confirming the previous results: slow rotation suppresses the formation of bipolar regions. A stronger imposed magnetic field alleviates the suppression somewhat and strengthens the structures.

These studies demonstrate the viability of NEMPI to form magnetic flux concentrations in both monopolar and bipolar structures. We find that NEMPI can only develop in the uppermost layers, where the local Coriolis number is small and the stratification strong.

Place, publisher, year, edition, pages
Stockholm: Department of Astronomy, Stockholm University , 2018. , p. 70
Keywords [en]
Magnetohydrodynamics (MHD), turbulence, dynamo, Sun: magnetic fields, Sun: rotation, Sun: activity, Sun: dynamo
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
URN: urn:nbn:se:su:diva-161765ISBN: 978-91-7797-434-5 (print)ISBN: 978-91-7797-435-2 (electronic)OAI: oai:DiVA.org:su-161765DiVA, id: diva2:1261124
Public defence
2019-01-08, sal FB42, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2018-12-18 Created: 2018-11-06 Last updated: 2018-12-18Bibliographically approved
List of papers
1. Rotational effects on the negative magnetic pressure instability
Open this publication in new window or tab >>Rotational effects on the negative magnetic pressure instability
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2012 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 548, article id A49Article in journal (Refereed) Published
Abstract [en]

Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims. We want to understand the effects of rotation on this instability in both two and three dimensions. Methods. We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results. We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions. We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.

Keywords
magnetohydrodynamics (MHD), hydrodynamics, turbulence, dynamo
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-86494 (URN)10.1051/0004-6361/201220078 (DOI)000311901200049 ()
Note

AuthorCount:5;

Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2018-11-06Bibliographically approved
2. Competition of rotation and stratification in flux concentrations
Open this publication in new window or tab >>Competition of rotation and stratification in flux concentrations
2013 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 556, article id A83Article in journal (Refereed) Published
Abstract [en]

Context. In a strongly stratified turbulent layer, a uniform horizontal magnetic field can become unstable and spontaneously form local flux concentrations due to a negative contribution of turbulence to the large-scale (mean-field) magnetic pressure. This mechanism, which is called negative effective magnetic pressure instability (NEMPI), is of interest in connection with dynamo scenarios in which most of the magnetic field resides in the bulk of the convection zone and not at the bottom, as is often assumed. Recent work using mean-field hydromagnetic equations has shown that NEMPI becomes suppressed at rather low rotation rates with Coriolis numbers as low as 0.1. Aims. Here we extend these earlier investigations by studying the effects of rotation both on the development of NEMPI and on the effective magnetic pressure. We also quantify the kinetic helicity resulting from direct numerical simulations (DNS) with Coriolis numbers and strengths of stratification comparable to values near the solar surface and compare it with earlier work at smaller scale separation ratios. Further, we estimate the expected observable signals of magnetic helicity at the solar surface. Methods. To calculate the rotational effect on the effective magnetic pressure we consider both DNS and analytical studies using the tau approach. To study the effects of rotation on the development of NEMPI we use both DNS and mean-field calculations of the three-dimensional hydromagnetic equations in a Cartesian domain. Results. We find that the growth rates of NEMPI from earlier mean-field calculations are well reproduced with DNS, provided the Coriolis number is below 0.06. In that case, kinetic and magnetic helicities are found to be weak and the rotational effect on the effective magnetic pressure is negligible as long as the production of flux concentrations is not inhibited by rotation. For faster rotation, dynamo action becomes possible. However, there is an intermediate range of rotation rates where dynamo action on its own is not yet possible, but the rotational suppression of NEMPI is being alleviated. Conclusions. Production of magnetic flux concentrations through the suppression of turbulent pressure appears to be possible only in the uppermost layers of the Sun, where the convective turnover time is less than two hours.

Keywords
magnetohydrodynamics (MHD), hydrodynamics, turbulence, Sun: dynamo
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-94587 (URN)10.1051/0004-6361/201220939 (DOI)000323893500083 ()
Funder
EU, European Research Council, 227952Swedish Research Council, 621-2011-5076Swedish Research Council, 2012-5797EU, European Research Council, 227915
Note

AuthorCount:4;

Available from: 2013-10-08 Created: 2013-10-07 Last updated: 2018-11-06Bibliographically approved
3. Magnetic flux concentrations in a polytropic atmosphere
Open this publication in new window or tab >>Magnetic flux concentrations in a polytropic atmosphere
2014 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 564, article id A2Article in journal (Refereed) Published
Abstract [en]

Context. Strongly stratified hydromagnetic turbulence has recently been identified as a candidate for explaining the spontaneous formation of magnetic flux concentrations by the negative effective magnetic pressure instability (NEMPI). Much of this work has been done for isothermal layers, in which the density scale height is constant throughout. Aims. We now want to know whether earlier conclusions regarding the size of magnetic structures and their growth rates carry over to the case of polytropic layers, in which the scale height decreases sharply as one approaches the surface. Methods. To allow for a continuous transition from isothermal to poly tropic layers, we employ a generalization of the exponential function known as the q-exponential. This implies that the top of the polytropic layer shifts with changing polytropic index such that the scale height is always the same at some reference height. We used both mean-field simulations (MPS) and direct numerical simulations (DNS) of forced stratified turbulence to determine the resulting flux concentrations in polytropic layers. Cases of both horizontal and vertical applied magnetic fields were considered. Results. Magnetic structures begin to form at a depth where the magnetic field strength is a small fraction of the local equipartition field strength with respect to the turbulent kinetic energy. Unlike the isothermal case where stronger fields can give rise to magnetic flux concentrations at larger depths, in the polytropic case the growth rate of NEMPI decreases for structures deeper down. Moreover, the structures that form higher up have a smaller horizontal scale of about four times their local depth. For vertical fields, magnetic structures of super-equipartition strengths are formed, because such fields survive downward advection that causes NEMPI with horizontal magnetic fields to reach premature nonlinear saturation by what is called the potato-sack effect. The horizontal cross-section of such structures found in DNS is approximately circular, which is reproduced with MFS of NEMPI using a vertical magnetic field. Conclusions. Results based on isothermal models can be applied locally to polytropic layers. For vertical fields, magnetic flux concentrations of super-equipartition strengths form, which supports suggestions that sunspot formation might be a shallow phenomenon.

Keywords
magnetohydrodynamics (MHD), hydrodynamics, turbulence, Sun: dynamo
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-103961 (URN)10.1051/0004-6361/201322315 (DOI)000334671000002 ()
Funder
EU, European Research Council, 227952EU, European Research Council, 227915Swedish Research Council, 621-2011-5076Swedish Research Council, 2012-5797
Note

AuthorCount:4;

Available from: 2014-06-09 Created: 2014-05-27 Last updated: 2018-11-06Bibliographically approved
4. Bipolar Magnetic Structures Driven by Stratified Turbulence with a Coronal Envelope
Open this publication in new window or tab >>Bipolar Magnetic Structures Driven by Stratified Turbulence with a Coronal Envelope
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2013 (English)In: Astrophysical Journal Letters, ISSN 2041-8205, E-ISSN 2041-8213, Vol. 777, no 2, article id L37Article in journal (Refereed) Published
Abstract [en]

We report the spontaneous formation of bipolar magnetic structures in direct numerical simulations of stratified forced turbulence with an outer coronal envelope. The turbulence is forced with transverse random waves only in the lower (turbulent) part of the domain. Our initial magnetic field is either uniform in the entire domain or confined to the turbulent layer. After about 1-2 turbulent diffusion times, a bipolar magnetic region of vertical field develops with two coherent circular structures that live during one turbulent diffusion time, and then decay during 0.5 turbulent diffusion times. The resulting magnetic field strengths inside the bipolar region are comparable to the equipartition value with respect to the turbulent kinetic energy. The bipolar magnetic region forms a loop-like structure in the upper coronal layer. We associate the magnetic structure formation with the negative effective magnetic pressure instability in the two-layer model.

Keywords
magnetohydrodynamics (MHD), starspots, Sun: corona, sunspots, turbulence
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-97026 (URN)10.1088/2041-8205/777/2/L37 (DOI)000326266500019 ()
Note

AuthorCount:5; 

Available from: 2013-12-03 Created: 2013-12-02 Last updated: 2018-11-07Bibliographically approved
5. Bipolar region formation in stratified two-layer turbulence
Open this publication in new window or tab >>Bipolar region formation in stratified two-layer turbulence
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2016 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 589, article id A125Article in journal (Refereed) Published
Abstract [en]

Aims. This work presents an extensive study of the previously discovered formation of bipolar flux concentrations in a two-layer model. We interpret the formation process in terms of negative effective magnetic pressure instability (NEMPI), which is a possible mechanism to explain the origin of sunspots. Methods. In our simulations, we use a Cartesian domain of isothermal stratified gas that is divided into two layers. In the lower layer, turbulence is forced with transverse nonhelical random waves, whereas in the upper layer no flow is induced. A weak uniform magnetic field is imposed in the entire domain at all times. In most cases, it is horizontal, but a vertical and an inclined field are also considered. In this study we vary the stratification by changing the gravitational acceleration, magnetic Reynolds number, strength of the imposed magnetic field, and size of the domain to investigate their influence on the formation process. Results. Bipolar magnetic structure formation takes place over a large range of parameters. The magnetic structures become more intense for higher stratification until the density contrast becomes around 100 across the turbulent layer. For the fluid Reynolds numbers considered, magnetic flux concentrations are generated at magnetic Prandtl number between 0.1 and 1. The magnetic field in bipolar regions increases with higher imposed field strength until the field becomes comparable to the equipartition field strength of the turbulence. A larger horizontal extent enables the flux concentrations to become stronger and more coherent. The size of the bipolar structures turns out to be independent of the domain size. A small imposed horizontal field component is necessary to generate bipolar structures. In the case of bipolar region formation, we find an exponential growth of the large-scale magnetic field, which is indicative of a hydromagnetic instability. Additionally, the flux concentrations are correlated with strong large-scale downward and converging flows. These findings imply that NEMPI is responsible for magnetic flux concentrations.

Keywords
magnetohydrodynamics (MHD), turbulence, sunspots, starspots, Sun: magnetic fields
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-131541 (URN)10.1051/0004-6361/201525880 (DOI)000375318300137 ()
Available from: 2016-07-01 Created: 2016-06-21 Last updated: 2018-11-06Bibliographically approved
6. Magnetic bipoles in rotating turbulence with coronal envelope
Open this publication in new window or tab >>Magnetic bipoles in rotating turbulence with coronal envelope
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2019 (English)In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 621, article id A61Article in journal (Refereed) Published
Abstract [en]

The formation of sunspots and starspots is not yet fully understood and is therefore one of the major open problems in solar and stellar physics. Magnetic flux concentrations can be produced by the negative effective magnetic pressure instability (NEMPI). This instability is strongly suppressed by rotation. However, the presence of an outer coronal envelope was previously found to strengthen the flux concentrations and make them more prominent. It also allows for the formation of bipolar regions (BRs). We want to know whether the presence of an outer coronal envelope also changes the excitation conditions and the rotational dependence of NEMPI. We use direct numerical simulations and mean-field simulations. We adopt a simple two-layer model of turbulence that mimics the jump between the convective turbulent and coronal layers below and above the surface of a star, respectively. The computational domain is Cartesian and located at a certain latitude of a rotating sphere. We investigate the effects of rotation on NEMPI by changing the Coriolis number, the latitude, and the box resolution. Rotation has a strong impact on the process of BR formation. Even rather slow rotation is found to suppress their formation. However, increasing the imposed magnetic field strength also makes the structures stronger and alleviates the rotational suppression somewhat. The presence of a coronal layer itself does not significantly alleviate the effects of rotational suppression.

Keywords
magnetohydrodynamics (MHD), turbulence, dyanmo, Sun:magnetic fields, Sun:rotation, Sun:activity
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Astronomy
Identifiers
urn:nbn:se:su:diva-161718 (URN)10.1051/0004-6361/201833018 (DOI)
Available from: 2018-11-05 Created: 2018-11-05 Last updated: 2019-01-19Bibliographically approved

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