On the turbulent decay of strong magnetic fields and the development of sunspot areas

Krause, F.; Ruediger, G.

doi:10.1007/bf00153288

Cited by 42 publications

(21 citation statements)

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“…Because turbulent diffusion is believed to be the dominating effect of spot decay, the decay rate of spot area is directly proportional to the turbulent diffusivity (Meyer et al 1974;Krause & Rüdiger 1975),…”

Section: Stellar Cycle Predictionmentioning

confidence: 99%

“…Martinez Pillet et al (1993) analyzed sunspot decay rates using the GPR data from 1874-1976 and found a lognormal distribution as well as some evidence for weak nonlinearities in the decay process of isolated spots. A linear area decay law has been studied from a theoretical point of view (Gokhale & Zwaan 1972;Meyer et al 1974;Krause & Rüdiger 1975). Meyer et al (1974) obtained a constant area decrease rate through a process of diffusion of magnetic field over the entire area of the spot.…”

Section: Introductionmentioning

confidence: 99%

“…This diffusion model predicts a linear area (and magnetic flux) decay, implying that dA/dt is proportional to the turbulent diffusivity η T . Krause & Rüdiger (1975) proposed a similar model based on turbulence, where the turbulent diffusion was related to the flux decay by dΦ/dt ∝ η T . Rüdiger & Kitchatinov (2000) used a mean-field formulation of diffusivity quenching and produced quasi-linear decays for both the spot area as well as the magnetic flux.…”

Section: Introductionmentioning

confidence: 99%

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Spot evolution on the red giant star XX Triangulum

Künstler

Carroll

Strassmeier

2015

A&A

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Context. Solar spots appear to decay linearly proportional to their size. The decay rate of solar spots is directly related to magnetic diffusivity, which itself is a key quantity for the length of a magnetic-activity cycle. Is a linear spot decay also seen on other stars, and is this in agreement with the large range of solar and stellar activity cycle lengths? Aims. We investigate the evolution of starspots on the rapidly-rotating (P rot ≈ 24 d) K0 giant XX Tri, using consecutive time-series Doppler images. Our aim is to obtain a well-sampled movie of the stellar surface over many years, and thereby detect and quantify a starspot decay law for further comparison with the Sun. Methods. We obtained continuous high-resolution and phase-resolved spectroscopy with the 1.2-m robotic STELLA telescope on Tenerife over six years, and these observations are ongoing. For each observing season, we obtained between 5 to 7 independent Doppler images, one per stellar rotation, making up a total of 36 maps. All images were reconstructed with our line-profile inversion code iMap. A wavelet analysis was implemented for denoising the line profiles. To quantify starspot area decay and growth, we match the observed images with simplified spot models based on a Monte Carlo approach. Results. It is shown that the surface of XX Tri is covered with large high-latitude and even polar spots and with occasional small equatorial spots. Just over the course of six years, we see a systematically changing spot distribution with various timescales and morphology, such as spot fragmentation and spot merging as well as spot decay and formation. An average linear decay of D = −0.022 ± 0.002 SH/day is inferred. We found evidence of an active longitude in phase toward the (unseen) companion star. Furthermore, we detect a weak solar-like differential rotation with a surface shear of α = 0.016 ± 0.003. From the decay rate, we determine a turbulent diffusivity of η T = (6.3 ± 0.5) × 10 14 cm 2 /s and predict a magnetic activity cycle of ≈26 ± 6 yr. Finally, we present a short movie of the spatially resolved surface of XX Tri.

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Section: Stellar Cycle Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spot evolution on the red giant star XX Triangulum

Künstler

Carroll

Strassmeier

2015

A&A

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“…The latter model, proposed independently by Meyer et al (1974) and by Krause and Rüdiger (1975), assumes that the decay of the spot is caused by turbulent diffusion throughout the whole cross-section of the tube, with a magnetically reduced but otherwise constant diffusivity. It was found that defining the boundary of the spot at some arbitrary fixed value of the flux density, such a diffusion naturally results in a linear decay law, and the Gnevyshev-Waldmeier relation is also returned.…”

Section: Modelsmentioning

confidence: 99%

Untitled

1997

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Abstract. In a statistical study of the decay of individual sunspots based on DPR data we find that the mean instantaneous area decay rate is related to the spot radius r and the maximal radius r0 as D = CD r/r0, CD = 32.0±0.26 MSH/day. This implies that sunspots on the mean follow a parabolic decay law; the traditional linear decay law is excluded by the data. The validity of the Gnevyshev-Waldmeier relationship between the maximal area A0 and lifetime T of a spot group, A0/T ≃ 10 MSH/day, is also demonstrated for individual sunspots. No evidence is found for a supposed supergranular "quantization" of sunspot areas. Our results strongly support the recent turbulent erosion model of sunspot decay while all other models are excluded.

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“…Early theories invoked turbulent diffusion of the magnetic field within the spot to model the observed rate of decay, yet such models predicted a linear decay law, corresponding to a constant area decay rate dA/dt (Meyer et al 1974;Krause & Rüdiger 1975). In order to explain a parabolic decay, Petrovay & Moreno-Insertis (1997) developed a model of sunspot disintegration by turbulent "erosion" of penumbral boundaries, which occurs when bits of magnetic field are sliced away from the edge of a sunspot and swept to the supergranular cell boundaries by supergranular flows (Simon & Leighton 1964).…”

Section: Introductionmentioning

confidence: 99%

Sunspot and Starspot Lifetimes in a Turbulent Erosion Model

Litvinenko

Wheatland

2017

ApJ

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Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient D: an inverse power-law dependence D ∝ B −ν and a stepfunction dependence of D on the magnetic field magnitude B. Analytical self-similar solutions are presented for the power-law case, including solutions exhibiting "superfast" diffusion. For the stepfunction case, the heat-balance integral method yields approximate solutions, valid for moderately suppressed diffusion in the spot. The accuracy of the resulting solutions is confirmed numerically, using a method which provides an accurate description of long-time evolution by imposing boundary conditions at infinite distance from the spot. The new models may allow insight into differences and similarities between sunspots and starspots.

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On the turbulent decay of strong magnetic fields and the development of sunspot areas

Cited by 42 publications

References 9 publications

Spot evolution on the red giant star XX Triangulum

Spot evolution on the red giant star XX Triangulum

Untitled

Sunspot and Starspot Lifetimes in a Turbulent Erosion Model

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