Differential Rotation Research Articles

Long-term stellar activity of M dwarfs. A combined K2 and TESS study of two early M-type stars

Studies of the rotation and activity of M type stars are essential in order to enhance our understanding of stellar dynamos and angular momentum evolution. Using the outstanding photometric capabilities of space telescopes, even those rotation signals with low amplitudes can now be investigated in previously unrivaled detail. By combining data of K2 and the TESS prime mission, the star spot activity of M dwarfs can be monitored over a timescale of half a decade. In the framework of our study on the rotation--activity relation for bright and nearby M dwarfs, we also aim to investigate their long-term activity. While K2 was observing fields distributed around the ecliptic plane, the TESS prime mission was oriented along a line of ecliptic longitude, with one camera centered on an ecliptic pole. Due to these different observing strategies, the overlap between K2 and the TESS prime mission is marginal. However, 45 stars from our sample were observed with both missions, and of these, two early M-type stars that fulfill our selection criteria, EPIC\,202059229 and EPIC\,245919787, were analyzed in more detail. We find that, for both stars, the rotation period did not change, while the rotational phase did change for EPIC\,245919787 by sim 0.2. The amplitude of the spot-induced variability changed for both stars but more significantly for EPIC\,245919787. By comparing the cumulative flare frequency distributions, we find that the flare activity for EPIC\,202059229 is unchanged, while it slightly changes for EPIC\,245919787 between the K2 and TESS epochs. Using a combination of light curves from K2 and TESS that span a baseline of up to 4.5 years, we are able to measure significant differential rotation for EPIC\,245919787. Furthermore, we show that combining missions like K2 and TESS is a promising method for detecting stellar activity cycles.

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

The Gasing Pangkah Collaboration. I. Asteroseismic Identification and Characterization of a Rapidly Rotating Engulfment Candidate* * Gasing pangkah is a traditional Malay competitive game of fighting spinning tops, whose name we adopt as the name of our collaboration.

We report the discovery and characterization of TIC 350842552 (“Zvrk”), an apparently isolated, rapidly rotating (P rot ∼ 99 days) red giant observed by TESS in its southern Continuous Viewing Zone. The star’s fast surface rotation is independently verified by the use of p-mode asteroseismology, strong periodicity in TESS and ASAS-SN photometry, and measurements of spectroscopic rotational broadening. A two-component fit to APOGEE spectra indicates a coverage fraction of its surface features consistent with the amplitude of the photometric rotational signal. Variations in the amplitude of its photometric modulations over time suggest the evolution of its surface morphology and therefore enhanced magnetic activity. We further develop and deploy new asteroseismic techniques to characterize radial differential rotation, but find at best only weak evidence for rotational shear within Zvrk’s convective envelope. This high surface rotation rate is incompatible with models of angular-momentum transport in single-star evolution. Spectroscopic abundance estimates also indicate a high lithium abundance, among other chemical anomalies. Taken together, all of these suggest a planet-ingestion scenario for the formation of this rotational configuration, various models for which we examine in detail.

3D pressure-corrected ballistic extrapolation of solar wind speed in the inner heliosphere

Solar wind parameters at different locations in the inner heliosphere can be estimated using various solar wind extrapolation methods. The simple ballistic method extrapolates solar wind parameters from the point of measurement to a chosen heliospheric position by assuming that major solar wind structures are persistent and arrive relatively unaltered to the target position. The method considers the rotation period of the Sun while assuming a constant solar wind speed during radial propagation. We improve the simple ballistic model by considering the interaction between the slow and the fast solar wind with a pressure-correction during the propagation. Instead of extrapolating from the position of a single spacecraft, we apply this pressure-corrected ballistic method to 2D speed maps of the solar source surface available from solar coronal models to determine the solar wind speed in the inner heliosphere in 3D, between latitudes of ±50°. We also take into account the effects of the solar differential rotation in our model. Our method is simple, fast and it can be applied to different source surface datasets. The results of our model are validated with in situ data from the ACE spacecraft. We find that the pressure-corrected ballistic method can give accurate predictions of the solar wind in 3D.

Exploiting Nonclassical Motion of a Trapped Ion Crystal for Quantum-Enhanced Metrology of Global and Differential Spin Rotations.

We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.

A Linear Model for Inertial Modes in a Differentially Rotating Sun

Inertial wave modes in the Sun are of interest owing to their potential to reveal new insight into the solar interior. These predominantly retrograde-propagating modes in the solar subsurface appear to deviate from the thin-shell Rossby–Haurwitz model at high azimuthal orders. We present new measurements of sectoral inertial modes at m > 15 where the modes appear to become progressively less retrograde compared to the canonical Rossby–Haurwitz dispersion relation in a corotating frame. We use a spectral eigenvalue solver to compute the spectrum of solar inertial modes in the presence of differential rotation. Focussing specifically on equatorial Rossby modes, we find that the numerically obtained mode frequencies lie along distinct ridges, one of which lies strikingly close to the observed mode frequencies in the Sun. We also find that the n = 0 ridge is deflected strongly in the retrograde direction. This suggests that the solar measurements may not correspond to the fundamental n = 0 Rossby–Haurwitz solutions as was initially suspected, but to those for a higher n. The numerically obtained eigenfunctions also appear to sit deep within the convection zone—unlike those for the n = 0 modes—which differs substantially from solar measurements and complicates inference.

How well does surface magnetism represent deep Sun-like star dynamo action?

Context. For Sun-like stars, the generation of toroidal magnetic field from poloidal magnetic field is an essential piece of the dynamo mechanism powering their magnetism. Previous authors have estimated the net toroidal flux generated in each hemisphere of the Sun by exploiting its conservative nature. This only requires observations of the photospheric magnetic field and surface differential rotation. Aims. We explore this approach using a 3D magnetohydrodynamic dynamo simulation of a cool star, for which the magnetic field and its generation are precisely known throughout the entire star. Methods. Changes to the net toroidal flux in each hemisphere were evaluated using a closed line integral bounding the cross-sectional area of each hemisphere, following the application of Stokes theorem to the induction equation; the individual line segments correspond to the stellar surface, base, equator, and rotation axis. We evaluated the influence of the large-scale flows, the fluctuating flows, and magnetic diffusion on each of the line segments, along with their depth-dependence. Results. In the simulation, changes to the net toroidal flux via the surface line segment typically dominate the total line integral surrounding each hemisphere, with smaller contributions from the equator and rotation axis. The surface line integral is governed primarily by the large-scale flows, and the diffusive current; the latter acting like a flux emergence term due to the use of an impenetrable upper boundary in the simulation. The bulk of the toroidal flux is generated deep inside the convection zone, with the surface observables capturing this due to the conservative nature of the net flux. Conclusions. Surface magnetism and rotation can be used to produce an estimate of the net toroidal flux generated in each hemisphere, allowing us to constrain the reservoir of magnetic flux for the next magnetic cycle. However, this methodology cannot identify the physical origin or the location of the toroidal flux generation. In addition, not all dynamo mechanisms depend on the net toroidal field produced in each hemisphere, meaning this method may not be able to characterise every magnetic cycle.

The Sun's differential rotation is controlled by high-latitude baroclinically unstable inertial modes.

Rapidly rotating fluids have a rotation profile that depends only on the distance from the rotation axis, in accordance with the Taylor-Proudman theorem. Although the Sun was expected to be such a body, helioseismology showed that the rotation rate in the convection zone is closer to constant on radii. It has been postulated that this deviation is due to the poles being warmer than the equator by a few degrees. Using numerical simulations, we show that the pole-to-equator temperature difference cannot exceed 7 kelvin as a result of the back-reaction of the high-latitude baroclinically unstable inertial modes. The observed amplitudes of the modes further indicate that this maximum temperature difference is reached in the Sun. We conclude that the Sun's latitudinal differential rotation reaches its maximum allowed value.

Modeling the effects of starspots on stellar magnetic cycles

Observations show that faster rotating stars tend to have stronger magnetic activity and shorter magnetic cycles. The cyclical magnetic activity of the Sun and stars is believed to be driven by the dynamo process. The success of the Babcock-Leighton (BL) dynamo in explaining the solar cycle suggests that starspots could play an important role in stellar magnetic cycles. We aim to extend the BL mechanism to solar-mass stars with various rotation rates and explore the effects of emergence properties of starspots in latitudes and tilt angles on stellar magnetic cycles. We adopt a kinematic BL-type dynamo model operating in the bulk of the convection zone. The profiles of the large-scale flow fields are from the mean-field hydrodynamical model for various rotators. The BL source term in the model is constructed based on the rotation dependence of starspot emergence; that is, faster rotators have starspots at higher latitudes with larger tilt angles. Faster rotators have poloidal flux appearing closer to about $ latitudes, where the toroidal field generation efficiency is the strongest because of the peak in the strength of the latitudinal differential rotation there. It takes a shorter time for faster rotators to transport the surface poloidal field from their emergence latitude to the $ latitudes of efficient Omega -effect, which shortens their magnetic cycles. The faster rotators operate in a more supercritical regime because of a stronger BL alpha -effect relating to the tilt angles, which leads to stronger saturated magnetic fields and makes the coupling of the poloidal field between two hemispheres more difficult. The magnetic field parity therefore shifts from the hemispherically asymmetric mixed mode to quadrupole, and further to dipole when a star spins down. The emergence of starspots plays an essential role in the large-scale stellar dynamo.

On the Inner‐Core Differential‐Rotation (Un)Resolvability From Earthquake Doublets: The Traps of Data Selection

AbstractThe phenomenon of differential rotation of the Earth's inner core relative to the mantle is a subject of interest in geodynamo modeling that has been validated by seismological observations, mainly via the earthquake‐doublets method. Although recent studies converge on the time‐varying differential rotation of the inner core relative to the mantle, favoring a decadal variation, the inferred models significantly differ. Here, considering the data selection, the observed data structure, and the subjective model parameterizations, which we avoid by employing a Bayesian transdimensional approach, we show that the recent best‐fit model by Yang and Song (2023, https://doi.org/10.1038/s41561‐022‐01112‐z) featuring the 70‐year decadal variation is not obtained when all available data are considered. Namely, including only a small number of discarded earthquake doublets (<10%) changes the period of the inner‐core differential rotation fluctuation to 20–30 years. More earthquake‐doublet data are required to address the non‐uniqueness of the inversion problem.

Budget equations and astrophysical nonlinear mean-field dynamos

Abstract Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, nonlinear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence and (iii) a convective turbulence. As the result of this effect, a nonlinear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2 and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field.

The Sun’s Large-Scale Flows I: Measurements of Differential Rotation & Torsional Oscillation

We have developed a comprehensive catalog of the variable differential rotation measured near the solar photosphere. This catalog includes measurements of these flows obtained using several techniques: direct Doppler, granule tracking, magnetic pattern tracking, global helioseismology, as well as both time-distance and ring-diagram methods of local helioseismology. We highlight historical differential rotation measurements to provide context, and thereafter provide a detailed comparison of the MDI-HMI-GONG-Mt. Wilson overlap period (April 2010 – Jan 2011) and investigate the differences between velocities obtained from different techniques and attempt to explain discrepancies. A comparison of the rotation rate obtained by magnetic pattern tracking with the rotation rates obtained using local and global helioseismic techniques shows that magnetic pattern tracking measurements correspond to helioseismic flows located at a depth of 25 to 28 Mm. In addition, we show the torsional oscillation from Sunspot Cycles 23 and 24 and discuss properties that are consistent across measurement techniques. We find that acceleration derived from torsional oscillation is a better indicator of long-term trends in torsional oscillation compared to the residual velocity magnitude. Finally, this analysis will pave the way toward understanding systematic effects associated with various flow measurement techniques and enable more accurate determination of the global patterns of flows and their regular and irregular variations.

The GAPS programme at TNG

Context. The intrinsic variability due to the magnetic activity of young active stars is one of the main challenges in detecting and characterising exoplanets. The stellar activity is responsible for jitter effects observed both in photometric and spectroscopic observations that can impact our planetary detection sensitivity. Aims. We present a method able to model the stellar photosphere and its surface inhomogeneities (starspots) in young, active, and fast-rotating stars based on the cross-correlation function (CCF) technique, and we extract information about the spot configuration of the star. Methods. We developed Spot CCF, a tool able to model the deformation of the CCF profile due to the presence of multiple spots on the stellar surface. Within the Global Architecture of Planetary Systems (GAPS) Project at the Telescopio Nazionale Galileo, we analysed more than 300 spectra of the young planet-hosting star V1298 Tau provided by the HARPS-N high-resolution spectrograph. By applying the SpotCCF model to the CCFs, we extracted the spot configuration (latitude, longitude, and projected filling factor) of this star, and provide a new radial velocity (RV) time series for this target. Results. We find that the features identified in the CCF profiles of V1298 Tau are modulated by the stellar rotation, supporting our assumption that they are caused by starspots. The analysis suggests a differential rotation velocity of the star with lower rotation at higher latitudes. Also, we find that SpotCCF provides an improvement in RV extraction, with a significantly lower dispersion with respect to the commonly used pipelines. This allows mitigation of the stellar activity contribution modulated with stellar rotation. A detection sensitivity test, involving the direct injection of a planetary signal into the data, confirms that the SpotCCF model improves the sensitivity and ability to recover planetary signals. Conclusions. Our method enables us to model the stellar photosphere and extract the spot configuration of young, active, and rapidly rotating stars. It also allows the extraction of optimised RV time series, thereby enhancing our detection capabilities for new exoplanets and advancing our understanding of stellar activity.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

ZPEKTR: A code for spectral synthesis of fast-rotating stars

Estimating the physical states of the surfaces of fast-rotating stars is challenging due to several intrinsic processes, which include radiative flux inhomogeneities on the photosphere induced by rotation and circumstellar signatures in their spectra. The analysis of their spectra ultimately requires the use of synthetic grids of spectra accounting for all these physical processes. In this paper, we present the `von ZeiPEl's code for gravity darKening specTRal synthesis' (ZPEKTR) code, which is designed to perform the spectral synthesis of fast-rotating stars, accounting for gravity darkening, limb-darkening effects in the continuum and geometrical deformation induced by fast rotation. We consider colatitudinal temperature and surface-gravity variations, assuming both the classical prescription developed by von Zeipel and the new formulation by Espinosa-Lara. The code runs either with a rectangular or a triangular mesh on the stellar surface. We compare the temperature and gravitational distribution as a function of the stellar latitude arising from both models. The line profiles of 4388, 4471, 4922, and 6678 produced with both formalisms are compared at three different rotation rates and illustrate differences in shape and central intensity. We also illustrate the fittings of 31 line spectra of classical Be stars averaged from the Be Stars Observation Survey (BeSOS) database and make a comparison among their apparent physical parameters and ages determined from plane-parallel non-local thermodynamical equilibrium (non-LTE) models and parameters determined from classical von Zeipel models, finding a displacement of more evolved objects towards the zero-age main sequence. We also compare the distributions of projected rotation velocities of these objects obtained with and without the inclusion of gravity-darkening effects with ZPEKTR. We observe a shift of the histogram of rotation velocities calculated accounting for effects of gravity darkening concerning rotation velocities obtained through the fittings with classical plane-parallel non-LTE models. We show that models that do not account for gravity darkening can underestimate the rotation velocity, because the stellar latitudes that contribute the higher velocities are those in the equator with the least radiative flux. We envisage near-future improvements to the code, such as the inclusion of differential rotation and treatment of tidal forces in binary stellar systems.

Post-dynamical inspiral phase of common envelope evolution

During common envelope evolution, an initially weak magnetic field may undergo amplification by interacting with spiral density waves and turbulence generated in the stellar envelope by the inspiralling companion. Using 3D magnetohydrodynamical simulations on adaptively refined spherical grids with excised central regions, we studied the amplification of magnetic fields and their effect on the envelope structure, dynamics, and the orbital evolution of the binary during the post-dynamical inspiral phase. About 95% of magnetic energy amplification arises from magnetic field stretching, folding, and winding due to differential rotation and turbulence while compression against magnetic pressure accounts for the remaining ∼5%. Magnetic energy production peaks at a scale of 3ab, where ab is the semimajor axis of the central binary’s orbit. Because the magnetic energy production declines at large radial scales, the conditions are not favorable for the formation of magnetically collimated bipolar jet-like outflows unless they are generated on small scales near the individual cores, which we did not resolve. Magnetic fields have a negligible impact on binary orbit evolution, mean kinetic energy, and the disk-like morphology of angular momentum transport, but turbulent Maxwell stress can dominate Reynolds stress when accretion onto the central binary is allowed, leading to an α-disk parameter of ≃0.034. Finally, we discovered accretion streams arising from the stabilizing effect of the magnetic tension from the toroidal field about the orbital plane, which prevents overdensities from being destroyed by turbulence and enables them to accumulate mass and eventually migrate toward the binary.

Mean flow induced by longitudinal libration of a fluid-filled rotating container bounded by two conical surfaces

The problem of determining a mean flow induced by longitudinal libration of a rapidly rotating fluid-filled container bounded by the surfaces of two oppositely oriented right circular cones is considered. It is shown that the problem is reduced, through introducing a cosine of the angle between the normal to the conical surfaces and the axis of rotation, to the problem of determining a mean flow induced by libration of a fluid-filled rotating cylindrical container of infinite radius. A theoretical scenario is proposed of how the solved problem can be applied to the approximate determination of the differential mean rotation in a significant part of a rotating spherical and/or oblate spheroidal cavity under the action of longitudinal libration forcing.

Stellar activity and differential rotation of HD 111395

Aims. Stellar activity cycles and rotation periods are important parameters for characterising the stellar dynamo, which operates in late-type main-sequence stars. However, the number of stars with well-known cycle and rotation periods is rather low, so new detections are still important. Methods. To find activity cycles and rotation periods, we utilised the TIGRE telescope to monitor stars for periodic variations in chromospheric activity indicators. We employed the widely used CaII H&K lines and the CaII infrared triplet lines as stellar activity indicators. To verify a periodic variation and to determine the corresponding period, we performed a frequency analysis via the generalised Lomb-Scargle method of the taken time series. Results. We studied CaII data of the G5V star HD 111395 and derive an activity cycle period of 949 ± 5 d (≈2.6 yr). This cycle is coincident with coronal measurements from the X-ray telescope eROSITA on board SRG. Furthermore, the TIGRE CaII time series show a long-term trend that indicates an additional long-term cycle. Using the few available literature S-index data points, we estimate a probable cycle length of 12–15 yr for this potential long-term cycle. Finally, we determined rotation periods from each observation season. We computed a mean rotation period of 16.76 ± 0.36 d averaged over all observation seasons and chromospheric indicators. However, we also find a strong variation in the mean seasonal rotation periods, which follows the derived cycle period; therefore, we interpret this behaviour as a sign of surface differential rotation.

Toroidal Magnetic Flux Budget in Mean-field Dynamo Model of Solar Cycles 23 and 24

We study the toroidal magnetic flux budget of the axisymmetric part of a data-driven 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes the effects of the formation and evolution of bipolar magnetic regions (BMRs) emerging on the solar surface. By applying Stokes’s theorem to the dynamo induction equation, we show that the hemispheric magnitude of the net axisymmetric toroidal magnetic field generation rate in the bulk of the convection zone can only partially be estimated from the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the radial integral along the equator, which is mostly due to the rotational radial shear at the bottom of the convection zone, has the same magnitude and is nearly in phase with the effect of the surface latitudinal differential rotation. Also, the toroidal field generation rate estimate strongly depends on the latitudinal profile of the surface radial magnetic field near the poles. This profile in our dynamo models significantly deviates from the polar magnetic field distribution observed during the minima of Solar Cycles 22, 23, and 24. The cause of this discrepancy requires further observational and theoretical studies. Comparing the 2D axisymmetric and the 3D nonaxisymmetric dynamo models, we find an increase in the toroidal field generation rate in the 3D model due to the surface effects of BMRs, resulting in an increase in the axisymmetric poloidal magnetic field magnitude.

Solar Tachocline Confinement by the Nonaxisymmetric Modes of a Dynamo Magnetic Field

We recently presented the first 3D numerical simulation of the solar interior for which tachocline confinement was achieved by a dynamo-generated magnetic field. In this follow-up study, we analyze the degree of confinement as the magnetic field strength changes (controlled by varying the magnetic Prandtl number) in a coupled radiative zone (RZ) and convection zone (CZ) system. We broadly find three solution regimes, corresponding to weak, medium, and strong dynamo magnetic field strengths. In the weak-field regime, the large-scale magnetic field is mostly axisymmetric with regular, periodic polarity reversals (reminiscent of the observed solar cycle) but fails to create a confined tachocline. In the strong-field regime, the large-scale field is mostly nonaxisymmetric with irregular, quasi-periodic polarity reversals and creates a confined tachocline. In the medium-field regime, the large-scale field resembles a strong-field dynamo for extended intervals but intermittently weakens to allow temporary epochs of strong differential rotation. In all regimes, the amplitude of poloidal field strength in the RZ is very well explained by skin-depth arguments, wherein the oscillating field that gives rise to the skin depth (in the medium- and strong-field cases) is a nonaxisymmetric field structure at the base of the CZ that rotates with respect to the RZ. These simulations suggest a new picture of solar tachocline confinement by the dynamo, in which nonaxisymmetric, very long-lived (effectively permanent) field structures rotating with respect to the RZ play the primary role, instead of the regularly reversing axisymmetric field associated with the 22 yr cycle.