Differential Rotation Profile Research Articles

Dependence of Stellar Differential Rotation on Effective Temperature and Rotation: An Analysis from Starspot Transit Mapping

Stellar rotation is crucial for studying stellar evolution, since it provides information about age, angular momentum transfer, and magnetic fields of stars. In the case of the Sun, due to its proximity, detailed observation of sunspots at various latitudes and longitudes allows a precise estimation of the solar rotation period and its differential rotation. Here, we present for the first time an analysis of stellar differential rotation using starspot transit mapping as a means of detecting differential shear in solar-type and M stars. The aim of this study is to investigate the relationship between rotational shear, ΔΩ, and both the star's effective temperature (T eff) and its average rotation period (). We present differential rotation profiles derived from previously collected spot transit mapping data for 13 slowly rotating stars (P rot ≥ 4.5 days), with spectral types ranging from M to F, which were observed by the Kepler and CoRoT satellites. Our findings reveal a significant negative correlation between rotational shear and the mean period of stellar rotation (correlation coefficient of −0.77), which may be an indicator of stellar age. On the other hand, a weak correlation was observed between differential rotation and the effective temperature of the stars. Overall, the study provides valuable insights into the complex relationship between stellar parameters and differential rotation, which may enhance our understanding of stellar evolution and magnetic dynamos.

Minuscule Corrections to Near-surface Solar Internal Rotation Using Mode Coupling

The observed solar oscillation spectrum is influenced by internal perturbations such as flows and structural asphericities. These features induce splitting of characteristic frequencies and distort the resonant-mode eigenfunctions. Global axisymmertric flow—differential rotation—is a very prominent perturbation. Tightly constrained rotation profiles as a function of latitude and radius are products of established helioseismic pipelines that use observed Dopplergrams to generate frequency-splitting measurements at high precision. However, the inference of rotation using frequency splittings does not consider the effect of mode coupling. This approximation worsens for modes with high angular degrees, as they become increasingly proximal in frequency. Since modes with high angular degrees probe the near-surface layers of the Sun, inversions considering coupled modes could potentially lead to more accurate estimates of rotation very close to the surface. In order to investigate if this is indeed the case, we perform inversions for solar differential rotation, considering coupling of modes for angular degrees 160 ≤ ℓ ≤ 300 in the surface gravity f-branch and first-overtone p modes. In keeping with the character of mode coupling, we carry out a nonlinear inversion using an eigenvalue solver. Differences in inverted profiles for frequency-splitting measurements from MDI and HMI are compared and discussed. We find that the corrections to the near-surface differential rotation profile, when accounting for mode-coupling effects, are smaller than 0.003 nHz and hence are insignificant. These minuscule corrections are found to be correlated with the solar cycle. We also present corrections to even-order splitting coefficients, which could consequently impact inversions for structure and magnetic fields.

Stellar Obliquity from Spot Transit Mapping of Kepler-210

Stellar obliquity, the angle between the stellar spin and the perpendicular to the planetary orbit, also known as the spin–orbit angle, holds clues to the formation and evolution of planetary systems. When a planet transits a star periodically, it may cross in front of a stellar spot, producing a noticeable signal on the transit light curve. Spot transit mapping can be used to measure stellar obliquity. Here we present the analysis of Kepler-210, a K-dwarf star with two mini-Neptune-size planets in orbit. Interestingly, the spot mapping from the outer planet, Kepler-210 c, resulted in a spot distribution with no spots detected at longitudes >38°, whereas the spots occulted by Kepler-210 b displayed all range of longitudes. The best explanation for this was that Kepler-210 c exhibited an inclined orbit, while the orbit of Kepler-210 b was parallel to the stellar equator. Thus, transits of Kepler-210 c occulted different latitude bands of the star. The observed maximum spot topocentric longitude of 38° implied an orbital obliquity of 18°–45° for Kepler-210 c. Further considering a symmetric spot distribution in latitude with respect to the stellar equator, the obliquity was restricted to 34.°8, implying a maximum spot latitude of 40°. The differential rotation profile calculated from the oblique orbit for Kepler-210 c agreed with that obtained from the spots occulted by Kepler-210 b. Combining results from both planets yields a rotational shear of ΔΩ = 0.0353 ± 0.0002 rad day−1 and a relative rotational shear of 6.9%. The causes of the Kepler-210 c misalignment remain to be explained.

Hunting for anti-solar differentially rotating stars using the Rossby number

Context. Anti-solar differential rotation profiles have been found for decades in numerical simulations of convective envelopes of solar-type stars. These profiles are characterized by a slow equator and fast poles (i.e., reversed with respect to the Sun) and have been found in simulations for high Rossby numbers. Rotation profiles like this have been reported in evolved stars, but have never been unambiguously observed for cool solar-type stars on the main sequence. As solar-type stars age and spin down, their Rossby numbers increase, which could therefore induce a transition toward an anti-solar differential rotation regime before the end of the main sequence. Such a rotational transition will impact the large-scale dynamo process and the magnetic activity. In this context, detecting this regime in old main-sequence solar-type stars would improve our understanding of their magnetorotational evolution. Aims. The goal of this study is to identify the most promising cool main-sequence stellar candidates for anti-solar differential rotation in the Kepler sample. Methods. First, we introduce a new theoretical formula to estimate fluid Rossby numbers, Rof, of main-sequence solar-type stars. We derived it from observational quantities such as Teff and Prot, and took the influence of the internal structure into account. Then, we applied it on a subset of the most recent catalog of Kepler rotation periods, after removing subgiants and selecting targets with solar metallicity. Next, we considered the highest computed Rof and inspected each target individually to select the most reliable anti-solar candidate. Finally, we extended our study to stars with metallicities different from that of the Sun. To this end, we developed a formulation for Rof dependent on the metallicity index [Fe/H] by using 1D stellar grids, and we also considered this compositional aspect for the selection of the targets. Results. We obtain a list of the most promising stars that are likely to show anti-solar differential rotation. We identify two samples: one at solar metallicity, including 14 targets, and another for other metallicities, including 8 targets. We find that the targets with the highest Rof are likely to be early-G or late-F stars at about log10g = 4.37 dex. Conclusions. We conclude that cool main-sequence stellar candidates for anti-solar differential rotation exist in the Kepler sample. The most promising candidate is KIC 10907436, and two other particularly interesting candidates are the solar analog KIC 7189915 and the seismic target KIC 12117868. Future characterization of these 22 stars is expected to help us understand how dynamics can impact magnetic and rotational evolution of old solar-type stars at high Rossby number.

Leptocline as a shallow substructure of near-surface shear layer in 3D radiative hydrodynamic simulations

ABSTRACT Understanding the effects driven by rotation in the solar convection zone is essential for many problems related to solar activity, such as the formation of differential rotation, meridional circulation, and others. We analyse realistic 3D radiative hydrodynamics simulations of solar subsurface dynamics in the presence of rotation in a local domain 80 Mm wide and 25 Mm deep, located at 30° latitude. The simulation results reveal the development of a shallow 10 Mm deep substructure of the near-surface shear layer (NSSL), characterized by a strong radial rotational gradient and self-organized meridional flows. This shallow layer (‘leptocline’) is located in the hydrogen ionization zone associated with enhanced anisotropic overshooting-type flows into a less unstable layer between the H and He ii ionization zones. We discuss current observational evidence of the presence of the leptocline and show that the radial variations of the differential rotation and meridional flow profiles obtained from the simulations in this layer qualitatively agree with helioseismic observations.

Ray Tracing of MHD Rossby Waves in the Solar Tachocline: Meridional Propagation and Implications for the Solar Magnetic Activity

Rossby waves have been recently recognised for their role in the large-scale spatio-temporal organisation of the solar magnetic activity. Here, we study the propagation of magnetohydrodynamic Rossby waves in a thin layer, representing the solar tachocline. We consider the waves embedded in a meridionally varying background state characterised by a mean zonal flow, which mimics the differential rotation profile of the Sun, and a toroidal magnetic field. Two anti-symmetric toroidal magnetic fields are utilised: one having a global structure with the maximum at around 50o and the other characterised by a narrow band centered at around 20o. We show that for a global structure toroidal magnetic field, the MHD Rossby modes undergo significant meridional propagation, either equatorward or poleward. In addition, the latitude where the waves exhibit a stationary behaviour is sensitive to the strength of the background magnetic field. On the other hand, a narrow band toroidal magnetic field is shown to work as a waveguide for the fast branch of MHD Rossby waves.

Numerical Equilibrium Configurations and Quadrupole Moments of Post-Merger Differentially Rotating Relativistic Stars

Numerical simulations of binary neutron star mergers invariably show that, when a long-lived remnant forms, its rotation profile is never a simple decaying function of the radius but rather exhibits a maximum rotation rate shifted away from the center. This is in contrast to the usual differential rotation profile employed for the numerical modeling of axisymmetric equilibria of relativistic stars. Two families of rotation rate functions that mimic post-merger profiles were proposed by Uryū et al. (2017). In this work we implement Uryū’s profiles into the XNS code by Bucciantini and Del Zanna (2011) and we present novel equilibrium sequences of differentially rotating neutron stars. These are constructed by using three different equations of state, in order to study the dependence of mass, radius, angular momentum, and other important physical quantities, especially the quadrupole deformation and metric quadrupole moment, from the rotation properties.

Effect of Differential Rotation on the Magnetic Braking of Low-mass and Solar-like Stars: A Proof-of-concept Study

Abstract On the main sequence, low-mass and solar-like stars are observed to spin down over time, and magnetized stellar winds are thought to be predominantly responsible for this significant angular momentum loss. Previous studies have demonstrated that the wind torque can be predicted via formulations dependent on stellar properties, such as magnetic field strength and geometry, stellar radius and mass, wind mass-loss rate, and stellar rotation rate. Although these stars are observed to experience surface differential rotation, torque formulations so far have assumed solid-body rotation. Surface differential rotation is expected to affect the rotation of the wind and thus the angular momentum loss. To investigate how differential rotation affects the torque, we use the PLUTO code to perform 2.5D magnetohydrodynamic, axisymmetric simulations of stellar winds, using a colatitude-dependent surface differential rotation profile that is solar-like (i.e., rotation is slower at the poles than the equator). We demonstrate that the torque is determined by the average rotation rate in the wind so that the net torque is less than that predicted by assuming solid-body rotation at the equatorial rate. The magnitude of the effect is essentially proportional to the magnitude of the surface differential rotation, for example, resulting in a torque for the Sun that is ∼20% smaller than predicted by the solid-body assumption. We derive and fit a semianalytic formulation that predicts the torque as a function of the equatorial spin rate, magnitude of differential rotation, and wind magnetization (depending on the dipolar magnetic field strength and mass-loss rate, combined).

Constraining Saturn’s Interior with Ring Seismology: Effects of Differential Rotation and Stable Stratification

Abstract Normal mode oscillations in Saturn excite density and bending waves in the C ring, providing a valuable window into the planet’s interior. Saturn’s fundamental modes (f-modes) excite the majority of the observed waves, while gravito-inertial modes (rotationally modified g-modes) associated with stable stratification in the deep interior provide a compelling explanation for additional density waves with low azimuthal wavenumbers m. However, multiplets of density waves with nearly degenerate frequencies, including an m = 3 triplet, still lack a definitive explanation. We investigate the effects of rapid and differential rotation on Saturn’s oscillations, calculating normal modes for independently constrained interior models. We use a non-perturbative treatment of rotation that captures the full effects of the Coriolis and centrifugal forces, and consequently the mixing of sectoral f-modes with g-modes characterized by very different spherical harmonic degrees. Realistic profiles for differential rotation associated with Saturn’s zonal winds can enhance these mode interactions, producing detectable oscillations with frequencies separated by less than 1%. Our calculations demonstrate that a three-mode interaction involving an f-mode and two g-modes can feasibly explain the finely split m = 3 triplet, although the fine-tuning required to produce such an interaction generally worsens agreement with seismological constraints provided by m = 2 density waves. Our calculations additionally demonstrate that sectoral f-mode frequencies are measurably sensitive to differential rotation in Saturn’s convective envelope. Finally, we find that including realistic equatorial antisymmetry in Saturn’s differential rotation profile couples modes with even and odd equatorial parity, producing oscillations that could in principle excite both density and bending waves simultaneously.

Chinese sunspot drawings and their digitization − (IV) differential rotation profile determined from hand-drawing records

Chinese sunspot drawings and their digitization − (IV) differential rotation profile determined from hand-drawing records

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions

Context.Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics. Furthermore, solar-like stars and giant gaseous planets in our Solar System experience differential rotation in their outer convective envelopes. In this respect, numerical simulations of tidal interactions in these objects have shown that the propagation and dissipation properties of tidally excited inertial waves can be strongly modified in the presence of differential rotation.Aims.In particular, tidal inertial waves may strongly interact with zonal flows at the so-called co-rotation resonances, where the wave’s Doppler-shifted frequency is cancelled out. The energy dissipation at such resonances could deeply modify the orbital and spin evolutions of tidally interacting systems. In this context, we aim to provide a deep physical understanding of the dynamics of tidal waves at co-rotation resonances in the presence of differential rotation profiles that are typical of low-mass stars and giant planets.Methods.In this work, we have developed an analytical local model of an inclined shearing box that describes a small patch of the differentially rotating convective zone of a star or a planet. We investigate the propagation and the transmission of free inertial waves at co-rotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model.Results.We find that inertial waves can be fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux in the fluid when damped at critical levels, or they can extract action flux from the fluid when amplified at critical levels. Both situations can lead to significant angular momentum exchange between the tidally interacting bodies.

Kepler-411 Differential Rotation from Three Transiting Planets

Abstract The differential rotation of the Sun is a crucial ingredient of the dynamo theory responsible for the generation of its magnetic field. Currently, the rotation profile of a star that hosts one or more transiting planet can be estimated. By detecting the same spot in a later transit, it is possible to infer the stellar rotation period at that latitude. In this work, we apply for the first time transit spot mapping to determine the differential rotation of Kepler-411, a K2V-type star with an average rotation period of 10.52 days, a radius of 0.79 R ⊙, and a mass of 0.83 M ⊙. Kepler-411 hosts at least four planets, the inner planet is a super-Earth with a radius of 1.88 R ⊕ and an orbital period of 3.0051 days, whereas the two larger transiting planets are mini Neptunes with radii of 3.27 and 3.31 R ⊕, and periods of 7.834435 and 58.0204 days, respectively. Their orbits are such that they transit the star at latitudes of −11°, −21°, and −49°. Analysis of the transit light curves of the three planets resulted in the detection of a total of 198 spots. For each transit latitude, the rotation period of the star was estimated and the differential rotation pattern estimated independently. Then a solar-like differential rotation profile was fit to the three rotation periods at the distinct latitudes, and the result agreed extremely well with the previous ones, resulting in a differential shear of 0.0500 ± 0.0006 rd day−1 or a relative differential rotation of 8.4% ± 0.1%.

Physically motivated heat-conduction treatment in simulations of solar-like stars: effects on dynamo transitions

Context.Results from global magnetoconvection simulations of solar-like stars are at odds with observations in many respects: simulations show a surplus of energy in the kinetic power spectrum at large scales; anti-solar differential rotation profiles with accelerated poles, and a slow equator for the solar rotation rate; and a transition from axi- to nonaxisymmetric dynamos at a much lower rotation rate than what is observed. Even though the simulations reproduce the observed active longitudes in fast rotators, their motion in the rotational frame (the so-called azimuthal dynamo wave, ADW) is retrograde, in contrast to the prevalent prograde motion in observations.Aims.We study the effect of a more realistic treatment of heat conductivity in alleviating the discrepancies between observations and simulations.Methods.We use physically motivated heat conduction by applying Kramers opacity law to a semi-global spherical setup that describes the convective envelopes of solar-like stars, instead of a prescribed heat conduction profile from mixing-length arguments.Results.We find that some aspects of the results now better correspond to observations: the axi- to nonaxisymmetric transition point is shifted towards higher rotation rates. We also find a change in the propagation direction of ADWs that means that prograde waves are also now found. However, the transition from an anti-solar to solar-like rotation profile is also shifted towards higher rotation rates, leaving the models in an even more unrealistic regime.Conclusions.Although Kramers-based heat conduction does not help in reproducing the solar rotation profile, it does help in the faster rotation regime, where the dynamo solutions now better match the observations.

Solar cycle-related variation in solar differential rotation and meridional flow in solar cycle 24

We studied temporal variation of the differential rotation and poleward meridional circulation during solar cycle 24 using the magnetic element feature tracking technique. We used line-of-sight magnetograms obtained using the helioseismic and magnetic imager aboard the Solar Dynamics Observatory from May 01, 2010 to March 26, 2020 (for almost the entire period of solar cycle 24, Carrington rotation from 2096 to 2229) and tracked the magnetic element features every 1 h. We also estimated the differential rotation and poleward meridional flow velocity profiles. The observed profiles are consistent with those of previous studies on different cycles. Typical properties resulting from torsional oscillations can also be observed from solar cycle 24. The amplitude of the variation was approximately ±10 m s^{-1}. Interestingly, we found that the average meridional flow observed in solar cycle 24 is faster than that observed in solar cycle 23. In particular, during the declining phase of the cycle, the meridional flow of the middle latitude is accelerated from 10 to 17 m s^{-1}, which is almost half of the meridional flow itself. The faster meridional flow in solar cycle 24 might be the result of the weakest cycle during the last 100 years.

Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone

Context. The interactions between magnetic fields and differential rotation in stellar radiative interiors could play a major role in achieving an understanding of the magnetism of intermediate-mass and massive stars and of the differential rotation profile observed in red-giant stars. Aims. The present study is aimed at studying the flow and field produced by a stellar radiative zone which is initially made to rotate differentially in the presence of a large-scale poloidal magnetic field threading the whole domain. We focus both on the axisymmetric configurations produced by the initial winding-up of the magnetic field lines and on the possible instabilities of those configurations. We investigate in detail the effects of the stable stratification and thermal diffusion and we aim, in particular, to assess the role of the stratification at stabilising the system. Methods. We performed 2D and 3D global Boussinesq numerical simulations started from an initial radial or cylindrical differential rotation and a large-scale poloidal magnetic field. Under the conditions of a large rotation frequency compared to the Alfvén frequency, we built a magnetic configuration strongly dominated by its toroidal component. We then perturbed this configuration to observe the development of non-axisymmetric instabilities. Results. The parameters of the simulations were chosen to respect the ordering of time scales of a typical stellar radiative zone. In this framework, the axisymmetric evolution is studied by varying the relative effects of the thermal diffusion, the Brunt-Väisälä frequency, the rotation, and the initial poloidal field strength. After a transient time and using a suitable adimensionalisation, we find that the axisymmetric state only depends on tes/tAp the ratio between the Eddington–Sweet circulation time scale and the Alfvén time scale. A scale analysis of the Boussinesq magnetohydrodynamical equations allows us to recover this result. In the cylindrical case, a magneto-rotational instability develops when the thermal diffusivity is sufficiently high to enable the favored wavenumbers to be insensitive to the effects of the stable stratification. In the radial case, the magneto-rotational instability is driven by the latitudinal shear created by the back-reaction of the Lorentz force on the flow. Increasing the level of stratification then leaves the growth rate of the instability mainly unaffected while its horizontal length scale grows. Conclusions. Non-axisymmetric instabilities are likely to exist in stellar radiative zones despite the stable stratification. They could be at the origin of the magnetic dichotomy observed in intermediate-mass and massive stars. They are also unavoidable candidates for the transport of angular momentum in red giant stars.

Instabilities in neutron-star postmerger remnants

Using nonlinear, fully relativistic, simulations we investigate the dynamics and gravitational-wave signature associated with instabilities in neutron star postmerger remnants. For simplified models of the remnant we establish the presence of an instability in stars with moderate $T/|W|$, the ratio between the kinetic and the gravitational potential energies. Detailed analysis of the density oscillation pattern reveals a local instability in the inner region of the more realistic differential rotation profile. We apply Rayleigh's inflection theorem and Fj\o{}rtoft's theorem to analyze the stability criteria concluding that this inner local instability originates from a shear instability close to the peak of the angular velocity profile, and that it later evolves into a fast-rotating $m=2$ oscillation pattern. We discuss the importance of the presence of a corotation point in the fluid, its connection with the shear instability, and comparisons to the Rossby wave and Papaloizou Pringle instabilities considered in the wider literature.

Generation of the Sun’s Radial Magnetic Field by Global Hydrodynamic Flows

A theory on the emergence of global hydrodynamic flows of matter and the generation of global magnetic fields in the solar convective zone is proposed. The unstable profile of differential rotation plays a crucial role in it: all hydrodynamic flows on the Sun (poloidal circulation, torsion oscillations, and spatiotemporal variations of the poloidal flow) are generated due to the loss of stability of differential rotation. None of the models known to us, wherein torsion oscillations and variations of the meridional circulation are typically calculated separately and are thus considered to be independent flows, reproduce this result. The calculations within our model suggest, on the contrary, that the indicated flows are actually toroidal and poloidal components of a single, 3-dimensional global flow. The decisive role of torsion oscillations in the generation of the radial alternating magnetic field is highlighted in the present study. It is demonstrated by numerical simulation that the time-varying radial magnetic field on the surface of the Sun reaches its maximum at the poles, where it changes polarity with a period of ~22 years. This process may be identified with the observed effect of polarity reversal of the polar field within the Hale magnetic cycle. It is demonstrated that the lines of zero values (polarity reversal) of the surface radial magnetic field pass through the maxima of the velocity modulus of zonal flows (torsion oscillations). In addition, the lines of magnetic polarity reversal of the radial field and the maximum velocities of surface zonal flows drift from the poles to the equator. It is noted that the obtained results on the latitudinal evolution of surface zonal flows correlate with the behavior of deep zonal flows determined by processing helioseismological data.

Activity and differential rotation of the early M dwarf Kepler-45 from transit mapping

ABSTRACT Little is known of the activity and differential rotation of low luminosity, early M dwarfs from direct observation. We present the first stellar activity analysis of star-spots and faculae for the hot Jupiter hosting M1V dwarf Kepler-45 from $\it Kepler$ transit light curves. We find star-spot and facula temperatures contrasting a few hundred degrees with the quiet photosphere, hence similar to other early M dwarfs having a convective envelope surrounding a radiative core. Star-spots are prominent close to the centre of the stellar disc, with faculae prominent towards the limbs, similar to what is observed for the Sun. Star-spot and facula mean sizes are about 40 and 45 × 103 km, respectively, and thus faculae occupy a 10 per cent larger surface area than the star-spots. A short-term activity cycle of about 295 d is observed that is reminiscent of those seen for other cool dwarfs. Adopting a solar-type differential rotation profile (faster equatorial rotation than polar rotation), our star-spot and facula temporal mapping indicates a rotation period of 15.520 ± 0.025 d at the transit latitude of −33.2°. From the mean stellar rotation of 15.762 d, we estimate a rotational shear of 0.031 ± 0.004 rad d−1, or a relative differential rotation of 7.8 ± 0.9 per cent. Kepler-45’s surface rotational shear is thus consistent with observations and theoretical modelling of other early M dwarfs that indicate a shear of less than 0.045 rad d−1 and no less than 0.03 rad d−1 for stars with similar stellar rotation periods.

Grand Minima in a spherical non-kinematic α2Ω mean-field dynamo model

We present a non-kinematic axisymetric α2Ω mean-field dynamo model in which the complete α-tensor and mean differential rotation profile are both extracted from a global magnetohydrodynamical simulation of solar convection producing cycling large-scale magnetic fields. The nonlinear backreaction of the Lorentz force on differential rotation is the only amplitude-limiting mechanism introduced in the mean-field model. We compare and contrast the amplitude modulation patterns characterizing this mean-field dynamo, to those already well-studied in the context of non-kinematic αΩ models using a scalar α-effect. As in the latter, we find that large quasi-periodic modulation of the primary cycle are produced at low magnetic Prandtl number (Pm), with the ratio of modulation period to the primary cycle period scaling inversely with Pm. The variations of differential rotation remain well within the bounds set by observed solar torsional oscillations. In this low-Pm regime, moderately supercritical solutions can also exhibit aperiodic Maunder Minimum-like periods of strongly reduced cycle amplitude. The inter-event waiting time distribution is approximately exponential, in agreement with solar activity reconstructions based on cosmogenic radioisotopes. Secular variations in low-latitude surface differential rotation during Grand Minima, as compared to epochs of normal cyclic behavior, are commensurate in amplitude with historical inferences based on sunspot drawings. Our modeling results suggest that the low levels of observed variations in the solar differential rotation in the course of the activity cycle may nonetheless contribute to, or perhaps even dominate, the regulation of the magnetic cycle amplitude.

I–Love–Q relations for realistic white dwarfs

ABSTRACT The space-borne gravitational wave interferometer, Laser Interferometer Space Antenna, is expected to detect signals from numerous binary white dwarfs. At small orbital separation, rapid rotation and large tidal bulges may allow for the stellar internal structure to be probed through such observations. Finite-size effects are encoded in quantities like the moment of inertia (I), tidal Love number (Love), and quadrupole moment (Q). The universal relations among them (I–Love–Q relations) can be used to reduce the number of parameters in the gravitational-wave templates. We here study I–Love–Q relations for more realistic white dwarf models than used in previous studies. In particular, we extend previous works by including (i) differential rotation and (ii) internal temperature profiles taken from detailed stellar evolution calculations. We use the publicly available stellar evolution code mesa to generate cooling models of both low- and high-mass white dwarfs. We show that differential rotation causes the I–Q relation (and similarly the Love–Q relation) to deviate from that of constant rotation. We also find that the introduction of finite temperatures causes the white dwarf to move along the zero-temperature mass sequence of I–Q values, moving towards values that suggest a lower mass. We further find that after only a few Myr, high-mass white dwarfs are well described by the zero-temperature model, suggesting that the relations with zero temperature may be good enough in most practical cases. Low-mass, He-core white dwarfs with thick hydrogen envelopes may undergo long periods of H burning which sustain the stellar temperature and allow deviations from the I–Love–Q relations for longer times.