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We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( ΔΩ∝(∣Ω∣/Ω⊙)0.46 ) in the MHD solutions than in their HD counterpart ∣Ω∣/Ω⊙0.66 ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker–Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star’s surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( BL,surf∼Rof−1.26 ) agrees better with observations ( BV∼Ros−1.4±0.1 ) and differs from dynamo scaling based on the global magnetic energy ( Bbulk∼Rof−0.5 ).

In order to address the generation of neutron star magnetic fields, with particular focus on the dichotomy between magnetars and radio pulsars, we consider the properties of dynamos as inferred from other astrophysical systems. With sufficiently low (modified) Rossby number, convective dynamos are known to produce dipole-dominated fields whose strength scales with convective flux, and we argue that these expectations should apply to the convective protoneutron stars (PNSs) at the centers of core-collapse supernovae. We analyze a suite of three-dimensional simulations of core collapse, featuring a realistic equation of state and full neutrino transport, in this context. All our progenitor models, ranging from 9 M ⊙ to 25 M ⊙, including one with initial rotation, have sufficiently vigorous PNS convection to generate dipole fields of order ∼1015 Gauss, if the modified Rossby number resides in the critical range. Thus, the magnetar/radio pulsar dichotomy may arise naturally in part from the distribution of core rotation rates in massive stars.

We review the state of the art of three dimensional numerical simulations of solar and stellar dynamos. We summarize fundamental constraints of numerical modelling and the techniques to alleviate these restrictions. Brief summary of the relevant observations that the simulations seek to capture is given. We survey the current progress of simulations of solar convection and the resulting large-scale dynamo. We continue to studies that model the Sun at different ages and to studies of stars of different masses and evolutionary stages. Both simulations and observations indicate that rotation, measured by the Rossby number which is the ratio of rotation period and convective turnover time, is a key ingredient in setting the overall level and characteristics of magnetic activity. Finally, efforts to understand global 3D simulations in terms of mean-field dynamo theory are discussed.

We investigate the evolution of magnetic fields generated by the crystallization-driven dynamo in carbon–oxygen white dwarfs (WDs) with masses ≲1.05 M ⊙. We use scalings for the dynamo to demonstrate that the initial magnetic field strength (B 0) has an upper limit that depends on the initial convection zone size (R out,0) and the WD mass. We solve the induction equation to follow the magnetic field evolution after the dynamo phase ends. We show that the predicted surface magnetic field strength (B surf) differs from B 0 by at least a factor of ∼0.3. This reduction depends on R out,0, where values smaller than half of the star radius give B surf ≲ 0.01 B 0. We implement electrical conductivities that account for the solid phase effect on the ohmic diffusion. We observe that the conductivity increases as the solid core grows, freezing in the magnetic field at a certain point of the evolution and slowing its outward transport. We study the effect of turbulent magnetic diffusivity induced by the convection and find that for a small R out,0, B surf is stronger than the nonturbulent diffusion cases because of the more rapid transport, but still orders of magnitude smaller than B 0. Given these limitations, the crystallization-driven dynamo theory could explain only magnetic C/O WDs with field strengths less than a few megagauss for the mass range 0.45–1.05 M ⊙. Our results also suggest that a buried fossil field must be at least 100 times stronger than observed surface fields if crystallization-driven convection is responsible for its transport to the surface.

Adenosine triphosphate (ATP) synthases are dynamos that interconvert rotational and chemical energy. Capturing the complete structure of these multisubunit membrane-bound complexes has been hindered by their inherent ability to adopt multiple conformations. Srivastava et al. used protein engineering to freeze mitochondrial ATP synthase from yeast in a single conformation and obtained a structure with the inhibitor oligomycin, which binds to the rotating c-ring within the membrane. Hahn et al. show that chloroplast ATP synthase contains a built-in inhibitor triggered by oxidizing conditions in the dark chloroplast. The mechanisms by which these machines are powered are remarkably similar: Protons are shuttled through a channel to the membrane-embedded c-ring, where they drive nearly a full rotation of the rotor before exiting through another channel on the opposite side of the membrane (see the Perspective by Kane). Science , this issue p. eaas9699 , p. eaat4318 ; see also p. 600 The mechanism by which protons find a path through the key enzyme involved in plant energy generation is elucidated. The chloroplast adenosine triphosphate (ATP) synthase uses the electrochemical proton gradient generated by photosynthesis to produce ATP, the energy currency of all cells. Protons conducted through the membrane-embedded F o motor drive ATP synthesis in the F 1 head by rotary catalysis. We determined the high-resolution structure of the complete cF 1 F o complex by cryo–electron microscopy, resolving side chains of all 26 protein subunits, the five nucleotides in the F 1 head, and the proton pathway to and from the rotor ring. The flexible peripheral stalk redistributes differences in torsional energy across three unequal steps in the rotation cycle. Plant ATP synthase is autoinhibited by a β-hairpin redox switch in subunit γ that blocks rotation in the dark.

The vast majority of stars in the nearby stellar neighborhood are M dwarfs. Their low masses and luminosities result in slow rates of nuclear evolution and minimal changes to the stars’ observable properties, even along astronomical timescales. However, they possess relatively powerful magnetic dynamos and resulting X-ray to UV (X–UV) activity, compared to their bolometric luminosities. This magnetic activity does undergo an observable decline over time, potentially making it a key age determinant for M dwarfs. Observing this activity is important for studying the outer atmospheres of these stars, but also for comparing the behaviors of different spectral type subsets of M dwarfs; e.g., those with partially versus fully convective interiors. Beyond stellar astrophysics, understanding the X–UV activity of M dwarfs over time is a key component when studying the atmospheres and habitability of any hosted exoplanets. Earth-sized exoplanets, in particular, are more commonly found orbiting M dwarfs than any other stellar type, and thermal escape (driven by the M dwarf X–UV activity) is believed to be the dominant atmospheric loss mechanism for these planets. Utilizing recently calibrated M dwarf age–rotation relationships, also constructed as part of the Living with a Red Dwarf program, we have analyzed the evolution of M dwarf activity over time, in terms of coronal (X-ray), chromospheric (Lyα, and Ca ii), and overall X–UV (5–1700 Å) emissions. The activity–age relationships presented here will be useful for studying exoplanet habitability and atmospheric loss, and also for studying the different dynamo and outer atmospheric heating mechanisms at work in M dwarfs.

M-type stars are crucial for stellar activity studies because they cover two types of magnetic dynamos and are particularly intriguing for habitability studies due to their abundance and long lifespans during the main-sequence stage. In this paper, we used the LAMOST DR9 catalog and the GALEX UV archive data to investigate the chromospheric and UV activities of M-type stars. All the chromospheric and UV activity indices clearly show that the saturated and unsaturated regimes, and the well-known activity–rotation relation, are consistent with previous studies. Both the FUV and NUV activity indices exhibit a single-peaked distribution, while the Hα and Ca ii H&K indices show a distinct double-peaked distribution. The gap between these peaks suggests a rapid transition from a saturated population to an unsaturated one. The smoothly varying distributions of different subtypes suggest a rotation-dependent dynamo for both early-type (partly convective) to late-type (fully convective) M stars. We identified a group of stars with high UV activity above the saturation regime (log RNUV′>−2.5 ) but low chromospheric activity, and the underlying reason is unknown. By calculating the continuously habitable zone and the UV habitable zone for each star, we found that about 70% stars in the total sample and 40% stars within 100 pc are located in the overlapping region of these two habitable zones, indicating that a number of M stars are potentially habitable. Finally, we examined the possibility of UV activity studies of M stars using the China Space Station Telescope.

The origin of large magnetic fields (≳106 G) in isolated white dwarfs is not clear. One possible explanation is that crystallization of the star’s core drives compositional convection, which when combined with the star’s rotation, can drive a dynamo. However, whether convection is efficient enough to explain the large intensity of the observed magnetic fields is still under debate. Recent work has shown that convection in cooling white dwarfs spans two regimes: efficient convection at the onset of crystallization, and thermohaline convection during most of the star’s cooling history. Here, we calculate the properties of crystallization-driven convection for cooling models of several white dwarfs of different masses. We combine mixing-length theory with scalings from magnetorotational convection to estimate the typical magnitude of the convective velocity and induced magnetic field for both scenarios. In the thermohaline regime, we find velocities ∼10−6–10−5 cm s−1, with fields restricted to ≲ 100 G. However, when convection is efficient, the flow velocity can reach magnitudes of ∼102–103 cm s−1, with fields of ∼106–108 G, independent of the star’s rotation rate. Thus, dynamos driven at the onset of crystallization could explain the large intensity magnetic fields measured for single white dwarfs.

We address the question whether the magnetorotational instability (MRI) can operate in the near-surface shear layer (NSSL) of the Sun and how it affects the interaction with the dynamo process. Using hydromagnetic mean-field simulations of αΩ-type dynamos in rotating shearing-periodic boxes, we show that for negative shear the MRI can operate above a certain critical shear parameter. This parameter scales inversely with the equipartition magnetic field strength above which α quenching set in. Like the usual Ω effect, the MRI produces toroidal magnetic field when the field is sufficiently strong. The work done by the Lorentz force is positive, so the magnetic field drives kinetic energy and not the other way around, as in a turbulent dynamo. This results in strong kinetic energy production and dissipation, which occurs at the expense of the magnetic energy. In view of the application to the solar NSSL, we conclude that the turbulent magnetic diffusivity may be too large for the MRI to be excited and that therefore only the standard Ω effect is expected to operate.

Adenosine triphosphate (ATP) synthases are dynamos that interconvert rotational and chemical energy. Capturing the complete structure of these multisubunit membrane-bound complexes has been hindered by their inherent ability to adopt multiple conformations. Srivastava et al. used protein engineering to freeze mitochondrial ATP synthase from yeast in a single conformation and obtained a structure with the inhibitor oligomycin, which binds to the rotating c-ring within the membrane. Hahn et al. show that chloroplast ATP synthase contains a built-in inhibitor triggered by oxidizing conditions in the dark chloroplast. The mechanisms by which these machines are powered are remarkably similar: Protons are shuttled through a channel to the membrane-embedded c-ring, where they drive nearly a full rotation of the rotor before exiting through another channel on the opposite side of the membrane (see the Perspective by Kane). Science , this issue p. eaas9699 , p. eaat4318 ; see also p. 600 The structure of an intact ATP synthase provides insight into how the motor and catalytic components are coupled. Mitochondrial adenosine triphosphate (ATP) synthase comprises a membrane embedded F o motor that rotates to drive ATP synthesis in the F 1 subunit. We used single-particle cryo–electron microscopy (cryo-EM) to obtain structures of the full complex in a lipid bilayer in the absence or presence of the inhibitor oligomycin at 3.6- and 3.8-angstrom resolution, respectively. To limit conformational heterogeneity, we locked the rotor in a single conformation by fusing the F6 subunit of the stator with the δ subunit of the rotor. Assembly of the enzyme with the F6-δ fusion caused a twisting of the rotor and a 9° rotation of the F o c 10 -ring in the direction of ATP synthesis, relative to the structure of isolated F o . Our cryo-EM structures show how F 1 and F o are coupled, give insight into the proton translocation pathway, and show how oligomycin blocks ATP synthesis.