Exploring Magnetic Activity from The Sun to the Stars

Sun-like stars are known to display a wide variety of magnetic activity which is likely to be the signature of a hydromagnetic dynamo mechanism working in stellar interiors. This dynamo mechanism has been studied extensively in the context of the Sun. Here we take ideas and experiences gained from solar dynamo modeling and build upon it to study the inferred scaling laws, involving stellar parameters, from observations of stellar magnetic activity. We also discuss how such a synthesis of theoretical dynamo modeling of Sun-like stars and stellar cycle observations may help us reconstruct the long-term variability of the Sun – an important ingredient for understanding the effects of solar forcing on space and global climate.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

The Solar-Stellar Connection: Magneto-Acoustic Pulsations in 1.5M ⊙ – 2M ⊙ Peculiar A Stars

Stellar astronomers look on in envy at the wealth of data, the incredible spatial resolution, and the maturity of the theoretical understanding of the Sun. Yet the Sun is but one star, so stellar astronomy is of great interest to solar astronomers for its range of different conditions under which to test theoretical understanding gained from the study of the Sun. The rapidly oscillating peculiar A stars are of particular interest to solar astronomers. They have strong, global, dipolar magnetic fields with strengths in the range 1?–?25?kG, and they pulsate in high-overtone p modes similar to those in the Sun; thus they offer a unique opportunity to study the interaction of pulsation, convection, and strong magnetic fields, as is now done in the local helioseismology of sunspots. Some of them even pulsate in modes with frequencies above the acoustic cutoff frequency, in analogy with the highest frequency solar modes, but with mode lifetimes up to decades in the roAp stars, very unlike the short mode lifetimes of the Sun. They offer the most extreme cases of atomic diffusion, a small, but important ingredient of the standard solar model with wide application in stellar astrophysics. They are compositionally stratified and are observed and modelled as a function of atmospheric depth and thus can inform plans to expand helioseismic observations to have atmospheric depth resolution. Study of this unique class of pulsating stars follows the advanced state of studies of the Sun and offers more extreme conditions for the understanding of physics shared with the Sun.     

X-ray emission from young stars and implications for the early solar system

Recent observations of soft X-ray emission from solar-type stars obtained with the Einstein X-Ray Observatory indicate that X-ray luminosity is inversely correlated with stellar age. If this result is applied to the Sun and if X-ray emission is a valid indicator of other manifestations of solar activity, then past solar wind and flare levels can be inferred. It can qualitatively explain the excess xenon and nitrogen found in the lunar regolith compared to the level expected from the comteporary solar wind. X-Ray emission from T Tauri and other low-mass pre-main-sequence stars is both highly luminous and variable, indicating the presence of flares ～4 × 10³ times stronger than the largest flares seen in the contemporary Sun. The proton flux from such solar flares during the 10⁶ to 10⁷-year pre-main-sequence phase would be sufficient to account for the ²⁶Al anomaly n meteorites.     

A heuristic remark on the periodic variation in the number of solar neutrinos detected on Earth

Four operating neutrino observatories confirm the long standing discrepancy between detected and predicted solar neutrino flux. Among these four experiments the Homestake experiment is taking data for almost 25 years. The reliability of the radiochemical method for detecting solar neutrinos has been tested recently by the GALLEX experiment. All efforts to solve the solar neutrino problem by improving solar, nuclear, and neutrino physics have failed so far. This may also mean that the average solar neutrino flux extracted from the four experiments may not be the proper quantity to explain the production of neutrinos in the deep interior of the Sun. Occasionally it has been emphasized that the solar neutrino flux may vary over time. In this paper we do address relations among specific neutrino fluxes produced in the proton-proton chain that are imposed by the coupled systems of nonlinear partial differential equations of solar structure and kinetic equations by focusing our attention on a statistical interpretation of selected kinetic equations of PPII/PPIII branch reactions of the protonproton chain. A fresh look at the statistical implications for the outcome of kinetic equations for nuclear reactions may shed light on recent claims that the⁷ Be-neutrino flux of the Sun is suppressed in comparison to the pp- and⁸B neutrino fluxes and may hint at that the solar neutrino flux is indeed varying over time as shown by the Homestake experiment.     

An analytic approach to the connection between stellar structure parameters and the neutrino emission rate in a simple stellar model

In order to obtain the internal structure of a main-sequence star such as the Sun usually one has to solve the detailed structure equations numerically. This paper is an attempt to construct analytic models for the stellar nuclear energy generation. We give closed-form analytic results for the stellar luminosity and stellar neutrino emission rate when the radial matter density of the spherical star under consideration is linear. For the numerical estimation of the neutrino flux of a specified stellar nuclear reaction we take into account parameters of the standard solar model. The present paper gives for the first time the connection between stellar structure parameters and neutrino fluxes in an analytic stellar model.     

Thin flux tube models for star spots

The possibility of understanding stellar activity as an up‐scaled version of the activity of our Sun is investigated. A theoretical model to explain properties of sunspots is used for explaining observed latitudes of star spots. The model is based on thin‐flux‐tube simulations that study the path of magnetic flux tubes from their origin in a stellar overshoot layer to photospheric layers. A direct comparison of the simulation results with individual stars is given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Standard and Non-Standard Solar Models

We summarize the physical input and assumptions commonly adopted in modern standard solar models that also produce good agreement with solar oscillation frequencies. We discuss two motivations for considering non-standard models: the solar neutrino problem and surface lithium abundance problem. We begin to explore the potential for mixed core models to solve the neutrino problem, and compare the structure, neutrino flux, and oscillation frequency predictions for several models in which the inner 25% of the radius is homogenized, taking into account the effects of non-local equilibrium abundances of ³He. The results for the neutrino flux and helioseismic predictions are far from satisfactory, but such models have the potential to reduce the predicted ⁷Be/⁸B neutrino flux ratio, and further studies are warranted. Finally, we discuss how much the neutrino problem can be alleviated in the framework of the standard solar model by using reaction rates, abundances and neutrino capture cross-sections at the limits of their uncertainties, while still satisfying the constraints of helioseismology.     

Rotational evolution of the Sun

The evolutionary behaviour of rotating solar models with different initial angular-momentum distributions has been investigated through the pre-Main-Sequence and Main-Sequence phases. The angular momentum was removed from the convective evelope of the solar models according to the Kawaler's model of magnetic stellar wind (Kawaler, 1988). The models show that (i) the surface rotational velocities of the solar mass stars are independent of initial angular momentum for ages greater than 10⁸ years and (ii) it is not possible to explain the neutrino problem and the sufficient depletion of lithium in the Sun.     

Cosmic and Galactic neutrino backgrounds from thermonuclear sources

We estimate energy spectra and fluxes at the Earth’s surface of the cosmic and Galactic neutrino backgrounds produced by thermonuclear reactions in stars. The extra-galactic component is obtained by combining the most recent estimates of the cosmic star formation history and the stellar initial mass function with accurate theoretical predictions of the neutrino yields all over the thermonuclear lifetime of stars of different masses. Models of the structure and evolution of the Milky Way are used to derive maps of the expected flux generated by Galactic sources as a function of sky direction. The predicted neutrino backgrounds depend only slightly on model parameters. In the relevant 50 keV–10 MeV window, the total flux of cosmic neutrinos ranges between 20 and 65 cm⁻² s⁻¹. Neutrinos reaching the Earth today have been typically emitted at redshift z2. Their energy spectrum peaks at E0.1–0.3 MeV. The energy and entropy densities of the cosmic background are negligible with respect to the thermal contribution of relic neutrinos originated in the early universe. In every sky direction, the cosmic background is outnumbered by the Galactic one, whose integrated flux amounts to 300–1000 cm⁻² s⁻¹. The emission from stars in the Galactic disk contributes more than 95% of the signal.     

Minimal models of cooling neutron stars with accreted envelopes

We study the 'minimal' cooling scenario of superfluid neutron stars with nucleon cores, where the direct Urca process is forbidden and enhanced cooling is produced by neutrino emission due to the Cooper pairing of neutrons. Extending our recent previous work, we include the effects of surface accreted envelopes of light elements. We employ the phenomenological density-dependent critical temperatures   T _cp(ρ)  and   T _cnt(ρ)  of singlet-state proton and triplet-state neutron pairing in a stellar core, as well as the critical temperature   T _cns(ρ)  of singlet-state neutron pairing in a stellar crust. We show that the presence of accreted envelopes simplifies the interpretation of observations of thermal radiation from isolated neutron stars in the scenario of our recent previous work and widens the class of models for nucleon superfluidity in neutron star interiors consistent with the observations.     

Jets from young stars

Most stars produce spectacular jets during their formation. There are thousands of young stars within 500 pc of the Sun and many power jets. Thus protostellar jets may be the most common type of collimated astrophysical outflow. Shocks powered by outflows excite many emission lines, exhibit a rich variety of structure, and motions with velocities ranging from 50 to over 500 km s⁻¹. Due to their relative proximity, proper motions and structural changes can be observed in less than a year. I review the general properties of protostellar jets, summarize some results from recent narrow-band imaging surveys of entire clouds, discuss irradiated jets, and end with some comments concerning outflows from high-mass young stellar objects. Protostellar outflows are ideal laboratories for the exploration of the jet physics.     

Time-varying sources derived from EUV spectroheliograms of the quiet Sun

Activity in the chromosphere-corona transition region of the quiet Sun is found both at network boundaries and in cell interiors using a time series of the EUV spectroheliograms obtained with the Harvard experiment on Skylab. We identify time-varying sources by subtracting the minimum count at each pixel in the time series from the counts at any time. Larger flux enhancements in emission lines occur only at the network boundary, though the cell interiors also have variable intensities. Time-varying sources in the cell interior appear often in the shape of streaks which seem to originate from sources at the network boundary, or as expanding network boundary sources. It is likely that the sources in the cell interior come from the transition sheaths of chromospheric inhomogenities. A multi-temperature analysis shows that two types of sources occur in the quiet Sun. One is due to heating of cool chromospheric inhomogenities like dark mottles. Sometimes cool matter is heated to coronal temperatures. The typical mass of the coronal material produced is 10¹¹-10¹²g. The other type seems to be due to draining of transition region material at the network boundary as the result of thermal instabilities. This quiet Sun activity is compatible with the time-varying sources at 6 cm wavelength.     

The instability of a horizontal magnetic field in an atmosphere stable against convection

The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3R beneath the surface of the Sun, a field of 10² G develops ripples over a scale of 10³ km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10¹⁰ years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001     

Stellar analogs of solar magnetic activity

The techniques and principal results of observational studies of stellar activity are summarized. Both chromospheric and coronal emission clearly track surface magnetic field properties, but it is not well known how the detailed relation between the emission and surface magnetic fields varies with spectral type. For lower Main-Sequence stars of the same spectral type, there is clear evidence of a close relationship between mean activity level and rotation period P _rot. There is also less definitive evidence for a similar dependence on convective overturn time _c , such that activity depends on the single parameter Ro = P _rot/ _c . For single stars, stellar rotation, and magnetic activity both decline smoothly with age. This implies a feedback between angular momentum loss rate and activity level. Temporal variations in mean stellar activity level mimic the solar cycle only for old stars like the Sun, being much more irregular for younger stars. The characteristic timescale of the variations (the cycle period) appears to depend on Ro for old stars, but shows no clear dependence on either rotation rate or spectral type for younger stars. Further data on mean activity and its variation for a large number of lower Main-Sequence stars should contribute significantly to our understanding of the causes of stellar magnetic activity.     

A young cooling neutron star in the remnant of Supernova 1987A

We describe the cooling theory for isolated neutron stars that are several tens of years old. Their cooling differs greatly from the cooling of older stars that has been well studied in the literature. It is sensitive to the physics of the inner stellar crust and even to the thermal conductivity of the stellar core, which is never important at later cooling stages. The absence of observational evidence for the formation of a neutron star during the explosion of Supernova 1987A is consistent with the fact that the star was actually born there. It may still be hidden in the dense center of the supernova remnant. If, however, the star is not hidden, then it should have a low thermal luminosity (below ～10³⁴ erg s^?1) and a short internal thermal relaxation time (shorter than 13 yr). This requires that the star undergo intense neutrino cooling (e.g., via the direct Urca process) and have a thin crust with strong superfluidity of free neutrons and/or an anomalously high thermal conductivity.     

Solar magnetic fields

Since the structuring and variability of the Sun and other stars are governed by magnetic fields, much of present-day stellar physics centers around the measurement and understanding of the magnetic fields and their interactions. The Sun, being a prototypical star, plays a unique role in astrophysics, since its proximity allows the fundamental processes to be explored in detail. The PRL anniversary gives us an opportunity to look back at past milestones and try to identify the main unsolved issues that will be addressed in the future.     

On the rotation–activity correlation for active binary stars

We present an investigation of rotation–activity correlations using International Ultraviolet Explorer ( IUE ) SWP measurements of the C  iv emission line at 1550Å for 72 active binary systems. We use a standard stellar evolution code to derive non-empirical Rossby numbers, R ₀, for each star in our sample and compare the resulting C  iv rotation–activity correlation to that found for empirically derived values of the Rossby number and that based on rotation alone. For dwarf stars our values of R ₀ do not differ greatly from empirical ones and we find a corresponding lack of improvement in correlation. Only a marginal improvement in correlation is found for evolved components in our sample. We discuss possible additional factors, other than rotation or convection, that may influence the activity levels in active binaries. Our observational data imply, in contrast to the theoretical predictions of convective motions, that activity is only weakly related to mass in evolved stars. We conclude that current dynamo theory is limited in its application to the study of active stars because of the uncertainty in the angular velocity-depth profile in stellar interiors and the unknown effects of binarity and surface gravity.     

Helioseismology as a diagnostic of the solar interior

Helioseismology has given us a unique window into the solar interior. Helioseismic data have enabled us to study the internal structure and dynamics with unprecedented detail. This has also allowed us to use the Sun as a laboratory to study the basic properties of stellar matter. We describe how helioseismology is used to determine solar structure and what we have learned about the Sun so far. We also describe how knowledge of the solar structure can be used to constrain the physics inputs.