The availability of large atomic data bases has made it possible to calculate stellar evolution models taking into detailed account the abundance variations of all important contributors to opacity. In a first step, in addition to nuclear reactions, the atomic diffusion, radiative accelerations and opacity are continuously calculated during evolution taking the abundance changes of 28 species into account. This leads to the first self consistent main sequence stellar evolution models. In A and F stars (M ≥ 1.5Mʘ) an iron peak convection zone is shown to appear at a temperature of 200000 K. The calculated surface abundance anomalies, that follow without any arbitrary parameter, are very similar to those observed in AmFm stars in open clusters except that they are larger by a factor of about 3. The second step, is then to introduce a competing hydrodynamical process. To reduce the calculated anomalies to the observed ones, turbulence has been introduced. It is found that the mixed zone must be about 5 times deeper than the iron convection zone. Detailed comparisons to a few AmFm stars have been carried out. The determination of the abundance anomalies of a large number of atomic species (20 to 30 are probably accessible) makes it possible to constrain stellar hydrodynamics. In clusters, the original abundances and age may be known and the accurate determination of surface abundances may constrain turbulence, mass loss and differential rotation when the required atomic data bases are available and used for the modeling of particle transport in stellar evolution.

We conduct numerical simulations of updated solar models including a physical treatment of the tachocline (Spiegel & Zahn 1992), the rotational transition layer localized at the base of the solar convection zone. We first describe what is the current understanding of this thin shear layer. We then show that we improve substantially the agreement between the models and the observed Sun by taking into account the macroscopic mixing occuring within this region.

Rotation brings significant surface He- and N-enhancements. The excesses are higher for higher masses and rotation. Rotating stellar models may account for the nitrogen enhancements observed at the surface of blue supergiants.

For the first time we propose a real physical mechanism for extra-mixing in red giants which can quantitatively interpret all the known star-to-star abundance variations in globular clusters. This is Zahn’s mechanism (Zahn 1992; Maeder & Zahn 1998). It considers extra-mixing in a radiative zone of a rotating star as a result of joint operation of meridional circulation and turbulent diffusion.

We discuss the impact of mixing and rotation along the red-giant branch (RGB) on the properties of horizontal-branch (HB) stars with emphasis on two problems: the nature of the unexpected blue HB population in the metal-rich globular clusters (GCs) NGC 6388 and NGC 6441 and the cause of the low gravities in the blue HB stars. New stellar models indicate that the sloped HBs in NGC 6388 and NGC 6441 might arise from a spread in metallicity, implying that these GCs may be metal-rich analogues of ω Cen. The low gravity problem can be largely explained by the radiative levitation of Fe in the atmospheres of the blue HB stars. We show that the onset of radiative levitation and the drop in HB rotation velocities at Teff ≈ 11,000 K coincide with the disappearance of surface convection. The low rotation velocities of the hotter HB stars may be due to the spin down of the surface layers by a weak stellar wind induced by the radiative levitation of Fe. We conclude that the impact of mixing and rotation on the HB remains to be clearly established.

Transport and mixing in stars is as important as it is difficult to quantify (Zahn 1992; Schatzman 1996; Maeder 1997; Pinsonneault 1997). A first difficulty is that both transport and mixing are dynamical processes which, given the low viscosities of stellar interiors, usually means that the flow is turbulent giving rise to technical difficulties for turbulence is still an incomplete chapter though recent studies have brought about considerable progress. A second difficulty is that turbulence is not self-sustaining and unless there is a source, dynamical mixing and transport will decay in time and eventually die out. Thus, the question: what is the source of turbulence, let alone how to describe it? In the convective zone, the source is the unstable stratification but the mixing there is so strong that one does not need a sophisticated theory to describe it. Strong turbulence is easier to describe than weak turbulence and yet the latter is when the problems become interesting and our descriptive power is less reliable. For example, below the solar CZ we don’t even know for sure the source of stirring, let alone how to describe it and yet, it is the region where we would like to be confident about models. The transport of Li is the best example of a mixing and transport that cannot be too strong or too weak (Schlattl and Weiss 1999). A third difficulty is the unstated assumption that “transport” (advection) and “mixing” (diffusion) have different origin.

Numerical radiation hydrodynamics simulations of stellar surface convection have gained a high level of reliability and perform very well in the confrontation with observations. Similar simulations of convection zones in stellar interiors are much more difficult to set up because of the huge range of time-scales to cover. Therefore, simplified models have to be used, where the results have to be carefully extrapolated to apply them to stellar interiors. Simulations of shallow surface convection zones show that the overshooting velocity fields extend far beyond the region with significant convective energy flux.

This short paper discusses various issues pertaining to the redistribution of angular momentum and mixing of chemical species in the radiative interior of solar-type stars. Results obtained to date indicate that models combining magnetically-mediated angular momentum transport with turbulent mixing of chemical species offer the best hope of explaining the observed rotation and light element evolution in open clusters, without doing excess violence to seismic measurements of the solar internal differential rotation.

In the 1950’s, Sweet (1950) and Öpik (1951) rediscussed the resolution of the von Zeipel paradox in a uniformly rotating stellar radiative zone, showing that the time-scale of the Eddington (1929)-Vogt (1925) thermally-driven circulation would be of the order of the Kelvin-Helmholtz time τK H, divided by an appropriate value for the ratio q of centrifugal to gravitational acceleration. In a Cowling-type star, the streamlines emerge near the poles of the convective core, traverse the radiative envelope, and return to the core at the equator. In a rapid rotator, the time τc of circulation is still short compared with the time-scale τn for transmutation in the core of H into He, and it seemed that the mean molecular weight μ would remain nearly uniform, with the star evolving up and slightly to the left of the Main Sequence in the H-R Diagram; while in a moderate rotator, there could still be enough mixing to affect noticeably the expected evolution towards the Giant Domain. Prima facie, significant mixing would occur provided the value q(rc) of q at the convective core surface exceeded τK H/τn ≈ 10−3.

Cuneiform tablets from Babylonia record lunar and solar eclipses, the presence and movement of comets, meteors and meteor showers. These have provided historical astronomers with much valuable data, but caution must be exercised when using such records, for accuracy of observation often ceded to astrological intent. In the future, texts from Assyria may also provide useful data for historical astronomers.

Chinese, Japanese and Korean celestial observations have made major contributions to Applied Historical Astronomy, especially in the study of supernovae, comets, Earth’s rotation (using eclipses) and solar variability (via sunspots and aurorae). Few original texts now survive; almost all extant records exist only in printed versions, often with the loss of much detail. The earliest Chinese astronomical observations extend back to before 1000 BC. However, fairly systematic records are only available since 200 BC - and even these have suffered losses through wars, etc. By around AD 800, many independent observations are available from Japan and Korea and these provide a valuable supplement to the Chinese data. Throughout East Asia dates were expressed in terms of a luni-solar calendar and conversion to the Julian or Gregorian calendar can be readily effected.

Because of insurmountable problems associated with absolute dating, the non-literate cultures of the Southern Hemisphere can contribute little to Applied Historical Astronomy, although Maori traditions document a possible supernova dating to the period 1000-1770AD. In contrast, the abundant nineteenth century solar, planetary, cometary and stellar observational data provided by Southern Hemisphere professional and amateur observatories can serve as an invaluable mine of information for present-day astronomers seeking to incorporate historical data in their investigations.

There is a great variety of planetary and lunar observations recorded throughout history. Even today, some of these are useful for the improvement of ephemerides, though one must use a lot of judgment and caution - for surprising reasons. Five different sets of observations are presented, each with a story and a lesson: Galileo’s observations of Neptune, Lalande’s observations of Neptune, Williams’ measurements of the 1780 solar eclipse, Robertson’s 1811 transit timings, and solar eclipses in general.

About 240 000 optical observations of the Sun, Mercury and Venus, accumulated during the era of classical astrometry from Bradley up to our days, are incorporated to analyse the secular variation of the longitudes of innermost planets. A significant discrepancy between modern ephemerides and optical observations is discovered. The possible sources of discrepancy are discussed. The tidal acceleration of the Moon has been revised to conform the lunar theory with the ephemerides of the planets. The offset and residual rotation of Hipparcos-based system with respect to the dynamical equinox is determined. Interpretation of this rotation is given.

We show that the spatial information in historical sunspot records, in particular the latitude of the spots, can be of great importance in determining the long term behaviour of the solar magnetic cycle. We examine a continuous record of sunspots with full spatial data from 1853-1996 compiled from the records of Carrington, Spörer, the GPR and SOON. Analysis of the latitudinally-weighted observations indicates that there is a previously unremarked oscillation of the solar magnetic equator with a period of approximately 90 years.

The analysis of historical eclipses shows that the length of the day is increasing on the average by 1.8 milliseconds per century, as distinct from the value of 2.3 milliseconds per century expected from tidal friction. The difference may be accounted for by the response of the Earth to post-glacial uplift following the end of the last ice-age.

Past endeavors in the field of Earth orientation have provided both service to astronomical users of the data and insight into the physical processes of the planet Earth. Since the study of Earth orientation has required a wide geographic distribution of astronomical observing sites, it has been an area of research that has depended heavily on international cooperation over long intervals of time. Recently, IAU Colloquium 178 pointed out that the need exists to find and collect observations that may have been made before the establishment of the current operational services. Reanalysis of such data could be important in our understanding of the physical processes affecting the Earth. All of these observations need to be analyzed in one system consistent with current definitions and conventions. The history of available observations is reviewed along with the contributions that have been made possible using these data. Possible sources for additional data are suggested.

Recent research on the scientific interpretation of historical auroral records is summarised, with special emphasis on topics that provide physical insight into possible variations in geomagnetic disturbance and solar activity during the past two millennia.

Historical records are available for nine supernova explosions seen in our Galaxy over the last two millennia. The observations of these ‘historical’ supernovae are very useful for the modern astrophysical interpretation of the remnants of these supernovae. The ages of the remnants of these historical supernovae are definitively known, which greatly aids understanding of the nature of the remnants. Also, the fact that the parent supernova was seen implies that it was relatively nearby in the Galaxy, giving further constraints on the distance, and hence other properties of their remnants. Here I briefly review the historical supernovae in our Galaxy, in the context of our understanding of their remnants from modern observations.