A view of the Galactic halo using beryllium as a time scale

Beryllium stellar abundances were suggested to be a good tracer of time in the early Galaxy. In an investigation of its use as a cosmochronometer, using a large sample of local halo and thick-disk dwarfs, evidence was found that in a log(Be/H) vs. [alpha/Fe] diagram the halo stars separate into two components. One is consistent with predictions of evolutionary models while the other is chemically indistinguishable from the thick-disk stars. This is interpreted as a difference in the star formation history of the two components and suggests that the local halo is not a single uniform population where a clear age-metallicity relation can be defined.Comment: To appear in Proceedings of the International Astronomical Union, IAU Symposium, Volume 265, Chemical abundances in the Universe: connecting first stars to planets, K. Cunha, M. Spite and B. Barbuy, eds. 2 Pages, 2 figure

Beryllium abundances and the formation of the halo and the thick disk

The single stable isotope of beryllium is a pure product of cosmic-ray spallation in the ISM. Assuming that the cosmic-rays are globally transported across the Galaxy, the beryllium production should be a widespread process and its abundance should be roughly homogeneous in the early-Galaxy at a given time. Thus, it could be useful as a tracer of time. In an investigation of the use of Be as a cosmochronometer and of its evolution in the Galaxy, we found evidence that in a log(Be/H) vs. [alpha/Fe] diagram the halo stars separate into two components. One is consistent with predictions of evolutionary models while the other is chemically indistinguishable from the thick-disk stars. This is interpreted as a difference in the star formation history of the two components and suggests that the local halo is not a single uniform population where a clear age-metallicity relation can be defined. We also found evidence that the star formation rate was lower in the outer regions of the thick disk, pointing towards an inside-out formation.Comment: 6 pages, 5 figures, To appear in the Proceedings of IAU Symp. 268 - Light Elements in the Universe (C. Charbonnel, M. Tosi, F. Primas, C. Chiappini, eds

Optimal Strategies for Prudent Investors

We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction \a of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed \a. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.Comment: 14 pages, LaTeX, epsfig.sty, 7 eps figures, minor changes; accepted for International J. of Theoretical and Applied Financ

The Be-test in the Li-rich star \#1657 of NGC 6397: evidence for Li-flash in RGB stars?

The Li-rich turn-off star in the globular cluster NGC 6397 could represent the smoking gun for some very rare episode of Li enrichment in globular clusters. We aim to understand the nature of the Li enrichment by performing a spectroscopic analysis of the star, in particular of its beryllium (Be) abundance, and by investigating its binary nature. We observe the near UV region where the Beii resonance doublet and the NH bands are located. We could not detect the Beii lines and derive an upper limit of log (Be/H)< -12.2, that is consistent with the Be observed in other stars of the cluster. We could detect a weak G-band, which implies a mild carbon enhancement [C/Fe]$+0.4\pm0.2$. We could not detect the UV NH band, and we derive an upper limit [N/Fe]$< 0.0$. For oxygen we could notdetect any of the near UV OH lines, which implies that oxygen cannot be strongly enhanced in this star. This is consistent with the detection of the Oi triplet at 777nm, which is consistent with [O/Fe]~0.5. Combining the UVES and Mike data, we could not detect any variation in the radial velocity greater than 0.95 kms$^{-1}$ over 8 years. The chemical composition of the star strongly resembles that of `first generation' NGC6397 stars, with the huge Li as the only deviating abundance. Not detecting Be rules out two possible explanations of the Li overabundance: capture of a substellar body and spallation caused by a nearby type II SNe. Discrepancies are also found with respect to other accretion scenarios,except for contamination by the ejecta of a star that has undergone the RGB Li-flash.Comment: Accepted for publication in A&

Beryllium in turnoff stars of NGC6397: early Galaxy spallation, cosmochronology and cluster formation

We present the first detection of beryllium in two turnoff stars of the old, metal-poor globular cluster NGC 6397. The beryllium lines are clearly detected and we determine a mean beryllium abundance of log(Be/H)=-12.35 +/- 0.2. The beryllium abundance is very similar to that of field stars of similar Fe content. We interpret the beryllium abundance observed as the result of primary spallation of cosmic rays acting on a Galactic scale, showing that beryllium can be used as a powerful cosmochronometer for the first stellar generations. With this method, we estimate that the cluster formed 0.2-0.3 Gyr after the onset of star formation in the Galaxy, in excellent agreement with the age derived from main sequence fitting. From the same spectra we also find low O (noticeably different for the two stars) and high N abundances, suggesting that the original gas was enriched in CNO processed material. Our beryllium results, together with the N, O, and Li abundances, provide insights on the formation of this globular cluster, showing that any CNO processing of the gas must have occurred in the protocluster cloud before the formation of the stars we observe now. We encounter, however, difficulties in giving a fully consistent picture of the cluster formation, able to explain the complex overall abundance pattern.Comment: to appear in A&

Evolution of lithium beyond the solar age: a Li survey of the old open cluster NGC 188

We have determined Li abundances for 11 G-type stars in the 6-8 Gyr old open cluster NGC 188. These data significantly enlarge the number of cluster stars with Li measurements, allowing us to extend the investigation of Li depletion in open clusters to ages well beyond the age of the Sun. We have also inferred the cluster metallicity which turns out to be solar. We find that solar-type stars in NGC 188 are only slightly more Li depleted than the much younger Hyades and no more Li depleted than stars of similar temperature in the 2-4 Gyr younger cluster M 67. At variance with M 67, NGC 188 members show virtually no scatter in their Li abundances. Surprisingly, no solar- type star in NGC 188 appears as Li depleted as the Sun or as the most Li depleted stars in M 67. We discuss the implications of these results for mechanisms of internal mixing and Li depletion in main sequence stars.Comment: to appear in A&

Lithium evolution in intermediate age and old open clusters: NGC 752 revisited

We present new high resolution spectroscopic observations of the intermediate age (~2 Gyr) open cluster NGC 752. We investigate the Li vs. Teff distribution and we obtain a new accurate determination of the cluster metallicity. We compare the results for NGC 752 with other intermediate age and old clusters spanning the age range from the Hyades (~0.6 Gyr) to NGC 188 (~6-8 Gyr). We find that NGC 752 has a solar iron content ([Fe/H]=+0.01+/-0.04), at variance with early reports of sub-solar metallicity. We find that NGC 752 is only slightly more Li depleted than the younger Hyades and has a Li pattern almost identical to that observed in the ~2 Gyr old IC 4651 and NGC 3680. As for the latter clusters, we find that NGC 752 is characterized by a tight Li vs. Teff distribution for solar-type stars, with no evidence for a Li spread as large as the one observed in the solar age solar metallicity M 67. We discuss these results in the framework of mixing mechanisms and Li depletion on the main sequence (MS). We conclude that the development of a large scatter in Li abundances in old open clusters might be an exception rather than the rule (additional observations of old clusters are required), and that metallicity variations of the order of ~0.2 dex do not affect Li depletion after the age of the Hyades.Comment: A&A accepted, 10 pages, 5 ps figure

Sivers and Boer-Mulders functions in Light-Cone Quark Models

Results for the naive-time-reversal-odd quark distributions in a light-cone quark model are presented. The final-state interaction effects are generated via single-gluon exchange mechanism. The formalism of light-cone wave functions is used to derive general expressions in terms of overlap of wave-function amplitudes describing the different orbital angular momentum components of the nucleon. In particular, the model predictions show a dominant contribution from S- and P-wave interference in the Sivers function and a significant contribution also from the interference of P and D waves in the Boer-Mulders function. The favourable comparison with existing phenomenological parametrizations motivates further applications to describe azimuthal asymmetries in hadronic reactions.Comment: references and explanations added; version to appear in Phys. Rev.