On a semiclassical formula for non-diagonal matrix elements

Let $H(\hbar)=-\hbar^2d^2/dx^2+V(x)$ be a Schr\"odinger operator on the real line, $W(x)$ be a bounded observable depending only on the coordinate and $k$ be a fixed integer. Suppose that an energy level $E$ intersects the potential $V(x)$ in exactly two turning points and lies below $V_\infty=\liminf_{|x|\to\infty} V(x)$. We consider the semiclassical limit $n\to\infty$, $\hbar=\hbar_n\to0$ and $E_n=E$ where $E_n$ is the $n$th eigen-energy of $H(\hbar)$. An asymptotic formula for $$, the non-diagonal matrix elements of $W(x)$ in the eigenbasis of $H(\hbar)$, has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.Comment: LaTeX2

Detection of the Vortex Dynamic Regimes in MgB2 by Third Harmonic AC Susceptibility Measurements

In a type-II superconductor the generation of higher harmonics in the magnetic response to an alternating magnetic field is a consequence of the non-linearity in the I-V relationship. The shape of the current-voltage (I-V) curve is determined by the current dependence of the thermal activation energy U(J) and is thus related to the dynamical regimes governing the vortex motion. In order to investigate the vortex dynamics in MgB2 bulk superconductors we have studied the fundamental (chi1) and third (chi3) harmonics of the ac magnetic susceptibility. Measurements have been performed as a function of the temperature and the dc magnetic field, up to 9 T, for various frequencies and amplitudes of the ac field. We show that the analysis of the behaviour in frequency of chi3(T) and chi3(B) curves can provide clear information about the non-linearity in different regions of the I-V characteristic. By comparing the experimental curves with numerical simulations of the non-linear diffusion equation for the magnetic field we are able to resolve the crossover between a dissipative regime governed by flux creep and one dominated by flux flow phenomena.Comment: to be published in "Horizons in Superconductivity Research" (Nova Science Publishers, Inc., NY, 2003

The Effects of Accretion Luminosity upon Fragmentation in the Early Universe

We introduce a prescription for the luminosity from accreting protostars into smoothed particle hydrodynamics simulation, and apply the method to simulations of five primordial minihalos generated from cosmological initial conditions. We find that accretion luminosity delays fragmentation within the halos, but does not prevent it. In halos that slowly form a low number of protostars, the accretion luminosity can reduce the number of fragments that are formed before the protostars start ionising their surroundings. However, halos that rapidly form many protostars become dominated by dynamical processes, and the effect of accretion luminosity becomes negligible. Generally the fragmentation found in the halos is highly dependent on the initial conditions. Accretion luminosity does not substantially affect the accretion rates experienced by the protostars, and is far less important than dynamical interactions, which can lead to ejections that effectively terminate the accretion. We find that the accretion rates onto the inner regions of the disks (20 AU) around the protostars are highly variable, in contrast to the constant or smoothly decreasing accretion rates currently used in models of the pre-main sequence evolution of Population III stars.Comment: 12 pages, 10 figures and 3 tables. Accepted by MNRA

Blue straggler stars in dwarf spheroidal galaxies

Blue straggler star (BSS) candidates have been observed in all old dwarf spheroidal galaxies (dSphs), however whether or not they are authentic BSSs or young stars has been a point of debate. To both address this issue and obtain a better understanding of the formation of BSSs in different environments, we have analysed a sample of BSS candidates in two nearby Galactic dSphs, Draco and Ursa Minor. We have determined their radial and luminosity distributions from wide field multicolour imaging data extending beyond the tidal radii of both galaxies. BSS candidates are uniformly distributed through the host galaxy, whereas a young population is expected to show a more clumpy distribution. Furthermore, the observed radial distribution of BSSs, normalized to both red giant branch (RGB) and horizontal branch (HB) stars, is almost flat, with a slight decrease towards the centre. Such a distribution is at odds with the predictions for a young stellar population, which should be more concentrated. Instead, it is consistent with model predictions for BSS formation by mass transfer in binaries (MT-BSSs). Such results, although not decisive, suggest that these candidates are indeed BSSs and that MT-BSSs form in the same way in Draco and Ursa Minor as in globular clusters. This favours the conclusion that Draco and Ursa Minor are truly ‘fossil' galaxies, where star formation ceased completely more than 8 billion years ag

Blue straggler stars in dwarf spheroidal galaxies - II. Sculptor and Fornax

The existence of blue straggler stars (BSSs) in dwarf spheroidal galaxies (dSphs) is still an open question. In fact, many BSS candidates have been observed in the Local Group dSphs, but it is unclear whether they are real BSSs or young stars. Shedding light on the nature of these BSS candidates is crucial in order to understand the star formation history of dSphs. In this paper, we consider BSS candidates in Sculptor and Fornax. In Fornax, there are strong hints that the BSS population is contaminated by young stars, whereas in Sculptor there is no clear evidence of recent star formation. We derive the radial and luminosity distribution of BSS candidates from wide field imaging data extending beyond the nominal tidal radius of these galaxies. The observations are compared with the radial distribution of BSSs expected from dynamical simulations. In Sculptor, the radial distribution of BSS candidates is consistent with that of red horizontal branch (RHB) stars and is in agreement with theoretical expectations for BSSs generated via mass transfer in binaries. On the contrary, in Fornax, the radial distribution of BSS candidates is more concentrated than that of all the considered stellar populations. This result supports the hypothesis that most of BSS candidates in Fornax are young stars, and this is consistent with previous studie

Dark Stars and Boosted Dark Matter Annihilation Rates

Dark Stars (DS) may constitute the first phase of stellar evolution, powered by dark matter (DM) annihilation. We will investigate here the properties of DS assuming the DM particle has the required properties to explain the excess positron and elec- tron signals in the cosmic rays detected by the PAMELA and FERMI satellites. Any possible DM interpretation of these signals requires exotic DM candidates, with an- nihilation cross sections a few orders of magnitude higher than the canonical value required for correct thermal relic abundance for Weakly Interacting Dark Matter can- didates; additionally in most models the annihilation must be preferentially to lep- tons. Secondly, we study the dependence of DS properties on the concentration pa- rameter of the initial DM density profile of the halos where the first stars are formed. We restrict our study to the DM in the star due to simple (vs. extended) adiabatic contraction and minimal (vs. extended) capture; this simple study is sufficient to illustrate dependence on the cross section and concentration parameter. Our basic results are that the final stellar properties, once the star enters the main sequence, are always roughly the same, regardless of the value of boosted annihilation or concentration parameter in the range between c=2 and c=5: stellar mass ~ 1000M\odot, luminosity ~ 10^7 L\odot, lifetime ~ 10^6 yrs (for the minimal DM models considered here; additional DM would lead to more massive dark stars). However, the lifetime, final mass, and final luminosity of the DS show some dependence on boost factor and concentration parameter as discussed in the paper.Comment: 37 pages, 11 figure

Low-Mass Relics of Early Star Formation

The earliest stars to form in the Universe were the first sources of light, heat and metals after the Big Bang. The products of their evolution will have had a profound impact on subsequent generations of stars. Recent studies of primordial star formation have shown that, in the absence of metals (elements heavier than helium), the formation of stars with masses 100 times that of the Sun would have been strongly favoured, and that low-mass stars could not have formed before a minimum level of metal enrichment had been reached. The value of this minimum level is very uncertain, but is likely to be between 10^{-6} and 10^{-4} that of the Sun. Here we show that the recent discovery of the most iron-poor star known indicates the presence of dust in extremely low-metallicity gas, and that this dust is crucial for the formation of lower-mass second-generation stars that could survive until today. The dust provides a pathway for cooling the gas that leads to fragmentation of the precursor molecular cloud into smaller clumps, which become the lower-mass stars.Comment: Offprint of Nature 422 (2003), 869-871 (issue 24 April 2003

Suppression of HD-cooling in protogalactic gas clouds by Lyman-Werner radiation

It has been shown that HD molecules can form efficiently in metal-free gas collapsing into massive protogalactic halos at high redshift. The resulting radiative cooling by HD can lower the gas temperature to that of the cosmic microwave background, T_CMB=2.7(1+z)K, significantly below the temperature of a few 100 K achievable via H_2-cooling alone, and thus reduce the masses of the first generation of stars. Here we consider the suppression of HD-cooling by UV irradiation in the Lyman-Werner (LW) bands. We include photo-dissociation of both H_2 and HD, and explicitly compute the self-shielding and shielding of both molecules by neutral hydrogen as well as the shielding of HD by H_2. We use a simplified dynamical collapse model, and follow the chemical and thermal evolution of the gas, in the presence of a UV background. We find that a LW flux of J_crit = 1e-22 erg/cm^2/sr/s/Hz is able to suppress HD cooling and thus prevent collapsing primordial gas from reaching temperatures below 100 K. The main reason for the lack of HD cooling for J>J_crit is the partial photo-dissociation of H_2, which prevents the gas from reaching sufficiently low temperatures (T<150K) for HD to become the dominant coolant; direct HD photo-dissociation is unimportant except for a narrow range of fluxes and column densities. Since the prevention of HD-cooling requires only partial H_2 photo-dissociation, the critical flux J_crit is modest, and is below the UV background required to reionize the universe at redshift z=10-20. We conclude that HD-cooling can reduce the masses of typical stars only in rare halos forming well before the epoch of reionization.Comment: 14 pages with 9 figures, submitted to MNRA

Dark Matter Capture in the First Stars: a Power Source and Limit on Stellar Mass

The annihilation of weakly interacting massive particles can provide an important heat source for the first (Pop. III) stars, potentially leading to a new phase of stellar evolution known as a "Dark Star". When dark matter (DM) capture via scattering off of baryons is included, the luminosity from DM annihilation may dominate over the luminosity due to fusion, depending on the DM density and scattering cross-section. The influx of DM due to capture may thus prolong the lifetime of the Dark Stars. Comparison of DM luminosity with the Eddington luminosity for the star may constrain the stellar mass of zero metallicity stars; in this case DM will uniquely determine the mass of the first stars. Alternatively, if sufficiently massive Pop. III stars are found, they might be used to bound dark matter properties.Comment: 19 pages, 4 figures, 3 Tables updated captions and graphs, corrected grammer, and added citations revised for submission to JCA