The Empirical Mass-Luminosity Relation for Low Mass Stars

This work is devoted to improving empirical mass-luminosity relations and mass-metallicity-luminosity relation for low mass stars. For these stars, observational data in the mass-luminosity plane or the mass-metallicity-luminosity space subject to non-negligible errors in all coordinates with different dimensions. Thus a reasonable weight assigning scheme is needed for obtaining more reliable results. Such a scheme is developed, with which each data point can have its own due contribution. Previous studies have shown that there exists a plateau feature in the mass-luminosity relation. Taking into account the constraints from the observational luminosity function, we find by fitting the observational data using our weight assigning scheme that the plateau spans from 0.28 to 0.50 solar mass. Three-piecewise continuous improved mass-luminosity relations in K, J, H and V bands, respectively, are obtained. The visual mass-metallicity-luminosity relation is also improved based on our K band mass-luminosity relation and the available observational metallicity data.Comment: 8 pages, 2 figures. Accepted for publication in Astrophysics & Space Scienc

The N/O Plateau of Blue Compact Galaxies: Monte Carlo Simulations of the Observed Scatter

Chemical evolution models and Monte Carlo simulation techniques have been combined for the first time to study the distribution of blue compact galaxies on the N/O plateau. Each simulation comprises 70 individual chemical evolution models. For each model, input parameters relating to a galaxy's star formation history (bursting or continuous star formation, star formation efficiency), galaxy age, and outflow rate are chosen randomly from ranges predetermined to be relevant. Predicted abundance ratios from each simulation are collectively overplotted onto the data to test its viability. We present our results both with and without observational scatter applied to the model points. Our study shows that most trial combinations of input parameters, including a simulation comprising only simple models with instantaneous recycling, are successful in reproducing the observed morphology of the N/O plateau once observational scatter is added. Therefore simulations which include delay of nitrogen injection are no longer favored over those which propose that most nitrogen is produced by massive stars, if only the plateau morphology is used as the principal constraint. The one scenario which clearly cannot explain plateau morphology is one in which galaxy ages are allowed to range below 250 Myr. We conclude that the present data for the N/O plateau are insufficient by themselves for identifying the portion of the stellar mass spectrum most responsible for cosmic nitrogen production.Comment: 41 pages, 15 figures; accepted by ApJ, to appear Aug. 20, 200

On the Slow Roll Expansion for Brane Inflation

One possibility for identifying the inflaton in the framework of string theory is that it is a $D$-brane modulus. This option involves a specific, non-canonical form of the kinetic energy -- the Dirac-Born-Infeld action. This note investigates the applicability of the slow roll approximation in inflationary models of this type. To this end the slow roll expansion of Liddle, Parsons and Barrow is derived for the case of the DBI action. The resulting slow roll conditions augment the standard ones valid in the case of canonical kinetic terms. It is also shown that in DBI models inflation does not require that the potential dominate the energy density.Comment: References adde

Duality Cascade in Brane Inflation

We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cosmic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.Comment: Corrections in Eq.(5.47), Eq (5.48), Eq(5.49) and Fig

RXJ1716.6+6708: a young cluster at z=0.81

Clusters of galaxies at redshifts nearing one are of special importance since they may be caught at the epoch of formation. At these high redshifts there are very few known clusters. We present follow-up ASCA, ROSAT HRI and Keck LRIS observations of the cluster RXJ1716.6+6708 which was discovered during the optical identification of X-ray sources in the North Ecliptic Pole region of the ROSAT All-Sky Survey. At z=0.809, RXJ1716.6+6708 is the second most distant X-ray selected cluster so far published and the only one with a large number of spectroscopically determined cluster member velocities. The optical morphology of RXJ1716.6+6708 resembles an inverted S-shape filament with the X-rays coming from the midpoint of the filament. The X-ray contours have an elongated shape that roughly coincide with the weak lensing contours. The cluster has a low temperature, kT=5.66{+1.37 -0.58} keV, and a very high velocity dispersion sigma_{los}=1522{+215 -150} km s^{-1}. While the temperature is commensurate with its X-ray luminosity of (8.19 +/- 0.43)x10^{44} h_{50}^{-2} erg s^{-1} (2-10 keV rest frame), its velocity dispersion is much higher than expected from the sigma-T_X relationship of present-day clusters with comparable X-ray luminosity. RXJ1716.6+6708 could be an example of a protocluster, where matter is flowing along filaments and the X-ray flux is maximum at the impact point of the colliding streams of matter.Comment: Latex file, 18 pages, 4 figures, accepted for publication in the Astronomical Journa

Stellar activity of planetary host star HD 189733

Extra-solar planet search programs require high-precision velocity measurements. They need to study how to disentangle radial-velocity variations due to Doppler motion from the noise induced by stellar activity. We monitored the active K2V star HD 189733 and its transiting planetary companion that has a 2.2-day orbital period. We used the high-resolution spectograph SOPHIE mounted on the 1.93-m telescope at the Observatoire de Haute-Provence to obtain 55 spectra of HD 189733 over nearly two months. We refined the HD 189733b orbit parameters and put limits on the eccentricity and on a long-term velocity gradient. After subtracting the orbital motion of the planet, we compared the variability of spectroscopic activity indices to the evolution of the radial-velocity residuals and the shape of spectral lines. The radial velocity, the spectral-line profile and the activity indices measured in HeI (5875.62 \AA), Halpha (6562.81 \AA) and the CaII H&K lines (3968.47 \AA and 3933.66 \AA, respectively) show a periodicity around the stellar rotation period and the correlations between them are consistent with a spotted stellar surface in rotation. We used such correlations to correct for the radial-velocity jitter due to stellar activity. This results in achieving high precision on the orbit parameters, with a semi-amplitude K = 200.56 \pm 0.88 m.s-1 and a derived planet mass of M_{P}=1.13 \pm 0.03 M$_{Jup}$.Comment: 9 pages, 2 tables, 9 figures, accepted for publication in A&A on 20/11/200

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between three and seven. We discuss some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure