Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Element abundances in the metal rich open cluster NGC6253

We have carried out a big FLAMES survey of 10 Galactic open clusters aiming at different goals. One of them is the determination of chemical abundances, in order to put constraints on the radial metallicity gradient in the disk and its evolution. One of the sample clusters is the very metal rich NGC 6253. We have obtained UVES high resolution spectra of seven candidate cluster members (from the turn off up to the red clump) with the goal of determining the chemical composition of NGC 6253 and to investigate its origin and role in the interpretation of the radial metallicity gradient in the disk. Equivalent width analysis and spectral synthesis were performed using MOOG and Kurucz model atmospheres. We derived abundances of Fe, alpha- and Fe-peak elements, the light element Na and the s-process element Ba. Excluding two likely non-members and the clump giant, whose metallicity from equivalent widths is overestimated, we find an average [Fe/H]=+0.36+/-0.07 (rms) for the cluster. For most of the other elements we derive solar abundance ratios.Comment: accepted by A&A (02/01/2007), 21 pages, 11 ps figure

Old open clusters in the outer Galactic disk

The outer parts of the Milky Way disk are believed to be one of the main arenas where the accretion of external material in the form of dwarf galaxies and subsequent formation of streams is taking place. The Monoceros stream and the Canis Major and Argo over-densities are notorious examples. VLT high resolution spectra have been acquired for five distant open clusters. We derive accurate radial velocities to distinguish field interlopers and cluster members. For the latter we perform a detailed abundance analysis and derive the iron abundance [Fe/H] and the abundance ratios of several $\alpha$ elements. Our analysis confirms previous indications that the radial abundance gradient in the outer Galactic disk does not follow the expectations extrapolated from the solar vicinity, but exhibits a shallower slope. By combining the metallicity of the five program clusters with eight more clusters for which high resolution spectroscopy is available, we find that the mean metallicity in the outer disk between 12 and 21 kpc from the Galactic center is [Fe/H] $\approx -0.35$, with only marginal indications for a radial variation. In addition, all the program clusters exhibit solar scaled or slightly enhanced $\alpha$ elements, similar to open clusters in the solar vicinity and thin disk stars. We investigate whether this outer disk cluster sample might belong to an extra-galactic population, like the Monoceros ring. However, close scrutiny of their properties - location, kinematics and chemistry - does not convincingly favor this hypothesis. On the contrary, they appear more likely genuine Galactic disk clusters. We finally stress the importance to obtain proper motion measurements for these clusters to constrain their orbits.Comment: 19 pages, 9 eps figure, in press in A&A, abstract rephrased to fit i

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

Open clusters as key tracers of Galactic chemical evolution. III. Element abundances in Berkeley 20, Berkeley 29, Collinder 261, and Melotte 66

Galactic open clusters are since long recognized as one of the best tools for investigating the radial distribution of iron and other metals. We employed FLAMES at VLT to collect UVES spectra of bright giant stars in a large sample of open clusters, spanning a wide range of Galactocentric distances, ages, and metallicities. We present here the results for four clusters: Berkeley 20 and Berkeley 29, the two most distant clusters in the sample; Collinder 261, the oldest and the one with the minimum Galactocentric distance; Melotte 66. Equivalent width analysis was carried out using the spectral code MOOG and Kurucz model atmospheres to derive abundances of Fe, Al, Mg, Si, Ca, Ti, Cr, Ni, Ba; non-LTE Na abundances were derived by direct line-profile fitting. We obtain subsolar metallicities for the two anticenter clusters Be 20 ([Fe/H]=-0.30, rms=0.02) and Be 29 ([Fe/H]=-0.31, rms=0.03), and for Mel 66 ([Fe/H]=-0.33, rms=0.03), located in the third Galactic quadrant, while Cr 261, located toward the Galactic center, has higher metallicity ([Fe/H]=+0.13, rms=0.05 dex). The alpha-elements Si, Ca and Ti, and the Fe-peak elements Cr and Ni are in general close to solar; the s-process element Ba is enhanced. Non-LTE computations of Na abundances indicate solar scaled values, suggesting that the enhancement in Na previously determined in giants in open clusters could be due to neglected non-LTE effects. Our results support the presence of a steep negative slope of the Fe radial gradient up to about 10-11 kpc from the Galactic center, while in the outer disk the [Fe/H] distribution seems flat. All the elemental ratios measured are in very good agreement with those found for disk stars of similar metallicity and no trend with Galactocentric distance seems to be present.Comment: Accepted for publication on A&

Extended Stromgren Photoelectric Photometry in NGC 752

Photoelectric photometry on the extended Stromgren system (uvbyCa) is presented for 7 giants and 21 main sequence stars in the old open cluster, NGC 752. Analysis of the hk data for the turnoff stars yields a new determination of the cluster mean metallicity. From 10 single-star members, [Fe/H] = -0.06 +/- 0.03, where the error quoted is the standard error of the mean and the Hyades abundance is set at [Fe/H] = +0.12. This result is unchanged if all 20 stars within the limits of the hk metallicity calibration are included. The derived [Fe/H] is in excellent agreement with past estimates using properly-zeroed m1 data, transformed moderate-dispersion spectroscopy, and recent high dispersion spectroscopy.Comment: 14 tex'd pages including 2 tables; 2 separate files with eps figures Accepted for PASP March 200

Binary coalescence from case A evolution -- mergers and blue stragglers

We constructed some main-sequence mergers from case A binary evolution and studied their characteristics via Eggleton's stellar evolution code. Both total mass and orbital angular momentum are conservative in our binary evolutions. Some mergers might be on the left of the ZAMS as defined by normal surface composition on a CMD because of enhanced surface helium content. The study also shows that central hydrogen content of the mergers is independent of mass. As a consequence, we fit the formula of magnitude and B-V of the mergers when they return back to thermal equilibrium with maximum error 0.29 and 0.037, respectively. Employing the consequences above, we performed Monte Carlo simulations to examine our models in NGC 2682 and NGC 2660. In NGC 2682, binary mergers from our models cover the region with high luminosity, but its importance is much less than that of AML. Our results are well-matched to the observations of NGC2660 if there is about 0.5Mo of mass loss in the merger process.Comment: 14 pages, 12 figures. accepted by MNRA

The evolution of the Galactic metallicity gradient from high-resolution spectroscopy of open clusters

Open clusters offer a unique possibility to study the time evolution of the radial metallicity gradients of several elements in our Galaxy, because they span large intervals in age and Galactocentric distance, and both quantities can be more accurately derived than for field stars. We re-address the issue of the Galactic metallicity gradient and its time evolution by comparing the empirical gradients traced by a sample of 45 open clusters with a chemical evolution model of the Galaxy. At variance with previous similar studies, we have collected from the literature only abundances derived from high--resolution spectra. The clusters have distances $7 < RGC<22$ kpc and ages from $\sim 30$ Myr to 11 Gyr. We also consider the $\alpha$-elements Si, Ca, Ti, and the iron-peak elements Cr and Ni. The data for iron-peak and $\alpha$-elements indicate a steep metallicity gradient for R_GC<12$kpc and a plateau at larger radii. The time evolution of the metallicity distribution is characterized by a uniform increase of the metallicity at all radii, preserving the shape of the gradient, with marginal evidence for a flattening of the gradient with time in the radial range 7-12 kpc. Our model is able to reproduce the main features of the metallicity gradient and its evolution with an infall law exponentially decreasing with radius and with a collapse time scale of the order of 8 Gyr at the solar radius. This results in a rapid collapse in the inner regions, i.e.$R_{\rm GC}\lesssim 12$ kpc (that we associate with an early phase of disk formation from the collapse of the halo) and in a slow inflow of material per unit area in the outer regions at a constant rate with time.Comment: 16 pages, 18 figures, A&A accepte

Lithium in the Intermediate-Age Open Cluster, NGC 3680

High-dispersion spectra centered on the Li 6708 A line have been obtained for 70 potential members of the open cluster NGC 3680, with an emphasis on stars in the turnoff region. A measurable Li abundance has been derived for 53 stars, 39 of which have radial velocities and proper motions consistent with cluster membership. After being transferred to common temperature and abundance scales, previous Li estimates have been combined to generate a sample of 49 members, 40 of which bracket the cluster Li-dip. Spectroscopic elemental analysis of 8 giants and 5 turnoff stars produces [Fe/H] = -0.17 +/- 0.07 (sd) and -0.07 +/- 0.02 (sd), respectively. We also report measurements of Ca, Si and Ni which are consistent with scaled-solar ratios within the errors. Adopting [Fe/H] = -0.08 (Sect. 3.6), Y^2 isochrone comparisons lead to an age of 1.75 +/- 0.10 Gyr and an apparent modulus of (m-M) = 10.30 +/- 0.15 for the cluster, placing the center of the Li-dip at 1.35 +/- 0.03 solar masses. Among the giants, 5 of 9 cluster members are now known to have measurable Li with A(Li) near 1.0. A combined sample of dwarfs in the Hyades and Praesepe is used to delineate the Li-dip profile at 0.7 Gyr and [Fe/H] = +0.15, establishing its center at 1.42 +/- 0.02 solar masses and noting the possible existence of secondary dip on its red boundary. When evolved to the typical age of the clusters NGC 752, IC 4651 and NGC 3680, the Hyades/Praesepe Li-dip profile reproduces the observed morphology of the combined Li-dip within the CMD's of the intermediate-age clusters while implying a metallicity dependence for the central mass of the Li-dip given by Mass = (1.38 +/-0.04) + (0.4 +/- 0.2)[Fe/H]. The implications of the similarity of the Li-dichotomy among giants in NGC 752 and IC 4651 and the disagreement with the pattern among NGC 3680 giants are discussed.Comment: Latex ms. is 56 pages, including 10 figures and 4 tables. Accepted for the Astronomical Journa

Transport behavior of holes in boron delta-doped diamond structures

Boron delta-doped diamond structures have been synthesized using microwave plasma chemical vapor deposition and fabricated into FET and gated Hall bar devices for assessment of the electrical characteristics. A detailed study of variable temperature Hall, conductivity, and field-effect mobility measurements was completed. This was supported by Schr€dinger-Poisson and relaxation time o calculations based upon application of Fermi’s golden rule. A two carrier-type model was developed with an activation energy of $0.2 eV between the delta layer lowest subband with mobility$1 cm2/Vs and the bulk valence band with high mobility. This new understanding of the transport of holes in such boron delta-doped structures has shown that although Hall mobility as high as 900 cm2/Vs was measured at room temperature, this dramatically overstates the actual useful performance of the device