Domain of validity of some atmospheric mesoscale models

The usual coordinate system in the mesoscale literature is a Cartesian system xyz with its origin at a point on a spherical earth model with the z-axis normal and exterior to the earth. The main form of the momentum equation for theoretical analysis has been dv/dt = −ρ−1∇ p + g−2Ω × v + f r where g is approximated by −gˆz. Several computational models use a version of this equation where z is replaced by a σ-type coordinate, and applications of such models have used a horizontal domain D(L) = 2L × 2L with L 650 km but the results of this paper suggest that the equation is valid with L 100 km. However, the necessity of including the effects of synoptic disturbances and reducing the errors from lateral boundaries impose the use of a large(L). This conflict is solved with the use of the correct gravitational acceleration g = −ga2Rr−3 which provides a momentum equation valid on any domain D(L). This is confirmed with an example which shows that the resulting momentum equation can yield the correct pressure field on the whole earth surface. Practical problems limit the use of the coordinate system xyz to L � 500 km. In this case, it is shown that the approximation g ∼ −g(xˆx + yˆy + aˆz)/a can be applied. Some mesoscale models incorporate map projections into model equations to consider the earth curvature. This has motivated the use of such models on a domain with L ∼ 882, 1665 km. Formally, the governing equations from map projections are written in terms of a curvilinear coordinate system xpypzp but it is shown that if xp, yp, zp are taken as x, y, z the resulting momentum equation is valid on a region with L � 100 km

Determination of transition frequencies in a single 138^{138}Ba+^{+} ion

Transition frequencies between low-lying energy levels in a single trapped $^{138}$Ba$^{+}$ ion have been measured with laser spectroscopy referenced to an optical frequency comb. By extracting the frequencies of one-photon and two-photon components of the line shape using an eight-level optical Bloch model, we achieved 0.1 MHz accuracy for the 5d $^{2}$D$_{3/2}$ - 6p $^{2}$P$_{1/2}$ and 6s $^{2}$S$_{1/2}$ - 5d $^{2}$D$_{3/2}$ transition frequencies, and 0.2 MHz for the 6s $^{2}$S$_{1/2}$ - 6p $^{2}$P$_{1/2}$ transition frequency.Comment: 5 pages, 7 figures, submitted to Phys. Rev.

Simulated Galactic methanol maser distribution to constrain Milky Way parameters

Using trigonometric parallaxes and proper motions of masers associated with massive young stars, the Bar and Spiral Structure Legacy (BeSSeL) survey has reported the most accurate values of the Galactic parameters so far. The determination of these parameters with high accuracy has a widespread impact on Galactic and extragalactic measurements. This research is aimed at establishing the confidence with which such parameters can be determined. This is relevant for the data published in the context of the BeSSeL survey collaboration, but also for future observations, in particular from the Southern Hemisphere. In addition, some astrophysical properties of the masers can be constrained, notably the luminosity function. We have simulated the population of maser-bearing young stars associated with Galactic spiral structure, generating several samples and comparing them with the observed samples used in the BeSSeL survey. Consequently, we checked the determination of Galactic parameters for observational biases introduced by the sample selection. Galactic parameters obtained by the BeSSeL survey do not seem to be biased by the sample selection used. In fact, the published error estimates appear to be conservative for most of the parameters. We show that future BeSSeL data and future observations with Southern arrays will improve the Galactic parameters estimates and smoothly reduce their mutual correlation. Moreover, by modeling future parallax data with larger distance and, thus, greater relative uncertainties for a larger numbers of sources, we found that parallax-distance biasing is an important issue. Hence, using fractional parallax uncertainty in the weighting of the motion data is imperative. Finally, the luminosity function for 6.7 GHz methanol masers was determined, allowing us to estimate the number of Galactic methanol masers.Comment: Accepted for publication in A&A. Language edition include

Finding evolved stars in the inner Galactic disk with Gaia

The Bulge Asymmetries and Dynamical Evolution (BAaDE) survey will provide positions and line-of-sight velocities of ~20,000 evolved, maser bearing stars in the Galactic plane. Although this Galactic region is affected by optical extinction, BAaDE targets may have Gaia cross-matches, eventually providing additional stellar information. In an initial attempt to cross-match BAaDE targets with Gaia, we have found more than 5,000 candidates. Of these, we may expect half to show SiO emission, which will allow us to obtain velocity information. The cross-match is being refined to avoid false positives using different criteria based on distance analysis, flux variability, and color assessment in the mid- and near-IR. Once the cross-matches can be confirmed, we will have a unique sample to characterize the stellar population of evolved stars in the Galactic bulge, which can be considered fossils of the Milky Way formation.Comment: To appear in the Proceedings of the IAU Symposium No. 330: "Astrometry and Astrophysics in the Gaia sky