The age distribution of stars in the Milky Way bulge

The age and chemical characteristics of the Galactic bulge link to the formation and evolutionary history of the Galaxy. Data-driven methods and large surveys enable stellar ages and precision chemical abundances to be determined for vast regions of the Milky Way, including the bulge. Here, we use the data-driven approach of The Cannon, to infer the ages and abundances for 125,367 stars in the Milky Way, using spectra from Apache Point Observatory Galaxy Evolution Experiment (APOGEE) DR14. We examine the ages and metallicities of 1654 bulge stars within $R_{\text{GAL}}<3.5$ kpc. We focus on fields with $b<12^\circ$, and out to longitudes of $l<15^\circ$. We see that stars in the bulge are about twice as old ($\tau=8$ Gyrs), on average, compared to those in the solar neighborhood ($\tau=4$ Gyrs), with a larger dispersion in [Fe/H] ($\approx0.38$ compared to 0.23 dex). This age gradient comes primarily from the low-$\alpha$ stars. Looking along the Galactic plane, the very central field in the bulge shows by far the largest dispersion in [Fe/H] ($\sigma_{[Fe/H]}\approx0.4$ dex) and line of sight velocity ($\sigma_{vr}\approx90$ km/s), and simultaneously the smallest dispersion in age. Moving out in longitude, the stars become kinematically colder and less dispersed in [Fe/H], but show a much broader range of ages. We see a signature of the X-shape within the bulge at a latitude of $b=8^\circ$, but not at $b=12^\circ$. Future APOGEE and other survey data, with larger sampling, affords the opportunity to extend our approach and study in more detail, to place stronger constraints on models of the Milky Way.Comment: Published in ApJ. 17 pages, 23 figures. Updated with minor text revisions and additional citations to match ApJ published versio

The Circular Velocity Curve of the Milky Way from 55 to 2525 kpc

We measure the circular velocity curve $v_{\rm c}(R)$ of the Milky Way with the highest precision to date across Galactocentric distances of $5\leq R \leq 25$ kpc. Our analysis draws on the $6$-dimensional phase-space coordinates of $\gtrsim 23,000$ luminous red-giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be $v_{\rm c}(R_{\odot}) = (229.0\pm0.2)\rm\,km\,s^{-1}$ with systematic uncertainties at the $\sim 2-5\%$ level. We find that the velocity curve is gently but significantly declining at $(-1.7\pm0.1)\rm\,km\,s^{-1}\,kpc^{-1}$, with a systematic uncertainty of $0.46\rm\,km\,s^{-1}\,kpc^{-1}$, beyond the inner $5$ kpc. We exclude the inner $5$ kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a non-axisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy's dark halo mass within the virial radius to be $M_{\rm vir} = (7.25\pm0.26)\cdot 10^{11}M_{\odot}$ and a local dark matter density of $\rho_{\rm dm}(R_{\odot}) = 0.30\pm0.03\,\rm GeV\,cm^{-3}$.Comment: Accepted for publication in ApJ. All data can be downloaded here: https://doi.org/10.5281/zenodo.146805

A kiloparsec-scale nuclear stellar disk in the milky way as a possible explanation of the high velocity peaks in the galactic bulge

The Apache Point Observatory Galactic Evolution Experiment has measured the stellar velocities of red giant stars in the inner Milky Way. We confirm that the line of sight velocity distributions (LOSVDs) in the mid-plane exhibit a second peak at high velocities, whereas those at | b| =2^\circ do not. We use a high resolution simulation of a barred galaxy, which crucially includes gas and star formation, to guide our interpretation of the LOSVDs. We show that the data are fully consistent with the presence of a thin, rapidly rotating, nuclear disk extending to ∼1 kpc. This nuclear disk is orientated perpendicular to the bar and is likely to be composed of stars on x2 orbits. The gas in the simulation is able to fall onto such orbits, leading to stars populating an orthogonal disk

Microwave Filter Design

Filters are an essential part of telecommunications and radar systems and are key items in the performance and cost of such systems, especially in the increasingly congested spectrum. There has been a particularly marked growth in the cellular communications industry in recent years. This has contributed to both very demanding performance specifications for filters and the commercial pressures for low cost, high volume and quick delivery. Through an investigation into and a subsequent implementation of filter theory, the techniques to produce optimal filter performance for a class of filters are developed in this thesis. This thesis presents an entire design process for filter synthesis of narrow to moderate bandwidth filters, from an investigation of the basic theory through to the development of a generalised synthesis program. This program is an exact design method based on the concept of a matrix representation of coupling coefficients. The outline of the processes required to implement this method have been obtained from a paper by Cameron[1]. To develop the program, Cameron’s summary of the filter synthesis method has been expanded in detail, using further mathematical derivations to produce a Matlab program for generalised Chebyshev filter synthesis.A description of how to transpose the obtained mathematical results to the physical filter structure is included and a filter has been designed and made to specifications using the synthesis program. The process of tuning the filter via the group delay method, using results obtained mathematically is detailed. The overall process is verified by the results obtained from the physical filter