Migration in the Tenth District : long-term trends and current developments

The movement of people into and out of a state can have important implications for the state’s economy. The total net inflow of people to a state matters because it affects the overall supply of workers in the state. Economists predict that growth in the national labor force will slow in coming decades as a result of such factors as the aging of the baby boomers and the decline in the fertility rate. As this happens, the availability of workers is likely to become an increasingly more important factor in the location decisions of firms. ; Migration matters not only for the size of a state’s workforce but also for the composition of the workforce. The spread of computers and advances in information technology have increased the demand for highly educated workers over the last two decades. Most economists expect the demand for such workers to continue growing in response to further advances in technology. But there will also continue to be a need for unskilled workers to perform jobs at the bottom of the job distribution. In deciding where to locate, firms are likely to pay careful attention to the educational composition of a state’s workforce in addition to the size. The most important determinant of the educational composition of the workforce is the quality of the state’s educational institutions. But also important is whether the state is retaining and attracting the kinds of workers in demand by businesses—for example, whether the state is suffering a net gain or net loss of college graduates to the rest of the nation, and whether the state is receiving too large or too small an influx of less educated immigrants from abroad. ; Focusing on the last half century, Keeton and Newton examine overall patterns in total migration and migration by level of education in Tenth District states. They show that the net inflow of people from other states has been consistently positive in only one state, Colorado, but has gradually improved in most other states. In addition, immigration increased greatly in most district states but ended up more important than in the nation only in Colorado. They also show that many district states have experienced both a net loss of college graduates to the rest of the nation and a net gain of people without high school degrees from abroad. The effects of these migration flows on the mix of workers have been greatly outweighed up till now by increases in education in the population at large. Finally, the authors show that in the current decade migration flows have taken a turn for the worse in several states, but this shift was due to temporary changes in relative economic conditions.Federal Reserve District, 10th

Asymmetric Light Bending in the Equatorial Kerr Metric

The observation of the bending of light by mass, now known as gravitational lensing, was key in establishing general relativity as one of the pillars of modern physics. In the past couple of decades, there has been increasing interest in using gravitational lensing to test general relativity beyond the weak deflection limit. Black holes and neutron stars produce the strong gravitational fields needed for such tests. For a rotating compact object, the distinction between prograde and retrograde photon trajectories becomes important. In this paper, we explore subtleties that arise in interpreting the bending angle in this context and address the origin of seemingly contradictory results in the literature. We argue that analogies that cannot be precisely quantified present a source of confusion

Lensing by Kerr Black Holes. II: Analytical Study of Quasi-Equatorial Lensing Observables

In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter epsilon, which is the ratio of the angular gravitational radius to the angular Einstein radius. We obtain new formulas and results for the bending angle, image positions, image magnifications, total unsigned magnification, and centroid, all to third order in epsilon and including the displacement. New results on the time delay between images are also given to second order in epsilon, again including displacement. For all lensing observables we show that the displacement begins to appear only at second order in epsilon. When there is no spin, we obtain new results on the lensing observables for Schwarzschild lensing with displacement.Comment: 23 pages; final published versio

Detection of microgauss coherent magnetic fields in a galaxy five billion years ago

Magnetic fields play a pivotal role in the physics of interstellar medium in galaxies, but there are few observational constraints on how they evolve across cosmic time. Spatially resolved synchrotron polarization maps at radio wavelengths reveal well-ordered large-scale magnetic fields in nearby galaxies that are believed to grow from a seed field via a dynamo effect. To directly test and characterize this theory requires magnetic field strength and geometry measurements in cosmologically distant galaxies, which are challenging to obtain due to the limited sensitivity and angular resolution of current radio telescopes. Here, we report the cleanest measurements yet of magnetic fields in a galaxy beyond the local volume, free of the systematics traditional techniques would encounter. By exploiting the scenario where the polarized radio emission from a background source is gravitationally lensed by a foreground galaxy at z = 0.439 using broadband radio polarization data, we detected coherent $\mu$G magnetic fields in the lensing disk galaxy as seen 4.6 Gyrs ago, with similar strength and geometry to local volume galaxies. This is the highest redshift galaxy whose observed coherent magnetic field property is compatible with a mean-field dynamo origin.Comment: 29 pages, 5 figures (including Supplementary Information). Published in Nature Astronomy on August 28, 201

Analytic Relations for Magnifications and Time Delays in Gravitational Lenses with Fold and Cusp Configurations

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton et al. (2005), this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies.Comment: 10 pages, 3 figures; reference added, minor correction