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When States Go Broke collects insights and analysis from leading academics and practitioners that discuss the ongoing fiscal crisis among the American states. No one disagrees with the idea that the states face enormous political and fiscal challenges. There is, however, little consensus on how to fix the perennial problems associated with these challenges. This volume fills an important gap in the dialogue by offering an academic analysis of the many issues broached by these debates. Leading scholars in bankruptcy, constitutional law, labor law, history, political science and economics have individually contributed their assessments of the origins, context and potential solutions for the states in crisis. It presents readers - academics, policy makers and concerned citizens alike - with the resources to begin and continue that important, solution-oriented conversation.
Less than a few hundred thousand years after the Big Bang, the temperature was high enough that cosmic gas consisted of protons, free electrons and light nuclei. Once the Universe cooled to about 3000 K, the electrons and protons were moving sufficiently slowly that they combined to form hydrogen atoms. With scattering of photons much reduced, they were able to move in straight lines indefinitely, and may be seen redshifted into the microwave part of the spectrum as the 2.7K CMB. So began the era of recombination, or so-called “dark ages” when the IGM became mostly neutral. Within the current cold Dark Matter model for the hierarchical formation of structure, mini-halos of mass ∼106M⊙ (Couchman & Rees 1986) provided the gravitational seeds for the first stars at z ≈ 20–30, ending the “dark ages” through re-ionization of the IGM. A comprehensive review of the astrophysical role of dark matter is provided by Jungman, Kamionkowski, & Griest (1996).
Galaxies formed as baryonic gas cooled in the centers of dark matter structures, from which galaxy mass built up via mergers of halos and proto-galaxies (White & Rees 1978; Davis et al. 1985). Since most present-day galaxies are relatively old, it follows that they formed at z ≥2. The timescale over which galaxies assembled remains unclear, particularly the bulges and disks which are the main components of present-day galaxies.
A detailed discussion of stellar atmospheres is beyond the scope of this book. Nevertheless, our means of studying the properties of hot massive stars relies upon our ability to properly interpret the stellar continuum and line information typically formed in the thin boundary layer between the unseen interior and effectively vacuum interstellar medium. An excellent monograph on the topic of stellar photospheres is provided by Gray (2005), whilst more advanced techniques are introduced by Mihalas (1978).
With respect to normal stars, our interpretation of hot, luminous stars is hindered by two effects. Firstly, the routine assumption of LTE breaks down for high-temperature stars, and particularly for supergiants, due to the intense radiation field, such that the solution of the statistical rate equations (non-LTE) is necessary. Secondly, the simplifying assumption of plane-parallel geometry is no longer valid for blue and red supergiants, so the scale heights of their atmospheres are no longer negligible with respect to their stellar radii. It is the combination of requiring non-LTE plus spherical geometry that has prevented the routine study of OB star atmospheres until recently.
Effective temperatures of early-type stars, essential for subsequent determinations of radii and luminosities, are derived from a comparison between observed photometry and/or spectroscopy and models. Surface gravities also require comparison between observed line profiles and models.
LTE model atmospheres developed by Robert Kurucz during the 1970s and 1980s account very thoroughly for metal line blanketing and are widely employed for both early- and late-type stars.