Algebraic Description of Shape Invariance Revisited

We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential problem. Following the prescription given by Gangopadhyaya et al., we first introduce certain nonlinear algebraic systems. We then show that, if the model parameters are appropriately quantized, the bound-state problems can be solved solely by means of representation theory.Comment: 12 pages, 8 eepic figures; minor correction

Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations

Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range

Includes bibliographical references (pages 016404-6-016404-7).We present the calculated prediction and the experimental confirmation that doubly ionized Ag and Sn plasmas can have an index of refraction greater than one for soft x-ray wavelengths. Interferometry experiments conducted using a capillary discharge soft x-ray laser operating at a wavelength of 46.9 nm (26.44 eV) confirm that in few times ionized laser-created plasmas of these elements the anomalous dispersion from bound electrons can dominate the free electron contribution, making the index of refraction greater than one. The results confirm that bound electrons can strongly influence the index of refraction of numerous plasmas over abroad range of soft x-ray wavelengths confirming recent observations. The understanding of index of refraction at short wavelengths will become even more essential during the next decade as x-ray free electron lasers will become available to probe a wider variety of plasmas at higher densities and shorter wavelengths

Prediction and observation of tin and silver plasmas with index of refraction greater than one in the soft x-ray range

Includes bibliographical references (pages 016404-6-016404-7).We present the calculated prediction and the experimental confirmation that doubly ionized Ag and Sn plasmas can have an index of refraction greater than one for soft x-ray wavelengths. Interferometry experiments conducted using a capillary discharge soft x-ray laser operating at a wavelength of 46.9 nm (26.44 eV) confirm that in few times ionized laser-created plasmas of these elements the anomalous dispersion from bound electrons can dominate the free electron contribution, making the index of refraction greater than one. The results confirm that bound electrons can strongly influence the index of refraction of numerous plasmas over abroad range of soft x-ray wavelengths confirming recent observations. The understanding of index of refraction at short wavelengths will become even more essential during the next decade as x-ray free electron lasers will become available to probe a wider variety of plasmas at higher densities and shorter wavelengths

The Mid-Infrared Emission of M87

We discuss Subaru and Spitzer Space Telescope imaging and spectroscopy of M87 in the mid-infrared from 5-35 um. These observations allow us to investigate mid-IR emission mechanisms in the core of M87 and to establish that the flaring, variable jet component HST-1 is not a major contributor to the mid-IR flux. The Spitzer data include a high signal-to-noise 15-35 $\mu$m spectrum of the knot A/B complex in the jet, which is consistent with synchrotron emission. However, a synchrotron model cannot account for the observed {\it nuclear} spectrum, even when contributions from the jet, necessary due to the degrading of resolution with wavelength, are included. The Spitzer data show a clear excess in the spectrum of the nucleus at wavelengths longer than 25 um, which we model as thermal emission from cool dust at a characteristic temperature of 55 \pm 10 K, with an IR luminosity \sim 10^{39} {\rm ~erg ~s^{-1}}. Given Spitzer's few-arcsecond angular resolution, the dust seen in the nuclear spectrum could be located anywhere within ~5'' (390 pc) of the nucleus. In any case, the ratio of AGN thermal to bolometric luminosity indicates that M87 does not contain the IR-bright torus that classical unified AGN schemes invoke. However, this result is consistent with theoretical predictions for low-luminosity AGNsComment: 9 pages, 7 figures, ApJ, in pres

Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction

Includes bibliographical references.We report anomalous fringe shifts observed in soft X-ray laser interferograms of laser-created Al plasmas. This clear experimental evidence shows that the contribution of bound electrons can dominate the index of refraction of laser-created plasmas at soft X-ray wavelengths, resulting in values greater than 1. The comparison of measured and simulated interferograms shows that this results from the dominant contribution of low-charge ions to the index of refraction. This usually neglected bound electron contribution can affect the propagation of soft X-ray radiation in plasmas and the interferometric diagnostics of plasmas for many elements.This work was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant # DE-FG03-02NA00062. Part of this work was performed under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory through the Institute of Laser Science and Application, under Contract No. W-7405-Eng-48. The CSU researchers also gratefully acknowledge the partial support of the NSF ERC Center for Extreme Ultraviolet Science and Technology, award EEC-0310717

Observation of multiply ionized plasmas with dominant bound electron contribution to the index of refraction

Includes bibliographical references.We report anomalous fringe shifts observed in soft X-ray laser interferograms of laser-created Al plasmas. This clear experimental evidence shows that the contribution of bound electrons can dominate the index of refraction of laser-created plasmas at soft X-ray wavelengths, resulting in values greater than 1. The comparison of measured and simulated interferograms shows that this results from the dominant contribution of low-charge ions to the index of refraction. This usually neglected bound electron contribution can affect the propagation of soft X-ray radiation in plasmas and the interferometric diagnostics of plasmas for many elements.This work was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grant # DE-FG03-02NA00062. Part of this work was performed under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory through the Institute of Laser Science and Application, under Contract No. W-7405-Eng-48. The CSU researchers also gratefully acknowledge the partial support of the NSF ERC Center for Extreme Ultraviolet Science and Technology, award EEC-0310717

The host galaxies of luminous quasars

We present results of a deep HST/WFPC2 imaging study of 17 quasars at z~0.4, designed to determine the properties of their host galaxies. The sample consists of quasars with absolute magnitudes in the range -24>M_V>-28, allowing us to investigate host galaxy properties across a decade in quasar luminosity, but at a single redshift. We find that the hosts of all the RLQs, and all the RQQs with nuclear luminosities M_V<-24, are massive bulge-dominated galaxies, confirming and extending the trends deduced from our previous studies. From the best-fitting model host galaxies we have estimated spheroid and black-hole masses, and the efficiency (with respect to Eddington luminosity) with which each quasar is radiating. The largest inferred black-hole mass in our sample is \~3.10^9 M_sun, comparable to those at the centres of M87 and Cygnus A. We find no evidence for super-Eddington accretion in even the most luminous objects. We investigate the role of scatter in the black-hole:spheroid mass relation in determining the ratio of quasar to host-galaxy luminosity, by generating simulated populations of quasars lying in hosts with a Schechter mass function. Within the subsample of the highest luminosity quasars, the observed variation in nuclear-host luminosity ratio is consistent with being the result of the scatter in the black-hole:spheroid relation. Quasars with high nuclear-host ratios can be explained by sub-Eddington accretion onto black holes in the high-mass tail of the black-hole:spheroid relation. Our results imply that, owing to the Schechter cutoff, host mass should not continue to increase linearly with quasar luminosity, at the very highest luminosities. Any quasars more luminous than M_V=-27 should be found in massive elliptical hosts which at the present day would have M_V ~ -24.5.Comment: Accepted for publication in MNRAS. 18 pages; 7 figures and 17 greyscale images are reproduced here at low quality due to space limitations. High-resolution figures are available from ftp://ftp.roe.ac.uk/pub/djef/preprints/floyd2004