Gaudin subalgebras and wonderful models

Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini-Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes.Comment: 13 pages, 2 figures; added detailed description of the B_2 and B_3 cases in the new versio

Absolute Magnitudes of Seismic Red Clumps in the Kepler Field and SAGA: the age dependency of the distance scale

Red clump stars are fundamental distance indicators in astrophysics, although theoretical stellar models predict a dependence of absolute magnitudes with ages. This effect is particularly strong below 2 Gyr, but even above this limit a mild age dependence is still expected. We use seismically identified red clump stars in the Kepler field for which we have reliable distances, masses and ages from the SAGA survey to first explore this effect. By excluding red clump stars with masses larger than 1.6 Msun (corresponding to ages younger than 2 Gyr), we derive robust calibrations linking intrinsic colors to absolute magnitudes in the following photometric systems: Str\"omgren $by$, Johnson $BV$, Sloan $griz$, 2MASS $JHK_s$ and WISE $W1W2W3$. With the precision achieved we also detect a slope of absolute magnitudes 0.020(0.003) mag per Gyrin the infrared, implying that distance calibrations of clump stars can be off by up to 0.2 mag in the infrared (over the range from 2 Gyr to 12 Gyr) if their ages are unknown. Even larger uncertainties affect optical bands, because of the stronger interdependency of absolute magnitudes on colors and age. Our distance calibrations are ultimately based on asteroseismology, and we show how the distance scale can be used to test the accuracy of seismic scaling relations. Within the uncertainties our calibrations are in agreement with those built upon local red clump with Hipparcos} parallaxes, although we find a tension which if confirmed would imply that scaling relations overestimate radii of red clump stars by 2(+-20%. Data-releases post Gaia DR1 will provide an important testbed for our results.Comment: 26 pages, 8 figures, accepted by Ap

Herschel and ALMA Observations of Massive SZE-selected Clusters

We present new Herschel observations of four massive, Sunyaev-Zel'dovich Effect (SZE)-selected clusters at $0.3 \leq z \leq 1.1$, two of which have also been observed with ALMA. We detect 19 Herschel/PACS counterparts to spectroscopically confirmed cluster members, five of which have redshifts determined via CO($4-3$) and [CI](${}^3P_1 - {}^3P_0$) lines. The mean [CI]/CO line ratio is $0.19 \pm 0.07$ in brightness temperature units, consistent with previous results for field samples. We do not detect significant stacked ALMA dust continuum or spectral line emission, implying upper limits on mean interstellar medium (H$_2$ + HI) and molecular gas masses. An apparent anticorrelation of $L_{IR}$ with clustercentric radius is driven by the tight relation between star formation rate and stellar mass. We find average specific star formation rate log(sSFR/yr$^{-1}$) = -10.36, which is below the SFR$-M_*$ correlation measured for field galaxies at similar redshifts. The fraction of infrared-bright galaxies (IRBGs; $\log (L_{IR}/L_\odot) > 10.6$) per cluster and average sSFR rise significantly with redshift. For CO detections, we find $f_{gas} \sim 0.2$, comparable to those of field galaxies, and gas depletion timescales of about 2 Gyr. We use radio observations to distinguish active galactic nuclei (AGNs) from star-forming galaxies. At least four of our 19 Herschel cluster members have $q_{IR} < 1.8$, implying an AGN fraction $f_{AGN} \gtrsim 0.2$ for our PACS-selected sample.Comment: Accepted in ApJ, 46 pages, 13 figure

Ray splitting in paraxial optical cavities

We present a numerical investigation of the ray dynamics in a paraxial optical cavity when a ray splitting mechanism is present. The cavity is a conventional two-mirror stable resonator and the ray splitting is achieved by inserting an optical beam splitter perpendicular to the cavity axis. We show that depending on the position of the beam splitter the optical resonator can become unstable and the ray dynamics displays a positive Lyapunov exponent.Comment: 13 pages, 7 figures, 1 tabl

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results

In the picture of eternal inflation, our observable universe resides inside a single bubble nucleated from an inflating false vacuum. Many of the theories giving rise to eternal inflation predict that we have causal access to collisions with other bubble universes, providing an opportunity to confront these theories with observation. We present the results from the first observational search for the effects of bubble collisions, using cosmic microwave background data from the WMAP satellite. Our search targets a generic set of properties associated with a bubble collision spacetime, which we describe in detail. We use a modular algorithm that is designed to avoid a posteriori selection effects, automatically picking out the most promising signals, performing a search for causal boundaries, and conducting a full Bayesian parameter estimation and model selection analysis. We outline each component of this algorithm, describing its response to simulated CMB skies with and without bubble collisions. Comparing the results for simulated bubble collisions to the results from an analysis of the WMAP 7-year data, we rule out bubble collisions over a range of parameter space. Our model selection results based on WMAP 7-year data do not warrant augmenting LCDM with bubble collisions. Data from the Planck satellite can be used to more definitively test the bubble collision hypothesis.Comment: Companion to arXiv:1012.1995. 41 pages, 23 figures. v2: replaced with version accepted by PRD. Significant extensions to the Bayesian pipeline to do the full-sky non-Gaussian source detection problem (previously restricted to patches). Note that this has changed the normalization of evidence values reported previously, as full-sky priors are now employed, but the conclusions remain unchange

The Bolocam 1.1 mm Lockman Hole Galaxy Survey: SHARC II 350 micron Photometry and Implications for Spectral Models, Dust Temperatures, and Redshift Estimation

We present 350 micron photometry of all 17 galaxy candidates in the Lockman Hole detected in a 1.1 mm Bolocam survey. Several of the galaxies were previously detected at 850 microns, at 1.2 mm, in the infrared by Spitzer, and in the radio. Nine of the Bolocam galaxy candidates were detected at 350 microns and two new candidates were serendipitously detected at 350 microns (bringing the total in the literature detected in this way to three). Five of the galaxies have published spectroscopic redshifts, enabling investigation of the implied temperature ranges and a comparison of photometric redshift techniques. Lambda = 350 microns lies near the spectral energy distribution peak for z = 2.5 thermally emitting galaxies. Thus, luminosities can be measured without extrapolating to the peak from detection wavelengths of lambda > 850 microns. Characteristically, the galaxy luminosities lie in the range 1.0 - 1.2 x 10^13 L_solar, with dust temperatures in the range of 40 K to 70 K, depending on the choice of spectral index and wavelength of unit optical depth. The implied dust masses are 3 - 5 x 10^8 M_solar. We find that the far-infrared to radio relation for star-forming ULIRGs systematically overpredicts the radio luminosities and overestimates redshifts on the order of Delta z ~ 1, whereas redshifts based on either on submillimeter data alone or the 1.6 micron stellar bump and PAH features are more accurate.Comment: In Press (to appear in Astrophysical Journal, ApJ 20 May 2006 v643 1) 47 pages, 10 figures, 4 table

A Search for Cosmic Microwave Background Anisotropies on Arcminute Scales with Bolocam

We have surveyed two science fields totaling one square degree with Bolocam at 2.1 mm to search for secondary CMB anisotropies caused by the Sunyaev- Zel'dovich effect (SZE). The fields are in the Lynx and Subaru/XMM SDS1 fields. Our survey is sensitive to angular scales with an effective angular multipole of l_eff = 5700 with FWHM_l = 2800 and has an angular resolution of 60 arcseconds FWHM. Our data provide no evidence for anisotropy. We are able to constrain the level of total astronomical anisotropy, modeled as a flat bandpower in C_l, with frequentist 68%, 90%, and 95% CL upper limits of 590, 760, and 830 uKCMB^2. We statistically subtract the known contribution from primary CMB anisotropy, including cosmic variance, to obtain constraints on the SZE anisotropy contribution. Now including flux calibration uncertainty, our frequentist 68%, 90% and 95% CL upper limits on a flat bandpower in C_l are 690, 960, and 1000 uKCMB^2. When we instead employ the analytic spectrum suggested by Komatsu and Seljak (2002), and account for the non-Gaussianity of the SZE anisotropy signal, we obtain upper limits on the average amplitude of their spectrum weighted by our transfer function of 790, 1060, and 1080 uKCMB^2. We obtain a 90% CL upper limit on sigma8, which normalizes the power spectrum of density fluctuations, of 1.57. These are the first constraints on anisotropy and sigma8 from survey data at these angular scales at frequencies near 150 GHz.Comment: 68 pages, 17 figures, 2 tables, accepted for publication in Ap

The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

High-precision abundances of elements in Kepler LEGACY stars. Verification of trends with stellar age

HARPS-N spectra with S/N > 250 and MARCS model atmospheres were used to derive abundances of C, O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, and Y in ten stars from the Kepler LEGACY sample (including the binary pair 16 Cyg A and B) selected to have metallicities in the range -0.15 < [Fe/H] < +0.15 and ages between 1 and 7 Gyr. Stellar gravities were obtained from seismic data and effective temperatures were determined by comparing non-LTE iron abundances derived from FeI and FeII lines. Available non-LTE corrections were also applied when deriving abundances of the other elements. The results support the [X/Fe]-age relations previously found for solar twins. [Mg/Fe], [Al/Fe], and [Zn/Fe] decrease by ~0.1 dex over the lifetime of the Galactic thin disk due to delayed contribution of iron from Type Ia supernovae relative to prompt production of Mg, Al, and Zn in Type II supernovae. [Y/Mg] and [Y/Al], on the other hand, increase by ~0.3 dex, which can be explained by an increasing contribution of s-process elements from low-mass AGB stars as time goes on. The trends of [C/Fe] and [O/Fe] are more complicated due to variations of the ratio between refractory and volatile elements among stars of similar age. Two stars with about the same age as the Sun show very different trends of [X/H] as a function of elemental condensation temperature Tc and for 16 Cyg, the two components have an abundance difference, which increases with Tc. These anomalies may be connected to planet-star interactions.Comment: 13 pages with 7 figures. Accepted for publication in A&