The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

Non-blind catalogue of extragalactic point sources from the Wilkinson Microwave Anisotropy Probe (WMAP) first 3--year survey data

We have used the MHW2 filter to obtain estimates of the flux densities at the WMAP frequencies of a complete sample of 2491 sources, mostly brighter than 500 mJy at 5 GHz, distributed over the whole sky excluding a strip around the Galactic equator (b < 5 degrees). After having detected 933 sources above the 3 sigma level in the MHW2 filtered maps - our New Extragalactic WMAP Point Source (NEWPS_3sigma) Catalogue - we are left with 381 sources above 5 sigma in at least one WMAP channel, 369 of which constitute our NEWPS_5sigma catalogue. It is remarkable to note that 98 (i.e. 26%) sources detected above 5 sigma are `new', they are not present in the WMAP catalogue. Source fluxes have been corrected for the Eddington bias. Our flux density estimates before such correction are generally in good agreement with the WMAP ones at 23 GHz. At higher frequencies WMAP fluxes tend to be slightly higher than ours, probably because WMAP estimates neglect the deviations of the point spread function from a Gaussian shape. On the whole, above the estimated completeness limit of 1.1 Jy at 23 GHz we detected 43 sources missed by the blind method adopted by the WMAP team. On the other hand, our low-frequency selection threshold left out 25 WMAP sources, only 12 of which, however, are 5 sigma detections and only 3 have fluxes S at 23 GHz > 1.1 Jy. Thus, our approach proved to be competitive with, and complementary to the WMAP one.Comment: 18 pages, 6 figures, 5 tables. Accepted for publication in ApJ

A near-IR line of Mn I as a diagnostic tool of the average magnetic energy in the solar photosphere

We report on spectropolarimetric observations of a near-IR line of Mn I located at 15262.702 A whose intensity and polarization profiles are very sensitive to the presence of hyperfine structure. A theoretical investigation of the magnetic sensitivity of this line to the magnetic field uncovers several interesting properties. The most important one is that the presence of strong Paschen-Back perturbations due to the hyperfine structure produces an intensity line profile whose shape changes according to the absolute value of the magnetic field strength. A line ratio technique is developed from the intrinsic variations of the line profile. This line ratio technique is applied to spectropolarimetric observations of the quiet solar photosphere in order to explore the probability distribution function of the magnetic field strength. Particular attention is given to the quietest area of the observed field of view, which was encircled by an enhanced network region. A detailed theoretical investigation shows that the inferred distribution yields information on the average magnetic field strength and the spatial scale at which the magnetic field is organized. A first estimation gives ~250 G for the mean field strength and a tentative value of ~0.45" for the spatial scale at which the observed magnetic field is horizontally organized.Comment: 42 pages, 17 figures, accepted for publication in the Astrophysical Journal. Figures 1 and 9 are in JPG forma

Water vapor emission from IRC+10216 and other carbon-rich stars: model predictions and prospects for multitransition observations

We have modeled the emission of H2O rotational lines from the extreme C-rich star IRC+10216. Our treatment of the excitation of H2O emissions takes into account the excitation of H2O both through collisions, and through the pumping of the nu2 and nu3 vibrational states by dust emission and subsequent decay to the ground state. Regardless of the spatial distribution of the water molecules, the H2O 1_{10}-1_{01} line at 557 GHz observed by the Submillimeter Wave Astronomy Satellite (SWAS) is found to be pumped primarily through the absorption of dust-emitted photons at 6 $\mu$m in the nu2 band. As noted by previous authors, the inclusion of radiative pumping lowers the ortho-H2O abundance required to account for the 557 GHz emission, which is found to be (0.5-1)x10^{-7} if the presence of H2O is a consequence of vaporization of orbiting comets or Fischer-Tropsch catalysis. Predictions for other submillimeter H2O lines that can be observed by the Herschel Space Observatory (HSO) are reported. Multitransition HSO observations promise to reveal the spatial distribution of the circumstellar water vapor, discriminating among the several hypotheses that have been proposed for the origin of the H2O vapor in the envelope of IRC+10216. We also show that, for observations with HSO, the H2O 1_{10}-1_{01} 557 GHz line affords the greatest sensitivity in searching for H2O in other C-rich AGB stars.Comment: 35 pages, 12 figures, to be published in The Astrophysical Journa