The properties of the stellar populations in ULIRGs I: sample, data and spectral synthesis modelling

We present deep long-slit optical spectra for a sample of 36 Ultraluminous Infrared Galaxies (ULIRGs), taken with the William Herschel Telescope (WHT) on La Palma with the aim of investigating the star formation histories and testing evolutionary scenarios for such objects. Here we present the sample, the analysis techniques and a general overview of the properties of the stellar populations. Spectral synthesis modelling has been used in order to estimate the ages of the stellar populations found in the diffuse light sampled by the spectra in both the nuclear and extended regions of the target galaxies. We find that adequate fits can be obtained using combinations of young stellar populations (YSPs,t_YSP<=2 Gyr), with ages divided into two groups: very young stellar populations (VYSPs, t_VYSP <=100 Myr) and intermediate-young stellar populations (IYSPs, 0.1 < t_IYSP <= 2 Gyr). Our results show that YSPs are present at all locations of the galaxies covered by our slit positions, with the exception of the northern nuclear region of the ULIRG IRAS 23327+2913. Furthermore, VYSPs are presents in at least 85% of the 133 extraction apertures used for this study. Old stellar populations (OSPs, t_{OSP} > 2 Gyr) do not make a major contribution to the optical light in the majority of the apertures extracted. In fact they are essential for fitting the spectra in only 5% (7) of the extracted apertures. The estimated total masses for the YSPs (VYSPs+IYSPs) are in the range 0.18 x 10^{10} <= M_YSP <= 50 x 10^{10} Msun. We have also estimated the bolometric luminosities associated with the stellar populations detected at optical wavelengths, finding that they fall in the range 0.07 x 10^{12} < L_bol < 2.2 x 10^{12} Lsun. In addition, we find that reddening is significant at all locations in the galaxies.Comment: accepted for publication in MNRA

Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A Haldane-Shastry spin chain of BC_N type in a constant magnetic field

We compute the spectrum of the trigonometric Sutherland spin model of BC_N type in the presence of a constant magnetic field. Using Polychronakos's freezing trick, we derive an exact formula for the partition function of its associated Haldane-Shastry spin chain.Comment: LaTeX, 13 page

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