Solvation in atomic liquids: connection between Gaussian field theory and density functional theory

For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory derived by David Chandler [Phys. Rev. E, 1993, 48, 2898] and classical density functional theory. We show that Chandler's results concerning the solvation of a hard core of arbitrary shape can be recovered by either minimising a linearised HNC functional using an auxiliary Lagrange multiplier field to impose a vanishing density inside the core, or by minimising this functional directly outside the core --- indeed a simpler procedure. Those equivalent approaches are compared to two other variants of DFT, either in the HNC, or partially linearised HNC approximation, for the solvation of a Lennard-Jones solute of increasing size in a Lennard-Jones solvent. Compared to Monte-Carlo simulations, all those theories give acceptable results for the inhomogeneous solvent structure, but are completely out-of-range for the solvation free-energies. This can be fixed in DFT by adding a hard-sphere bridge correction to the HNC functional.Comment: 14 pages, 4 figure

Effective interactions in the colloidal suspensions from HNC theory

The HNC Ornstein-Zernike integral equations are used to determine the properties of simple models of colloidal solutions where the colloids and ions are immersed in a solvent considered as a dielectric continuum and have a size ratio equal to 80 and a charge ratio varying between 1 and 4000. At an infinite dilution of colloids, the effective interactions between colloids and ions are determined for ionic concentrations ranging from 0.001 to 0.1 mol/l and compared to those derived from the Poisson-Boltzmann theory. At finite concentrations, we discuss on the basis of the HNC results the possibility of an unambiguous definition of the effective interactions between the colloidal molecules.Comment: 26 pages, 15 figure

The impact of mass-loss on the evolution and pre-supernova properties of red supergiants

The post main-sequence evolution of massive stars is very sensitive to many parameters of the stellar models. Key parameters are the mixing processes, the metallicity, the mass-loss rate and the effect of a close companion. We study how the red supergiant lifetimes, the tracks in the Hertzsprung-Russel diagram (HRD), the positions in this diagram of the pre-supernova progenitor as well as the structure of the stars at that time change for various mass-loss rates during the red supergiant phase (RSG), and for two different initial rotation velocities. The surface abundances of RSGs are much more sensitive to rotation than to the mass-loss rates during that phase. A change of the RSG mass-loss rate has a strong impact on the RSG lifetimes and therefore on the luminosity function of RSGs. At solar metallicity, the enhanced mass-loss rate models do produce significant changes on the populations of blue, yellow and red supergiants. When extended blue loops or blue ward excursions are produced by enhanced mass-loss, the models predict that a majority of blue (yellow) supergiants are post RSG objects. These post RSG stars are predicted to show much smaller surface rotational velocities than similar blue supergiants on their first crossing of the HR gap. The position in the HRD of the end point of the evolution depends on the mass of the hydrogen envelope. More precisely, whenever, at the pre-supernova stage, the H-rich envelope contains more than about 5\% of the initial mass, the star is a red supergiant, and whenever the H-rich envelope contains less than 1\% of the total mass the star is a blue supergiant. For intermediate situations, intermediate colors/effective temperatures are obtained. Yellow progenitors for core collapse supernovae can be explained by the enhanced mass-loss rate models, while the red progenitors are better fitted by the standard mass-loss rate models.Comment: 19 pages, 11 figures, 6 tables, accepted for publication in Astronomy and Astrophysic

Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619, 2013] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields, the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density. It makes the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.Comment: 24 pages, 8 figure

Supernova 2008bk and its red supergiant progenitor

Indexación: ISIHemos obtenido pocos datos fotométricos y espectroscópicos de supernova (SN) 2008bk en NGC 7793, principalmente a 150 días después de la explosión. Nos parece que se trata de un tipo II-Plateau (II-P) SN que más se asemeja a la de baja luminosidad SN 1999br en NGC 4900. Dada la similitud general entre las curvas de luz observadas y colores de SNs 2008bk y 1999br, inferimos que la extinción total visual a SN 2008bk ( A V = 0,065 mag) debe ser casi en su totalidad debido a un primer plano galáctico, similar a lo que ha supuesto para SN 1999br. Confirmamos la identificación de la supergigante roja putativo (RSG) estrella progenitora de SN en la alta calidad de g ' r ' i imágenes "que había obtenido en 2007 en el Gemini-Sur 8 telescopio m. Existe poca ambigüedad en esta identificación progenitor, calificándolo como el mejor ejemplo hasta la fecha, junto con la identificación de la estrella Sk -69 ° 202 como el progenitor de SN 1987A. A partir de una combinación de fotometría de las imágenes de Gemini con el de archivo, pre-SN, el Telescopio Muy Grande de JHK s imágenes, derivamos una precisa distribución observada energía espectral (SED) para el progenitor. Nos encontramos con índices de nebulares fuerte intensidad de emisiones de línea para varios H II regiones cercanas a la SN que la metalicidad en el medio ambiente es probable subsolar ( Z 0.6 Z ☉ ). El SED observado de la estrella concuerda bastante bien con SED sintéticos obtenidos a partir de modelos de atmósferas RSG eficaz con temperatura T eff = 3600 ± 50 K. Nos encontramos, por tanto, que la estrella tenía una luminosidad bolométrica con respecto al Sol de log ( L bol / L ☉ ) = 4,57 ± 0,06 y el radio R = 496 ± 34 R ☉ a ~ 6 meses antes de la explosión. Al comparar las propiedades del progenitor con teóricos masiva estrella modelos evolutivos, llegamos a la conclusión de que el progenitor RSG tenía una masa inicial en el rango de 8-8,5 M ☉ . Esta masa es consistente con, aunque en el extremo bajo de la gama inferido de masas iniciales para SN II-P progenitores. También es coherente con el límite superior estimado de la masa inicial de la progenitora de SN 1999br, y concuerda con las masas iniciales bajos encontrados para los progenitores RSG de otras supernovas de baja luminosidad II-P.http://www.sherpa.ac.uk/romeo/issn/0004-6256/es/http://iopscience.iop.org/1538-3881/143/1/19

Supernova 2008bk and Its Red Supergiant Progenitor

We have obtained limited photometric and spectroscopic data for supernova (SN) 2008bk in NGC 7793, primarily at ≳ 150 days after explosion. We find that it is a Type II-Plateau (II-P) SN that most closely resembles the low-luminosity SN 1999br in NGC 4900. Given the overall similarity between the observed light curves and colors of SNe 2008bk and 1999br, we infer that the total visual extinction to SN 2008bk (A_V = 0.065 mag) must be almost entirely due to the Galactic foreground, similar to what has been assumed for SN 1999br. We confirm the identification of the putative red supergiant (RSG) progenitor star of the SN in high-quality g'r'i' images we had obtained in 2007 at the Gemini-South 8 m telescope. Little ambiguity exists in this progenitor identification, qualifying it as the best example to date, next to the identification of the star Sk –69°202 as the progenitor of SN 1987A. From a combination of photometry of the Gemini images with that of archival, pre-SN, Very Large Telescope JHK_s images, we derive an accurate observed spectral energy distribution (SED) for the progenitor. We find from nebular strong-intensity emission-line indices for several H II regions near the SN that the metallicity in the environment is likely subsolar (Z ≈ 0.6 Z_☉). The observed SED of the star agrees quite well with synthetic SEDs obtained from model RSG atmospheres with effective temperature T_(eff) = 3600 ± 50 K. We find, therefore, that the star had a bolometric luminosity with respect to the Sun of log (L_(bol)/L_☉) = 4.57 ± 0.06 and radius R* = 496 ± 34 R_☉ at ~6 months prior to explosion. Comparing the progenitor's properties with theoretical massive-star evolutionary models, we conclude that the RSG progenitor had an initial mass in the range of 8-8.5 M_☉. This mass is consistent with, albeit at the low end of, the inferred range of initial masses for SN II-P progenitors. It is also consistent with the estimated upper limit on the initial mass of the progenitor of SN 1999br, and it agrees with the low initial masses found for the RSG progenitors of other low-luminosity SNe II-P

The High-Metallicity Explosion Environment of the Relativistic Supernova 2009bb

We investigate the environment of the nearby (d ~ 40Mpc) broad-lined Type Ic supernova SN 2009bb. This event was observed to produce a relativistic outflow likely powered by a central accreting compact object. While such a phenomenon was previously observed only in long-duration gamma-ray bursts (LGRBs), no LGRB was detected in association with SN 2009bb. Using an optical spectrum of the SN 2009bb explosion site, we determine a variety of ISM properties for the host environment, including metallicity, young stellar population age, and star formation rate. We compare the SN explosion site properties to observations of LGRB and broad-lined SN Ic host environments on optical emission line ratio diagnostic diagrams. Based on these analyses, we find that the SN 2009bb explosion site has a very high metallicity of ~2x solar, in agreement with other broad-lined SN Ic host environments and at odds with the low-redshift LGRB host environments and recently proposed maximum metallicity limits for relativistic explosions. We consider the implications of these findings and the impact that SN 2009bb's unusual explosive properties and environment have on our understanding of the key physical ingredient that enables some SNe to produce a relativistic outflow.Comment: 7 pages, 4 figures, 1 table; accepted for publication in ApJ Letters (replaced to include missing figure

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

Recent experimental and theoretical results have shown the existence of a liquid-liquid phase transition in isotropic systems, such as biological solutions and colloids, whose interaction can be represented via an effective potential with a repulsive soft-core and an attractive part. We investigate how the phase diagram of a schematic general isotropic system, interacting via a soft-core squared attractive potential, changes by varying the parameters of the potential. It has been shown that this potential has a phase diagram with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition and that, for a short-range soft-core, the phase diagram resulting from molecular dynamics simulations can be interpreted through a modified van der Waals equation. Here we consider the case of soft-core ranges comparable with or larger than the hard-core diameter. Because an analysis using molecular dynamics simulations of such systems or potentials is too time-demanding, we adopt an integral equation approach in the hypernetted-chain approximation. Thus we can estimate how the temperature and density of both critical points depend on the potential's parameters for large soft-core ranges. The present results confirm and extend our previous analysis, showing that this potential has two fluid-fluid critical points that are well separated in temperature and in density only if there is a balance between the attractive and repulsive part of the potential. We find that for large soft-core ranges our results satisfy a simple relation between the potential's parameters

Generalized Heisenberg algebras and k-generalized Fibonacci numbers

It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al. corespond to k=2.Comment: 8 page

SN 2010ay is a Luminous and Broad-lined Type Ic Supernova within a Low-metallicity Host Galaxy

We report on our serendipitous pre-discovery detection and detailed follow-up of the broad-lined Type Ic supernova (SN) 2010ay at z = 0.067 imaged by the Pan-STARRS1 3pi survey just ~4 days after explosion. The SN had a peak luminosity, M_R ~ -20.2 mag, significantly more luminous than known GRB-SNe and one of the most luminous SNe Ib/c ever discovered. The absorption velocity of SN 2010ay is v_Si ~ 19,000 km/s at ~40 days after explosion, 2-5 times higher than other broad-lined SNe and similar to the GRB-SN 2010bh at comparable epochs. Moreover, the velocity declines ~2 times slower than other SNe Ic-BL and GRB-SNe. Assuming that the optical emission is powered by radioactive decay, the peak magnitude implies the synthesis of an unusually large mass of 56 Ni, M_Ni = 0.9 M_solar. Modeling of the light-curve points to a total ejecta mass, M_ej ~ 4.7 M_sol, and total kinetic energy, E_K ~ 11x10^51 ergs. The ratio of M_Ni to M_ej is ~2 times as large for SN 2010ay as typical GRB-SNe and may suggest an additional energy reservoir. The metallicity (log(O/H)_PP04 + 12 = 8.19) of the explosion site within the host galaxy places SN 2010ay in the low-metallicity regime populated by GRB-SNe, and ~0.5(0.2) dex lower than that typically measured for the host environments of normal (broad-lined) Ic supernovae. We constrain any gamma-ray emission with E_gamma < 6x10^{48} erg (25-150 keV) and our deep radio follow-up observations with the Expanded Very Large Array rule out relativistic ejecta with energy, E > 10^48 erg. We therefore rule out the association of a relativistic outflow like those which accompanied SN 1998bw and traditional long-duration GRBs, but place less-stringent constraints on a weak afterglow like that seen from XRF 060218. These observations challenge the importance of progenitor metallicity for the production of a GRB, and suggest that other parameters also play a key role.Comment: 19 pages, 10 figures, V3 has revisions following referee's report; more information at http://www.cfa.harvard.edu/~nsanders/papers/2010ay/summary.htm