Miracle-dz/UniFAR-FTUs huggingface dataset:
Lie sphere geometry and integrable systems

Two basic Lie-invariant forms uniquely defining a generic (hyper) surface in Lie sphere geometry are introduced. Particularly interesting classes of surfaces associated with these invariants are considered. These are the diagonally cyclidic surfaces and the Lie-minimal surfaces, the latter being the extremals of the simplest Lie-invariant functional generalizing the Willmore functional in conformal geometry. Equations of motion of a special Lie sphere frame are derived, providing a convenient unified treatment of surfaces in Lie sphere geometry. In particular, for diagonally cyclidic surfaces this approach immediately implies the stationary modified Veselov-Novikov equation, while the case of Lie-minimal surfaces reduces in a certain limit to the integrable coupled Tzitzeica system. In the framework of the canonical correspondence between Hamiltonian systms of hy- drodynamic type and hypersurfaces in Lie sphere geometry, it is pointed out that invariants of Lie-geometric hypersurfaces coincide with the reciprocal invariants of hydrodynamic type systems. Integrable evolutions of surfaces in Lie sphere geometry are introduced. This provides an interpretation of the simplest Lie-invariant functional as the first local conservation law of the (2 + 1)-dimensional modified Veselov-Novikov hierarchy. Parallels between Lie sphere geometry and projective differential geometry of surfaces are drawn in the conclusion.
Recent results in relativistic heavy ion collisions: from ‘a new state of matter’ to ‘the perfect fluid’

Experimental physics with relativistic heavy ions dates from 1992 when a beam of 197Au of energy greater than 10 A GeV/c first became available at the Alternating Gradient Synchrotron at Brookhaven National Laboratory (BNL) soon followed in 1994 by a 208Pb beam of 158A GeV/c at the Super Proton Synchrotron at CERN (European Center for Nuclear Research). Previous pioneering measurements at the Berkeley Bevalac (Gutbrod et al 1989 Rep. Prog. Phys. 52 1267–132) in the late 1970s and early 1980s were at much lower bombarding energies (≲1A GeV/c) where nuclear breakup rather than particle production is the dominant inelastic process in A+A collisions. More recently, starting in 2000, the relativistic heavy ion collider at BNL has produced head-on collisions of two 100 A GeV beams of fully stripped Au ions, corresponding to nucleon–nucleon centre-of-mass (cm) energy, , total cm energy 200 A GeV. The objective of this research program is to produce nuclear matter with extreme density and temperature, possibly resulting in a state of matter where the quarks and gluons normally confined inside individual nucleons (r < 1 fm) are free to act over distances an order of magnitude larger. Progress from the period 1992 to the present will be reviewed, with reference to previous results from light ion and proton–proton collisions where appropriate. Emphasis will be placed on the measurements which formed the basis for the announcements by the two major laboratories: ‘A new state of matter’, by CERN on Febraury 10 2000 and ‘The perfect fluid’ by BNL on April 19 2005.
XMM–Newton observations of 3C 273

ABSTRACT A series of nine XMM-Newton observations of the radio-loud quasar 3C 273 arepresented, concentrating mainly on the soft excess. Although most of the individ-ual observations do not show evidence for iron emission, co-adding them reveals aweak, broad line (EW ∼ 56 eV). The soft excess component is found to vary, con-ﬁrming previous work, and can be well ﬁtted with multiple blackbody components,with temperatures ranging between ∼ 40 and ∼ 330 eV, together with a power-law.Alternatively, a Comptonisation model also provides a good ﬁt, with a mean electrontemperature of ∼ 350 eV, although this value is higher when the soft excess is moreluminous over the 0.5–10 keV energy band. In the RGS spectrum of 3C 273, a strongdetection of the Ovii Heα absorption line at zero redshift is made; this may originatein warm gas in the local intergalactic medium, consistent with the ﬁndings of bothFang et al. (2003) and Rasmussen et al. (2003). Key words: galaxies: active – X-rays: galaxies – galaxies: individual: 3C 273
Stellar populations of galaxies in the ALHAMBRA survey up to $z \sim 1$. IV. Properties of quiescent galaxies on the stellar mass$-$size plane

We perform a comprehensive study of the stellar population properties of quiescent galaxies as a function of size and stellar mass to constrain the physical mechanism governing the stellar mass assembly and the likely evolutive scenarios that explain their growth in size. After selecting all the quiescent galaxies from the ALHAMBRA survey by the dust-corrected stellar mass$-$colour diagram, we built a shared sample of $\sim850$ quiescent galaxies with reliable sizes from the HST. The stellar population properties were retrieved using the SED-fitting code MUFFIT with various sets of composite stellar population models. Age, formation epoch, metallicity, and extinction were studied on the stellar mass$-$size plane as function of size through a Monte Carlo approach. This accounted for uncertainties and degeneracy effects amongst stellar population properties. The stellar population properties of quiescent galaxies and their stellar mass and size since $z\sim1$ are correlated. At fixed stellar mass, the more compact the quiescent galaxy, the older and richer in metals it is ($1$Gyr and $0.1$dex, respectively). In addition, more compact galaxies may present slight lower extinctions than their more extended counterparts at the same stellar mass ($<0.1$ mag). By means of studying constant regions of stellar population properties across the stellar mass$-$size plane, we obtained empirical relations to constrain the physical mechanism that governs the stellar mass assembly of the form $M_\star \propto r_\mathrm{c}^\alpha$, where $\alpha$ amounts to $0.50-0.55 \pm 0.09$. There are indications that support the idea that the velocity dispersion is tightly correlated with the stellar content of galaxies. The mechanisms driving the evolution of stellar populations can therefore be partly linked to the dynamical properties of galaxies, along with their gravitational potential.
On the relation between the mass of Compact Massive Objects and their host galaxies

Supermassive black holes and/or very dense stellar clusters are found in the central regions of galaxies. Nuclear star clusters are present mainly in faint galaxies while upermassive black holes are common in galaxies with masses $\geq 10^{10}$ M$_\odot $. In the intermediate galactic mass range both types of central massive objects (CMOs) are found. Here we present our collection of a huge set of nuclear star cluster and massive black hole data that enlarges significantly already existing data bases useful to investigate for correlations of their absolute magnitudes, velocity dispersions and masses with structural parameters of their host galaxies. In particular, we directed our attention to some differences between the correlations of nuclear star clusters and massive black holes as subsets of CMOs with hosting galaxies. In this context, the mass-velocity dispersion relation plays a relevant role because it seems the one that shows a clearer difference between the supermassive black holes and nuclear star clusters. The $M_{MBH}-{\sigma}$ has a slope of $5.19\pm 0.28$ while $M_{NSC}-{\sigma}$ has the much smaller slope of $1.84\pm 0.64$. The slopes of the CMO mass- host galaxy B magnitude of the two types of CMOs are indistinguishable within the errors while that of the NSC mass-host galaxy mass relation is significantly smaller than for supermassive black holes. Another important result is the clear depauperation of the NSC population in bright galaxy hosts, which reflects also in a clear flattening of the NSC mass vs host galaxy mass at high host masses.
Probing the dark side: Constraints on the dark energy equation of state from CMB, large scale structure and Type Ia supernovae

We have reanalyzed constraints on the equation of state parameter, ${w}_{Q}\ensuremath{\equiv}P/\ensuremath{\rho},$ of the dark energy, using several cosmological data sets and relaxing the usual constraint ${w}_{Q}g~\ensuremath{-}1. $ We find that combining cosmic microwave background, large scale structure, and type Ia supernova data yields a nontrivial lower bound on ${w}_{Q}. $ At 95.4% confidence we find, assuming a flat geometry of the universe, a bound of $\ensuremath{-}2.68l{w}_{Q}l\ensuremath{-}0.78$ if ${w}_{Q}$ is taken to be a completely free parameter. Reassuringly we also find that the constraint ${w}_{Q}g~\ensuremath{-}1$ does not significantly bias the overall allowed region for ${w}_{Q}. $ When this constraint is imposed the 95.4% confidence bound is $\ensuremath{-}1l~{w}_{Q}l\ensuremath{-}0.71. $ Also, a pure cosmological constant $(w=\ensuremath{-}1)$ is an excellent fit to all available data. Based on simulations of future data from the Planck CMB experiment and the SNAP and SNfactory supernova experiments we estimate that it will be possible to constrain ${w}_{Q}$ at the 5% level in the future.
The Lensed Arc Production Efficiency of Galaxy Clusters: A Comparison of Matched Observed and Simulated Samples

We compare the statistical properties of giant gravitationally lensed arcs produced in matched simulated and observed cluster samples. The observed sample consists of 10 X-ray-selected clusters at redshifts zc ~ 0.2 imaged with HST by Smith et al. The simulated data set is produced by lensing the Hubble Deep Field, which serves as a background source image, with 150 realizations (different projections and shifts) of five simulated zc = 0.2 clusters from a ΛCDM N-body simulation. The real and simulated clusters have similar masses, the real photometric redshift is used for each background source, and all the observational effects influencing arc detection in the real data set, including light from cluster galaxies, are simulated in the artificial data set. We develop, and apply to both data sets, an objective automatic arc-finding algorithm. We find consistent arc statistics in the real and in the simulated sample, with an average of ~1 detected giant (length-to-width ratio l/w ≥ 10) arc per cluster and ~0.2 giant luminous (RST < 22.3 mag) arcs per cluster. Thus, taking into account a realistic source population and observational effects, the clusters predicted by ΛCDM have the same arc production efficiency as the observed clusters. If, as suggested by other studies, there is a discrepancy between the predicted and the observed total number of arcs on the sky, it must be the result of differences between the redshift-dependent cluster mass functions and not due to differences in the lensing efficiency of the most massive clusters.
An exact solution of the partition function for mean-field quantum spin systems without the static approximation

Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to explicitly treat the imaginary-time dependence of the partition function, we usually neglect the imaginary-time dynamical effect, which is called the static approximation. Although the static approximation is the first approach, it is not even clear when the static approximation is justified for mean-field quantum spin systems, that is, mean-field quantum spin systems have not been solved exactly so far. In this study, we solve exactly the partition function for a particular class of mean-field quantum spin systems including randomness without the static approximation. The partition function can be regarded as a result of time evolution in the imaginary-time Schr\"odinger equation, and solving the exact solution of the partition function is equivalent to solving the optimal control problem in the imaginary-time Schr\"odinger equation. As the result, the solution of the optimal control problem coincides exactly with the static approximate solution of the partition function and, therefore, the static approximation is exact for the particular class of mean-field quantum spin systems including randomness in general. Furthermore, we prove that the analysis of the previous study in quantum annealing is exact where the non-stoquastic interaction and the inhomogeneous transverse field accelerate the computational time exponentially for mean-field quantum spin systems.
Hubble Space Telescope WFPC2 Proper Motions in Two Bulge Fields: Kinematics and Stellar Population of the Galactic Bulge

We report proper-motion dispersions for stars in the direction of two fields of the Galactic bulge, using Hubble Space Telescope Wide Field Planetary Camera 2 images taken 6 years apart. Our two fields are Baade's window [(l, b) = (1.°13, -3.°77)] and Sgr I [(l, b) = (1.°25, -2.°65)]. Our proper-motion dispersions are in good agreement with prior ground- and space-based proper-motion studies in bulge fields, but in contrast to some prior studies, we do not exclude any subset of stars from our sample. In Baade's window, we find the l and b proper-motion dispersions are 2.9 and 2.5 mas yr-1, while in Sgr I, they are 3.3 and 2.7 mas yr-1, respectively. For the first time, we can clearly separate the foreground disk stars out from the bulge because of their large mean apparent proper motion. The population with nondisk kinematics (which we conclude to be the bulge) has an old main-sequence turnoff point, similar to those found in old, metal-rich bulge globular clusters, while those stars selected to have disk kinematics lie on a fully populated main sequence. Separating main-sequence stars by luminosity, we find strong evidence that the bulge population is rotating, largely explaining observations of proper-motion anisotropy in bulge fields. Because we have isolated such a pure sample of stars in the bulge, we have one of the clearest demonstrations that the old stellar population of the inner bulge/bar is in fact rotating.
Coexistence of charge density waves, bond order waves and spin density waves in quasi-one dimensional charge transfer salts

Charge, spin, as well as lattice instabilities are investigated in isolated or weakly coupled chains of correlated electrons at quarter filling. Our analysis is based on extended Hubbard models including nearest-neighbor repulsion and Peierls coupling to lattice degrees of freedom. While treating the electronic quantum fluctuations exactly, the lattice structure is optimized self-consistently. We show that, generically, isolated chains undergo instabilities towards coexisting charge-density waves (CDW's) and bond order waves (BOW's) insulating spin-gapped phases. The spin and charge gaps of the BOW-CDW phase are computed. In the presence of an interchain magnetic coupling spin-density waves phases including a CDW or a BOW component are also found. Our results are discussed in the context of insulating charge-transfer salts.
The Herschel-PACS North Ecliptic Pole Survey

A detailed analysis of Herschel-PACS observations at the North Ecliptic Pole is presented. High quality maps, covering an area of 0.44 square degrees, are produced and then used to derive potential candidate source lists. A rigorous quality control pipeline has been used to create final legacy catalogues in the PACS Green 100 micron and Red 160 micron bands, containing 1384 and 630 sources respectively. These catalogues reach to more than twice the depth of the current archival Herschel/PACS Point Source Catalogue, detecting 400 and 270 more sources in the short and long wavelength bands respectively. Galaxy source counts are constructed that extend down to flux densities of 6mJy and 19mJy (50% completeness) in the Green 100 micron and Red 160 micron bands respectively. These source counts are consistent with previously published PACS number counts in other fields across the sky. The source counts are then compared with a galaxy evolution model identifying a population of luminous infrared galaxies as responsible for the bulk of the galaxy evolution over the flux range (5-100mJy) spanned by the observed counts, contributing approximate fractions of 50% and 60% to the cosmic infrared background (CIRB) at 100 microns and 160 microns respectively.
A new approach to turbulent transport of a mean scalar

We develop a simple mean field approach to the transport of a passive scalar for which the fundamental equation is a second order differential equation in the transported quantity, not a first order equation. Triple correlations are included, as they must be for any realistic description of turbulence. No correlation time enters the theory, only an eddy turnover time. The approach is simpler than standard approaches which incorporate triple correlations, but more realistic than Gaussian or short correlation time closures which do not. A similar approach has proven useful in magnetohydrodynamics.
Periodic boundary data for an integrable model of stimulated Raman scattering: long-time asymptotic behavior

We study the long-time asymptotic behavior of the solution to the initial-boundary value (IBV) problem in the quarter plane (x > 0, t > 0) for nonlinear integrable equations of stimulated Raman scattering. We consider the case of zero initial condition and periodic boundary data (p eiωt). Using the steepest descent method for oscillatory matrix Riemann–Hilbert problems we show that the solution of the IBV problem has different asymptotic behavior in different regions. The solution takes the form of a plane wave of finite amplitude, when 0 < x < ω20t, a modulated elliptic wave of finite amplitude, when ω20t < x < ω2t, and a self-similar vanishing (as t → ∞) wave, when x > ω2t. For the IBV problem with nonzero initial condition and the same periodic boundary data, the solution to this problem is qualitatively similar to that of this study with the only difference that the solitons (of finite amplitude) can appear in the region x > ω2t. a plane wave of finite amplitude, when 0 < x < ω20t, a modulated elliptic wave of finite amplitude, when ω20t < x < ω2t, and a self-similar vanishing (as t → ∞) wave, when x > ω2t.
X-ray and optical bursts and flares in YSOs: results from a 5-day XMM-Newton monitoring campaign of L1551

We present the results of a five-day monitoring campaign with XMM- Newton of six X-ray bright young stellar objects (YSOs) in the star-forming complex L1551 in Taurus. All stars present significant variability on the five-day time scale. Modulation of the light curve on time scales comparable with the star's rotational period appeared to be present in the case of one weak-lined T Tauri star. Significant spectral variations between the 2000 and the 2004 observations were detected in the (unresolved) classical T Tauri binary system XZ Tau: a hot plasma component which was present in the X-ray spectrum in 2000 had significantly weakened in 2004. As XZ Tau N was undergoing a strong optical outburst in 2000, which had terminated since then, we speculate on the possible relationship between episodic, burst accretion, and X-ray heating. The transition object HL Tau underwent a strong flare with a complex temperature evolution, which is indicative of an event confined within a very large magnetic structure (few stellar radii), similar to the ones found in YSOs in the Orion Nebula Cluster.
All-optical signatures of quantum vacuum nonlinearities in generic laser fields

All-optical experiments at the high-intensity frontier offer a promising route to unprecedented precision tests of quantum electrodynamics in strong macroscopic electromagnetic fields. So far, most theoretical studies of all-optical signatures of quantum vacuum nonlinearity are based on simplifying approximations of the beam profiles and pulse shapes of the driving laser fields. Since precision tests require accurate quantitative theoretical predictions, we introduce an efficient numerical tool facilitating the quantitative theoretical study of all-optical signatures of quantum vacuum nonlinearity in generic laser fields. Our approach is based on the vacuum emission picture, and makes use of the fact that the dynamics of the driving laser fields are to an excellent approximation governed by classical Maxwell theory in vacuum. In combination with a Maxwell solver, which self-consistently propagates any given laser field configuration, this allows for accurate theoretical predictions of photonic signatures of vacuum nonlinearity in high-intensity laser experiments from first principles. We employ our method to simulate photonic signatures of quantum vacuum nonlinearity in laser pulse collisions involving a few-cycle pulse, and show that the angular and spectral distributions of the emitted signal photons deviate from those of the driving laser beams.
A long term study of AGN X-ray variability. Structure function analysis on a ROSAT-XMM quasar sample

Variability in the X-rays is a key ingredient in understanding and unveiling active galactic nuclei (AGN) properties. In this band flux variations occur on short time scales (hours) as well as on larger times scales. While short time scale variability is often investigated in single source studies, only few works are able to explore flux variation on very long time scales.This work provides a statistical analysis of the AGN long term X-ray variability. We study variability on the largest time interval ever investigated for the 0.2-2 keV band, up to $\sim 20$ years rest-frame for a sample of 220 sources. Moreover, we study variability for 2,700 quasars up to $\sim 8$ years rest-frame in the same (soft) band.We build our source sample using the 3XMM serendipitous source catalogue data release 5, and data from ROSAT All Sky Survey Bright and Faint source catalogues. In order to select only AGN we use the Sloan Digital Sky Survey quasar catalogues data releases 7 and 12. Combining ROSAT and XMM-Newton observations, we investigate variability using the structure function analysis which describes the amount of variability as a function of the lag between the observations.Our work shows an increase of the structure function up to 20 years. We do not find evidence of a plateau in the structure function on these long time scales.The increase of the structure function at long time lags suggests that variability in the soft X-rays can be influenced by flux variations originated in the accretion disk or that they take place in a region large enough to justify variation on such long time scales.
Early-type Galaxies in the Sloan Digital Sky Survey. II. Correlations between Observables

A magnitude-limited sample of nearly 9000 early-type galaxies, in the redshift range 0.01 ≤ z ≤ 0.3, was selected from the Sloan Digital Sky Survey using morphological and spectral criteria. The sample was used to study how early-type galaxy observables, including luminosity L, effective radius Ro, surface brightness Io, color, and velocity dispersion σ, are correlated with one another. Measurement biases are understood with mock catalogs that reproduce all of the observed scaling relations and their dependences on fitting technique. At any given redshift, the intrinsic distribution of luminosities, sizes, and velocity dispersions in our sample are all approximately Gaussian. A maximum likelihood analysis shows that σ ∝ L0.25±0.012, Ro ∝ L0.63±0.025, and Ro ∝ I-0.75±0.02 in the r* band. In addition, the mass-to-light ratio within the effective radius scales as Mo/L ∝ L0.14±0.02 or Mo/L ∝ M, and galaxies with larger effective masses have smaller effective densities: Δo ∝ M. These relations are approximately the same in the g*, i*, and z* bands. Relative to the population at the median redshift in the sample, galaxies at lower and higher redshifts have evolved only little, with more evolution in the bluer bands. The luminosity function is consistent with weak passive luminosity evolution and a formation time of about 9 Gyr ago.