Transitions Of CS Research Articles

AN OVERALL PICTURE OF THE GAS FLOW IN A MASSIVE CLUSTER-FORMING REGION: THE CASE OF G10.6–0.4

The massive clump G10.6-0.4 is an OB cluster forming region, in which multiple UC HII regions have been identified. In the present study, we report arcsecond resolution observations of the CS (1-0) transition, the NH$_{3}$ (3,3) main hyperfine inversion transition, the CH$_{3}$OH J=5 transitions, and the centimeter free-free continuum emissions in this region. The comparisons of the molecular line emissions with the free--free continuum emissions reveal a 0.5 pc scale massive molecular envelope which is being partially dispersed by the dynamically-expanding bipolar ionized cavity. The massive envelope is rotationally flattened and has an enhanced molecular density in the mid-plane. In the center of this massive clump lies a compact ($<$0.1 pc) hot ($\gtrsim$100 K) toroid, in which a cluster of O--type stars has formed. This overall geometry is analogous to the standard core collapse picture in the low-mass star forming region, with a central (proto-)stellar object, a disk, an envelope, and a bipolar outflow and outflow cavity. However, G10.6-0.4 has a much larger physical size scale ($\le$0.1 pc for typical low--mass star forming core). Based on the observations, we propose a schematic picture of the OB cluster forming region, which incorporates the various physical mechanisms. This model will be tested with the observations of other embedded OB clusters, and with numerical simulations.

CS LINE PROFILES IN HOT CORES

We present a theoretical study of CS line profiles in archetypal hot cores. We provide estimates of line fluxes from the CS(1-0) to the CS(15-14) transitions and present the temporal variation of these fluxes. We find that \textit{i)} the CS(1-0) transition is a better tracer of the Envelope of the hot core whereas the higher-J CS lines trace the ultra-compact core; \textit{ii)} the peak temperature of the CS transitions is a good indicator of the temperature inside the hot core; \textit{iii)} in the Envelope, the older the hot core the stronger the self-absorption of CS; \textit{iv)} the fractional abundance of CS is highest in the innermost parts of the ultra-compact core, confirming the CS molecule as one of the best tracers of very dense gas.

Evolution of the ISM in luminous infrared galaxies

Molecules that trace the high-density regions of the interstellar medium may be used to evaluate the changing physical and chemical environment during the ongoing nuclear activity in (Ultra-)Luminous Infrared Galaxies. The changing ratios of the HCN(1-0), HNC(1-0), HCO+(1-0), CN(1-0) and CN(2-1), and CS(3-2) transitions were compared with the HCN(1-0)/CO(1-0) ratio, which is proposed to represent the progression time scale of the starburst. These diagnostic diagrams were interpreted using the results of theoretical modeling using a large physical and chemical network to describe the state of the nuclear ISM in the evolving galaxies. Systematic changes are seen in the line ratios as the sources evolve from early stage for the nuclear starburst (ULIRGs) to later stages. These changes result from changing environmental conditions and particularly from the lowering of the average density of the medium. A temperature rise due to mechanical heating of the medium by feedback explains the lowering of the ratios at later evolutionary stages. Infrared pumping may affect the CN and HNC line ratios during early evolutionary stages. Molecular transitions display a behavior that relates to changes of the environment during an evolving nuclear starburst. Molecular properties may be used to designate the evolutionary stage of the nuclear starburst. The HCN(1-0)/CO(1-0) and HCO+(1-0)/HCN(1-0) ratios serve as indicators of the time evolution of the outburst.

MOLECULAR OUTFLOWS WITHIN THE FILAMENTARY INFRARED DARK CLOUD G34.43+0.24

We present molecular line observations, made with angular resolutions of ~20", toward the filamentary infrared dark cloud G34.43+0.24 using the APEX [CO(3-2), 13CO(3-2), C18O(3-2) and CS(7-6) transitions], Nobeyama 45 m [CS(2-1), SiO(2-1), C34S(2-1), HCO+(1-0), H13CO+(1-0) and CH3OH(2-1) transitions], and SEST [CS(2-1) and C18O(2-1) transitions] telescopes. We find that the spatial distribution of the molecular emission is similar to that of the dust continuum emission observed with 11" resolution showing a filamentary structure and four cores. The cores have local thermodynamic equilibrium masses ranging from 3.3x10^2 - 1.5x10^3 solar masses and virial masses from 1.1x10^3 - 1.5x10^3 solar masses, molecular hydrogen densities between 1.8x10^4 and 3.9x10^5 cm^{-3}, and column densities >2.0x10^{22} cm^{-2}; values characteristics of massive star forming cores. The 13CO(3-2) profile observed toward the most massive core reveals a blue profile indicating that the core is undergoing large-scale inward motion with an average infall velocity of 1.3 km/s and a mass infall rate of 1.8x10^{-3} solar masses per year. We report the discovery of a molecular outflow toward the northernmost core thought to be in a very early stage of evolution. We also detect the presence of high velocity gas toward each of the other three cores, giving support to the hypothesis that the excess 4.5 $\mu$ emission ("green fuzzies") detected toward these cores is due to shocked gas. The molecular outflows are massive and energetic, with masses ranging from 25 -- 80 solar masses, momentum 2.3 - 6.9x10^2 \Msun km/s, and kinetic energies 1.1 - 3.6x10^3 \Msun km^2 s^{-2}; indicating that they are driven by luminous, high-mass young stellar objects.

S-bearing molecules in massive dense cores

<i>Context. <i/>Although few in number, high-mass stars play a major role in the interstellar energy budget and the shaping of the Galactic environment; however, the formation of high-mass stars is not well understood, because of their large distances, short time scales, and heavy extinction.<i>Aims. <i/>The chemical composition of the massive cores forming high-mass stars can put some constraints on the time scale of the massive star formation: sulfur chemistry is of specific interest thanks to its rapid evolution in warm gas and because the abundance of sulfur-bearing species increases significantly with the temperature.<i>Methods. <i/>Two mid-infrared quiet and two brighter massive cores were observed in various transitions (<i>E<i/><sub>up<sub/> up to 289 K) of CS, OCS, H<sub>2<sub/>S, SO, and SO<sub>2<sub/> and of their <sup>34<sup/>S isotopologues at mm wavelengths with the IRAM 30m and CSO telescopes. The 1D modeling of the dust continuum is used to derive the density and temperature laws, which were then applied in the RATRAN code to modeling the observed line emission and to deriving the relative abundances of the molecules.<i>Results. <i/>All lines are detected, except the highest energy SO<sub>2<sub/> transition. Infall (up to 2.9 km s<sup>-1<sup/>) may be detected towards the core W43MM1. The inferred mass rate is 5.8–9.4 10yr. We propose an evolutionary sequence of our sources (W43MM1IRAS18264-1152IRAS05358+3543IRAS18162-2048), based on the SED analysis. The analysis of the variations in abundance ratios from source to source reveals that the SO and SO<sub>2<sub/> relative abundances increase with time, while CS and OCS decrease.<i>Conclusions. <i/>Molecular ratios, such as [ OCS/H<sub>2<sub/>S] , [ CS/H<sub>2<sub/>S] , [SO/OCS], [ SO<sub>2<sub/>/OCS] , [CS/SO], and [ SO<sub>2<sub/>/SO] may be good indicators of evolution, depending on layers probed by the observed molecular transitions. Observations of molecular emission from warmer layers, so that involving higher upper energy levels must be included.

Theoretical Analysis of Gas-Phase Front-Side Attack Identity SN2(C) and SN2(Si) Reactions with Retention of Configuration

Gas-phase front-side attack identity S(N)2(C) and S(N)2(Si) reactions, CH(3)X1 + X2(-) --> CH(3)X2 + X1(-) and SiH(3)X1 + X2(-) --> SiH(3)X2 + X1(-) (X = F, Cl), are investigated by the ab initio method and molecular face (MF) theory. The computations have been performed at the CCSD(T)/aug-cc-pVTZ//MP2/6-311++G(3df,3pd) and CISD/aug-cc-pVDZ levels. Front-side attack identity S(N)2 reactions for both SiH(3)X and CH(3)X have double-well potential energy surfaces (PESs), but their transition-state positions are different relative to the positions of reactants and products: it is lower for SiH(3)X, and it is higher for CH(3)X. The minimum energy path for an S(N)2(Si) reaction with retention of configuration proceeds from a stable pentacoordinated anion intermediate of C(s) symmetry (TBP) via a C(s) transition state (SP) to a complementary pentacoordinated intermediate (TBP) and finally up to separate products. Berry pseudorotation has been observed in the front-side attack identity S(N)2(Si) reactions with F(-) and Cl(-) along the intrinsic reaction coordinate (IRC) routes. In addition, the geometrical transformations of front-side attack identity S(N)2(C) and S(N)2(Si) reactions based on the IRC calculations at the MP2/6-311++G(3df, 3pd) level of theory are described compared with those of corresponding back-side attack reactions. The difference between front-side attack identity S(N)2(C) and S(N)2(Si) reactions has been demonstrated. In MF theory, the potential acting on an electron in a molecule (PAEM) is an important quantity; in particular, its D(pb) can measure the strength of a chemical bond in a molecule. It is found that the difference between D(pb) values of reactant and transition state may be related to the activation energy for front-side and back-side attack S(N)2(C) and S(N)2(Si) reactions, and the D(pb) curves along the IRC routes have features similar to those of the potential energy profiles for all of the back-side attack S(N)2 reactions and front-side attack S(N)2(Si) reaction with F(-). Furthermore, according to the MF theory, the spatial dynamic changing features of the molecular shapes and the face electron density are vividly depicted for the course of the reactions.

Observations of the Goldreich-Kylafis effect in star-forming regions with XPOL at the IRAM 30 m telescope

Context. The Goldreich-Kylafis (GK) effect causes certain molecular line emission to be weakly linearly polarized, e.g., in the presence of a magnetic field. Compared to polarized dust emission, the GK effect potentially yields additional information along the line of sight through its dependence on velocity in the line profile. Aims. Our goal was to detect polarized molecular line emission toward the DR21(OH), W3OH/H2O, G34.3+0.2, and UYSO 1 dense molecular cloud cores in transitions of rare CO isotopologues and CS. The feasibility of such observations had to be established by studying the influence of polarized sidelobes, e.g., in the presence of extended emission in the surroundings of compact sources. Methods. The observations were carried out with the IRAM 30 m telescope employing the correlation polarimeter XPOL and using two orthogonally polarized receivers. We produced beam maps to investigate instrumental polarization. Results. While a polarized signal is found in nearly all transitions toward all sources, its degree of polarization in only one case surpasses the polarization that can be expected from instrumental effects. It is shown that any emission in the polarized sidelobes of the system can produce instrumental polarization, even if the source is unpolarized. Tentative evidence of astronomically polarized line emission with pL 1.5% was found in the CS(2-1) line toward G34.3+0.2.

Tracing High-Density Gas in M82 and NGC 4038

We present the first detection of CS in the Antennae galaxies toward the NGC 4038 nucleus, as well as the first detections of two high-J (5-4 and 7-6) CS lines in the center of M82. The CS(7-6) line in M82 shows a profile that is surprisingly different from those of other low-J CS transitions we observed. This implies the presence of a separate, denser and warmer molecular gas component. The derived physical properties and the likely location of the CS(7-6) emission suggest an association with the supershell in the center of M82.

Molecular line profiles as diagnostics of protostellar collapse: modelling the ‘blue asymmetry’ in inside-out infall

The evolution of star-forming core analogues undergoing inside-out collapse is studied with a multipoint chemodynamical model which self-consistently computes the abundance distribution of chemical species in the core. For several collapse periods the output chemistry of infalling tracer species such as HCO+, CS and N2H+ is then coupled to an accelerated Λ-iteration radiative transfer code, which predicts the emerging molecular line profiles using two different input gas/dust temperature distributions. We investigate the sensitivity of the predicted spectral line profiles and line asymmetry ratios to the core temperature distribution, the time-dependent model chemistry, as well as to ad hoc abundance distributions. The line asymmetry is found to be strongly dependent on the adopted chemical abundance distribution. In general, models with a warm central region show higher values of blue asymmetry in optically thick HCO+ and CS lines than models with a starless core temperature profile. We find that in the formal context of Shu-type inside-out infall, and in the absence of rotation or outflows, the relative blue asymmetry of certain HCO+ and CS transitions is a function of time and, subject to the foregoing caveats, can act as a collapse chronometer. The sensitivity of simulated HCO+ line profiles to linear radial variations, subsonic or supersonic, of the internal turbulence field is investigated in the separate case of static cores.

Experimental Determination of Energy Disposal in the Dissociative Electron Recombinations of CS2+ and HCS2+

Vibronic optical emissions from CS(A1pi --> X1sigma+) and CS(a3pi --> X1sigma+) transitions have been identified from dissociative recombination (DR) of CS2(+) and HCS2(+) plasmas. All of the spectra were taken in flowing afterglow plasmas using an optical monochromator in the UV-visible wavelength region of 180-800 nm. For the CS(A --> X) and CS(a --> X) emissions, the relative vibrational distributions have been calculated for v' < 5 and v' < 3 in both types of plasmas for the CS(A) and CS(a) states, respectively. Both recombining plasmas show a population inversion from the v' = 0 to v' = 1 level of the CS(A) state, similar to other observations of the CS(A) state populations, which were generated using two other energetic processes. The possibility of spectroscopic cascading is addressed, such that transitions from upper level electronic states into the CS(A) and CS(a) states would affect the relative vibrational distribution, and there is no spectroscopic evidence supporting the cascading effect. Additionally, excited-state transitions from neutral sulfur (S(5S(2)0 --> 3P(2)) and S(5S(2)0 --> 3P(1))) and the products of ion-molecule reactions (CS(B1sigma+ --> A1pi), CS(+)(B2sigma+ --> A2pi(i)), and CS2(+) (A2pi(u) --> X2pi(g))) have been observed and are discussed.

Dense gas in luminous infrared galaxies

Aims. Molecules that trace the high-density regions of the interstellar medium have been observed in (ultra-) luminous (far-) infrared galaxies, in order to initiate multiple-molecule multiple-transition studies to evaluate the physical and chemical environment of the nuclear medium and its response to the ongoing nuclear activity. Methods. The HCN(1-0), HNC(1-0), HCO+ (1-0), CN(1-0) and CN(2-1), CO(2-1), and CS(3-2) transitions were observed in sources covering three decades of infrared luminosity including sources with known OH megamaser activity. The data for the molecules that trace the high-density regions were augmented with data available in the literature. Results. The integrated emissions of high-density tracer molecules show a strong relation to the far-infrared luminosity. Ratios of integrated line luminosities were used for a first-order diagnosis of the integrated molecular environment of the evolving nuclear starbursts. Diagnostic diagrams display significant differentiation among the sources that relate to the initial conditions and the radiative excitation environment. Initial differentiation was introduced between the FUV radiation field in photon-dominated-regions and the X-ray field in X-ray-dominated-regions. The galaxies displaying OH megamaser activity have line ratios typical of photon-dominated regions.

The [formula omitted] and [formula omitted] states of Cs 2: Observation and calculation

Potential energy curves of the 3 3 Σ g + and a 3 Σ u + states of Cs 2 have been determined in the framework of the pseudopotential method. Fifty 3 3 Σ g + v = 2 – 9 ← X 1 Σ g + two-photon transitions of Cs 2 have been observed in the near infrared wavelength range. Resolved fluorescence into bound levels and the continuum of the a 3 Σ u + state has been recorded with a monochromator/photomultiplier detection system. Calculated 3 3 Σ g + → a 3 Σ u + fluorescence spectra are compared with observed spectra.

Toward the SI System Based on Fundamental Constants: Weighing the Electron

A modified International System of Units (SI) based on simply specifying exact numeric values of seven physical constants is described. This "set of constants" approach fixes the scale for all measurements, and the result is that both base units and derived units have equal footing. The seven quantities are the Cs transition frequency, the speed of light, the spectral luminous efficacy, the electron charge, the Avogadro constant, the Planck constant, and the Boltzmann constant. The first three quantities ensure that the second, the meter, and the candela are, in practice, the same as in the present SI. However, this approach requires that the definition of the ampere, mole, kilogram, and kelvin be changed to provide consistency with these constants. A major challenge in ensuring acceptable continuity is in advancing the measure of the kilogram and kelvin in terms of fundamental constants of nature

Calculation of the franck-condon factors for the transitions of CS +2 ions and comparison with related photodissociation spectra

On the basis of the approximation of harmonic oscillation between SC and S for the symmetric stretching vibration of the CS 2 + ions, the Franck-Condon factors for the C ˜ 2 Σ g + ← B ˜ 2 Σ u + transitions of CS + 2 ions have been calculated using the potential curves and wavefunctions of the harmonic oscillator. The calculation results have been used for comparison with the photodissociation spectra via the C ˜ 2 Σ g + ← B ˜ 2 Σ u + transition, and for estimating the validity of the rotation constants and the bond length of C ˜ 2 Σ g + state given in the previous studies. The photodissociation mechanism via the C ˜ 2 Σ g + ← B ˜ 2 Σ u + transitions of CS + 2 ions has also been discussed.

Theoretical Studies of Quantum Amplified Isomerizations for Imaging Systems Involving Hexamethyl Dewar Benzene and Related Systems

The ring-opening reactions of the radical cations of hexamethyl Dewar benzene (1) and Dewar benzene have been studied using density functional theory (DFT) and complete active-space self-consistent field (CASSCF) calculations. Compound 1 is known to undergo photoinitiated ring opening by a radical cation chain mechanism, termed "quantum amplified isomerization" (QAI), which is due to the high quantum yield. Why QAI is efficient for 1 but not other reactions is explained computationally. Two radical cation minima of 1 and transition states located near avoided crossings are identified. The state crossings are characterized by conical intersections corresponding to degeneracy between doublet surfaces. Ring opening occurs by formation of the radical cation followed by a decrease in the flap dihedral angle. A rate-limiting Cs transition state leads to a second stable radical cation with an elongated transannular C-C bond and an increased flap dihedral. This structure proceeds through a conrotatory-like pathway of Cs symmetry to give the benzene radical cation. The role of electron transfer was investigated by evaluating oxidation of various systems using adiabatic ionization energies and electron affinities calculated from neutral and cation geometries. Electron-transfer theory was applied to 1 to investigate the limiting effects of back-electron transfer as it is related to the unusual stability of the two radical cations. Expected changes in optical properties between reactants and products of Dewar benzene compounds and other systems known to undergo QAI were characterized by computing frequency-dependent indices of refraction from isotropic polarizabilities. In particular, the reaction of 1 shows greater contrast in index of refraction than that of the Dewar benzene parent system.

A BIMA Array Survey of Molecules in Comets LINEAR (C/2002 T7) and NEAT (C/2001 Q4)

We present an interferometric search for large molecules, including methanol, methyl cyanide, ethyl cyanide, ethanol, and methyl formate in comets LINEAR (C/2002 T7) and NEAT (C/2001 Q4) with the Berkeley-Illinois-Maryland Association (BIMA) array. In addition, we also searched for transitions of the simpler molecules CS, SiO, HNC, HN13C and 13CO . We detected transitions of methanol and CS around Comet LINEAR and one transition of methanol around Comet NEAT within a synthesized beam of ~20''. We calculated the total column density and production rate of each molecular species using the variable temperature and outflow velocity (VTOV) model described by Friedel et al.(2005).Considering the molecular production rate ratios with respect to water, Comet T7 LINEAR is more similar to Comet Hale-Bopp while Comet Q4 NEAT is more similar to Comet Hyakutake. It is unclear, however, due to such a small sample size, whether there is a clear distinction between a Hale-Bopp and Hyakutake class of comet or whether comets have a continuous range of molecular production rate ratios.

Star formation in the Vela Molecular Clouds: A new protostar powering a bipolar jet

We have performed a detailed study of the star-forming region associated with the IRAS source 08448-4343 in the cloud D of the Vela Molecular Ridge. Our investigation covers a wide spectral range from the near IR, through the thermal IR to the mm-band exploiting both imaging and spectroscopic facilities in each spectral regime. A picture emerges of a dust structure which hosts a near IR cluster and multiple well-collimated H2 jets; these jets originate from different sources lying in a compact region at the cluster centre. The peak of the 1.2 mm map does not coincide with the IRAS peak, thus tracing a less evolved and denser region with a colder dust with respect to that traced by IRAS. This view is also confirmed by the observations of CS transitions from J = 2− 1t oJ = 7−6. The mm peak can be associated with the position of a red object, already proposed in previous studies as the driving source of the main jet in the field. This jet, extended along more than 0.3 pc, is composed of individual knots whose radial velocities decrease with increasing distance from the central source, which is resolved into at least six 2 µm peaks. The reddest and coldest of these peaks is well aligned with the inner knots of the jet. The spectral energy distribution of the central source resembles that of an intermediate luminosity, Class I protostar, whose youth is discussed in terms of the efficiency of the energy transfer into the jet.

Search for massive protostellar candidates in the southern hemisphere

We have observed two rotational transitions of both CS and C 17 O, and the 1.2 mm continuum emission towards a sample of 130 high-mass protostellar candidates with δ δ ≥ $-30^{\circ}$, we have selected from the IRAS Point Source Catalogue 429 sources which potentially are compact molecular clouds on the basis of their IR colours. The sample has then been divided into two groups according to the colour indices [25–12] and [60–12]: the 298 sources with [25–12] ≥ 0.57 and [60–12] ≥ 1.30 have been called High sources, the remaining 131 have been called Low sources. In this paper, we check the association with dense gas and dust in 130 Low sources. We have obtained a detection rate of ~$85\%$ in CS, demonstrating a tight association of the sources with dense molecular clumps. Among the sources detected in CS, ~$76\%$ have also been detected in C 17 O and ~$93\%$ in the 1.2 mm continuum. Millimeter-continuum maps show the presence of clumps with diameters in the range $0.2{-}2$ pc and masses from a few $M_{\odot}$ to $10^{5}~M_{\odot}$; H 2 volume densities computed from CS line ratios lie between ~10 4.5 and 10 5.5 cm -3 . The bolometric luminosities of the sources, derived from IRAS data, are in the range $10^{3}{-}10^{6}~L_{\odot}$, consistent with embedded high-mass objects. Based on our results and those found in the literature for other samples of high-mass young stellar objects, we conclude that our sources are massive objects in a very early evolutionary stage, probably prior to the formation of an Hii region. We propose a scenario in which High and Low sources are both made of a massive clump hosting a high-mass protostellar candidate and a nearby stellar cluster. The difference might be due to the fact that the 12 μ m IRAS flux, the best discriminant between the two groups, is dominated by the emission from the cluster in Lows and from the massive protostellar object in Highs .

Field-Induced Phase Transitions Driven by Quantum Fluctuation inS=1/2 Anisotropic Triangular Antiferromagnet Cs2CuBr4

The field induced magnetic phase transitions of Cs 2 CuBr 4 were investigated by means of magnetization process and neutron scattering experiments. Cs 2 CuBr 4 should be characterized as S = 1/2 two-dimensional triangular antiferromagnet. Below the ordering temperature T N = 1.4 K, the Spin structure is the helical incommensurate structure almost within the triangular lattice plane. In the field direction within the triangular lattice plane, Cs 2 CuBr 4 exhibits the magnetization plateaux at one-third and two-thirds of the saturation magnetization. The spin structure in the one-third plateau phase is found to be almost collinear up-up-down structure which should be stabilized by quantum fluctuation as predicted by the theoretical studies.

W49A North: Global or Local or No Collapse?

We attempt to fit observations with resolution of the J=2-1 transition of CS in the directions of H II regions A, B, and G of W49A North as well as observations with 20 resolution of the J=2-1, 3-2, 5-4, and 7-6 transitions in the directions of H II regions A and G by using radiative transfer calculations. These calculations predict the intensity profiles resulting from several spherical clouds along the line of sight. We consider three models: global collapse of a very large (5 pc radius) cloud, localized collapse from smaller (1 pc) clouds around individual H II regions, and multiple, static clouds. For all three models we can find combinations of parameters that reproduce the CS profiles reasonably well provided that the component clouds have a core-envelope structure with a temperature gradient. Cores with high temperature and high molecular hydrogen density are needed to match the higher transitions (e.g. J=7-6) observed towards A and G. The lower temperature, low density gas needed to create the inverse P-Cygni profile seen in the CS J=2-1 line (with beam) towards H II region G arises from different components in the 3 models. The infalling envelope of cloud G plus cloud B creates the absorption in global collapse, cloud B is responsible in local collapse, and a separate cloud, G', is needed in the case of many static clouds. The exact nature of the velocity field in the envelopes for the case of local collapse is not important as long as it is in the range of 1 to 5 km/s for a turbulent velocity of about 6 km/s. High resolution observations of the J=1-0 and 5-4 transitions of CS and C34S may distinguish between these three models. Modeling existing observations of HCO+ and C18O does not allow one to distinguish between the three models but does indicate the existence of a bipolar outflow.