Nebula NGC Research Articles

CHARACTERIZING THE INFRARED SPECTRA OF SMALL, NEUTRAL, FULLY DEHYDROGENATED POLYCYCLIC AROMATIC HYDROCARBONS

We present the results of a computational study to investigate the infrared spectroscopic properties of a large number of polycyclic aromatic hydrocarbon (PAH) molecules and their fully dehydrogenated counterparts. We constructed a database of fully optimized geometries for PAHs that is complete for eight or fewer fused benzene rings, thus containing 1550 PAHs and 805 fully dehydrogenated aromatics. A large fraction of the species in our database have clearly non-planar or curved geometries. For each species, we determined the frequencies and intensities of their normal modes using density functional theory calculations. Whereas most PAH spectra are fairly similar, the spectra of fully dehydrogenated aromatics are much more diverse. Nevertheless, these fully dehydrogenated species show characteristic emission features at 5.2$\mu$m, 5.5$\mu$m and 10.6$\mu$m; at longer wavelengths, there is a forest of emission features in the 16--30$\mu$m range that appears as a structured continuum, but with a clear peak centered around 19$\mu$m. We searched for these features in Spitzer-IRS spectra of various positions in the reflection nebula NGC 7023. We find a weak emission feature at 10.68$\mu$m in all positions except that closest to the central star. We also find evidence for a weak 19$\mu$m feature at all positions that is not likely due to C$_{60}$. We interpret these features as tentative evidence for the presence of a small population of fully dehydrogenated PAHs, and discuss our results in the framework of PAH photolysis and the formation of fullerenes.

XMM-NewtonRGS observations of the Cat’s Eye Nebula

We present an analysis of XMM-Newton Reflection Grating Spectrometer (RGS) observations of the planetary nebula (PN) NGC 6543, rendering it the second PN with high resolution X-ray spectroscopic observations besides BD+30 3639. The observations consist of 26 pointings, of which 14 included RGS observations for a total integration time of 435 ks. Many of these observations, however, were severely affected by high-background levels, and the net useful exposure time is drastically reduced to 25 ks. Only the O VII triplet at 22 \AA\ is unambiguously detected in the RGS spectrum of NGC 6543. We find this spectrum consistent with an optically thin plasma at 0.147 keV (1.7 MK) and nebular abundances. Unlike the case of BD+30 3639, the X-ray emission from NGC 6543 does not reveal overabundances of C and Ne. The results suggest the N/O ratio of the hot plasma is consistent with that of the stellar wind, i.e., lower than the nebular N/O ratio, but this result is not conclusive.

The Goldilocks Theory

The Goldilocks Theory

Echelle spectroscopy and photoionization modelling of the entire planetary nebula NGC 6210

Echelle spectroscopy and photoionization modelling of the entire planetary nebula NGC 6210

SHAPEMOL: a 3D code for calculating CO line emission in planetary and protoplanetary nebulae

Modern instrumentation in radioastronomy constitutes a valuable tool for studying the Universe: ALMA has reached unprecedented sensitivities and spatial resolution, while Herschel/HIFI has opened a new window for probing molecular warm gas (~50-1000 K). On the other hand, the software SHAPE has emerged in the past few years as a standard tool for determining the morphology and velocity field of different kinds of gaseous emission nebulae via spatio-kinematical modelling. SHAPE implements radiative transfer solving, but it is only available for atomic species and not for molecules. Being aware of the growing importance of the development of tools for simplifying the analyses of molecular data, we introduce shapemol, a complement to SHAPE, with which we intend to fill the so-far under-developed molecular niche. shapemol enables user-friendly, spatio-kinematic modelling with accurate non-LTE calculations of excitation and radiative transfer in CO lines. It allows radiative transfer solving in the 12CO and 13CO J=1-0 to J=17-16 lines, but its implementation permits easily extending the code to different molecular species. shapemol allows easily generating synthetic maps and line profiles to match against interferometric or single-dish observations. We fully describe shapemol and discuss its limitations and the sources of uncertainty to be expected in the final synthetic profiles or maps. As an example of the power and versatility of shapemol, we build a model of the molecular envelope of the planetary nebula NGC 6302 and compare it with 12CO and 13CO J=2-1 interferometric maps from SMA and high-J transitions from Herschel/HIFI. We find the molecular envelope to have a complex, broken ring-like structure with an inner, hotter region and several 'fingers' and high-velocity blobs, emerging outwards from the plane of the ring. We derive a mass of 0.11 Msun for the molecular envelope.

NGC 6309, a planetary nebula that shifted from round to multipolar★†

We present new narrow-band Ha, [N II], and [O III] high-resolution images of the quadrupolar planetary nebula (PN) NGC 6309 that show in great detail its bipolar lobes and reveal new morphological features. New high- and low-dispersion long-slit spectra have been obtained to help in the investigation of the new nebular components. The images and spectra unveil two diffuse blobs, one of them located at 55 arcsec from the central star along the NE direction (PA= +71) and the other at 78 arcsec in the SW direction (PA= -151). Therefore, these structures do not share the symmetry axes of the inner bipolar outflows. Their radial velocities relative to the system are quite low: +3 and -4 km/s, respectively. Spectroscopic data confirm a high [O III] to Ha ratio, indicating that the blobs are being excited by the UV flux from the central star. Our images convincingly show a spherical halo 60 arcsec in diameter encircling the quadrupolar nebula. The expansion velocity of this shell is low, 66 km/s. The software SHAPE has been used to construct a morpho-kinematic model for the ring and the bipolar flows that implies an age of 4,000 yrs, the expansion of the halo sets a lower limit for its age 46,000 yrs, and the very low expansion of the blobs suggests they are part of a large structure corresponding to a mass ejection that took place 150,000 yrs ago. In NGC 6309 we have direct evidence of a change in the geometry of mass-loss, from spherical in the halo to axially-symmetric in the two pairs of bipolar lobes.

On the diffuse X-ray emission from the Wolf–Rayet bubble NGC 2359

A recent XMM-Newton observation (Zhekov 2014) has revealed diffuse X-ray emission inside the nebula NGC 2359 around the Wolf-Rayet star WR 7. Taking advantage of an improved point-source rejection and background subtraction, and a detailed comparison of optical and X-ray morphology, we have reanalyzed these X-ray observations. Our analysis reveals diffuse X-ray emission from a blowout and the presence of emission at energies from 1.0 to 2.0 keV. The X-ray emission from NGC 2359 can be described by an optically-thin plasma emission model, but contrary to previous analysis, we find that the chemical abundances of this plasma are similar to those of the optical nebula, with no magnesium enhancement, and that two components at temperatures T_1=2x10^6 K and T_2=5.7x10^7 K are required. The estimated X-ray luminosity in the 0.3 - 2.0 keV energy range is L_X=2x10^33 erg s^-1. The averaged rms electron density of the X-ray-emitting gas (n_e \lesssim 0.6 cm^-3) reinforces the idea of mixing of material from the outer nebula into the hot bubble.

Variability of the planetary nebula NGC 6572 and its central star during the interval covered by optical observations

Estimates of relative line intensities available in the literature and integrated Hβ fluxes of the planetary nebula NGC 6572 during the time covered by optical observations (1938–2013) are compared to search for possible variations. Line intensities measured from observations obtained at the Crimean Station of the Sternberg Astronomical Institute in 2013 are presented, as well as previously unpublished photographic spectroscopic data obtained 1972–2005. Our analysis of all the available data shows that the line intensities do not vary within the observational uncertainties, with the possible exception of the [OIII] 4959 and 5007 A lines, which show a tendency for their intensity increase with time. This can be interpreted as a manifestation of a temperature increase of the central star, or radial stratification of the [OIII] emission in the nebula, with the latter explanation being less probable. However, stratification is clearly visible in the [OII] and [NII] line intensities. The integrated Hβ flux is most probably constant at F(Hβ) = (1.50 ± 0.03) × 10−10 erg cm−2 s−1. A refined estimate of the interstellar extinction toward NGC 6572 has been obtained from radio and optical data, c(Hβ) = 0.42 ± 0.03. The MAST spectroscopy data were used to derive the central star’s UBV magnitudes in 2004. Integrated photoelectric UBV observations of the nebula and central star for 1971–2005 are presented.

HIP 3678: a hierarchical triple stellar system in the centre of the planetary nebula NGC 246★

We report the detection of a new low-mass stellar companion to the white dwarf HIP 3678 A, the central star of the planetary nebula NGC 246. The newly found companion is located about 1 arcsec (at projected separation of about 500 au) north-east of HIP 3678 A, and shares a common proper motion with the white dwarf and its known comoving companion HIP 3678 B. The hypothesis that the newly detected companion is a non-moving background object can be rejected on a significance level of more than 8 $\sigma$, by combining astrometric measurements from the literature with follow-up astrometry, obtained with Wild Field Planetary Camera 2/\textit{Hubble Space Telescope} and NACO/Very Large Telescope. From our deep NACO imaging data, we can rule out additional stellar companions of the white dwarf with projected separations between 130 up to 5500 au. In the deepest high-contrast NACO observation, we achieve a detection limit in the \textit{Ks} band of about 20 mag, which allows the detection of brown dwarf companions with masses down to 36$\,\rmn{M_{jup}}$ at an assumed age of the system of 260 Myr. To approximate the masses of the companions HIP 3678 B and C, we use the evolutionary Baraffe et al. models and obtain about 0.85\,M$_{\sun}$ for HIP 3678 B and about 0.1 M$_{\sun}$ for HIP 3678 C. According to the derived absolute photometry, HIP 3678 B should be a early to mid-K dwarf (K2--K5), while HIP 3678 C should be a mid-M dwarf with a spectral type in the range between M5 and M6.

Kinematic study of planetary nebulae in NGC 6822

By measuring precise radial velocities of planetary nebulae (which belong to the intermediate age population), H II regions, and A-type supergiant stars (which are members of the young population) in NGC 6822, we aim to determine if both types of population share the kinematics of the disk of H I found in this galaxy. Spectroscopic data for four planetary nebulae were obtained with the high spectral resolution spectrograph Magellan Inamori Kyocera Echelle (MIKE) on the Magellan telescope at Las Campanas Observatory. Data for other three PNe and one H II region were obtained from the SPM Catalog of Extragalactic Planetary Nebulae which employed the Manchester Echelle Spectrometer attached to the 2.1m telescope at the Observatorio Astron\'omico Nacional, M\'exico. In the wavelength calibrated spectra, the heliocentric radial velocities were measured with a precision better than 5-6 km s$^{-1}$. Data for three additional H II regions and a couple of A-type supergiant stars were collected from the literature. The heliocentric radial velocities of the different objects were compared to the velocities of the H i disk at the same position. From the analysis of radial velocities it is found that H II regions and A-type supergiants do share the kinematics of the H I disk at the same position, as expected for these young objects. On the contrary, planetary nebula velocities differ significantly from that of the H I at the same position. The kinematics of planetary nebulae is independent from the young population kinematics and it is closer to the behavior shown by carbon stars, which are intermediate-age members of the stellar spheroid existing in this galaxy. Our results are confirming that there are at least two very different kinematical systems in NGC 6822.

Modelling the 3D morphology and proper motions of the planetary nebula NGC 6302

We present 3D hydrodynamical simulations of an isotropic fast wind interacting with a previously ejected toroidally shaped slow wind in order to model both the observed morphology and the kinematics of the planetary nebula (PN) NGC 6302. This source, also known as the Butterfly nebula, presents one of the most complex morphologies ever observed in PNe. From our numerical simulations, we have obtained an intensity map for the Hα emission to make a comparison with the Hubble Space Telescope (HST) observations of this object. We have also carried out a proper motion (PM) study from our numerical results, in order to compare with previous observational studies. We have found that the two interacting stellar wind model reproduce well the morphology of NGC 6302, and while the PMs in the models are similar to the observations, our results suggest that an acceleration mechanism is needed to explain the Hubble-type expansion found in HST observations.

Rummaging inside the Eskimo's parka: variable asymmetric planetary nebula fast wind and a binary nucleus?

We report on high-resolution optical time-series spectroscopy of the central star of the `Eskimo' planetary nebula NGC~2392. Datasets were secured with the ESO 2.3m in 2006 March and CFHT 3.6m in 2010 March to diagnose the fast wind and photospheric properties of the central star. The HeI and HeII recombination lines reveal evidence for clumping and temporal structures in the fast wind that are erratically variable on timescales down to ~ 30 min. (i.e. comparable to the characteristic wind flow time). We highlight changes in the overall morphology of the wind lines that cannot plausibly be explained by line-synthesis model predictions with a spherically homogeneous wind. Additionally we present evidence that the UV line profile morphologies support the notion of a high-speed, high-ionization polar wind in NGC~2392. Analyses of deep-seated, near-photospheric absorption lines reveals evidence for low-amplitude radial velocity shifts. Fourier analysis points tentatively to a ~ 0.12-d modulation in the radial velocities, independently evident in the ESO and CFHT data. We conclude that the overall spectroscopic properties support the notion of a (high inclination) binary nucleus in NGC~2392 and an asymmetric fast wind.

Expansion velocities of the planetary nebula NGC 7009—the high dispersion spectra line profiles

We investigated the line profiles of the high dispersion spectra of He I, He II, N III, [N II], [O III], [Ar III], [Ar IV], [S II], [S III ], and [Cl IV], secured at the center of the planetary nebula NGC 7009 with the fiber-fed Bohyunsan Echelle Spectrograph (BOES). The expansion velocities for the main shell and the faint outer thin shell were derived based on stronger double Gaussian profiles and the fast blue wing component, respectively. With the Keck 2D spectral images, we set the main shell boundaries as R∼4″ and 6″ and the faint outer thin shell boundaries as R∼11″ and 13″. The radial variation of expansion velocities of both shells does not follow a linear acceleration. The acceleration of the main shell gas seems to be in a retarded mode, while that of the outer faint shell gas seems to be affected by an additional force. The fast wing component appears also in the He I, He II, and N III line profiles which are likely to have been formed in a compact region, located inside the main shell. The additional deceleration factor, such as the rotation of the central star or the dust gas in the gas shell might cause the non-linear acceleration. Based on the line profiles responsible for the three zones, we conclude that there were at least three major changes occurred in the central star temperature since the first outflow from the central star.

A Study on the CO Isotopic Lines of the Star Forming Region AFGL 5157

By the mapping observations simultaneously at the 12CO (J=1-0), 13CO (J=1-0), and C18O (J=1-0) lines on the area of 24’×24’ (12 pc×12 pc) of the star forming region AFGL 5157, we have obtained the distribution and averaged physical parameters for the respective 13CO and C18O cores of this molecu- lar cloud. At the edge of the molecular cloud, the isotopic abundance ratio is X [(13CO)/(C18O)] ≈ 10, close to the ratio of a giant molecular cloud. The viral masses of the 13CO and C18O cores are less than the masses of the molecu-lar cloud cores, so the molecular cloud cores are gravitationally unstable, and the C18O molecular cloud core is more easy to collapse. The column density distributions of the C18O molecular cloud core in the northeast and southwest directions are, respectively, 1.1 × 1023× z−0.43 and 4.6 × 1025× z−0.58, where z is the distance from the center of the molecular cloud core. The high velocity molecular outflow has been confirmed from our 12CO spectra, the mass loss rate of the outflow has been estimated, and the mass-velocity relation of the outflow is fitted by a power-law function of m ∝ v−1.8. The star formation rate of the 13CO molecular cloud core is as high as 23%, probably, under the influence ofthe reflection nebula NGC 1985, this region is forming medium and large mass stars or clusters.

Spatially resolved physical and chemical properties of the planetary nebula NGC 3242

Optical integral-field spectroscopy was used to investigate the planetary nebula NGC 3242. We analysed the main morphological components of this source, including its knots, but not the halo. In addition to revealing the properties ofthe physical and chemical nature of this nebula, we also provided reliable spatially resolved constraints that can be used for future photoionisation modelling of the nebula. The latter is ultimately necessary to obtain a fully self-consistent 3D picture of the physical and chemical properties of the object. The observations were obtained with the VIMOS instrument attached to VLT-UT3. Maps and values for specific morphological zones for the detected emission-lines were obtained and analysed with routines developed by the authors to derive physical and chemical conditions of the ionised gas in a 2D fashion. We obtained spatially resolved maps and mean values of the electron densities, temperatures, and chemical abundances, for specific morphological structures in NGC 3242. These results show the pixel-to-pixel variations of the the small- and large-scale structures of the source. These diagnostic maps provide information free from the biases introduced by traditional single long-slit observations. In general, our results are consistent with a uniform abundance distribution for the object, whether we look at abundance maps or integrated fluxes from specified morphological structures. The results indicate that special care should be taken with the calibration of the data and that only data with extremely good signal-to-noise ratio and spectral coverage should be used to ensure the detection of possible spatial variations.

AHerschelstudy of NGC 650

As part of the Herschel Guaranteed Time Key Project MESS (Mass loss of Evolved StarS) we have imaged a sample of planetary nebulae. In this paper we present the PACS and SPIRE images of the classical bipolar planetary nebula NGC 650. We used these images to derive a temperature map of the dust. We also constructed a photoionization and dust radiative transfer model using the spectral synthesis code Cloudy. To constrain this model, we used the PACS and SPIRE fluxes and combined these with hitherto unpublished IUE and Spitzer IRS spectra as well as various other data from the literature. The temperature map combined with the photoionization model were used to study various aspects of the central star, the nebula, and in particular the dust grains in the nebula. The central star parameters are determined to be T_eff = 208 kK and L = 261 L_sol assuming a distance of 1200 pc. The stellar temperature is much higher than previously published values. We confirm that the nebula is carbon-rich with a C/O ratio of 2.1. The nebular abundances are typical for a type IIa planetary nebula. With the photoionization model we determined that the grains in the ionized nebula are large (assuming single-sized grains, they would have a radius of 0.15 micron. Most likely these large grains were inherited from the asymptotic giant branch phase. The PACS 70/160 micron temperature map shows evidence for two radiation components heating the grains. The first component is direct emission from the central star, while the second component is diffuse emission from the ionized gas (mainly Ly alpha). We show that previous suggestions that there is a photo-dissociation region surrounding the ionized region are incorrect. The neutral material resides in dense clumps inside the ionized region. These may also harbor stochastically heated very small grains in addition to the large grains.

Book Review: Sublime Images from Hubble, Picturing the Cosmos: Hubble Space Telescope Images and the Astronomical Sublime

SUBLIME IMAGES FROM HUBBLE Picturing the Cosmos: Hubble Space Telescope Images and the Astronomical Sublime. Elizabeth A. Kessler (University of Minnesota Press, Minneapolis, 2012). Pp. viii + 279. $30 (paperback). ISBN 978-0-8166-7957-7.In 1998, the Hubble Heritage Team was preparing to release a new image of the planetary nebula NGC 3132. Hubble Heritage images appear not just in research papers but on calendars, coffee mugs, and the walls of art galleries. They literally shape how many citizens and scientists around the world see the universe. When describing how a balance between aesthetic inclinations and scientific veracity was found for the NGC 3132 picture, one team member explained, We tend to look for things that 'look right.' And what exactly looks right is maybe a little hard to quantify (p. 162).This quote, found toward the end of Elizabeth A. Kessler's excellent and thought-provoking new book, captures a great deal of the tension inherent in making and viewing contemporary images. Such scientific images have an inherent aesthetic and artistic quality. As Kessler's book reveals, they do all sorts of work besides merely conveying scientific information.As the book's title suggests, the astronomical is central to Kessler's analysis of Hubble images. Primarily focusing on the work of the Hubble Heritage Project, she expands on the sublime's characteristic features (astonishment, the infinite, and even terror) and extends it beyond its origins with eighteenth-century scholars like Immanuel Kant and Edmund Burke. Kessler convincingly shows how contemporary Hubble images not only reflect qualities of the sublime but also resemble earlier traditions in Western art. In particular, she compares Hubble images to famous nineteenth-century landscape paintings by artists such as Thomas Moran and Albert Bierstadt. The famous 1995 Pillars of Creation image - a view of the Eagle Nebula has parallels to, for example, the towering cloud and rock formations found in Romantic scenes of the American West.Nineteenth-century scenes of the American frontier once conveyed natural splendour to parlour-bound citizens, and tempted scientists with their geological mysteries. They also communicated the ideology of Manifest Destiny and the transformative power of the frontier as Frederick Jackson Turner famously noted. In similar fashion, images from Hubble reflect their own historical moment by stimulating public interest and continued funding for NASA's exploration of the cosmic frontier. In the early 1990s, when the telescope's initial spherical aberration threatened to undermine public and political support altogether, images from Hubble proved especially critical. They convinced scientists, politicians and taxpayers that a hobbled Hubble could still produce good science and a repaired telescope even more so.The strength of Kessler's argument lies in her skilful blending of the histories of art and astronomy with oral history interviews and observations from contemporary astronomers at work. She also engages with the work of other scholars who have considered the nature and use of images. This book, for example, finds common ground with Samuel Edgerton and Michael Lynch's earlier work on digital image processing while critiquing the sceptical view of the art historian James Elkins. …

THE REMARKABLE MOLECULAR CONTENT OF THE RED SPIDER NEBULA (NGC 6537)

Millimeter and sub-millimeter molecular-line observations of planetary nebula (PN) NGC 6537 (Red Spider) have been carried out using the Sub-Millimeter Telescope and the 12 m antenna of the Arizona Radio Observatory in the frequency range 86-692 GHz. CN, HCN, HNC, CCH, CS, SO, H2CO, HCO+ and N2H+, along with the J = 3 → 2 and 6 → 5 lines of CO and those of several isotopologues, were detected toward the Red Spider, estimated to be ~1600 yr old. This extremely high excitation PN evidently fosters a rich molecular environment. The presence of CS and SO suggest that sulfur may be sequestered in molecular form in such nebulae. A radiative transfer analysis of the CO and CS spectra indicate a kinetic temperature of T K ~ 60-80 K and gas densities of n(H2) ~ 1-8 × 105 cm–3 in NGC 6537. Column densities of the molecules in the nebula and their fractional abundances relative to H2 ranged from N tot ~ 1016 cm–2 and f ~ 10–4 for CO, to ~7 × 1011 cm–2 and f ~ 8 × 10–9 for the least abundant species, N2H+. For SO and CS, N tot ~ 2 × 1012 cm–2 and 1013 cm–2, respectively, with f ~ 10–7 and 2 × 10–8. It was also found that HCN/HNC 2. A low 12C/13C ratio of ~4 was measured, indicative of hot-bottom burning. These results, coupled with past observations, suggest that molecular abundances in PNe are governed principally by the physical and chemical properties of the individual object and its progenitor star, rather than nebular age.

Multiple outflows in the planetary nebula NGC 6058

We present narrow-band [O III]lambda5007 and H-alpha images, as well as long-slit high-resolution echelle spectra of the planetary nebula NGC 6058. Our data reveal that NGC 6058 is a multipolar planetary nebula of about ~45 arcsec in extent and formed by four bipolar outflows that are oriented at different position angles. Assuming homologous expansion for all the structures, and a distance of 3.5 kpc, we obtain polar velocities around ~68 km s^-1 for three of them. The estimated kinematical ages suggest that the three oldest outflows have been ejected in intervals of ~ 1100 and ~ 400 yr during which, the ejection axis has changes its orientation by ~ 60 degrees and ~ 40 degrees, respectively. Although a inner ring-like structure is suggested by the direct images, its kinematics shows that no equatorial ring or toroid exists in the nebula. At the contrary, the long-slit spectra reveal that the ring-like structure corresponds to a fourth outflow that is oriented almost perpendicular to the other three. This fourth outflow is the youngest one and appears to be interacting with the other three, creating a protruding zone that sweeps material in a region almost perpendicular to the major axes of the oldest outflows. This structure also presents two bright arcuate regions along the same direction of the older outflows, and at opposite sides from the central star. From our model, we suggest that NGC 6058 could be anintermediate evolutionary stage between starfish planetary nebulae and multipolar planetary nebula with apparent equatorial lobes.

Kepler photometry and optical spectroscopy of the ZZ Lep central star of the planetary nebula NGC 6826: rotational and wind variability

We present three years of long-cadence and over one year of short-cadence photometry of the central star of the Planetary Nebula NGC 6826 obtained with the Kepler spacecraft, and temporally coinciding optical spectroscopy. The light curves are dominated by incoherent variability on time scales of several hours, but contain a lower-amplitude periodicity of 1.23799 d. The temporal amplitude and shape changes of this signal are best explicable with a rotational modulation, and are not consistent with a binary interpretation. We argue that we do not observe stellar pulsations within the limitations of our data, and show that a binary central star with an orbital period less than seven days could only have escaped our detection in the case of low orbital inclination. Combining the photometric and spectroscopic evidence, we reason that the hourly variations are due to a variable stellar wind, and are global in nature. The physical cause of the wind variability of NGC 6826 and other ZZ Leporis stars is likely related to the mechanism responsible for wind variations in massive hot stars.