Compact Active Galactic Nuclei Research Articles

Compact Symmetric Objects. I. Toward a Comprehensive Bona Fide Catalog

Compact symmetric objects (CSOs) are jetted active galactic nuclei (AGN) with overall projected size <1 kpc. The classification was introduced to distinguish these objects from the majority of compact jetted AGN in centimeter-wavelength very long baseline interferometry observations, where the observed emission is relativistically boosted toward the observer. The original classification criteria for CSOs were (i) evidence of emission on both sides of the center of activity and (ii) overall size <1 kpc. However, some relativistically boosted objects with jet axes close to the line of sight appear symmetric and have been misclassified as CSOs, thereby undermining the CSO classification. This is because two essential CSO properties, pointed out in the original papers, have been neglected: (iii) low variability and (iv) low apparent speeds along the jets. As a first step toward creating a comprehensive catalog of “bona fide” CSOs, we identify 79 bona fide CSOs, including 15 objects claimed as confirmed CSOs here for the first time, that match the CSO selection criteria. This sample of bona fide CSOs can be used for astrophysical studies of CSOs without contamination by misclassified CSOs. We show that the fraction of CSOs in complete flux density limited AGN samples with S 5GHz > 700 mJy is between (6.8 ± 1.6)% and (8.5 ± 1.8)%.

SPARCS-North Wide-field VLBI Survey: exploring the resolved μJy extragalactic radio source population with EVN + e-MERLIN

ABSTRACT The SKA PAthfinder Radio Continuum Surveys (SPARCS) are providing deep-field imaging of the faint (sub-mJy) extragalactic radio source populations through a series of reference surveys. One of the key science goals for SPARCS is to characterize the relative contribution of radio emission associated with active galactic nucleus (AGN) from star formation (SF) in these faint radio source populations, using a combination of high sensitivity and high angular resolution imaging over a range of spatial scales (arcsec to mas). To isolate AGN contribution from SF, we hypothesize that there exists a brightness temperature cut-off point separating pure AGN from SF. We present a multiresolution (10–100 mas) view of the transition between compact AGN and diffuse SF through a deep wide-field EVN + e-MERLIN, multiple phase centre survey of the centre of the Northern SPARCS (SLOAN) reference field at 1.6 GHz. This is the first (and only) VLBI (+ e-MERLIN) milliarcsecond angular resolution observation of this field, and of the wider SPARCS reference field programme. Using these high spatial resolution (9 pc–0.3 kpc at z ∼ 1.25) data, 11 milliarcsec-scale sources are detected from a targeted sample of 52 known radio sources from previous observations with the e-MERLIN, giving a VLBI detection fraction of $\sim 21{{\ \rm per\ cent}}$. At spatial scales of $\sim 9\,$pc, these sources show little to no jet structure whilst at $\sim 0.3\,$kpc one-sided and two-sided radio jets begin to emerge on the same sources, indicating a possible transition from pure AGN emissions to AGN and SF systems.

A molecular absorption line survey towards the AGN of Hydra-A

ABSTRACT We present Atacama Large Millimetre/submillimetre Array observations of the brightest cluster galaxy Hydra-A, a nearby (z = 0.054) giant elliptical galaxy with powerful and extended radio jets. The observations reveal CO(1−0), CO(2–1), 13CO(2–1), CN(2–1), SiO(5–4), HCO+(1–0), HCO+(2–1), HCN(1–0), HCN(2–1), HNC(1–0), and H2CO(3–2) absorption lines against the galaxy’s bright and compact active galactic nucleus. These absorption features are due to at least 12 individual molecular clouds that lie close to the centre of the galaxy and have velocities of approximately −50 to +10 km s−1 relative to its recession velocity, where positive values correspond to inward motion. The absorption profiles are evidence of a clumpy interstellar medium within brightest cluster galaxies composed of clouds with similar column densities, velocity dispersions, and excitation temperatures to those found at radii of several kpc in the Milky Way. We also show potential variation in a ∼10 km s−1 wide section of the absorption profile over a 2 yr time-scale, most likely caused by relativistic motions in the hot spots of the continuum source that change the background illumination of the absorbing clouds.

H i absorption towards radio active galactic nuclei of different accretion modes

ABSTRACT We present results of H i absorption experiment done using the Giant Metrewave Radio Telescope (GMRT) towards 27 low- and intermediate-luminosity ($P_{\rm 1.4 GHz}\, \sim 10^{23}$-1026 W Hz−1) radio active galactic nuclei (AGNs), classified as either low excitation radio galaxies (LERGs) or high excitation radio galaxies (HERGs) and with WISE colour W2[4.6 μm]−W3[12 μm]&amp;gt; 2. We report H i absorption detection towards seven radio AGNs, six of which are new. Combined with other sources from literature classified as LERGs or HERGs, we confirm our earlier result that compact radio AGNs with WISE colour W2−W3 &amp;gt; 2 have higher detection rates compared to those with W2−W3 &amp;lt; 2. We find that H i absorption detection rate is higher for HERGs (37.0$^{+15.8}_{-11.5}$ per cent) compared to LERGs (22.0$^{+3.9}_{-3.4}$ per cent), mainly due to a larger fraction of HERGs being gas and dust rich with a younger stellar population compared to LERGs. However, for similar compact radio structures and host galaxies with WISE colours W2−W3 &amp;gt; 2, we don’t find any significant difference in detection rates of two types of AGNs implying detection of H i gas may not necessarily mean high excitation mode AGN. We further analysed the kinematics towards these sources. We find that while LERGs show a wide range in the shift of centroid velocities ($\sim \, -$479 to +356 km s−1) relative to the optical systemic velocity, most of the HERGs have centroid velocity shift less than 200 km s−1, possibly due to differences in jet-interstellar medium interaction.

WISE mid-infrared properties of compact active galactic nuclei selected from the high radio frequency AT20G survey

ABSTRACT Past studies of compact active galactic nuclei (AGNs), the dominant population at high radio frequencies, selected them using flat spectral index criteria. This biases the sample due to the steepening of AGN spectra at high radio frequencies. We improve upon this by selecting 3610 compact AGNs using their angular size information ($\lesssim$0.15 arcsec scale) from the Australia Telescope 20 GHz (AT20G) high-angular resolution catalogue. We cross-match these against the Wide-field Infrared Survey Explorer AllWISE catalogue and present a catalogue with 3300 (91 per cent) matches, 91 (3 per cent) rejects, and 219 (6 per cent) non-detections that are excellent high-redshift candidates. Of the matched compact AGNs, 92 per cent exhibit QSO mid-infrared colours (W1−W2 &amp;gt; 0.5). Therefore, our sample of high frequency compact sources has a very high rate of identification with mid-infrared QSOs. We find counterparts for 88 per cent of 387 compact steep-spectrum (CSS) sources in the AT20G survey, 82 ± 5 per cent of which exhibit QSO mid-infrared colours and have moderate redshifts (zmedian = 0.82), while those dominated by host galaxy colours in mid-infrared have lower redshifts (zmedian = 0.13). The latter classified into late- and early-type galaxies using their mid-infrared colours shows a majority (68 ± 4 per cent) have colours characteristic of late-type galaxies. Thus, we find that a larger fraction of these CSS sources are embedded in hosts with higher gas densities than average early-type galaxies. We compare mid-infrared colours of our AGNs against those reported for AGNs primarily selected using non-radio techniques. This shows that mid-infrared SED of high frequency selected compact radio AGN is comparatively less red, possibly due to contributions from their hosts.

Unveiling Sizes of Compact AGN Hosts with ALMA

Abstract We present rest-frame far-infrared (FIR) and optical size measurements of active galactic nucleus (AGN) hosts and star-forming galaxies (SFGs) in the COSMOS field, enabled by high-resolution Atacama Large Millimeter/submillimeter Array (ALMA)/1 mm (0.″1–0.″4) and Hubble Space Telescope (HST)/F814W imaging (∼0.″1). Our sample includes 27 galaxies at z &lt; 2.5, classified as infrared-selected AGN (three sources), X-ray selected AGN (four sources), and non-AGN SFGs (20 sources), for which high-resolution Band 6/7 ALMA images are available at 1 mm from our own observing program as well as archival observations. The sizes and star formation rate surface densities measured from both ALMA/1 mm and HST/F814W images show that obscured AGN host galaxies are more compact than non-AGN SFGs at similar redshift and stellar mass. This result suggests that the obscured accretion phase may be related to galaxies experiencing a compaction of their gaseous component, which could be associated with enhanced central star formation before a subsequent quenching driving the formation of compact passive galaxies. Moreover, most of the detected and stacked rest-frame FIR sizes of AGNs in our sample are similar or more compact than their rest-frame optical sizes, which is consistent with recent results of ALMA-detected sources. This might be explained by the fact that the dusty starbursts take place in the compact regions, and suggests that the star formation mechanisms in the compact regions of AGN hosts are similar to those observed in SFGs observed with ALMA.

Multifrequency Study of GHz-peaked Spectrum Sources

Gigahertz-Peaked spectrum (GPS) sources are compact active galactic nuclei, presumably young precursors of bright radio sources. The study of GPS radio properties provides information about the features of synchrotron radiation in extragalactic sources. Also in applied research GPS sources are useful as compact stationary radio sources in the sky for astrometric purposes. This paper presents the results of a multifrequency GPS study based on quasi-simultaneous measurements with the RATAN-600 radio telescope during the 2006-2017. The catalog containing spectral flux densities measured at six frequencies (1.1, 2.3, 4.8, 7.7/8.2, 11.2, and 21.7 GHz) have been obtained. In addition, for the analysis of radio spectra, data from the following low-frequency surveys have been used: GLEAM (GaLactic and Extragalactic All-sky Murchison widefield array survey) and TGSS (Tata institute for fundamental research GMRT Sky Survey) and high-frequency measurements from Planck survey. A total number of 164 GPS and candidates to GPS have been identified (17 of them are new discoveries), which makes up a small fraction of GPS in the initial sample of bright AGNs, about 2%. The physical properties and formation conditions of synchrotron radiation is found to be quite different in GPS of different AGN types. The deficit of distant GPS ($z > 2$) with low maximum frequencies (less than 1 GHz) is confirmed. The existing 'size - peak frequency' anticorrelation is continuous. The continuum radio spectra are found to become statistically steeper with increasing redshift.

General-relativistic rotation: Self-gravitating fluid tori in motion around black holes

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spin-less black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or modelling of compact active galactic nuclei.

Probing the Large Faraday Rotation Measure Environment of Compact Active Galactic Nuclei

Knowing how the ambient medium in the vicinity of active galactic nuclei (AGNs) is shaped is crucial to understanding generally the evolution of such cosmic giants as well as AGN jet formation and launching. Thanks to the new broadband capability now available at the Jansky Very Large Array (JVLA), we can study changes in polarization properties, fractional polarization, and polarization angles, together with the total intensity spectra of a sample of 14 AGNs, within a frequency range from 1 to 12 GHz. Depolarization modeling has been performed by means of so-called “qu-fitting” to the polarized data, and a synchrotron self absorption model has been used for fitting to the total intensity data. We found complex behavior both in the polarization spectra and in the total intensity spectra, and several Faraday components with a large rotation measure (RM) and several synchrotron components were needed to represent these spectra. Here, results for three targets are shown. This new method of analyzing broadband polarization data through qu-fitting successfully maps the complex surroundings of unresolved objects.

Local Swift-BAT active galactic nuclei prefer circumnuclear star formation

We use Herschel data to analyze the size of the far-infrared 70 μm emission for z &lt; 0.06 local samples of 277 hosts of Swift-BAT selected active galactic nuclei (AGN), and 515 comparison galaxies that are not detected by BAT. For modest far-infrared luminosities 8.5 &lt;log (LFIR [L⊙]) &lt; 10.5, we find large scatter of half light radii Re,70 for both populations, but a typical Re,70≲ 1 kpc for the BAT hosts that is only half that of comparison galaxies of same far-infrared luminosity. The result mostly reflects a more compact distribution of star formation (and hence gas) in the AGN hosts, but compact AGN heated dust may contribute in some extremely AGN dominated systems. Our findings are in support of an AGN-host coevolution where accretion onto the central black hole and star formation are fed from the same gas reservoir, with more efficient black hole feeding if that reservoir is more concentrated. The significant scatter in the far-infrared sizes emphasizes that we are mostly probing spatial scales much larger than those of actual accretion, and that rapid accretion variations can smear the distinction between the AGN and comparison categories. Large samples are hence needed to detect structural differences that favor feeding of the black hole. No size difference between AGN host and comparison galaxies is observed at higher far-infrared luminosities log(LFIR [L⊙]) &gt; 10.5 (star formation rates ≳6 M⊙ yr-1), possibly because these are typically reached in more compact regions.

INTERSTELLAR SCINTILLATION AND THE RADIO COUNTERPART OF THE FAST RADIO BURST FRB 150418

ABSTRACT Keane et al. have recently reported the discovery of a new fast radio burst (FRB), FRB 150418, with a promising radio counterpart at 5.5 and 7.5 GHz—a rapidly decaying source, falling from 200–300 μJy to 100 μJy on timescales of ∼6 days. This transient source may be associated with an elliptical galaxy at redshift z = 0.492, providing the first firm spectroscopic redshift for an FRB and the ability to estimate the density of baryons in the intergalactic medium via the combination of known redshift and radio dispersion of the FRB. An alternative explanation, first suggested by Williams &amp; Berger, is that the identified counterpart may instead be a compact active galactic nucleus (AGN). The putative counterpart’s variation may then instead be extrinsic, caused by refractive scintillation in the ionized interstellar medium of the Milky Way, which would invalidate the association with FRB 150418. We examine this latter explanation in detail and show that the reported observations are consistent with scintillating radio emission from the core of a radio-loud AGN having a brightness temperature T b ≳ 109 K. Using numerical simulations of the expected scattering for the line of sight to FRB 150418, we provide example images and light curves of such an AGN at 5.5 and 7.5 GHz. These results can be compared with continued radio monitoring to conclusively determine the importance of scintillation for the observed radio variability, and they show that scintillation is a critical consideration for continued searches for FRB counterparts at radio wavelengths.

Dichotomy in the population of young AGN: Optical, radio, and X‐ray properties

AbstractThere are numerous examples of radio sources with various sizes which surprisingly exhibit very similar morphology. This observational fact helped to create a standard evolutionary model in which young and small radio‐loud active galactic nuclei (AGN), called gigahertz‐peaked spectrum (GPS) sources and compact steep spectrum (CSS) sources, become largescale radio objects. However, many details of this evolutionary process are still unclear. We explored evolution scenarios of radio‐loud AGN using new radio, optical and X‐ray data of so far unstudied low luminosity compact (LLC) sources and we summarize the results in this paper. Our studies show that the evolutionary track is very “individualized” although we can mention common factors affecting it. These are interaction with the ambient medium and AGN power. The second feature affects the production of the radio jets which, if they are weak, are more vulnerable for instabilities and disruption. Thus not all GPS and CSS sources will be able to develop large scale morphologies. Many will fade away being middleaged (105 yr). It seems that only radio strong, high excitation compact AGN can be progenitors of large‐scale FRII radio sources. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Finding binary active galactic nuclei by the centroid shift in imaging surveys

The census of binary active galactic nuclei (AGNs) is important in order to understand the merging history of galaxies and the triggering of AGNs. However, there is still no efficient method for selecting the candidates of binary AGNs. The non-synchronous variations of the two AGNs in one binary system will induce the shift of the image centroid. Since the astrometric error is normally much smaller than the angular resolution of telescopes, it is possible to detect such shifts even in the unresolved system via multi-epoch observations. We perform some simulations and find that hundreds of observations are required to discover compact binary AGNs. This method is suitable for the future large-scale surveys, e.g., the Large Synoptic Survey Telescope, and it might lead to a large sample of binary AGNs with a 1-2 yr survey.

The most compact bright radio-loud AGN—I. A new target sample selected for the space VLBI

We investigated the archival ground-based VLBI images of the extragalactic radio sources included in both the {\it Wilkinson Microwave Anisotropy Probe (WMAP)} and the {\it Planck} catalogues, and selected 49 bright and compact sources as potential targets for space Very Long Baseline Interferometry (VLBI) observations at mm wavelengths. These sources have a flat radio continuum spectrum between 33 and 94~GHz. They are identified as core-dominated active galactic nuclei (AGN), located at declinations above $-40\degr$, and have never been observed with ground-based VLBI at 86~GHz. The radio properties of the 49 new sources are presented. We compare this new sample with similar samples of compact AGN available from earlier studies. The new candidates, together with the existing bright compact AGN sample identified from 86-GHz ground-based VLBI imaging surveys, form a catalogue of more than 160 AGN. These could be primary targets for mm-VLBI observations on the ground, as well as for future mm-wavelength space VLBI missions such as the project with two satellites currently under study in China.

The AT20G high-angular-resolution catalogue

We present the high angular resolution catalogue for the Australia Telescope 20 GHz (AT20G) survey, using the high angular resolution 6-km antenna data at the baselines of ~ 4500 m of the Australia Telescope Compact Array (ATCA). We have used the data to produce the visibility catalogue that separates the compact Active Galactic Nuclei (AGNs) from the extended radio sources at the 0.15 arcsec angular scale, corresponding to the linear size scale of 1 kpc at redshifts higher than 0.7. We find the radio population at 20 GHz to be dominated by compact AGNs constituting 77% of the total sources in the AT20G. We introduce the visibility-spectra diagnostic plot, produced using the AT20G cross-matches with lower frequency radio surveys at 1 GHz (the NRAO-VLA Sky Survey (NVSS) and the Sydney University Molonglo Sky Survey (SUMSS)), that separates the 20 GHz population into distinct sub-populations of the compact AGNs, the compact steep-spectrum sources, the extended AGN-powered sources and extended flat-spectrum sources. The extended flat-spectrum sources include a local thermal emitting population of high latitude planetary nebulae and also gravitational lens and binary black hole candidates among the AGNs. We find a smooth transition in properties between the compact CSS sources and the AGN populations. The visibility catalogue, together with the main AT20G survey, provides an estimate of angular size scales for sources in the AT20G and an estimate of the flux arising from central cores of extended radio sources. The identification of the compact AGNs in the AT20G survey provides high quality calibrators for high frequency radio telescope arrays and VLBI observations.

HOW TO MONITOR AGN INTRA-DAY VARIABILITY AT 230GHZ

We probe the feasibility of high-frequency radio observations of very rapid flux variations in compact active galactic nuclei (AGN). Our study assumes observations at 230GHz with a small 6-meter class observatory, using the SNU Radio Astronomical Observatory (SRAO) as an example. We find that 33 radio-bright sources are observable with signal-to-noise ratios larger than ten. We derive statistical detection limits via exhaustive Monte Carlo simulations assuming (a) periodic, and (b) episodic flaring flux variations on time-scales as small as tens of minutes. We conclude that a wide range of flux variations is observable. This makes high-frequency radio observations – even with small observatories – a powerful probe of AGN intra-day variability; especially, those which complement observations at lower radio frequencies with larger observatories like the Korean VLBI Network (KVN).

Optical-radio positional offsets for active galactic nuclei

Context. It will soon become possible to directly link the most accurate radio reference frame with the Gaia optical reference frame using many common extragalactic objects. It is important to know the level of coincidence between the radio and optical positions of compact active galactic nuclei (AGN). Aims. Using the best catalogues available at present, we investigate how many AGN with significantly large optical-radio positional offsets exist as well as the possible causes of these offsets. Methods. We performed a case study by finding optical counterparts to the International Celestial Reference Frame (ICRF2) radio sources in the Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9). The ICRF2 catalogue was used as a reference because the radio positions determined by Very Long Baseline Interferometry (VLBI) observations are about two orders of magnitude more accurate than the optical positions. Results. We find 1297 objects in common for ICRF2 and SDSS DR9. Statistical analysis of the optical-radio differences verifies that the SDSS DR9 positions are accurate to ~55 mas in both coordinates, with no systematic offset with respect to ICRF2. We find 51 sources (~4% of the sample) for which the positional offset exceeds 170 mas (~3{\sigma}). Astrophysical explanations must exist for most of these outliers. There are 3 known strong gravitational lenses among them. Dual AGN or recoiling supermassive black holes may also be possible. Conclusions. The most accurate Gaia-VLBI reference frame link will require a careful selection of a common set of objects by eliminating the outliers. On the other hand, the significant optical-radio positional non-coincidences may offer a new tool for finding e.g. gravitational lenses or dual AGN candidates. Detailed follow-up radio interferometric and optical spectroscopic observations are encouraged to investigate the outlier sources found in this study.

WHY DO COMPACT ACTIVE GALACTIC NUCLEI AT HIGH REDSHIFT SCINTILLATE LESS?

The fraction of compact active galactic nuclei (AGNs) that exhibit interstellar scintillation (ISS) at radio wavelengths, as well as their scintillation amplitudes, have been found to decrease significantly for sources at redshifts z > 2. This can be attributed to an increase in the angular sizes of the \muas-scale cores or a decrease in the flux densities of the compact \muas cores relative to that of the mas-scale components with increasing redshift, possibly arising from (1) the space-time curvature of an expanding Universe, (2) AGN evolution, (3) source selection biases, (4) scatter broadening in the ionized intergalactic medium (IGM) and intervening galaxies, or (5) gravitational lensing. We examine the frequency scaling of this redshift dependence of ISS to determine its origin, using data from a dual-frequency survey of ISS of 128 sources at 0 < z < 4. We present a novel method of analysis which accounts for selection effects in the source sample. We determine that the redshift dependence of ISS is partially linked to the steepening of source spectral indices ({\alpha}^8.4_4.9) with redshift, caused either by selection biases or AGN evolution, coupled with weaker ISS in the {\alpha}^8.4_4.9 < -0.4 sources. Selecting only the -0.4 < {\alpha}^8.4_4.9 < 0.4 sources, we find that the redshift dependence of ISS is still significant, but is not significantly steeper than the expected (1+z)^0.5 scaling of source angular sizes due to cosmological expansion for a brightness temperature and flux-limited sample of sources. We find no significant evidence for scatter broadening in the IGM, ruling it out as the main cause of the redshift dependence of ISS. We obtain an upper limit to IGM scatter broadening of < 110\muas at 4.9 GHz with 99% confidence for all lines of sight, and as low as < 8\muas for sight-lines to the most compact, \sim 10\muas sources.

Spectral properties and the effect on redshift cut-off of compact active galactic nuclei from the AT20G survey

We use high angular resolution data, measured from visibility of sources at the longest baseline of 4500 m of the Australia Telescope Compact Array (ATCA), for the Australia Telescope 20 GHz (AT20G) survey to obtain angular size information for > 94% of AT20G sources. We confirm the previous AT20G result that due to the high survey frequency of 20 GHz, the source population is strongly dominated by compact sources (79%). At 0.15 arcseconds angular resolution limit, we show a very strong correlation between the compact and extended sources with flat and steep-spectrum sources respectively. Thus, we provide a firm physical basis for the traditional spectral classification into flat and steep-spectrum sources to separate compact and extended sources. We find the cut-off of -0.46 to be optimum for spectral indices between 1 and 5 GHz and, hence, recommend the continued use of -0.5 for future studies. We study the effect of spectral curvature on redshift cut-off of compact AGNs using recently published redshift data. Using spectral indices at different frequencies, we correct for the redshift effect and produce restframe frequency spectra for compact sources for redshift up to ~5. We show that the flat spectra of most compact sources start to steepen at ~30 GHz. At higher frequencies, the spectra of both populations are steep so the use of spectral index does not separate the compact and extended source populations as well as in lower frequencies. We find that due to the spectral steepening, surveys of compact sources at higher frequencies (>5 GHz) will have redshift cut-off due to spectral curvature but at lower frequencies, the surveys are not significantly affected by spectral curvature, thus, the evidence for a strong redshift cut-off in AGNs found in lower frequency surveys is a real cut-off and not a result of K-correction.

MEM and CLEAN Imaging of VLBA Polarisation Observations of Compact Active Galactic Nuclei

The Maximum Entropy Method (MEM) for the deconvolution of radio interferometry images is mathematically well based and presents a number of advantages over the usual CLEAN deconvolution, such as appreciably higher resolution. The application of MEM for polarisation imaging remains relatively little studied. CLEAN and MEM intensity and polarisation techniques are discussed in application to recently obtained 18cm VLBA polarisation data for a sample of Active Galactic Nuclei.