Merger History Research Articles

Effects of environment on sSFR profiles of late-type galaxies in the CALIFA survey

Aims. We explore the effects of environment on star formation in late-type galaxies by studying the dependence of the radial profiles of specific star formation rate (sSFR) on environment and the stellar mass, using a sample of 275 late-type galaxies drawn from the CALIFA survey. Methods. We consider three different discrete environments: field galaxies, galaxies in pairs, and galaxies in groups, with stellar masses 9 ≤ log(M⋆/M⊙) ≤ 12, and compare their sSFR profiles across the environments. Results. Our results suggest that the stellar mass is the main factor determining the sSFR profiles of late-type galaxies; the influence of AGNs and bars are secondary. We find that the relative size of the bulge plays a key role in depressing star formation towards the center of late-type galaxies. The group environment determines clear differences in the sSFR profiles of galaxies. We find evidence of an outside-in action upon galaxies with stellar masses 9 ≤ log(M⋆/M⊙) ≤ 10 in groups. We find a much stronger suppression of star formation in the inner regions of massive galaxies in groups, which may be an indication of a different merger history.

Studying dynamical models of the core galaxy NGC 1399 with merging remnants

An investigation on the possible dynamical models of the core galaxy NGC 1399 is performed. Because early-type galaxies are likely to be formed through merging events, remnant rings are considered in the modeling process. A numerical survey over three parameters is employed to obtain the best-fit models that are completely consistent with observations. It is found that the inner slope of the dark matter profile is cuspy for this core galaxy. The existence of remnant rings in best-fit models indicates a merging history. The remnant ring explains the flattened surface brightness and thus could be the physical counterpart of the core structure of NGC 1399.

Identification of low surface brightness tidal features in galaxies using convolutional neural networks

Faint tidal features around galaxies record their merger and interaction histories over cosmic time. Due to their low surface brightnesses and complex morphologies, existing automated methods struggle to detect such features and most work to date has heavily relied on visual inspection. This presents a major obstacle to quantitative study of tidal debris features in large statistical samples, and hence the ability to be able to use these features to advance understanding of the galaxy population as a whole. This paper uses convolutional neural networks (CNNs) with dropout and augmentation to identify galaxies in the CFHTLS-Wide Survey that have faint tidal features. Evaluating the performance of the CNNs against previously-published expert visual classifications, we find that our method achieves high (76%) completeness and low (20%) contamination, and also performs considerably better than other automated methods recently applied in the literature. We argue that CNNs offer a promising approach to effective automatic identification of low surface brightness tidal debris features in and around galaxies. When applied to forthcoming deep wide-field imaging surveys (e.g. LSST, Euclid), CNNs have the potential to provide a several order-of-magnitude increase in the sample size of morphologically-perturbed galaxies and thereby facilitate a much-anticipated revolution in terms of quantitative low surface brightness science.

The infrared-luminous progenitors of high-zquasars

Here we explore the infrared (IR) properties of the progenitors of high-z quasar host galaxies. Adopting the cosmological, data constrained semi-analytic model GAMETE/QSOdust, we simulate several independent merger histories of a luminous quasar at z ~ 6, following black hole growth and baryonic evolution in all its progenitor galaxies. We find that a fraction of progenitor galaxies (about 0.4 objects per single luminous quasar) at 6.5 < z < 8 has an IR luminosity of L_IR > 10^13 Lsun (hyper-luminous IR galaxies; HyLIRGs). HyLIRGs progenitors reside in the most massive halos, with dark matter (DM) masses of M_DM ~ 10^12.5 - 10^13 Msun. These systems can be easily observed in their ~ 1 mm-continuum emission in a few seconds of integration time with the Atacama Large Millimeter/submillimeter Array (ALMA), and at least 40% of them host nuclear BH activity that is potentially observable in the soft and hard X-ray band. Our findings are in line with recent observations of exceptional massive DM halos hosting HyLIRGs at z ~ 7, suggesting that z ~ 6 luminous quasars are indeed the signposts of these observed rare peaks in the high-z cosmic density field, and that massive IR-luminous galaxies at higher z are their natural ancestors.

The Complementary Roles of Feedback and Mergers in Building the Gaseous Halo and the X-Ray Corona of Milky-Way-sized Galaxies

Abstract We use high-resolution cosmological hydrodynamical simulations of Milky-Way-sized galaxies with varying supernova feedback strengths and merger histories to investigate the formation of their gaseous halos and especially their hot (&gt;106 K) X-ray-luminous coronae. Our simulations predict the presence of significant hot gas in the halos as early as z = 3–4, well before the halos ought to be able to sustain hot mode accretion in the conventional picture. The nascent coronae grow inside-out and initially do so primarily as a result of outflows from the central galaxies powered by merger-induced shock heating and strong supernova feedback, both of which are elemental features of today’s successful galaxy formation models. Furthermore, the outflows and the forming coronae also accelerate the transition from cold to hot mode accretion by contributing to the conditions for sustaining stable accretion shocks. They also disrupt the filamentary streams funneling cold gas onto the central galaxies by causing their mouths to fray into a broad delta, detach from the galaxies, and be pushed away to larger radii. And even though at early times the filaments repeatedly re-form, the hot gas and the outflows act to weaken the filaments and accelerate their ultimate disruption. Although galactic outflows are generally thought of as ejective feedback, we find that their action on the filaments suggests a preventive role as well.

Galaxy and Mass Assembly (GAMA): Accurate number densities and environments of massive ultra-compact galaxies at 0.02 &lt; z &lt; 0.3

Context. Massive ultra-compact galaxies (MUGs) are common at z = 2−3, but very rare in the nearby Universe. Simulations predict that the few surviving MUGs should reside in galaxy clusters, whose large relative velocities prevent them from merging, thus maintaining their original properties (namely stellar populations, masses, sizes and dynamical state). Aims. Our goal is to obtain a complete census of the MUG population at 0.02 &lt; z &lt; 0.3, determining the number density, population properties and environment. Methods. We have taken advantage of the high-completeness, large-area spectroscopic GAMA survey, complementing it with deeper imaging from the KiDS and VIKING surveys. We find a set of 22 bona-fide MUGs, defined as having high stellar mass (&gt; 8 × 1010 M⊙) and compact size (Re &lt; 2 kpc). An additional set of seven lower-mass objects (6 × 1010 &lt; M⋆/M⊙ &lt; 8 × 1010) are also potential candidates according to typical mass uncertainties. Results. The comoving number density of MUGs at low redshift (z &lt; 0.3) is constrained at (1.0 ± 0.4)×10−6 Mpc−3, consistent with galaxy evolution models. However, we find a mixed distribution of old and young galaxies, with a quarter of the sample representing (old) relics. MUGs have a predominantly early or swollen disk morphology (Sérsic index 1 &lt; n &lt; 2.5) with high stellar surface densities (⟨Σe⟩∼1010 M⊙ Kpc−2). Interestingly, a large fraction feature close companions – at least in projection – suggesting that many (but not all) reside in the central regions of groups. Halo masses show these galaxies inhabit average-mass groups. Conclusions. As MUGs are found to be almost equally distributed among environments of different masses, their relative fraction is higher in more massive overdensities, matching the expectations that some of these galaxies fell in these regions at early times. However, there must be another channel leading some of these galaxies to an abnormally low merger history because our sample shows a number of objects that do not inhabit particularly dense environments.

Gas accretion in Milky Way-like galaxies: temporal and radial dependencies

One of the fundamental assumptions of chemical evolution models (CEMs) of the Milky Way (MW) and other spirals is that higher gas accretion rates are expected in the past, and in the inner regions of the Galaxy. This leads to the so-called `inside-out disc formation scenario'. Yet, these are probably the most unconstrained inputs of such models. In the present paper, we aim at investigating these main assumptions by studying how gas is accreted in four simulated MW-like galaxies assembled within the $\Lambda$CDM scenario. The galaxies were obtained using two different simulation techniques, cosmological setups and initial conditions. Two of them are MW candidates corresponding to the chemodynamical model of Minchev et al. (2013, 2014) (known as MCM) and the Local Group cosmological simulation of Nuza et al. (2014). We investigate vertical and radial gas accretion on to galaxy discs as a function of cosmic time and disc radius. We find that accretion in the MW-like galaxies seem to happen in two distinct phases, namely: an early, more violent period; followed by a subsequent, slowly declining phase. Our simulations seem to give support to the assumption that the amount of gas incorporated into the MW disc exponentially decreases with time, leading to current net accretion rates of $0.6-1\,$M$_\odot\,$yr$^{-1}$. In particular, accretion timescales on to the simulated thin-disc-like structures are within $\sim5-7\,$Gyr, consistent with expectations from CEMs. Moreover, our simulated MW discs are assembled from the inside-out with gas in the inner disc regions accreted in shorter timescales than in external ones, in qualitative agreement with CEMs of the Galaxy. However, this type of growth is not general to all galaxies and it is intimately linked to their particular merger and gas accretion history.

The oxygen abundance gradients in the gas discs of galaxies in the EAGLE simulation

We use the EAGLE simulations to study the oxygen abundance gradients of gas discs in galaxies within the stellar mass range [10^9.5, 10^10.8]Mo at z=0. The estimated median oxygen gradient is -0.011 (0.002) dex kpc^-1, which is shallower than observed. No clear trend between simulated disc oxygen gradient and galaxy stellar mass is found when all galaxies are considered. However, the oxygen gradient shows a clear correlation with gas disc size so that shallower abundance slopes are found for increasing gas disc sizes. Positive oxygen gradients are detected for ~40 per cent of the analysed gas discs, with a slight higher frequency in low mass galaxies. Galaxies that have quiet merger histories show a positive correlation between oxygen gradient and stellar mass, so that more massive galaxies tend to have shallower metallicity gradients. At high stellar mass, there is a larger fraction of rotational-dominated galaxies in low density regions. At low stellar mass, non-merger galaxies show a large variety of oxygen gradients and morphologies. The normalization of the disc oxygen gradients in non-merger galaxies by the effective radius removes the trend with stellar mass. Conversely, galaxies that experienced mergers show a weak relation between oxygen gradient and stellar mass. Additionally, the analysed EAGLE discs show no clear dependence of the oxygen gradients on local environment, in agreement with current observational findings.

Multimessenger Signatures of Massive Black Holes in Dwarf Galaxies

Recent discoveries of massive black holes (MBHs) in dwarf galaxies suggest that they may have a more common presence than once thought. Systematic searches are revealing more candidates, but this process could be accelerated by predictions from simulations. We perform a study of several high-resolution, cosmological, zoom-in simulations focusing on dwarf galaxies that host massive black holes at z = 0, with the aim of determining when the black holes are most observable. Larger dwarf galaxies are more likely to host MBHs than those of lower mass. About 50% of the MBHs in dwarfs are not centrally located, but rather are wandering within a few kpc of the galaxy center. The accretion luminosities of MBHs in dwarfs are low throughout cosmic time, rendering them extremely difficult to detect. However, the merger history of these MBHs is optimal for gravitational wave detection by LISA.

Proving the short-wavelength approximation in Pulsar Timing Array gravitational-wave background searches

A low-frequency gravitational-wave background (GWB) from the cosmic merger history of supermassive black holes is expected to be detected in the next few years by pulsar timing arrays. A GWB induces distinctive correlations in the pulsar residuals—the expected arrival time of the pulse less its actual arrival time. Simplifying assumptions are made in order to write an analytic expression for this correlation function, called the Hellings and Downs curve for an isotropic GWB, which depends on the angular separation of the pulsar pairs, the gravitational-wave frequency considered, and the distance to the pulsars. This is called the short-wavelength approximation, which we prove here rigorously and analytically for the first time.

The origin of the diverse morphologies and kinematics of Milky Way-mass galaxies in the FIRE-2 simulations.

We use hydrodynamic cosmological zoom-in simulations from the Feedback in Realistic Environments project to explore the morphologies and kinematics of 15 Milky Way (MW)-mass galaxies. Our sample ranges from compact, bulge-dominated systems with 90 per cent of their stellar mass within 2.5 kpc to well-ordered discs that reach ≳15 kpc. The gas in our galaxies always forms a thin, rotation-supported disc at z = 0, with sizes primarily determined by the gas mass. For stars, we quantify kinematics and morphology both via the fraction of stars on disc-like orbits and with the radial extent of the stellar disc. In this mass range, stellar morphology and kinematics are poorly correlated with the properties of the halo available from dark matter-only simulations (halo merger history, spin, or formation time). They more strongly correlate with the gaseous histories of the galaxies: those that maintain a high gas mass in the disc after z ~ 1 develop well-ordered stellar discs. The best predictor of morphology we identify is the spin of the gas in the halo at the time the galaxy formed 1/2 of its stars (i.e. the gas that builds the galaxy). High-z mergers, before a hot halo emerges, produce some of the most massive bulges in the sample (from compact discs in gas-rich mergers), while later-forming bulges typically originate from internal processes, as satellites are stripped of gas before the galaxies merge. Moreover, most stars in z = 0 MW-mass galaxies (even z = 0 bulge stars) form in a disc: ≳60-90 per cent of stars begin their lives rotationally supported.

Andromeda’s violent past

The Andromeda galaxy’s stellar halo and disk show signs of an active recent merger history. Recent work suggests that most of the disturbances in Andromeda’s disk and the inner halo may be due to a single merger event.

Merger History of Central Galaxies in Semi-analytic Models of Galaxy Formation

Abstract We investigate the dynamical evolution of galaxies in groups with different formation epochs. Galaxy groups have been selected to be in different dynamical states, namely dynamically old and dynamically young, which reflect their early and late formation times, respectively, based on their halo mass assembly. The brightest galaxies in dynamically young groups have suffered their last major galaxy merger typically ∼2 Gyr more recently than their counterparts in dynamically old groups. Furthermore, we study the evolution of velocity dispersion in these two classes and compare them with the analytic models of isolated halos. The velocity dispersion of dwarf galaxies in high-mass, dynamically young groups increases slowly in time, while the analogous dispersion in dynamically old, high-mass groups is constant. In contrast, the velocity dispersion of giant galaxies in low-mass groups decreases rapidly at late times. This increasing velocity bias is caused by dynamical friction, and starts much earlier in the dynamically old groups. The recent Radio-SAGE model of galaxy formation suggests that radio luminosities of central galaxies, considered to be tracers of AGN activity, are enhanced in halos that assembled more recently, independent of the time since the last major merger.

Massive black hole and Population III galaxy formation in overmassive dark-matter haloes with violent merger histories

We propose the formation of massive pristine dark-matter (DM) halos with masses of $\sim 10^8~M_\odot$, due to the dynamical effects of frequent mergers in rare regions of the Universe with high baryonic streaming velocity relative to DM. Since the streaming motion prevents gas collapse into DM halos and delays prior star formation episodes, the gas remains metal-free until the halo virial temperatures $\gtrsim 2\times 10^4~{\rm K}$. The minimum cooling mass of DM halos is boosted by a factor of $\sim 10-30$ because frequent major mergers of halos further inhibit gas collapse. We use Monte Carlo merger trees to simulate the DM assembly history under a streaming velocity of twice the root-mean-square value, and estimate the number density of massive DM halos containing pristine gas as $\simeq 10^{-4}~{\rm cMpc}^{-3}$. When the gas infall begins, efficient Ly$\alpha$ cooling drives cold streams penetrating inside the halo and feeding a central galactic disk. When one stream collides with the disk, strong shock forms a dense and hot gas cloud, where the gas never forms H$_2$ molecules due to effective collisional dissociation. As a result, a massive gas cloud forms by gravitational instability and collapses directly into a massive black hole (BH) with $M_\bullet \sim 10^5~M_\odot$. Almost simultaneously, a galaxy with $M_{\star, \rm tot}\sim 10^6~M_\odot$ composed of Population III stars forms in the nuclear region. If the typical stellar mass is as high as $\sim 100~M_\odot$, the galaxy could be detected with the James Webb Space Telescope even at $z\gtrsim 15$. These massive seed BHs would be fed by continuous gas accretion from the host galaxy, and grow to be bright quasars observed at $z\gtrsim 6$.

Exploring the astrophysics of dark atoms

A component of the dark matter could consist of two darkly charged particles with a large mass ratio and a massless force carrier. This `atomic' dark sector could behave much like the baryonic sector, cooling and fragmenting down to stellar-mass or smaller scales. Past studies have shown that cosmic microwave background and large-scale structure constraints rule out $\gtrsim 5\%$ of the dark matter to behave in this manner. However, we show that, even with percent level mass fractions, a dark atomic sector could affect some extragalactic and galactic observables. We track the cooling and merger history of an atomic dark component for much of the interesting parameter space. Unlike the baryons, where stellar feedback (driven by nuclear physics) delays the formation and growth of galaxies, cooling dark atomic gas typically results in disks forming earlier, leaving more time for their destruction via mergers. Rather than disks in Milky Way sized halos, we find the end product is typically spheroidal structures on galactic scales or dark atom fragments distributed on halo scales. This result contrasts with previous studies, which had assumed that the dark atoms would result in dark disks. Furthermore the dark atoms condense into dense clumps, analogous to how the baryons fragment on solar-mass scales. We estimate the size of these dark clumps, and use these estimates to show that viable atomic dark matter parameter space is ruled out by stellar microlensing, by the half-light radii of ultra-faint dwarf galaxies, and by Milky Way mass-to-light inferences.

No assembly required: mergers are mostly irrelevant for the growth of low-mass dwarf galaxies

We investigate the merger histories of isolated dwarf galaxies based on a suite of 15 high-resolution cosmological zoom-in simulations, all with masses of $M_{\rm halo} \approx 10^{10}\,{\rm M}_{\odot}$ (and M$_\star\sim10^5-10^7\,{\rm M}_{\odot}$) at $z=0$, from the Feedback in Realistic Environments (FIRE) project. The stellar populations of these dwarf galaxies at $z=0$ are formed essentially entirely "in situ": over 90$\%$ of the stellar mass is formed in the main progenitor in all but two cases, and all 15 of the galaxies have >70$\%$ of their stellar mass formed in situ. Virtually all galaxy mergers occur prior to $z\sim3$, meaning that accreted stellar populations are ancient. On average, our simulated dwarfs undergo 5 galaxy mergers in their lifetimes, with typical pre-merger galaxy mass ratios that are less than 1:10. This merger frequency is generally comparable to what has been found in dissipationless simulations when coupled with abundance matching. Two of the simulated dwarfs have a luminous satellite companion at $z=0$. These ultra-faint dwarfs lie at or below current detectability thresholds but are intriguing targets for next-generation facilities. The small contribution of accreted stars make it extremely difficult to discern the effects of mergers in the vast majority of dwarfs either photometrically or using resolved-star color-magnitude diagrams (CMDs). The important implication for near-field cosmology is that star formation histories of comparably massive galaxies derived from resolved CMDs should trace the build-up of stellar mass in one main system across cosmic time as opposed to reflecting the contributions of many individual star formation histories of merged dwarfs.

SMHASH: anatomy of the Orphan Stream using RR Lyrae stars

Stellar tidal streams provide an opportunity to study the motion and structure of the disrupting galaxy as well as the gravitational potential of its host. Streams around the Milky Way are especially promising as phase space positions of individual stars will be measured by ongoing or upcoming surveys. Nevertheless, it remains a challenge to accurately assess distances to stars farther than 10 kpc from the Sun, where we have the poorest knowledge of the Galaxy's mass distribution. To address this we present observations of 32 candidate RR Lyrae stars in the Orphan tidal stream taken as part of the Spitzer Merger History and Shape of the Galactic Halo (SMHASH) program. The extremely tight correlation between the periods, luminosities, and metallicities of RR Lyrae variable stars in the Spitzer IRAC $\mathrm{3.6 \mu m}$ band allows the determination of precise distances to individual stars; the median statistical distance uncertainty to each RR Lyrae star is $2.5\%$. By fitting orbits in an example potential we obtain an upper limit on the mass of the Milky Way interior to 60 kpc of $\mathrm{5.6_{-1.1}^{+1.2}\times 10^{11}\ M_\odot}$, bringing estimates based on the Orphan Stream in line with those using other tracers. The SMHASH data also resolve the stream in line--of--sight depth, allowing a new perspective on the internal structure of the disrupted dwarf galaxy. Comparing with N--body models we find that the progenitor had an initial dark halo mass of approximately $\mathrm{3.2 \times 10^{9}\ M_\odot}$, placing the Orphan Stream's progenitor amongst the classical dwarf spheroidals.

Merger types forming the Virgo cluster in recent gigayears

Context. As our closest cluster-neighbor, the Virgo cluster of galaxies is intensely studied by observers to unravel the mysteries of galaxy evolution within clusters. At this stage, cosmological numerical simulations of the cluster are useful to efficiently test theories and calibrate models. However, it is not trivial to select the perfect simulacrum of the Virgo cluster to fairly compare in detail its observed and simulated galaxy populations that are affected by the type and history of the cluster. Aims. Determining precisely the properties of Virgo for a later selection of simulated clusters becomes essential. It is still not clear how to access some of these properties, such as the past history of the Virgo cluster from current observations. Therefore, directly producing effective simulacra of the Virgo cluster is inevitable. Methods. Efficient simulacra of the Virgo cluster can be obtained via simulations that resemble the local Universe down to the cluster scale. In such simulations, Virgo-like halos form in the proper local environment and permit assessing the most probable formation history of the cluster. Studies based on these simulations have already revealed that the Virgo cluster has had a quiet merging history over the last seven gigayears and that the cluster accretes matter along a preferential direction. Results. This paper reveals that in addition such Virgo halos have had on average only one merger larger than about a tenth of their mass at redshift zero within the last four gigayears. This second branch (by opposition to main branch) formed in a given sub-region and merged recently (within the last gigayear). These properties are not shared with a set of random halos within the same mass range. Conclusions. This study extends the validity of the scheme used to produce the Virgo simulacra down to the largest sub-halos of the Virgo cluster. It opens up great prospects for detailed comparisons with observations, including substructures and markers of past history, to be conducted with a large sample of high resolution “Virgos” and including baryons, in the near future.

Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe

Abstract Profiles of dark matter-dominated halos at the group and cluster scales play an important role in modern cosmology. Using results from two very large cosmological N-body simulations, which increase the available volume at their mass resolution by roughly two orders of magnitude, we robustly determine the halo concentration–mass (c−M) relation over a wide range of masses, employing multiple methods of concentration measurement. We characterize individual halo profiles, as well as stacked profiles, relevant for galaxy–galaxy lensing and next-generation cluster surveys; the redshift range covered is 0 ≤ z ≤ 4, with a minimum halo mass of M 200c ∼ 2 × 1011 M ⊙. Despite the complexity of a proper description of a halo (environmental effects, merger history, nonsphericity, relaxation state), when the mass is scaled by the nonlinear mass scale M ⋆(z), we find that a simple non-power-law form for the c–M/M ⋆ relation provides an excellent description of our simulation results across eight decades in M/M ⋆ and for 0 ≤ z ≤ 4. Over the mass range covered, the c–M relation has two asymptotic forms: an approximate power law below a mass threshold M/M ⋆ ∼ 500–1000, transitioning to a constant value, c 0 ∼ 3 at higher masses. The relaxed halo fraction decreases with mass, transitioning to a constant value of ∼0.5 above the same mass threshold. We compare Navarro–Frenk–White (NFW) and Einasto fits to stacked profiles in narrow mass bins at different redshifts; as expected, the Einasto profile provides a better description of the simulation results. At cluster scales at low redshift, however, both NFW and Einasto profiles are in very good agreement with the simulation results, consistent with recent weak lensing observations.

A relation between the characteristic stellar ages of galaxies and their intrinsic shapes

Stellar population and stellar kinematic studies provide unique but complementary insights into how galaxies build-up their stellar mass and angular momentum. A galaxy's mean stellar age reveals when stars were formed, but provides little constraint on how the galaxy's mass was assembled. Resolved stellar dynamics trace the change in angular momentum and orbital distribution of stars due to mergers, but major mergers tend to obscure the effect of earlier interactions. With the rise of large multi-object integral field spectroscopic (IFS) surveys, such as SAMI and MaNGA, and single-object IFS surveys (e.g., ATLAS$^{\rm{3D}}$, CALIFA, MASSIVE), it is now feasible to connect a galaxy's star formation and merger history on the same resolved physical scales, over a large range in galaxy mass, and across the full range of optical morphology and environment. Using the SAMI Galaxy Survey, here we present the first study of spatially-resolved stellar kinematics and global stellar populations in a large IFS galaxy survey. We find a strong correlation of stellar population age with location in the ($V / \sigma$, $\epsilon_{\rm{e}}$) diagram that links the ratio of ordered rotation to random motions in a galaxy to its observed ellipticity. For the large majority of galaxies that are oblate rotating spheroids, we find that characteristic stellar age follows the intrinsic ellipticity of galaxies remarkably well. This trend is still observed when galaxies are separated into early-type and late-type samples.