We present the results for the galaxy NGC 628 observed with the Planetary Nebulae Spectrograph (PN.S) equipped with the Hα arm. With the third PN.S arm, the Hα arm, we measure the Hα fluxes, in addition to fluxes and line-of-sight velocities (LOSV) of monochromatic spatially unresolved [OIII] 5007Å sources. The narrow band color ([OIII] 5007Å-Hα) vs m5007 magnitude diagram separates planetary nebulae (PNe) from single compact ionized HII regions and supernovae remnants (SNRs), which also emit in [OIII]5007 Å. The goals are to detect bona-fide PNe in the face-on spiral galaxy NGC 628 (M74) so that we can measure the velocity dispersion of the stars perpendicular to the main plane of the disc. This study validates the empirical selection criteria for PNe with the PN.S in star forming discs. We classified 442 PNe and 251 spatially isolated, unresolved HII regions: the PN.S with the Hα arm increased the number of known PNe by a factor 4. We find evidence for two kinematically distinct PN populations in the NGC 628 disc. The kinematically cold PN population dominates the PN luminosity function close to the bright cut-off magnitude, indicating that the PN massive, short-lived progenitors dominate the PNLF bright cut-off in NGC 628. The warmer PN component increasingly dominates at fainter magnitudes. The velocity dispersion orthogonal to the disc plane are σz,cold = 8.8 kms-1 and σz,warm =26.1 kms-1 respectively, over a range of radii 80 to 425 arcsec. These components contribute with the ratio 46

Global m=1 asymmetries are observed in many self-gravitating astrophysical systems and are often interpreted as large-scale slow modes in near-Keplerian potentials. Prominent examples include eccentric nuclear disks in galactic centres, such as the double nucleus of M31. However, the origin and long-term stability of such modes remain unclear. We investigate the evolution and stability of a collisionless, self-gravitating torus orbiting a dominant central mass, aiming to determine whether a slow non-axisymmetric (m=1) mode can arise spontaneously. We perform direct N-body simulations exploring different torus-to-central mass ratios and initial conditions. The calculations use the high-order Hermite GPU integrator (ϕ-GPU), allowing us to follow long-term evolution with many particles. We find that a global slow m=1 mode forms spontaneously from initially axisymmetric configurations. The lopsided structure is sustained by coherent apsidal alignment and persists over secular timescales. Its maintenance requires nonlinear coupling of low-order modes, including the m=3 component, as well as a sufficient vertical thickness of the torus. As a result of the long-lived overdensity, the central mass is displaced from the system barycenter. These results provide a framework for understanding eccentric nuclear disks, such as those in M31 and NGC4486B, as well as molecular tori in AGNs, and suggest that such asymmetries may produce observable offsets of the central supermassive black hole.

Toroidal/ring structures are a common feature in a wide variety of astrophysical objects, including dusty tori in active galactic nuclei (AGNs), rings in galaxies, protoplanetary disks, and others. The matter distribution in such structures is not homogeneous and can be flattened by self-gravity or become elongated in the vertical direction, as is the case with obscuring tori in AGNs. This led us to consider the more general case of the gravitational potential of an inhomogeneous torus with an elliptical cross-section. We begin by showing that the outer potential of a homogeneous elliptical torus can be effectively approximated with less than 1

The recent ALMA maps together with observations of H$_2$O maser emission seem to suggest the presence of a counter-rotation in the obscuring torus of NGC 1068. We propose to explain this phenomenon as due to the influence of a wind, considered as radiation pressure, and the effects of torus orientation. In order to test this idea: 1. we make $N$-body simulation of a clumpy torus taking into account mutual forces between particles (clouds); 2. we apply ray-tracing algorithm with the beams from the central engine to choose the clouds in the torus throat that can be under direct influence of the accretion disk emission; 3. we use semi-analytical model to simulate the influence of the asymmetrical radiation pressure (wind) forced on the clouds in the torus throat. An axis of such a wind is tilted with respect to the torus symmetry axis; 4. we orient the torus relative to an observer and again apply ray-tracing algorithm. In this step the beams go from an observer to the optically thick clouds that allows us to take into account the mutual obscuration of clouds; 5. after projecting on the picture plane, we impose a grid on the resulting cloud distribution and find the mean velocity of clouds in each cells to mimic the ALMA observational maps. By choosing the parameters corresponding to NGC 1068 we obtain the model velocity maps that emulate the effect of an apparent counter-rotation and can explain the discovery made by ALMA.

The basic task of classical celestial mechanics, set by the need to model and predict the motions of Solar System bodies in the context of Newton’s mechanics and gravitational lawGravitationallaw, is to determine the dynamical evolution of systems with a finite number N of distinct bodies that are subject to mutual gravitational forces. The classic formulation of the problem, given by the system of equations (1.2), is straightforward, but the exact solution does not exist for $$N\!>\!2$$ even under oversimplified assumptions, i.e., when: i. the external forces are deliberately disregarded (the system is then said to be isolated), ii. there are no other internal forces but gravitational interactions, and iii. the bodies in play are all assimilated to massive pointsMassive points.

In the previous chapters we have limited ourselves to consider only massive pointsMassive points, fictitious bodies that attract each other according to a law of force with a seemingly simple mathematical expression This approximation is successfully applied to many real situations.

Celestial Mechanics: An introduction to the field based on lectures delivered at Padua University (MC) and V.N. Karazin Kharkiv National University (EB).

The VST Early-type GAlaxy Survey (VEGAS) is a deep, multi-band (u, g, r, i) imaging survey, carried out with the 2.6-metre VLT Survey Telescope (VST) at ESO's Paranal Observatory in Chile. VEGAS combines the wide (1-square-degree) OmegaCAM imager and long integration times, together with a specially designed observing strategy. It has proven to be a gold mine for studies of features at very low surface brightness, down to levels of mu_g 27-30 magnitudes arcsec^(-2), over 5-8 magnitudes fainter than the dark sky at Paranal. In this article we highlight the main science results obtained with VEGAS observations of galaxies across different environments, from dense clusters of galaxies to unexplored poor groups and in the field.

We present the first data release (DR1) of the VST Early-type GAlaxy Survey (VEGAS). This is a deep multi-band (u'g'r'i') imaging survey, carried out with the ESO VLT Survey Telescope (VST). To date, using about 90 observing time, VEGAS has already collected 43 targets (groups and clusters of galaxies) covering a total area on the sky of about 95 square degrees. Taking advantage of the wide (1 deg^2) field-of-view of OmegaCAM@VST, the long integration time and the wide variety of targets, VEGAS has proven to be a gold mine to explore the structure of galaxies down to the faintest surface brightness levels of about 27-30 mag/arcsec^2 in the SDSS g' band, for the dense clusters of galaxies and for the unexplored poor groups of galaxies. Based on the analysed data, VEGAS allowed us to i) study the galaxy outskirts, detect the intra-cluster light and low-surface brightness features in the intra-cluster/group space, ii) trace the mass assembly in galaxies, by estimating the accreted mass fraction in the stellar halos and provide results that can be directly compared with the predictions of galaxy formation models, iii) trace the spatial distribution of candidate globular clusters, and iv) detect the ultra-diffuse galaxies. With the DR1, we provide the reduced VST mosaics of 10 targets, which have been presented in the VEGAS publications. The data products are available via the ESO Science Portal (see http://www.eso.org/sci/observing/phase3/news.html#VEGAS-DR1).

VEGAS is a deep multi-band (u’g’r’i’) imaging survey, carried out with the ESO VLT Survey Telescope (VST). VST is a 2.6-m wide-field optical survey telescope, located at ESO Paranal Observatory (Chile). First VEGAS observations started in October 2011 (former PI: M. Capaccioli, see also Capaccioli et al. 2015). Later the program was approved for an extension to the period 2016-2021 (PI: E. Iodice). The whole VEGAS sample is made by selecting groups and clusters of galaxies with an early-type galaxy in the core brighter than MB = −21 mag, in the local volume within 54 Mpc/h, mainly located in the Southern hemisphere. The total observing time allocated to the survey is 500 hours for five years (2016-2021). With the data release 1 (DR1), we provide the reduced VST mosaics of 10 targets, which have been presented in the VEGAS publications. Taking advantage of the wide (1 deg2) field-of-view of OmegaCAM@VST, the long integration time and the wide variety of targets, VEGAS has proven to be a gold mine to explore the structure of galaxies down to the faintest surface brightness levels of ~ 27-30 mag/arcsec2 in the SDSS g’-band, for the dense clusters of galaxies as well as for the unexplored poor groups of galaxies. As such, in the wide panorama of deep imaging surveys, VEGAS has occupied a pivotal role in exploring the galaxy properties as a function of the environments down to the low surface brightness (LSB) regime. About 30% of the VEGAS observing time was dedicated to the Fornax Deep Survey (FDS), a new multiband deep imaging survey of the Fornax cluster, where the reduced data have been recently released (Peletier et al. 2020, arXiv:2008.12633). To date, using about 400 hours of the total observing time, VEGAS has already collected 43 targets (groups and clusters of galaxies) covering a total area on the sky of ∼ 95 deg2. Based on the analyzed data, VEGAS allowed us to i) study the galaxy outskirts, detect the intra-cluster light and LSB features in the intra-cluster/group space (Iodice et al. 2016, 2017a; Spavone et al. 2018; Cattapan et al. 2019; Raj et al. 2019, 2020; Iodice et al. 2019a, 2020a), ii) trace the mass assembly in galaxies, by estimating the accreted mass fraction in the stellar halos and provide results that can be directly compared with the predictions of galaxy formation models (Iodice et al. 2017b; Spavone et al. 2017, 2020), iii) trace the spatial distribution of candidate globular clusters (D’Abrusco et al. 2016; Cantiello et al. 2018, 2020); iv) detect the ultra-diffuse galaxies (Forbes et al. 2019, 2020; Iodice et al. 2020b). Overview of Observations Targets, covered area, filters and total exposure times of the DR1 are listed in Table 1. In this table, the adopted observing strategy for each target is also included. We have tested that for the brightest and most extended galaxies (with mB ≤ 10 mag and a major axis diameter ≥ 3 arcmin), the best background estimate is achieved by adopting the step-dither observing strategy. This mimics the ON-OFF procedure devised in infrared astronomy where the background is estimated from exposures taken as close as possible, in space and time, to the scientific ones. Therefore, the step-dither strategy used for the VEGAS images consists of a cycle of short exposures (150 sec) on the science target and on an adjacent field (close in space and time) to the science frame. We adopted an offset of ≤ 0.3 deg in the observing sequence and the directions of these small offsets were randomly chosen around the center of each field. An average sky image, for each night, is derived from the sky frames, which is then scaled and subtracted from the science frames. For less extended objects (with a major axis diameter D ≤ 3 arcmin), we adopted the standard diagonal observing strategy, since the sky background can be estimated on the science frame, by using a polynomial surface fit over the entire frame (see Capaccioli et al. 2015). E S O S c i e n c e A r c h i v e F a c i l i t y P h a s e 3 D a t a R e l e a s e D e s c r i p t i o n E S O p ro gr am m e V S T s ur ve y of E ar ly -t yp e G A la xi eS ( V E G A S ), D at a R el ea se D R 1 pr ov id ed b y E nr ic he tta Io di ce , s ub m itt ed b et w ee n 20 20 -1 223 a nd 2 02 101 -2 5 p ub lis he d on 2 02 102 -0 1

In this work we use Max-Tree Objects, (MTO) on the FDS data in order to detect previously undetected Low surface brightness (LSB) galaxies. After extending the existing Fornax dwarf galaxy catalogs with this sample, our goal is to understand the evolution of LSB dwarfs in the cluster. We also study the contribution of the newly detected galaxies to the faint end of the luminosity function. We test the detection completeness and parameter extraction accuracy of MTO. We then apply MTO to the FDS images to identify LSB candidates. The identified objects are fitted with 2D S\'ersic models using GALFIT and classified based on their morphological appearance, colors, and structure. With MTO, we are able to increase the completeness of our earlier FDS dwarf catalog (FDSDC) 0.5-1 mag deeper in terms of total magnitude and surface brightness. Due to the increased accuracy in measuring sizes of the detected objects, we also add many small galaxies to the catalog that were previously excluded as their outer parts had been missed in detection. We detect 265 new LSB dwarf galaxies in the Fornax cluster, which increases the total number of known dwarfs in Fornax to 821. Using the extended catalog, we show that the luminosity function has a faint-end slope of -1.38+/-0.02. We compare the obtained luminosity function with different environments studied earlier using deep data but do not find any significant differences. On the other hand, the Fornax-like simulated clusters in the IllustrisTNG cosmological simulation have shallower slopes than found in the observational data. We also find several trends in the galaxy colors, structure, and morphology that support the idea that the number of LSB galaxies is higher in the cluster center due to tidal forces and the age dimming of the stellar populations. The same result also holds for the subgroup of large LSB galaxies, so-called ultra-diffuse galaxies.

ABSTRACT We have developed the dynamical model of a clumpy torus in an active galactic nucleus (AGN) and compared to recent The Atacama Large Millimeter Array (ALMA) observations. We present N-body simulations of a torus in the field of a supermassive black hole (SMBH), made of up to N = 105 gravitationally interacting clouds. As initial conditions, we choose random distributions of the orbital elements of the clouds with a cut-off in the inclination to mimic the presence of wind cones produced at the early AGN stage. When the torus reaches an equilibrium, it has a doughnut shape. We discuss the presence of box orbits. We have then constructed the velocity and velocity dispersion maps using the resulting distributions of the clouds at equilibrium. The effects of torus inclination and cloud sizes are duly analysed. We discuss the obscuration effects of the clouds using a ray tracing simulation matching the model maps to ALMA resolution. By comparing the model with the observational maps of NGC 1068, we find that the SMBH mass is $M_\text{smbh}=5\times 10^6 \, \mathrm{M}_\odot$ for the range of the torus inclination angles 45°–60°. We also construct the velocity dispersion maps for NGC 1326 and NGC 1672. They show that the peaks in the ALMA dispersion maps are related to the emission of the torus throat. Finally, we obtain the temperature distribution maps with parameters that correspond to our model velocity maps for NGC 1068. They show stratification in temperature distribution with the shape of the high-temperature region as in the VLTI/MIDI map.

We present the first data release of the Fornax Deep Survey (FDS), an imaging survey using using the wide-field imager OmegaCAM mounted on the VST in the SDSS u', g', r', and i'-bands covering the Fornax Galaxy Cluster and the infalling Fornax A Group. FDS is a joint project between NOVA (previously called FOCUS - PI: R. F. Peletier) and INAF (as part of VEGAS - PIs: M. Capaccioli and E. Iodice). With exposure times of about 9 hours over an area of ~28 square degrees, this survey is a legacy dataset for studies of members of the Fornax Galaxy Cluster and the infalling Fornax A Group down to a surface brightness limit of ~28 mag/arcsec^2 (1-sigma surface brightness over a 1 arcsecond^2 area) and opens a new parameter regime to investigate the role of the cluster environment in shaping the properties of its galaxy population. After the Virgo cluster,Fornax is the second nearest galaxy cluster to us, and with its different mass and evolutionary state, it provides a valuable comparison that makes it possible to understand the various evolutionary effects on galaxies and galaxy clusters. Details about the survey can be found in A. Venhola, R. F. Peletier, E. Laurikainen et al., 2018, A&A 620, 165. In this release, 181 Gb of (compressed) fits files reduced using the system are present. Catalogues with the complete sample of sources including dwarf galaxies part of the cluster, globular clusters, and background galaxies will be provided in forthcoming releases. The data products are available via the ESO Science Portal at https://archive.eso.org/scienceportal/home?publ_date=2020-08-26

We present the study of the south-west group in the Fornax cluster centred on the brightest group galaxy (BGG) Fornax A, observed as part of the Fornax Deep Survey (FDS). This includes the analysis of the bright group members (mB < 16 mag) and the intra-group light (IGL). The main objective of this work is to investigate the assembly history of the Fornax A group and to compare its physical quantities as a function of the environment to that of the Fornax cluster core. For all galaxies, we extract the azimuthally averaged surface brightness profiles in three optical bands (g, r, i) by modelling the galaxy's isophotes. We derive their colour profiles and structural parameters in all respective bands. The long integration time and large covered area of the FDS allow us to also estimate the amount of IGL. The majority of galaxies in the Fornax A group are late-type galaxies (LTGs), spanning a range of stellar mass of $8 < log (M_* M_{\odot}) < 10.5$. Six out of nine LTGs show a Type III (up-bending) break in their light profiles, which is either suggestive of strangulation halting star-formation in their outskirts or their HI-richness causing enhanced star-formation in their outer-discs. The estimated luminosity of the IGL is $6 \pm 2 \times 10^{10} L_{\odot}$ in g-band, which corresponds to about 16% of the total light in the group. The Fornax A group appears to be in an early stage of assembly with respect to the cluster core. The environment of the Fornax A group is not as dense as that of the cluster core, with all galaxies except the BGG showing similar morphology, comparable colours and stellar masses, and Type III disc-breaks, without any clear trend of these properties with group-centric distances. The main contribution to the IGL is from the minor merging in the outskirts of the BGG NGC1316 and, probably, the disrupted dwarf galaxies close to the group centre.

The VST Optical Imaging of the CDFS and ES1 Fields (VOICE) Survey, in synergy with the SUDARE survey, is a deep optical $ugri$ imaging of the CDFS and ES1 fields using the VLT Survey Telescope (VST). The observations for the CDFS field comprise about 4.38 deg$^2$ down to $r\sim26$ mag. The total on-sky time spans over four years in this field, distributed over four adjacent sub-fields. In this paper, we use the multi-epoch $r$-band imaging data to measure the variability of the detected objects and search for transients. We perform careful astrometric and photometric calibrations and point spread function (PSF) modeling. A new method, referring to as differential running-average photometry, is proposed to measure the light curves of the detected objects. With the method, the difference of PSFs between different epochs can be reduced, and the background fluctuations are also suppressed. Detailed uncertainty analysis and detrending corrections on the light curves are performed. We visually inspect the light curves to select variable objects, and present some objects with interesting light curves. Further investigation of these objects in combination with multi-band data will be presented in our forthcoming paper.