In this paper we introduce a new method for analysing Milky Way phase-space which allows us to reveal the imprint left by the Milky Way bar and spiral arms in the stars with full phase-space data in Gaia Data Release 2. The unprecedented quality and extended spatial coverage of these data enable us to discover six prominent stellar density structures in the disc to a distance of 5 kpc from the Sun. Four of these structures correspond to the spiral arms detected previously in the gas and young stars (Scutum-Centaurus, Sagittarius, Local and Perseus), while the remaining two are associated with two main resonances of the Milky Way bar. For the first time we provide evidence of the imprint left by spiral arms and resonances in the stellar densities not relying on a specific tracer, through a mean of enhancing the signatures left by these asymmetries. Our method offers new avenues for studying how the stellar populations in our Galaxy are shaped. Article number, page 2 of 10 S. Khoperskov et al.: Hic sunt dracones: Cartography of the Milky Way spiral arms and bar resonances with Gaia Data Release 2 Model I Milky Way -Gaia DR2 Model II

A. Khoperskov et al.: Numerical modelling of disc galaxies Astron. Nachr./AN XXX (200X) XThe non-linear dynamics of bending instability and vertical structure of a galactic stellar disc embedded into a spherical halo are studied with N-body numerical modelling. Development of the bending instability in stellar galactic disc is considered as the main factor that increases the disc thickness. Correlation between the disc vertical scale height and the halo-to-disc mass ratio is predicted from the simulations. The method of assessment of the spherical-todisc mass ratio for edge-on spiral galaxies with a small bulge is considered. Modelling of eight edge-on galaxies: NGC 891, NGC 4738, NGC 5170, UGC 6080, UGC 7321, UGC 8286, UGC 9422 and UGC 9556 is performed. Parameters of stellar discs, dark haloes and bulges are estimated. The lower limit of the dark-toluminous mass ratio in our galaxies is of the order of 1 within the limits of their stellar discs. The dark haloes dominate by mass in the galaxies with very thin stellar discs (NGC 5170, UGC 7321 and UGC 8286).

We use the marginal stability condition for galactic disks and the stellar velocity dispersion data published by different authors to place upper limits on the disk local surface density at two radial scalelengths R = 2h. Extrapolating these estimates, we constrain the total mass of the disks and compare these estimates to those based on the photometry and color of stellar populations.The comparison reveals that the stellar disks of most of spiral galaxies in our sample cannot be substantially overheated and are therefore unlikely to have experienced a significant merging event in their history. The same conclusion applies to some, but not all of the S0 galaxies we consider. However, a substantial part of the early type galaxies do show the stellar velocity dispersion well in excess of the gravitational stability threshold suggesting a major merger event in the past. We find dynamically overheated disks among both seemingly isolated galaxies and those forming pairs. The ratio of the marginal stability disk mass estimate to the total galaxy mass within four radial scalelengths remains within a range of 0.4-0.8. We see no evidence for a noticeable running of this ratio with either the morphological type or color index.

We used N -body dynamical simulations to analyze the conditions for the gravitational stability of a three-dimensional stellar disk in the gravitational field of two rigid spherical components -a bulge and a halo, whose central concentrations and relative masses vary over wide ranges. The number of point masses N in the simulations varied from 40 to 500 thousands and the evolution of the simulated models is followed over 10-20 rotation periods of the outer edge of the disk. The initially unstable disks are heated and, as a rule, reach a quasi-stationary equilibrium with a steady-state radial-velocity dispersion c r over five to eight periods of rotation. The radial behavior of the Toomre stability parameter Q T (r) for the final state of the disk is estimated. Numerical models are used to analyze the dependence of the gravitational stability of the disk on the relative masses of the spherical components, disk thickness, degree of differential rotation, and initial state of the disk. Formal application of existing analytical local criteria for marginal stability of the disk can lead to errors in c r of more than a factor of 1.5. It is suggested that the approximate constancy of Q T ≃ 1.2 ÷ 1.5 for r ≃ (1 ÷ 2) × L (where L is the radial scale of a disk surface density), valid for a wide range of models, can be used to estimate upper limits for the disc mass and density based on the observed distributions of the rotational velocity of the gaseous component and of the stellar velocity dispersion.

Spectroscopic observations of three lenticular (S0) galaxies (NGC 1167, NGC 4150, and NGC 6340) and one SBa galaxy (NGC 2273) have been taken with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences aimed to study the structure and kinematic properties of early-type disk galaxies. The radial profiles of the stellar radial velocities and the velocity dispersion are measured. N -body simulations are used to construct dynamical models of galaxies containing a stellar disk, bulge, and halo. The masses of individual components are estimated for maximum-mass disk models. A comparison of models with estimated rotational velocities and the stellar velocity dispersion suggests that the stellar disks in lenticular galaxies are "overheated"; i.e., there is a significant excess velocity dispersion over the minimum level required to maintain the stability of the disk. This supports the hypothesis that the stellar disks of S0 galaxies were subject to strong gravitational perturbations. The relative thickness of the stellar disks in the S0 galaxies we consider substantially exceed the typical disk thickness of spiral galaxies.