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We report high-quality H${\alpha}$/CO, imaging spectroscopy of nine massive (log median stellar mass = 10.65 $M_{\odot}$), disk galaxies on the star-forming, main sequence (henceforth `SFGs'), near the peak of cosmic galaxy evolution ($z\sim$1.1-2.5), taken with the ESO-Very Large Telescope, IRAM-NOEMA and Atacama Large Millimeter/submillimeter Array. We fit the major axis position-velocity cuts with beam-convolved, forward models with a bulge, a turbulent rotating disk, and a dark matter (DM) halo. We include priors for stellar and molecular gas masses, optical light effective radii and inclinations, and DM masses from our previous rotation curve analyses of these galaxies. We then subtract the inferred 2D model-galaxy velocity and velocity dispersion maps from those of the observed galaxies. We investigate whether the residual velocity and velocity dispersion maps show indications for radial flows. We also carry out kinemetry, a model-independent tool for detecting radial flows. We find that all nine galaxies exhibit significant non-tangential flows. In six SFGs, the inflow velocities ($v_r\sim$30-90 km s$^{-1}$, 10%-30% of the rotational component) are along the minor axis of these galaxies. In two cases the inflow appears to be off the minor axis. The magnitudes of the radial motions are in broad agreement with the expectations from analytic models of gravitationally unstable, gas-rich disks. Gravitational torques due to clump and bar formation, or spiral arms, drive gas rapidly inward and result in the formation of central disks and large bulges. If this interpretation is correct, our observations imply that gas is transported into the central regions on ~10 dynamical time scales., Comment: 31 pages, 27 figures, 3 tables. The Astrophysical Journal in press

We present a high-resolution kinematic study of the massive main-sequence star-forming galaxy (SFG) SDSS J090122.37+181432.3 (J0901) at z=2.259, using 0.36 arcsec ALMA CO(3-2) and 0.1-0.5 arcsec SINFONI/VLT H-alpha observations. J0901 is a rare, strongly-lensed but otherwise normal massive (log(M_star/M_sun)~11) main sequence SFG, offering a unique opportunity to study a typical massive SFG under the microscope of lensing. Through forward dynamical modeling incorporating lensing deflection, we fit the CO and H-alpha kinematics in the image plane out to about one disk effective radius (R_e ~ 4 kpc) at a ~600pc delensed physical resolution along the kinematic major axis. Our results show high intrinsic dispersions of the cold molecular and warm ionized gas (sig0_mol ~ 40 km/s and sig0_ion ~ 66 km/s) that remain constant out to R_e; a moderately low dark matter fraction (f_DM(R_e) ~ 0.3-0.4) within R_e; and a centrally-peaked Toomre Q-parameter -- agreeing well with the previously established sig0 vs. z, f_DM vs. Sig_baryon, and Q's radial trends using large-sample non-lensed main sequence SFGs. Our data further reveal a high stellar mass concentration within ~1-2 kpc with little molecular gas, and a clumpy molecular gas ring-like structure at R ~ 2-4 kpc, in line with the inside-out quenching scenario. Our further analysis indicates that J0901 had assembled half of its stellar mass only ~400 Myrs before its observed cosmic time, and cold gas ring and dense central stellar component are consistent with signposts of a recent wet compaction event of a highly turbulent disk found in recent simulations., Comment: 29 pages and 21 figures in total (14 pages and 10 figures in main text and the rest in appendix). Accepted for publication in ApJ

We analyze Ha or CO rotation curves (RCs) extending out to several galaxy effective radii for 100 massive, large, star-forming disk galaxies (SFGs) across the peak of cosmic galaxy star formation (z~0.6-2.5), more than doubling the previous sample presented by Genzel et al. (2020) and Price et al. (2021). The observations were taken with SINFONI and KMOS integral-field spectrographs at ESO-VLT, LUCI at LBT, NOEMA at IRAM, and ALMA. We fit the major axis kinematics with beam-convolved, forward models of turbulent rotating disks with bulges embedded in dark matter (DM) halos, including the effects of pressure support. The fraction of dark to total matter within the disk effective radius ($R_e ~ 5 kpc$), $f_DM (R_e)=V_{DM}^2 (R_e)/V_{circ}^2 (R_e)$, decreases with redshift: At z~1 (z~2) the median DM fraction is $0.38\pm 0.23$ ($0.27\pm 0.18$), and a third (half) of all galaxies are "maximal" disks with $f_{DM} (R_e)<0.28$. Dark matter fractions correlate inversely with the baryonic surface density, and the low DM fractions require a flattened, or cored, inner DM density distribution. At z~2 there is ~40% less dark matter mass on average within $R_e$ compared to expected values based on cosmological stellar-mass halo-mass relations. The DM deficit is more evident at high star formation rate (SFR) surface densities ($\Sigma_{SFR}>2.5 M_{\odot} yr^{-1} kpc^{-2}$) and galaxies with massive bulges ($M_{bulge}>10^{10} M_{\odot}$). A combination of stellar or active galactic nucleus (AGN) feedback, and/or heating due to dynamical friction, either from satellite accretion or clump migration, may drive the DM from cuspy into cored mass distributions. The observations plausibly indicate an efficient build-up of massive bulges and central black holes at z~2 SFGs., Comment: Submitted to ApJ (34 pages, 12 figures, 4 tables)

We propose a new type of effective densities via the potential distribution theorem. These densities are for the sake of enabling the mapping of the free energy of a uniform fluid onto that of a nonuniform fluid. The potential distribution theorem gives the work required to insert a test particle into the bath molecules under the action of the external (wall) potential. This insertion work W_ins can be obtained from Monte Carlo (MC) simulation (e.g. from Widom's test particle technique) or from an analytical theory. The pseudo-densities are constructed thusly so that when their values are substituted into a uniform-fluid equation of state (e.g. the Carnahan-Starling equation for the hard-sphere chemical potentials), the MC nonuniform insertion work is reproduced. We characterize the pseudo-density behavior for the hard spheres/hard wall system at moderate to high densities (from \rho^*= 0.5745 to 0.9135). We adopt the MC data of Groot et al. for this purpose. The pseudo-densities show oscillatory behavior out of phase (opposite) to that of the singlet densities. We also construct a new closure-based density functional theory (the star-function based density functional theory) that can give accurate description of the MC density profiles and insertion works. A viable theory is established for several cases in hard sphere adsorption., Comment: 15 pages, 10 figures