We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds, or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable unstable system of counter-rotating disks, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided (m=1) mode.Comment: 28 pages, 11 figures; minor changes to text and figures. To be published in MNRA

Starburst galaxies are galaxies or regions of galaxies undergoing intense periods of star formation. Understanding the heating and cooling mechanisms in these galaxies can give us insight to the driving mechanisms that fuel the starburst. Molecular emission lines play a crucial role in the cooling of the excited gas. With Herschel Spectral and Photometric Imaging Receiver we have been able to observe the rich molecular spectrum towards the central region of NGC 253. Carbon monoxide (CO, J = 4−3 to 13−12) is the brightest molecule in the Herschel wavelength range and together with ground-based low-J observations, the line fluxes trace the excitation of CO. By studying the CO excitation ladder and comparing the intensities to models, we investigate whether the gas is excited by UV radiation, X-rays, cosmic rays, or turbulent heating. Comparing the 12 CO and 13 CO observations to large velocity gradient models and photon-dominated region (PDR) models we find three main interstellar medium (ISM) phases. We estimate the density, temperature, and masses of these ISM phases. By adding 13 CO, HCN, and HNC line intensities, we are able to constrain these degeneracies and determine the heating sources. The first ISM phase responsible for the low-J CO lines is excited by PDRs, but the second and third phases, responsible for the mid to high-J CO transitions, require an additional heating source. We find three possible combinations of models that can reproduce our observed molecular emission. Although we cannot determine which of these is preferable, we can conclude that mechanical heating is necessary to reproduce the observed molecular emission and cosmic ray heating is a negligible heating source. We then estimate the mass of each ISM phase; 6 × 10 7 M for phase 1 (low-J CO lines), 3 × 10 7 M for phase 2 (mid-J CO lines), and 9 × 10 6 M for phase 3 (high-J CO lines) for a total system mass of 1 × 10 8 M .

CO observations in active galactic nuclei and star-bursts reveal high kinetic temperatures. Those environments are thought to be very turbulent due to dynamic phenomena such as outflows and high supernova rates. We investigate the effect of mechanical heating on atomic fine-structure and molecular lines, and their ratios. We try to use those ratios as a diagnostic to constrain the amount of mechanical heating in an object and also study its significance on estimating the H 2 mass. Equilibrium photo-dissociation models (PDRs hereafter) were used to compute the thermal and chemical balance for the clouds. The equilibria were solved for numerically using the optimized version of the Leiden PDR-XDR code. Large velocity gradient calculations were done as post-processing on the output of the PDR models using RADEX. High-J CO line ratios are very sensitive to mechanical heating (Γ mech hereafter). Emission becomes at least one order of magnitude brighter in clouds with n ∼ 10 5 cm −3 and a star formation rate of 1 M yr −1 (corresponding to Γ mech = 2 × 10 −19 erg cm −3 s −1 ). Emission of low-J CO lines is not as sensitive to Γ mech , but they do become brighter in response to Γ mech . Generally, for all of the lines we considered, Γ mech increases excitation temperatures and decreases the optical depth at the line centre. Hence line ratios are also affected, strongly in some cases. Ratios involving HCN are a good diagnostic for Γ mech , where the HCN(1-0)/CO(1-0) increases from 0.06 to 0.25 and the HCN(1-0)/HCO + (1-0) increase from 0.15 to 0.5 for amounts of Γ mech equivelent to 5% of the surface heating rate. Both ratios increase to more than 1 for higher Γ mech , as opposed to being much less than unity in pure PDRs. The first major conclusion is that low-J to high-J intensity ratios will yield a good estimate of the mechanical heating rate (as opposed to only low-J ratios). The second one is that the mechanical heating rate should be taken into account when determing A V or equivalently N H , and consequently the cloud mass. Ignoring Γ mech will also lead to large errors in density and radiation field estimates.

Context. Multitransition CO observations of galaxy centers have revealed that significant fractions of the dense circumnuclear gas have high kinetic temperatures, which are hard to explain by pure photon excitation, but may be caused by dissipation of turbulent energy. Aims. We aim to determine to what extent mechanical heating should be taken into account while modeling PDRs. To this end, the effect of dissipated turbulence on the thermal and chemical properties of PDRs is explored. Methods. Clouds are modeled as 1D semi-infinite slabs whose thermal and chemical equilibrium is solved for using the Leiden PDR-XDR code, where mechanical heating is added as a constant term throughout the cloud. An extensive parameter space in hydrogen gas density, FUV radiation field and mechanical heating rate is considered, covering almost all possible cases for the ISM relevant to the conditions that are encountered in galaxies. Effects of mechanical heating on the temperature profiles, column densities of CO and H 2 O and column density ratios of HNC, HCN and HCO + are discussed. Results. In a steady-state treatment, mechanical heating seems to play an important role in determining the kinetic temperature of the gas in molecular clouds. Particularly in high-energy environments such as starburst galaxies and galaxy centers, model gas temperatures are underestimated by at least a factor of two if mechanical heating is ignored. The models also show that CO, HCN and H 2 O column densities increase as a function of mechanical heating. The HNC/HCN integrated column density ratio shows a decrease by a factor of at least two in high density regions with n ∼ 10 5 cm −3 , whereas that of HCN/HCO + shows a strong dependence on mechanical heating for this same density range, with boosts of up to three orders of magnitude. Conclusions. The effects of mechanical heating cannot be ignored in studies of the molecular gas excitation whenever the ratio of the star formation rate to the gas density (SFR/n 3/2 ) is close to, or exceeds, 7 × 10 −6 M yr −1 cm 4.5 . If mechanical heating is not included, predicted column densities (such as those of CO) are underestimated, sometimes (as in the case of HCN and HCO + ) even by a few orders of magnitude. As a lower bound to its importance, we determined that it has non-negligible effects already when mechanical heating is as little as 1% of the UV heating in a PDR.

The HD molecules are key species for the cooling of pristine gas at temperatures below 100 K. They are also known to be key tracers of H2 in protoplanetary disks and thus, they can be used as a measure of protoplanetary disks mass. Accurate modeling of the cooling mechanism and of HD abundance in astrophysical media requires a proper modeling for its excitation by both radiative and collisional processes. Here, we report quantum time-independent calculations of collisional rate coefficients for the rotational excitation of HD by H for temperatures ranging from 10 to 1000 K. The reactive and hydrogen exchange channels are taken into account in the scattering calculations. New exact quantum results are compared to previous calculations performed neglecting reactive and exchange channels. We found that for temperatures higher than ∼300 K, the impact of these channels on the rate coefficients cannot be neglected. Such results suggest that the new HD–H collisional data have to be used for properly modeling HD cooling function and HD abundance in all the astrophysical environments where HD plays a role, e.g. in photon-dominated regions, protoplanetary disks, early Universe chemistry, and primordial star forming regions.