On the turbulence driving mode of expanding HII regions

We investigate the turbulence driving mode of ionizing radiation from massive stars on the surrounding interstellar medium (ISM). We run hydrodynamical simulations of a turbulent cloud impinged by a plane-parallel ionization front. We find that the ionizing radiation forms pillars of neutral gas reminiscent of those seen in observations. We quantify the driving mode of the turbulence in the neutral gas by calculating the driving parameter $b$, which is characterised by the relation $\sigma_s^2 = \ln({1+b^2\mathcal{M}^2})$ between the variance of the logarithmic density contrast $\sigma_s^2$ (where $s = \ln({\rho/\rho_0})$ with the gas density $\rho$ and its average $\rho_0$), and the turbulent Mach number $\mathcal{M}$. Previous works have shown that $b\sim1/3$ indicates solenoidal (divergence-free) driving and $b\sim1$ indicates compressive (curl-free) driving, with $b\sim1$ producing up to ten times higher star formation rates than $b\sim1/3$. The time variation of $b$ in our study allows us to infer that ionizing radiation is inherently a compressive turbulence driving source, with a time-averaged $b\sim 0.76 \pm 0.08$. We also investigate the value of $b$ of the pillars, where star formation is expected to occur, and find that the pillars are characterised by a natural mixture of both solenoidal and compressive turbulent modes ($b\sim0.4$) when they form, and later evolve into a more compressive turbulent state with $b\sim0.5$--$0.6$. A virial parameter analysis of the pillar regions supports this conclusion. This indicates that ionizing radiation from massive stars may be able to trigger star formation by producing predominately compressive turbulent gas in the pillars.Comment: 10 pages, 6 figures. Accepted for publication in MNRA

Outflows Driven by Direct and Reprocessed Radiation Pressure in Massive Star Clusters

We use three-dimensional radiation hydrodynamic (RHD) simulations to study the formation of massive star clusters under the combined effects of direct ultraviolet (UV) and dust-reprocessed infrared (IR) radiation pressure. We explore a broad range of mass surface density $\Sigma \sim 10^2$-$10^5 \, \mathrm{M}_{\odot} \, \mathrm{pc}^{-2}$, spanning values typical of weakly star-forming galaxies to extreme systems such as clouds forming super-star clusters, where radiation pressure is expected to be the dominant feedback mechanism. We find that star formation can only be regulated by radiation pressure for $\Sigma \lesssim 10^3 \, \mathrm{M}_{\odot} \, \mathrm{pc}^{-2}$, but that clouds with $\Sigma \lesssim 10^5 \, \mathrm{M}_{\odot} \, \mathrm{pc}^{-2}$ become super-Eddington once high star formation efficiencies ($\sim 80 \%$) are reached, and therefore launch the remaining gas in a steady outflow. These outflows achieve mass-weighted radial velocities of $\sim 15$ - $30 \,\mathrm{km} \, \mathrm{s}^{-1}$, which is $\sim 0.5$ - $2.0$ times the cloud escape speed. This suggests that radiation pressure is a strong candidate to explain recently observed molecular outflows found in young super-star clusters in nearby starburst galaxies. We quantify the relative importance of UV and IR radiation pressure in different regimes, and deduce that both are equally important for $\Sigma \sim 10^3 \, \mathrm{M}_{\odot} \, \mathrm{pc}^{-2}$, whereas clouds with higher (lower) density are increasingly dominated by the IR (UV) component. Comparison with control runs without either the UV or IR bands suggests that the outflows are primarily driven by the impulse provided by the UV component, while IR radiation has the effect of rendering a larger fraction of gas super-Eddington, and thereby increasing the outflow mass flux by a factor of $\sim 2$.Comment: 15 pages, 11 figures. MNRAS accepted. v2: Minor changes in text made to address referee comment

Infrared Radiation Feedback Does Not Regulate Star Cluster Formation

We present 3D radiation-hydrodynamical (RHD) simulations of star cluster formation and evolution in massive, self-gravitating clouds, whose dust columns are optically thick to infrared (IR) photons. We use \texttt{VETTAM} -- a recently developed, novel RHD algorithm, which uses the Variable Eddington Tensor (VET) closure -- to model the IR radiation transport through the cloud. We also use realistic temperature ($T$) dependent IR opacities ($\kappa$) in our simulations, improving upon earlier works in this area, which used either constant IR opacities or simplified power laws ($\kappa \propto T^2$). We investigate the impact of the radiation pressure of these IR photons on the star formation efficiency (SFE) of the cloud, and its potential to drive dusty winds. We find that IR radiation pressure is unable to regulate star formation or prevent accretion onto the star clusters, even for very high gas surface densities ($\Sigma > 10^5 M_{\odot} \, \mathrm{pc}^{-2}$), contrary to recent semi-analytic predictions and simulation results using simplified treatments of the dust opacity. We find that the commonly adopted simplifications of $\kappa \propto T^2$ or constant $\kappa$ for the IR dust opacities leads to this discrepancy, as those approximations overestimate the radiation force. By contrast, with realistic opacities that take into account the micro-physics of the dust, we find that the impact of IR radiation pressure on star formation is very mild, even at significantly high dust-to-gas ratios ($\sim 3$ times solar), suggesting that it is unlikely to be an important feedback mechanism in controlling star formation in the ISM.Comment: 28 pages, 19 figures. MNRAS accepted. v2: Minor changes made to address referee comment

Probing the evolution of molecular cloud structure II: From chaos to confinement

We present an analysis of the large-scale molecular cloud structure and of the stability of clumpy structures in nearby molecular clouds. In our recent work, we identified a structural transition in molecular clouds by studying the probability distributions of gas column densities in them. In this paper, we further examine the nature of this transition. The transition takes place at the visual extinction of A_V^tail = 2-4 mag, or equivalently, at \Sigma^tail = 40-80 Ms pc^{-2}. The clumps identified above this limit have wide ranges of masses and sizes, but a remarkably constant mean volume density of n = 10^3 cm^{-3}. This is 5-10 times larger than the density of the medium surrounding the clumps. By examining the stability of the clumps, we show that they are gravitationally unbound entities, and that the external pressure from the parental molecular cloud is a significant source of confining pressure for them. Then, the structural transition at A_V^tail may be linked to a transition between this population and the surrounding medium. The star formation rates in the clouds correlate strongly with the total mass in the clumps, i.e, with the mass above A_V^tail, dropping abruptly below that threshold. These results imply that the formation of pressure confined clumps introduces a prerequisite for star formation. Furthermore, they give a physically motivated explanation for the recently reported relation between the star formation rates and the amount of dense material in molecular clouds. Likewise, they give rise to a natural threshold for star formation at A_V^tail.Comment: 11 pages, 12 figures, accepted for publication in Astronomy and Astrophysic

Probing the evolution of molecular cloud structure: From quiescence to birth

Aims: We derive the probability density functions (PDFs) of column density for a complete sample of prominent molecular cloud complexes closer than 200 pc. Methods: We derive near-infrared dust extinction maps for 23 molecular cloud complexes, using the "nicest" colour excess mapping technique and data from the 2MASS archive. The extinction maps are then used to examine the column density PDFs in the clouds. Results: The column density PDFs of most molecular clouds are well-fitted by log-normal functions at low column densities (0.5 mag < A_v < 3-5 mag). However, at higher column densities prominent, power-law-like wings are common. In particular, we identify a trend among the PDFs: active star-forming clouds always have prominent non-log-normal wings. In contrast, clouds without active star formation resemble log-normals over the whole observed column density range, or show only low excess of higher column densities. This trend is also reflected in the cumulative PDFs, showing that the fraction of high column density material is significantly larger in star-forming clouds. These observations are in agreement with an evolutionary trend where turbulent motions are the main cloud-shaping mechanism for quiescent clouds, but the density enhancements induced by them quickly become dominated by gravity (and other mechanisms) which is strongly reflected by the shape of the column density PDFs. The dominant role of the turbulence is restricted to the very early stages of molecular cloud evolution, comparable to the onset of active star formation in the clouds.Comment: 7 pages, 11 figures, accepted to A&A Letter

A semi-analytic model of the turbulent multi-phase interstellar medium

We present a semi-analytic model for the interstellar medium that considers local processes and structures of turbulent star-forming gas. A volume element of the interstellar medium is described as a multiphase system, comprising a cold and a warm gas phase in effective (thermal plus turbulent) pressure equilibrium, and a stellar component. Since turbulence has a critical impact on the shape of the gaseous phases, on the production of molecular hydrogen and on the formation of stars, the consistent treatment of turbulence energy -- the kinetic energy of unresolved motions -- is an important new feature of our model. Besides turbulence production by supernovae and by the cooling instability, we also take into account the forcing by large scale motions. We formulate a set of ordinary differential equations, which statistically describes star formation and the exchange between the different budgets of mass and energy in a region of the interstellar medium with given mean density, size, metallicity and external turbulence forcing. By exploring the behaviour of the solutions, we find equilibrium states, in which the star formation efficiencies are consistent with observations. Kennicutt-Schmidt-like relations naturally arise from the equilibrium solutions, while conventional star formation models in numerical simulations impose such relations with observed efficiency parameters as phenomenological calibrations. Beyond the semi-analytic approach, a potential application is a complete subgrid scale model of the unresolved multi-phase structure, star formation and turbulence in simulations of galaxies or in cosmological simulations. The formulation presented in this article combines various models focusing on particular processes and yet can be adopted to specific applications, depending on the range of resolved length scales.Comment: 25 pages, 22 figures, 1 table, accepted for publication by MNRA

Do Lognormal Column-Density Distributions in Molecular Clouds Imply Supersonic Turbulence?

Recent observations of column densities in molecular clouds find lognormal distributions with power-law high-density tails. These results are often interpreted as indications that supersonic turbulence dominates the dynamics of the observed clouds. We calculate and present the column-density distributions of three clouds, modeled with very different techniques, none of which is dominated by supersonic turbulence. The first star-forming cloud is simulated using smoothed particle hydrodynamics (SPH); in this case gravity, opposed only by thermal-pressure forces, drives the evolution. The second cloud is magnetically subcritical with subsonic turbulence, simulated using nonideal MHD; in this case the evolution is due to gravitationally-driven ambipolar diffusion. The third cloud is isothermal, self-gravitating, and has a smooth density distribution analytically approximated with a uniform inner region and an r^-2 profile at larger radii. We show that in all three cases the column-density distributions are lognormal. Power-law tails develop only at late times (or, in the case of the smooth analytic profile, for strongly centrally concentrated configurations), when gravity dominates all opposing forces. It therefore follows that lognormal column-density distributions are generic features of diverse model clouds, and should not be interpreted as being a consequence of supersonic turbulence.Comment: 6 pages, 6 figures, accepted for publication in MNRA

The <i>Herschel</i> view of the massive star-forming region NGC 6334

Aims: Fundamental to any theory of high-mass star formation are gravity and turbulence. Their relative importance, which probably changes during cloud evolution, is not known. By investigating the spatial and density structure of the high-mass star-forming complex NGC 6334 we aim to disentangle the contributions of turbulence and gravity. Methods: We used Herschel PACS and SPIRE imaging observations from the HOBYS key programme at wavelengths of 160, 250, 350, and 500 μm to construct dust temperature and column density maps. Using probability distribution functions (PDFs) of the column density determined for the whole complex and for four distinct sub-regions (distinguished on the basis of differences in the column density, temperature, and radiation field), we characterize the density structure of the complex. We investigate the spatial structure using the Δ-variance, which probes the relative amount of structure on different size scales and traces possible energy injection mechanisms into the molecular cloud. Results: The Δ-variance analysis suggests that the significant scales of a few parsec that were found are caused by energy injection due to expanding HII regions, which are numerous, and by the lengths of filaments seen everywhere in the complex. The column density PDFs have a lognormal shape at low densities and a clearly defined power law at high densities for all sub-regions whose slope is linked to the exponent α of an equivalent spherical density distribution. In particular with α = 2.37, the central sub-region is largly dominated by gravity, caused by individual collapsing dense cores and global collapse of a larger region. The collapse is faster than free-fall (which would lead only to α = 2) and thus requires a more dynamic scenario (external compression, flows). The column density PDFs suggest that the different sub-regions are at different evolutionary stages, especially the central sub-region, which seems to be in a more evolved stage

Turbulent Mixing in the Interstellar Medium -- an application for Lagrangian Tracer Particles

We use 3-dimensional numerical simulations of self-gravitating compressible turbulent gas in combination with Lagrangian tracer particles to investigate the mixing process of molecular hydrogen (H2) in interstellar clouds. Tracer particles are used to represent shock-compressed dense gas, which is associated with H2. We deposit tracer particles in regions of density contrast in excess of ten times the mean density. Following their trajectories and using probability distribution functions, we find an upper limit for the mixing timescale of H2, which is of order 0.3 Myr. This is significantly smaller than the lifetime of molecular clouds, which demonstrates the importance of the turbulent mixing of H2 as a preliminary stage to star formation.Comment: 10 pages, 5 figures, conference proceedings "Turbulent Mixing and Beyond 2007