3D-PDR: a new three-dimensional astrochemistry code for treating photodissociation regions

Photodissociation regions (PDRs) define the transition zone between an ionized and a dark molecular region. They consist of neutral gas which interacts with far-ultraviolet radiation and are characterized by strong infrared line emission. Various numerical codes treating one-dimensional PDRs have been developed in the past, simulating the complexity of chemical reactions occurring and providing a better understanding of the structure of a PDR. In this paper we present the three-dimensional code, 3D-PDR, which can treat PDRs of arbitrary density distribution. The code solves the chemistry and the thermal balance self-consistently within a given three-dimensional cloud. It calculates the total heating and cooling functions at any point in a given PDR by adopting an escape probability method. It uses a HEALPIx-based ray tracing scheme to evaluate the attenuation of the far-ultraviolet radiation in the PDR and the propagation of the far-infrared/submm line emission out of the PDR. We present benchmarking results and apply 3D-PDR to (i) a uniform-density spherical cloud interacting with a plane-parallel external radiation field, (ii) a uniform-density spherical cloud interacting with a two-component external radiation field and (iii) a cometary globule interacting with a plane-parallel external radiation field. We find that the code is able to reproduce the benchmarking results of various other one-dimensional numerical codes treating PDRs. We also find that the accurate treatment of the radiation field in the fully three-dimensional treatment of PDRs can in some cases leads to different results when compared to a standard one-dimensional treatment

Smoothed Particle Hydrodynamics simulations of expanding HII regions. I. Numerical methods and tests

We describe a new algorithm for including the dynamical effects of ionizing radiation in SPH simulations, and we present several examples of how the algorithm can be applied to problems in star formation. We use the HEALPix software to tessellate the sky and to solve the equation of ionization equilibrium along a ray towards each of the resulting tesserae. We exploit the hierarchical nature of HEALPix to make the algorithm adaptive, so that fine angular resolution is invoked only where it is needed, and the computational cost is kept low. We present simulations of (i) the spherically symmetric expansion of an HII region inside a uniform-density, non--self-gravitating cloud; (ii) the spherically symmetric expansion of an HII region inside a uniform-density, self-gravitating cloud; (iii) the expansion of an off-centre HII region inside a uniform-density, non--self-gravitating cloud, resulting in rocket acceleration and dispersal of the cloud; and (iv) radiatively driven compression and ablation of a core overrun by an HII region. The new algorithm provides the means to explore and evaluate the role of ionizing radiation in regulating the efficiency and statistics of star formation.Comment: 12 pages, 16 figures, simulation movies available at http://galaxy.ig.cas.cz/~richard/HIIregion

ALMA observations of atomic carbon in z~4 dusty star-forming galaxies

We present ALMA [CI]($1-0$) (rest frequency 492 GHz) observations for a sample of 13 strongly-lensed dusty star-forming galaxies originally discovered at 1.4mm in a blank-field survey by the South Pole Telescope. We compare these new data with available [CI] observations from the literature, allowing a study of the ISM properties of $\sim 30$ extreme dusty star-forming galaxies spanning a redshift range $2 < z < 5$. Using the [CI] line as a tracer of the molecular ISM, we find a mean molecular gas mass for SPT-DSFGs of $6.6 \times 10^{10}$ M$_{\odot}$. This is in tension with gas masses derived via low-$J$ $^{12}$CO and dust masses; bringing the estimates into accordance requires either (a) an elevated CO-to-H$_2$ conversion factor for our sample of $\alpha_{\rm CO} \sim 2.5$ and a gas-to-dust ratio $\sim200$, or (b) an high carbon abundance $X_{\rm CI} \sim 7\times10^{-5}$. Using observations of a range of additional atomic and molecular lines (including [CI], [CII], and multiple transitions of CO), we use a modern Photodissociation Region code (3D-PDR) to assess the physical conditions (including the density, UV radiation field strength, and gas temperature) within the ISM of the DSFGs in our sample. We find that the ISM within our DSFGs is characterised by dense gas permeated by strong UV fields. We note that previous efforts to characterise PDR regions in DSFGs may have significantly underestimated the density of the ISM. Combined, our analysis suggests that the ISM of extreme dusty starbursts at high redshift consists of dense, carbon-rich gas not directly comparable to the ISM of starbursts in the local Universe.Comment: 21 pages, 12 figures. Accepted for publication in MNRA

Dispersal of molecular clouds by ionising radiation

The role of feedback from massive stars is believed to be a key element in the evolution of molecular clouds. We use high-resolution 3D SPH simulations to explore the dynamical effects of a single O7 star located at the centre of a molecular cloud with mass 10^4M_sun and radius 6.4pc. The initial internal structure of the cloud is characterised by its fractal dimension, D=2.0 - 2.8, and its log-normal density PDF. (i) As regards star formation, in the short term ionising feedback is positive, in the sense that star formation occurs much more quickly in gas that is compressed by the high pressure of the ionised gas. However, in the long term ionising feedback is negative, in the sense that most of the cloud is dispersed with an outflow rate of up to ~0.01M_sun/yr, on a timescale comparable with the sound-crossing time for the ionised gas (~1-2Myr), and triggered star formation is therefore limited to a few percent of the cloud's mass. (ii) As regards the morphology of the ionisation fronts (IFs) bounding the HII region and the systematics of outflowing gas, we distinguish two regimes. For low D<=2.2, the initial cloud is dominated by large-scale structures, so the neutral gas tends to be swept up into a few extended coherent shells, and the ionised gas blows out through a few large holes between these shells; we term these HII regions "shell-dominated". Conversely, for high D>=2.6, the initial cloud is dominated by small-scale structures, and these are quickly overrun by the advancing IF, thereby producing neutral pillars whilst the ionised gas blows out through a large number of small holes between the pillars; we term these HII regions "pillar-dominated". (iii) As regards the injection of bulk kinetic energy, by ~1Myr, the expansion of the HII region has delivered a rms velocity of ~6km/s; this represents less than 0.1% of the total energy radiated by the O7 star.Comment: 13 pages, 8 figures, 2 tables; submitted to MNRA

Comparing simulations of ionisation triggered star formation and observations in RCW 120

Massive clumps within the swept-up shells of bubbles, like that surrounding the galactic HII region RCW 120, have been interpreted in terms of the Collect and Collapse (C&C) mechanism for triggered star formation. The cold, dusty clumps surrounding RCW 120 are arranged in an almost spherical shell and harbour many young stellar objects. By performing high-resolution, three-dimensional SPH simulations of HII regions expanding into fractal molecular clouds, we investigate whether the formation of massive clumps in dense, swept-up shells necessarily requires the C&C mechanism. In a second step, we use RADMC-3D to compute the synthetic dust continuum emission from our simulations, in order to compare them with observations of RCW 120 made with APEX-LABOCA at 870 micron. We show that a distribution of clumps similar to the one seen in RCW 120 can readily be explained by a non-uniform initial molecular cloud structure. Hence, a shell-like configuration of massive clumps does not imply that the C&C mechanism is at work. Rather, we find a hybrid form of triggering, which combines elements of C&C and Radiatively Driven Implosion (RDI). In addition, we investigate the reliability of deriving clump masses from their 870 micron emission. We find that for clumps with more than 100 M_sun the observational estimates are accurate to within a factor of two and that, even at these long wavelengths, it is important to account for the radiative heating from triggered, embedded protostars.Comment: 10 pages, 7 figures, submitted to MNRA

The Milky Way Project: A statistical study of massive star formation associated with infrared bubbles

The Milky Way Project citizen science initiative recently increased the number of known infrared bubbles in the inner Galactic plane by an order of magnitude compared to previous studies. We present a detailed statistical analysis of this dataset with the Red MSX Source catalog of massive young stellar sources to investigate the association of these bubbles with massive star formation. We particularly address the question of massive triggered star formation near infrared bubbles. We find a strong positional correlation of massive young stellar objects (MYSOs) and H II regions with Milky Way Project bubbles at separations of < 2 bubble radii. As bubble sizes increase, a statistically significant overdensity of massive young sources emerges in the region of the bubble rims, possibly indicating the occurrence of triggered star formation. Based on numbers of bubble-associated RMS sources we find that 67+/-3% of MYSOs and (ultra)compact H II regions appear associated with a bubble. We estimate that approximately 22+/-2% of massive young stars may have formed as a result of feedback from expanding H II regions. Using MYSO-bubble correlations, we serendipitously recovered the location of the recently discovered massive cluster Mercer 81, suggesting the potential of such analyses for discovery of heavily extincted distant clusters.Comment: 16 pages, 17 figures. Accepted for publication in ApJ, comments welcome. Milky Way Project public data release available at http://www.milkywayproject.org/dat

Radiative transfer and the energy equation in SPH simulations of star formation

We introduce and test a new and highly efficient method for treating the thermal and radiative effects influencing the energy equation in SPH simulations of star formation. The method uses the density, temperature and gravitational potential of each particle to estimate a mean optical depth, which then regulates the particle's heating and cooling. The method captures -- at minimal computational cost -- the effects of (i) the rotational and vibrational degrees of freedom of H2, H2 dissociation, H0 ionisation, (ii) opacity changes due to ice mantle melting, sublimation of dust, molecular lines, H-, bound-free and free-free processes and electron scattering; (iv) external irradiation; and (v) thermal inertia. The new algorithm reproduces the results of previous authors and/or known analytic solutions. The computational cost is comparable to a standard SPH simulation with a simple barotropic equation of state. The method is easy to implement, can be applied to both particle- and grid-based codes, and handles optical depths 0<tau<10^{11}.Comment: Submitted to A&A, recommended for publicatio

Gravitational Instabilities in a proto-solar like disc I.: Dynamics and Chemistry

To date, most simulations of the chemistry in protoplanetary discs have used 1 + 1D or 2D axisymmetric α-disc models to determine chemical compositions within young systems. This assumption is inappropriate for non-axisymmetric, gravitationally unstable discs, which may be a significant stage in early protoplanetary disc evolution. Using 3D radiative hydrodynamics, we have modelled the physical and chemical evolution of a 0.17 M⊙ self-gravitating disc over a period of 2000 yr. The 0.8 M⊙ central protostar is likely to evolve into a solar-like star, and hence this Class 0 or early Class I young stellar object may be analogous to our early Solar system. Shocks driven by gravitational instabilities enhance the desorption rates, which dominate the changes in gas-phase fractional abundances for most species. We find that at the end of the simulation, a number of species distinctly trace the spiral structure of our relatively low-mass disc, particularly CN. We compare our simulation to that of a more massive disc, and conclude that mass differences between gravitationally unstable discs may not have a strong impact on the chemical composition. We find that over the duration of our simulation, successive shock heating has a permanent effect on the abundances of HNO, CN and NH3, which may have significant implications for both simulations and observations. We also find that HCO+ may be a useful tracer of disc mass. We conclude that gravitational instabilities induced in lower mass discs can significantly, and permanently, affect the chemical evolution, and that observations with high-resolution instruments such as Atacama Large Millimeter/submillimeter Array (ALMA) offer a promising means of characterizing gravitational instabilities in protosolar discs

STARBENCH: the D-type expansion of an HII region

STARBENCH is a project focused on benchmarking and validating different star formation and stellar feedback codes. In this first STARBENCH paper we perform a comparison study of the D-type expansion of an H II region. The aim of this work is to understand the differences observed between the 12 participating numerical codes against the various analytical expressions examining the D-type phase of H II region expansion. To do this, we propose two well-defined tests which are tackled by 1D and 3D grid- and smoothed particle hydrodynamics-based codes. The first test examines the ‘early phase’ D-type scenario during which the mechanical pressure driving the expansion is significantly larger than the thermal pressure of the neutral medium. The second test examines the ‘late phase’ D-type scenario during which the system relaxes to pressure equilibrium with the external medium. Although they are mutually in excellent agreement, all 12 participating codes follow a modified expansion law that deviates significantly from the classical Spitzer solution in both scenarios. We present a semi-empirical formula combining the two different solutions appropriate to both early and late phases that agrees with high-resolution simulations to ≲ 2 per cent. This formula provides a much better benchmark solution for code validation than the Spitzer solution. The present comparison has validated the participating codes and through this project we provide a data set for calibrating the treatment of ionizing radiation hydrodynamics codes

Evolution of prolate molecular clouds at H II boundaries - II. Formation of BRCs of asymmetrical morphology

A systematic investigation on the evolution of a prolate cloud at an H II boundary is conducted using smoothed particle hydrodynamics in order to understand the mechanism for a variety of irregular morphological structures found at the boundaries of various H II regions. The prolate molecular clouds in this investigation are set with their semimajor axes at inclinations between 0° and 90° to a plane-parallel ionizing radiation flux. A set of four parameters, the number density n, the ratio of major to minor axis γ, the inclination angle Φ and the incident flux FEUV, are used to define the initial state of the simulated clouds. The dependence of the evolution of a prolate cloud under radiation-driven implosion (RDI) on each of the four parameters is investigated. It is found that (i) in addition to the well-studied standard type A, B or C bright-rimmed clouds (BRCs), many other types such as asymmetrical BRCs, filamentary structures and irregular horse-head structures could also be developed at H II boundaries with only simple initial conditions; (ii) the final morphological structures are very sensitive to the four initial parameters, especially to the initial density and the inclination; (iii) the previously defined ionizing radiation penetration depth can still be used as a good indicator of the final morphology. Based on the simulation results, the formation time-scales and masses of the early RDI-triggered star formation from clouds of different initial conditions are also estimated. Finally a unified mechanism for the various morphological structures found in many different H II boundaries is suggested