We present a new set of analytic models for the expansion of HII regions powered by UV photoionisation from massive stars and compare them to a new suite of radiative magnetohydrodynamic simulations of turbulent, self-gravitating molecular clouds. To
perform these simulations we use the Eulerian adaptive mesh magnetohydrodynamics code RAMSES-RT, including radiative transfer of UV photons. Our analytic models successfully predict the global behaviour of the HII region provided the density and velocity structure of the cloud is known. We give estimates for the HII region behaviour based on a power law fit to the density field assuming that the system is virialised. We give a radius at which the ionisation front should stop expanding (stall). If this radius is smaller than the distance to the edge of the cloud, the HII region will be trapped by the cloud. This effect is more severe in collapsing clouds than in virialised clouds, since the density in the former increases dramatically over time, with much larger photon emission rates needed for the HII region to escape a collapsing cloud. We also measure the response of Jeans unstable gas to the HII regions to predict the impact of UV radiation on star formation in the cloud. We find that the mass in unstable gas can be explained by a model in which the clouds are evaporated by UV photons, suggesting that the net feedback on star formation should be negative
Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of fragmentation and the
number of fragments seem to be determined to a large degree by the initial conditions. In this work we study the fate of the linear perturbations of a homogeneous gas sphere both analytically and numerically. In particular, we investigate the stability of the well-known homologous solution that describes the collapse of a uniform spherical cloud. The difficulty of the mathematical singularity in the perturbation equations is surpassed here by explicitly introducing a weak shock next to the sonic point. In parallel, we perform adaptive mesh refinement (AMR) numerical simulations of the linear stages of the collapse and compared the growth rates obtained by each method. With this combination of analytical and numerical tools, we explore the behavior of both spherically symmetric and non-axisymmetric perturbations. The numerical experiments provide the linear growth rates as a function of the cores initial virial parameter and as a function of the azimuthal wave number of the perturbation. The overlapping regime of the numerical experiments and the analytical predictions is the situation of a cold and large cloud, and in this regime the analytically calculated growth rates agree very well with the ones obtained from the simulations. The use of a weak shock as part of the perturbation allows us to find a physically acceptable solution to the equations for a continuous range of growth rates. The numerical simulations agree very well with the analytical prediction for the most unstable cores, while they impose a limit of a virial parameter of 0.1 for core fragmentation in the absence of rotation.
Context. Molecular clouds are known to be turbulent and strongly affected by stellar feedback. Moreover, stellar feedback is believed to drive turbulence at large scales in galaxies. Aims. We study the role played by supernovae in molecular clouds
and the influence of the magnetic field on this process. Methods. We performed three-dimensional numerical simulations of supernova explosions, in and near turbulent self-gravitating molecular clouds. In order to study the influence of the magnetic field, we performed both hydrodynamical and magnetohydrodynamical simulations. We also ran a series of simple uniform density medium simulations and developed a simple analytical model. Results. We find that the total amount of momentum that is delivered during supernova explosions typically varies by a factor of about 2, even when the gas density changes by 3 orders of magnitude. However, the amount of momentum delivered to the dense gas varies by almost a factor of 10 if the supernova explodes within or outside the molecular cloud. The magnetic field has little influence on the total amount of momentum injected by the supernova explosions but increases the momentum injected into the dense gas. Conclusions. Supernovae that explode inside molecular clouds remove a significant fraction of the cloud mass. Supernovae that explode outside have a limited influence on the cloud. It is thus essential to know sufficiently well the correlation between supernovae and the surrounding dense material in order to know whether supernovae can regulate star formation effectively.
Context. Ultraviolet radiation plays a crucial role in molecular clouds. Radiation and matter are tightly coupled and their interplay influences the physical and chemical properties of gas. In particular, modeling the radiation propagation requires c
alculating column densities, which can be numerically expensive in high-resolution multidimensional simulations. Aims. Developing fast methods for estimating column densities is mandatory if we are interested in the dynamical influence of the radiative transfer. In particular, we focus on the effect of the UV screening on the dynamics and on the statistical properties of molecular clouds. Methods. We have developed a tree-based method for a fast estimate of column densities, implemented in the adaptive mesh refinement code RAMSES. We performed numerical simulations using this method in order to analyze the influence of the screening on the clump formation. Results. We find that the accuracy for the extinction of the tree-based method is better than 10%, while the relative error for the column density can be much more. We describe the implementation of a method based on precalculating the geometrical terms that noticeably reduces the calculation time. To study the influence of the screening on the statistical properties of molecular clouds we present the probability distribution function (PDF) of gas and the associated temperature per density bin and the mass spectra for different density thresholds. Conclusions. The tree-based method is fast and accurate enough to be used during numerical simulations since no communication is needed between CPUs when using a fully threaded tree. It is then suitable to parallel computing. We show that the screening for far UV radiation mainly affects the dense gas, thereby favoring low temperatures and affecting the fragmentation.
Context: Star formation efficiency (SFE) theories are currently based on statistical distributions of turbulent cloud structures and a simple model of star formation from cores. They remain poorly tested, especially at the highest densities. Aims: We
investigate the effects of gas density on the SFE through measurements of the core formation efficiency (CFE). With a total mass of $sim2times10^4$ M$_odot$, the W43-MM1 ridge is one of the most convincing candidate precursor of starburst clusters and thus one of the best place to investigate star formation. Methods: We used high-angular resolution maps obtained at 3 mm and 1 mm within W43-MM1 with the IRAM Plateau de Bure Interferometer to reveal a cluster of 11 massive dense cores (MDCs), and, one of the most massive protostellar cores known. An Herschel column density image provided the mass distribution of the cloud gas. We then measured the instantaneous CFE and estimated the SFE and the star formation rate (SFR) within subregions of the W43-MM1 ridge. Results: The high SFE found in the ridge ($sim$6% enclosed in $sim$8 pc$^3$) confirms its ability to form a starburst cluster. There is however a clear lack of dense cores in the northern part of the ridge, which may be currently assembling. The CFE and the SFE are observed to increase with volume gas density while the SFR steeply decreases with the virial parameter, $alpha_{vir}$. Statistical models of the SFR may well describe the outskirts of the W43-MM1 ridge but struggle to reproduce its inner part, which corresponds to measurements at low $alpha_{vir}$. It may be that ridges do not follow the log-normal density distribution, Larson relations, and stationary conditions forced in the statistical SFR models.
Cosmic rays (CR) play an important role in dense molecular cores, affecting their thermal and dynamical evolution and initiating the chemistry. Several studies have shown that the formation of protostellar discs in collapsing clouds is severely hampe
red by the braking torque exerted by the entrained magnetic field on the infalling gas, as long as the field remains frozen to the gas. We examine the possibility that the concentration and twisting of the field lines in the inner region of collapse can produce a significant reduction of the ionisation fraction. To check whether the CR ionisation rate (CRir) can fall below the critical value required to maintain good coupling, we first study the propagation of CRs in a model of a static magnetised cloud varying the relative strength of the toroidal/poloidal components and the mass-to-flux ratio. We then follow the path of CRs using realistic magnetic field configurations generated by numerical simulations of a rotating collapsing core. We find that an increment of the toroidal component of the magnetic field, or, in general, a more twisted configuration of the field lines, results in a decrease in the CR flux. This is mainly due to the magnetic mirroring effect that is stronger where larger variations in the field direction are present. In particular, we find a decrease of the CRir below 10^-18 s-1 in the central 300-400 AU, where density is higher than about 10^9 cm-3. This very low value of the CRir is attained in the cases of intermediate and low magnetisation (mass-to-flux ratio lambda=5 and 17, respectively) and for toroidal fields larger than about 40% of the total field. Magnetic field effects can significantly reduce the ionisation fraction in collapsing clouds. We provide a handy fitting formula to compute approximately the attenuation of the CRir in a molecular cloud as a function of the density and the magnetic configuration.
Our main purpose is to estimate the effect of assuming uniform density on the line-of-sight in PDR chemistry models, compared to a more realistic distribution for which total gas densities may well vary by several orders of magnitude. A secondary goa
l of this paper is to estimate the amount of molecular hydrogen which is not properly traced by the CO (J = 1 -> 0) line, the so-called dark molecular gas. We use results from a magnetohydrodynamical (MHD) simulation as a model for the density structures found in a turbulent diffuse ISM with no star-formation activity. The Meudon PDR code is then applied to a number of lines of sight through this model, to derive their chemical structures. It is found that, compared to the uniform density assumption, maximal chemical abundances for H2, CO, CH and CN are increased by a factor 2 to 4 when taking into account density fluctuations on the line of sight. The correlations between column densities of CO, CH and CN with respect to those of H2 are also found to be in better overall agreement with observations. For instance, at N(H2) > 2.10^{20} cm-2, while observations suggest that d[log N(CO)]=d[log N(H2)] = 3.07 +/- 0.73, we find d[log N(CO)]=d[log N(H2)] =14 when assuming uniform density, and d[log N(CO)]=d[log N(H2)] = 5.2 when including density fluctuations.
We present a simple dimensional argument to illustrate the impact of nonthermal support from turbulent velocity dispersion on the shape of the prestellar core mass function (CMF), precursor of the stellar initial mass function (IMF). The argument dem
onstrates the need to invoke such support to recover the Salpeter slope in the high-mass part of the CMF/IMF, whereas pure thermal support leads to a much steeper slope. This simple dimensional argument clearly highlights the results obtained in the complete Hennebelle-Chabrier theory of the IMF.
We present a simple statistical analysis of recent numerical simulations exploring the correlation between the core mass function obtained from the fragmentation of a molecular cloud and the stellar mass function which forms from these collapsing cor
es. Our analysis shows that the distributions of bound cores and sink particles obtained in the simulations are consistent with the sinks being formed predominantly from their parent core mass reservoir, with a statistical dispersion of the order of one third of the core mass. Such a characteristic dispersion suggests that the stellar initial mass function is relatively tightly correlated to the parent core mass function, leading to two similar distributions, as observed. This in turn argues in favor of the IMF being essentially determined at the early stages of core formation and being only weakly affected by the various environmental factors beyond the initial core mass reservoir, at least in the mass range explored in the present study. Accordingly, the final IMF of a star forming region should be determined reasonably accurately, statistically speaking, from the initial core mass function, provided some uniform efficiency factor. The calculations also show that these statistical fluctuations, due e.g. to variations among the core properties, broaden the low-mass tail of the IMF compared with the parent CMF, providing an explanation for the fact that this latter appears to underestimate the number of pre brown dwarf cores compared with the observationally-derived brown dwarf IMF.
We study the rotational properties of magnetized and self-gravitating molecular cloud cores formed in 2 very high resolution 3D molecular cloud simulations.The simulations have been performed using the code RAMSES at an effective resolution of 4096^3
.One simulation represents a mildly magnetically-supercritical cloud and the other a strongly magnetically-supercritical cloud.A noticeable difference between the 2 simulations is the core formation efficiency (CFE) of the high density cores.In the strongly supercritical simulations the CFE is ~33 % per free-fall time of the cloud tff,cl, whereas in the mildly supercritical simulations this value goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular momentum j3D distributions of the cores with the distribitions of j2D derived using synthetic 2D velocity maps of the cores,shows that the synthetic observations tend to overestimate the true value of j by a factor of ~10.The origin of this discrepancy lies in the fact that contrary to the intrinsic determination which sums up the individual gas parcels contributions to j, the determination of j using the observational procedure which is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation smoothes out the complex fluctuations present in the 3D velocity field. Our results provide a natural explanation for the discrepancy by a factor ~10 observed between the intrinsic 3D distributions of j and the corresponding distributions derived in real observations.We suggest that measurements of j which are based on the measurement of the observed global velocity gradients may need to be reduced by a factor of ~10 in order to derive a more accurate estimate of j in the cores.
