Turbulent Cloud Research Articles

Environmental effects on the dynamical evolution of star clusters in turbulent molecular clouds

Context. Star clusters form within giant molecular clouds that are strongly altered by the feedback action of the massive stars, but the cluster still remains embedded in a dense, highly turbulent medium and interactions with ambient structures may modify its dynamical evolution from that expected if it were isolated. Aims. We aim to study coupling mechanisms between the dynamical evolution of the cluster, accelerated by the mass segregation process, with harassment effects caused by the gaseous environment. Methods. We simulated the cluster dynamical evolution combining N-body and hydrodynamic codes within the Astronomical Multipurpose Software Environment (AMUSE). Results. Tidal harassment produces a sparser configuration more rapidly than the isolated reference simulations. The evolution of the asymptotic power-law density distribution exponent also shows substantially different behaviour in the two cases. The background is more effective on clusters in advanced stages of dynamical development.

Saturation Level of Turbulence in Collapsing Gas Clouds

We investigate the physical mechanism that determines the saturation level of the turbulence in collapsing gas clouds. We perform a suite of high-resolution numerical simulations that follow the collapse of turbulent gas clouds, with various effective polytropic exponents γ eff, initial Mach numbers , and initial turbulent seeds. Equating the energy injection rate from gravitational contraction and the dissipation rate of the turbulence, we obtain an analytic expression for the saturation level of the turbulence, and compare it with the numerical results. Consequently, the numerical results are well described by the analytic model, given that the turbulent driving scale in collapsing gas clouds is one-third the Jeans length of the collapsing core. These results indicate that the strength of the turbulence at first-core formations in the early universe/the present-day star formation process can be estimated solely by γ eff.

SIMULATIONS OF UNEQUAL BINARY COLLISIONS EMBEDDED IN A TURBULENT GAS CLOUD FAR FROM A MASSIVE GRAVITATIONAL CENTER

We simulate the collapse of a turbulent gas cloud, in which we choose two sub-clouds. A translational velocity $\vec{r}_L$ or $\vec{r}_R$ is added, so that the sub-clouds move towards each other to collide. The radius and pre-collision velocity of the sub-clouds are chosen to be unequal, and both head-on and oblique collisions are considered. The simulations are all calibrated to have the same total mass and initial energy ratio α = 0.16, which is defined as the ratio of thermal energy to gravitational energy. We compare low-β models to a high-β models, where β is defined as the ratio of kinetic energy to gravitational energy. Finally, we consider the turbulent cloud to be under the gravitational influence of an object located far enough, in order to approximate the tidal effects by means of an azimuthal velocity Vcir added to the cloud particles apart from the translational and turbulent velocities mentioned above. We compare a low-Vcir model with a high-Vcir one.

Impact of Advection Schemes on Tracer Interrelationships in Large-Eddy Simulations of Deep Convection

Abstract This study investigates the preservation of tracer interrelationships during advection in large-eddy simulations of an idealized deep convective cloud, which is particularly relevant to chemistry, aerosol, and cloud microphysics models. Employing the Cloud Model 1, advection is represented using third-, fifth-, and seventh-order weighted essentially non-oscillatory schemes. As a simplified analogy for cloud hydrometeors and aerosols, several inert passive tracers following linear and nonlinear relationships are initialized after the cloud reaches ∼6-km depth. Numerical mixing in the simulated turbulent convective clouds leads to significant deviations from the initial nonlinear relationships between tracers. In these simulations, a considerable fraction of the grid points where the tracers’ nonlinear relationships are altered from advection are classified as unrealistic (e.g., ∼13% for the environmental tracers on average), including errors from range-preserving unmixing and overshooting. Errors in the sum of three tracers are also relatively large, ranging between ∼1% and 16% for 5% of the grid points in and near the cloud. The magnitude of unrealistic mixing and errors in the sum of three tracers generally increase with the order of accuracy of the advection scheme. These results are consistent across model grid spacings ranging from 50 to 200 m, and across three different flow realizations for each combination of grid spacing and advection scheme tested. Tests employing a previously proposed scalar normalization procedure show substantially reduced errors in the sum of three tracers with a relatively small negative impact on other tracer relationships. This analysis, therefore, suggests efficacy of the normalization procedure when applied to turbulent three-dimensional cloud simulations. Significance Statement In nature, transporting several quantities through bulk motions of a fluid does not affect preexisting relationships between them. However, this is not always accomplished in numerical models of the atmosphere, because of intrinsic limitations in the transport algorithms employed. We aim to investigate how these errors behave in 3D realistic simulations of a cumulus cloud, where the turbulent flow constitutes a particular challenge. We show that relationships between quantities are significantly and frequently perturbed during bulk transport in the model. Moreover, our results suggest that increasing complexity of the bulk-transport algorithms (in a way that is conventionally employed for improving the representation of individual quantities) tends to worsen the representation of relationships between two or three quantities.

Large‐eddy simulations of drizzling shallow cumuli using a turbulence‐aware autoconversion parametrization

AbstractTurbulence in clouds enhances collision between cloud droplets, which is critical to drizzle formation in shallow cumulus clouds. In this study, we develop an autoconversion parametrization that considers the turbulence‐induced collision enhancement (TICE) obtained from a particle trajectory model. We implement the developed parametrization to a large‐eddy simulation model and simulate the Rain In Cumulus over the Ocean (RICO) case to investigate the effects of TICE on shallow cumulus clouds and their sensitivities to the cloud droplet number concentration and horizontal grid resolution. TICE significantly increases the autoconversion rate, leading to large increases in the accretion rate, rainwater path and surface rain rate. The simulations of shallow cumulus clouds are highly sensitive to the cloud droplet number concentration and horizontal grid resolution, and the inclusion of TICE overall reduces the sensitivities. For example, the large rainwater path and surface rain rate that appear when cloud droplet number concentration is relatively low are reduced by TICE, whereas the very small rainwater path and surface rain rate that appear when cloud droplet number concentration is relatively high are increased by TICE. Comparisons with two other TICE‐aware parametrizations based on direct numerical simulation results of droplet collisions in turbulence show that there are substantial differences in TICE effects for different parametrizations, which implies a large uncertainty in simulating turbulent clouds. Among the three parametrizations, the parametrization developed in this study shows intermediate TICE‐induced increases in rainwater path and surface rain rate.

Detecting Nonequilibrium States in Atmospheric Turbulence

Abstract In this work we show how to retrieve information about temporal changes of turbulence in the atmosphere based on in situ wind velocity measurements performed by aircraft. We focus on the stratocumulus-topped boundary layer high-resolution data taken by a helicopter-borne platform Airborne Cloud Turbulence Observation System (ACTOS). We calculate two nondimensional indicators, the dissipation factor and the integral-to-Taylor-scale ratio, and study their dependence on the Taylor-scale-based Reynolds number. By analyzing these results, we can identify regions where turbulence is in its stationary state and regions where turbulence decays in time or, on the contrary, becomes stronger. We can also detect nonequilibrium turbulence states, which indicate the presence of rapidly changing external conditions. Significance Statement The purpose of this work is to retrieve new information on turbulence in the atmosphere. We consider data from a field study based on in situ observations from a measurement payload below a slow-flying helicopter. We show that it is possible to retrieve information on temporal tendencies in a given region from such measurements. We attempt to estimate whether turbulence is in its stationary state, or possibly, turbulence decays due to insufficient production, or, on the contrary, becomes stronger. Such information provide useful knowledge of small-scale processes in the atmospheric boundary layer and can be used to improve their parameterizations.

Turbulence, coherence, and collapse: Three phases for core evolution

ABSTRACT We study the formation, evolution, and collapse of dense cores by tracking structures in a magnetohydrodynamic simulation of a star-forming cloud. We identify cores using the dendrogram algorithm and utilize machine learning techniques, including Neural Gas prototype learning and Fuzzy c-means clustering to analyse the density and velocity dispersion profiles of cores together with six bulk properties. We produce a 2-d visualization using a Uniform Manifold Approximation and Projection (UMAP), which facilitates the connection between physical properties and three partially-overlapping phases: i) unbound turbulent structures (Phase I), ii) coherent cores that have low turbulence (Phase II), and iii) bound cores, many of which become protostellar (Phase III). Within Phase II, we identify a population of long-lived coherent cores that reach a quasi-equilibrium state. Most prestellar cores form in Phase II and become protostellar after evolving into Phase III. Due to the turbulent cloud environment, the initial core properties do not uniquely predict the eventual evolution, i.e. core evolution is stochastic, and cores follow no one evolutionary path. The phase lifetimes are 1.0 ± 0.1 × 105 yr, 1.3 ± 0.2 × 105 yr, and 1.8 ± 0.3 × 105 yr for Phase I, II, and III, respectively. We compare our results to NH3 observations of dense cores. Known coherent cores predominantly map into Phase II, while most turbulent pressure-confined cores map to Phase I or III. We predict that a significant fraction of observed starless cores have unresolved coherent regions and that ≳20 per cent of observed starless cores will not form stars. Measurements of core radial profiles in addition to the usual bulk properties will enable more accurate predictions of core evolution.

Super‐Droplet Method to Simulate Lagrangian Microphysics of Nuclear Fallout in a Homogeneous Cloud

AbstractNuclear detonations produce hazardous local and global particles or fallout. Predicting fallout size, chemical components, and location is necessary to inform officials and determine immediate guidance for the public. However, existing nuclear detonation fallout models prescribe the particle size distributions based on limited observations. In this work, we apply the super‐droplet method, which is a numerical modeling technique developed for cloud microphysics, to simulate size distributions of particles in a mushroom cloud formed post‐detonation of a nuclear device. We model fallout formation and evolution with homogeneous nucleation and condensation of a single species and a Monte Carlo coagulation algorithm. We verify the numerical methods representing coagulation and condensation processes against analytical test problems. Additionally, we explore several scenarios for the integral system mass and yield in equivalent kilotons (kt) of TNT (trinitrotoluene). The fallout size distribution median diameter dpg follows a scaling law based on the integral system mass mv0 kg and yield Y kt: nm. We test the effect of cloud turbulence, enhanced nucleation and growth, and vapor volatility with a sensitivity study. The range in median diameter predictions for simulations of historical tests performed over the Pacific encompass the measurements of particles sampled from the cloud caps. Predicted median particle size ranges up to 217, 123, 86, and 35 nm for historical tests with yields of 0.2, 0.7, 2, and 10 Mt, respectively. This work can be expanded in many different directions to build a more predictive model for fallout formation.

Density distribution function of a self-gravitating isothermal turbulent fluid in the context of molecular cloud ensembles – III. Virial analysis

ABSTRACT In this work, we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov & Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not only for supersonic flows but for trans- and subsonic ones as well. Making use of the Eulerian virial theorem at an arbitrary scale, far from the cloud core, we derive an equation for the density profile and solve it in approximate way. The result confirms the solution ϱ(ℓ) = ℓ−2 found in the previous papers. This solution corresponds to three possible configurations for the energy balance. For trans- or subsonic flows, we obtain a balance between the gravitational and thermal energy (Case 1) or between the gravitational, turbulent, and thermal energies (Case 2) while for supersonic flows, the possible balance is between the gravitational and turbulent energy (Case 3). In Cases 1 and 2, the energy of the fluid element can be negative or zero; thus the solution is dynamically stable and shall be long lived. In Case 3, the energy of the fluid element is positive or zero, i.e. the solution is unstable or at best marginally bound. At scales near the core, one cannot neglect the second derivative of the moment of inertia of the gas, which prevents derivation of an analytic equation for the density profile. However, we obtain that gas near the core is not virialized and its state is marginally bound since the energy of the fluid element vanishes.

Star cluster formation in clouds with externally driven turbulence

ABSTRACT Star clusters are known to be formed in turbulent molecular clouds. How turbulence is driven in molecular clouds and what effect this has on star formation is still unclear. We compare a simulation setup with turbulent driving everywhere in a periodic box with a setup where turbulence is only driven around the outside of the box. We analyse the resulting gas distribution, kinematics, and the population of stars that are formed from the cloud. Both setups successfully produce a turbulent velocity field with a power-law structure function, the externally driven cloud has a more central, monolithic, clump, while the fully driven cloud has many smaller, more dispersed, clumps. The star formation follows the cloud morphology producing large clusters, with high star-forming efficiency in the externally driven simulations and sparse individual star formation with much lower star formation efficiency in the fully driven case. We conclude that the externally driven method, which resembles a Global Hierarchical Collapse (GHC) scenario, produces star clusters that more closely match with observations.

Multi‐Scale Kelvin‐Helmholtz Instability Dynamics Observed by PMC Turbo on 12 July 2018: 1. Secondary Instabilities and Billow Interactions

AbstractThe Polar Mesospheric Cloud (PMC) Turbulence experiment performed optical imaging and Rayleigh lidar PMC profiling during a 6‐day flight in July 2018. A mosaic of seven imagers provided sensitivity to spatial scales from ∼20 m to 100 km at a ∼2‐s cadence. Lidar backscatter measurements provided PMC brightness profiles and enabled definition of vertical displacements of larger‐scale gravity waves (GWs) and smaller‐scale instabilities of various types. These measurements captured an interval of strong, widespread Kelvin‐Helmholtz instabilities (KHI) occurring over northeastern Canada on July 12, 2018 during a period of significant GW activity. This paper addresses the evolution of the KHI field and the characteristics and roles of secondary instabilities within the KHI. Results include the imaging of secondary KHI in the middle atmosphere and multiple examples of KHI “tube and knot” (T&K) dynamics where two or more KH billows interact. Such dynamics have been identified clearly only once in the atmosphere previously. Results reveal that KHI T&K arise earlier and evolve more quickly than secondary instabilities of uniform KH billows. A companion paper by Fritts et al. (2022), https://doi.org/10.1029/2021JD035834 reveals that they also induce significantly larger energy dissipation rates than secondary instabilities of individual KH billows. The expected widespread occurrence of KHI T&K events may have important implications for enhanced turbulence and mixing influencing atmospheric structure and variability.

Peak Rain Rate Sensitivity to Observed Cloud Condensation Nuclei and Turbulence in Continental Warm Shallow Clouds During CACTI

AbstractWarm clouds strongly affect Earth's energy budget but remain imperfectly represented in climate models, partly due to the complexity and covariability of relevant processes influencing warm rain. This work presents a detailed analysis of different factors affecting rain rate peak intensity (RR) in continental warm clouds. Clouds were identified with vertically pointing radar and lidar observations and categorized via a temperature‐based cloud type classification algorithm from which warm clouds were isolated. Observations and retrievals of liquid water path (LWP), cloud condensation nuclei concentration (NCCN), cloud depth, and cloud duration of more than 3,000 separate warm clouds sampled during the Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign are analyzed in this work. Multiple linear regression (MLR) and random forest (RF) models are applied to assess the relative impact of these variables on RR. Overall, RR tends to increase as cloud depth, LWP, and cloud duration increase, or NCCN decreases. Cloud depth affects RR the most while NCCN impacts it the least. When considering over 170 warm clouds observed at least 1 hr in which in‐cloud turbulence is retrieved, the effect of NCCN on RR remains most likely suppressive, but it is not significant at a 75% level for MLR and is highly uncertain for RF. The impact of in‐cloud turbulence depends on the moment and location it is sampled. Cloud base turbulence around the time of RR suppresses RR, while cloud top turbulence effects are inconclusive. Possible difficulties in isolating robust CCN and turbulence effects on RR are discussed.

Turbulence analysis on the flight of Etihad airways in Bangka Island using the WRF case study May 4, 2016

<p>Accurate weather forecasts should support the increase in safety of aviation operations in Indonesia. This weather forecast is needed, especially in detecting turbulence, considering that geographically Indonesia has effective solar radiation resulting in convective cloud formation. Convective clouds can trigger turbulence then produce disruption and even accidents on flights. This research uses a case study on the Etihad Airways flight on Bangka Island on May 4, 2016. At the time of the incident, there was turbulence at 39,000 feet altitude, and the aircraft did not enter the cloudy area. The Weather Research and Forecasting (WRF) model is used to simulate the turbulence in this study, which is downscaled up to 3 km with a microphysics parameterization of WRF Single Moment 6 Class (WSM6). The results were then verified using correlation and linear regression for temperature, wind direction, wind speed, and pattern resemblance between cloud fraction and the convective nuclei distribution. The turbulence is analyzed from the south-north and west-east vertical airflow. The turbulence spotted at 06.40 UTC when there is a quite strong updraft which can cause turbulence. The turbulence parameters used, such as the eddy dissipation rate (EDR) parameter, which has a value of 0.05 , Richardson number with a value of less than 0.25, and turbulence index (TI 1) with a maximum value of 4 x 10<sup>-7</sup> s<sup>-2</sup> found that turbulence was in a strong category. The turbulence that occurs in this study is identified as near cloud turbulence (NCT) event due to cloud formation observed in the west of the turbulence and intense updraft activity at the location of turbulence.</p>

Vertical aerosol particle exchange in the marine boundary layer estimated from helicopter-borne measurements in the Azores region

Abstract. Aerosol particles are important for radiation effects, cloud formation, and therefore the climate system. A detailed understanding of the spatial distribution of aerosol particles within the atmospheric boundary layer, which depends on sources and sinks, as well as long-range transport and vertical exchange, is important. Especially in marine regions, where the climate effect of clouds is comparably high, long-range transport with subsequent vertical mixing dominates over local aerosol sources. In this study, three different methods were applied to estimate the vertical aerosol particle flux in the marine boundary layer (MBL) and the vertical exchange between the MBL and the free troposphere (FT): eddy covariance (EC), flux–gradient similarity (K theory), and the mixed-layer gradient method (MLG). For the first time, MBL aerosol fluxes derived from these three methods were compared in the framework of the “Azores Stratocumulus Measurements of Radiation, Turbulence and Aerosols” (ACORES) field campaign in the Azores region in the northeastern Atlantic Ocean in July 2017. Meteorological parameters and aerosol and cloud properties were measured in the marine troposphere using the helicopter-borne measurement platform ACTOS (Airborne Cloud Turbulence Observation System). All three methods were applied to estimate the net particle exchange between MBL and FT. In many cases, the entrainment fluxes of the MLG method agreed within the range of uncertainty with the EC and K-theory flux estimates close to the top of the MBL, while the surface flux estimates of the different methods diverged. It was not possible to measure directly above the surface with the helicopter-borne payload, which might be a source of uncertainty in the surface fluxes. The observed particle fluxes at the top of the MBL ranged from 0 to 10×106 m−2 s−1 both in the upward and the downward direction, and the associated uncertainties were on the same order of magnitude. Even though the uncertainties of all three methods are considerable, the results of this study contribute to an improved understanding of the transport of particles between the MBL and FT and their distribution in the MBL.

Revealing the Drag Instability in One-fluid Nonideal Magnetohydrodynamic Simulations of a 1D Isothermal C-shock

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in nonideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the post-shock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed.

Impact of Radiation Feedback on the Formation of Globular Cluster Candidates during Cloud–Cloud Collisions

To understand the impact of radiation feedback during the formation of a globular cluster (GC), we simulate a head-on collision of two turbulent giant molecular clouds (GMCs). A series of idealized radiation-hydrodynamic simulations is performed, with and without stellar radiation or Type II supernovae. We find that a gravitationally bound, compact star cluster of mass M GC ∼ 105 M ⊙ forms within ≈3 Myr when two GMCs with mass M GMC = 3.6 × 105 M ⊙ collide. The GC candidate does not form during a single collapsing event but emerges due to the mergers of local dense gas clumps and gas accretion. The momentum transfer due to the absorption of the ionizing radiation is the dominant feedback process that suppresses the gas collapse, and photoionization becomes efficient once a sufficient number of stars form. The cluster mass is larger by a factor of ∼2 when the radiation feedback is neglected, and the difference is slightly more pronounced (16%) when extreme Lyα feedback is considered in the fiducial run. In the simulations with radiation feedback, supernovae explode after the star-forming clouds are dispersed, and their metal ejecta are not instantaneously recycled to form stars.

Flow Characteristics Study of High-Parameter Multi-Stage Sleeve Control Valve

This study considers a multi-stage sleeve control valve with different opening degrees. The flow capacity of the numerical model is calculated using the actual working conditions of the control valve in a nuclear power plant as a baseline. A flow resistance test bench is then used to measure the flow capacity under each opening degree, and the flow characteristic curve is plotted to verify the accuracy of the numerical model. Based on CFX software simulations of different opening speeds, pressures, turbulent kinetic energy clouds, and set detection curves, analysis of the flow characteristics of the multi-stage sleeve valve with high parameters shows that, with an increase in the degree of opening, the valve speed will also increase. However, the speed at the socket orifice is slightly different, exhibiting a higher opening in the middle and lower openings on both sides. A maximum speed of 792.4 m/s is found in the 40% valve orifice. A maximum value of the turbulent kinetic energy of 1.4 × 10 4m2/s2 occurs in the throttle hole of the valve seat with an opening of 80%. The source of the aerodynamic noise is obtained in this study, which is of great significance to the decompression and noise reduction in multi-stage sleeve valves.

Helicity dynamics in viscous vortex links

The dynamics of two slender Hopf-linked vortex rings at vortex Reynolds numbers ( $Re \equiv \varGamma /\nu, \mathrm {circulation/viscosity}$ ) $2000$ , $3000$ and $4000$ is studied using direct numerical simulations of the incompressible Navier–Stokes equations. Under self-induction, the initially perpendicularly placed vortex rings approach each other and reconnect to form two separate vortex rings. The leading ring is closely cuddled and further undergoes secondary reconnection to form two even smaller rings. At high $Re$ , the leading ring and the subsequent smaller rings are unstable and break up into turbulent clouds consisting of numerous even smaller-scale structures. Although the global helicity $H$ remains constant before reconnection, it increases and then rapidly decays during reconnection – both the growth and decay rates increase with $Re$ . In the two higher $Re$ (i.e. 3000 and 4000) cases, $H$ further rises after the first reconnection and reaches a quasi-plateau with the asymptotic value continuously increasing with $Re$ – suggesting that $H$ for viscous flows is not conserved at very high $Re$ . Further flow analysis demonstrates that significant numbers of positive and negative helical structures are simultaneously generated before and during reconnection, and their different decay rates is the main reason for the complex evolution of $H$ . By examining the topological aspects of the helicity dynamics, we find that, different from $H$ , the sum of link and writhe ( $L_k+W_r$ ) continuously drop during reconnection. Our results also clearly demonstrate that the twist, which increases with $Re$ , plays a significant role in the helicity dynamics, particularly at high $Re$ .

Collision Fluctuations of Lucky Droplets with Superdroplets

Abstract It was previously shown that the superdroplet algorithm for modeling the collision–coalescence process can faithfully represent mean droplet growth in turbulent clouds. An open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space (“lucky droplet model”). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

Impact of the cosmic background radiation on the initial mass function of metal-poor stars

ABSTRACT We study star cluster formation at low metallicities of Z/Z⊙ = 10−4–10−1 using three-dimensional hydrodynamics simulations. Particular emphasis is put on how the stellar mass distribution is affected by the cosmic microwave background radiation (CMB), which sets the temperature floor to the gas. Starting from the collapse of a turbulent cloud, we follow the formation of a protostellar system resolving ∼au scale. In relatively metal-enriched cases of Z/Z⊙ ≳ 10−2, where the mass function resembles the present-day one in the absence of CMB, high-temperature CMB suppresses cloud fragmentation and reduces the number of low-mass stars, making the mass function more top-heavy than in the cases without CMB heating at z ≳ 10. In lower-metallicity cases with Z/Z⊙ ≲ 10−3, where the gas temperature is higher than the CMB value due to inefficient cooling, the CMB has only a minor impact on the mass distribution, which is top-heavy, regardless of the redshift. In cases either with a low metallicity of Z/Z⊙ ≲ 10−2 or at a high redshift z ≳ 10, the mass spectrum consists of a low-mass Salpeter-like component, peaking at 0.1 M⊙, and a top-heavy component with 10–50 M⊙, with the fraction in the latter increasing with increasing redshift. In galaxies forming at z ≳ 10, the major targets of the future instruments including JWST, CMB heating makes the stellar mass function significantly top-heavy, enhancing the number of supernova explosions by a factor of 1.4 (2.8) at z = 10 (20, respectively) compared to the prediction by Chabrier initial mass function when Z/Z⊙ = 0.1.