Sufficiently massive clumps of molecular gas collapse under self-gravity and fragment to spawn a cluster of stars that have a range of masses. We investigate observationally the early stages of formation of a stellar cluster in a massive filamentary infrared dark cloud, G28.34+0.06 P1, in the 1.3mm continuum and spectral line emission using the ALMA. Sensitive continuum data reveal further fragmentation in five dusty cores at a resolution of several 10^3 AU. Spectral line emission from C18O, CH3OH, 13CS, H2CO and N2D+ are detected for the first time toward these dense cores. We found that three cores are chemically more evolved as compared with the other two; interestingly though, all of them are associated with collimated outflows as suggested by evidence from the CO, SiO, CH3OH, H2CO and SO emissions. The parsec-scale kinematics in NH3 exhibit velocity gradients along the filament, consistent with accretion flows toward the clumps and cores. The moderate luminosity and the chemical signatures indicate that the five cores harbor low- to intermediate-mass protostars that likely become massive ones at the end of the accretion. Despite the fact that the mass limit reached by the 1σdust continuum sensitivity is 30 times lower than the thermal Jeans mass, there is a lack of a distributed low-mass protostellar population in the clump. Our observations indicate that in a protocluster, low-mass stars form at a later stage after the birth of more massive protostars.
We present a catalogue of starless and protostellar clumps associated with infrared dark clouds (IRDCs) in a 40 degrees wide region of the inner Galactic Plane (b<1). We have extracted the far-infrared (FIR) counterparts of 3493 IRDCs with known distance in the Galactic longitude range 15<l<55 and searched for the young clumps using Hi-GAL, the survey of the Galactic Plane carried out with the Herschel satellite. Each clump is identified as a compact source detected at 160, 250 and 350 mum. The clumps have been classified as protostellar or starless, based on their emission (or lack of emissio…
A grid of 20 millions 3-1100$μ$m SED models is presented for synthetic young clusters embedded in dense clumps. The models depend on four primary parameters: the clump mass M$_{clump}$ and dust temperature T$_{dust}$, the fraction of mass f$_{core}$ locked in dense cores, and the age of the clump t$_{SF}$. We populate the YSO clusters using the IMF from Kroupa(2001) and the YSOs SED models grid of Robitaille et al. (2006). We conduct extensive testing of SED fitting using a simulated dataset and we find that M$_{clump}$ essentially depends on the submillimeter portion of the SED, while T$_{dus…
We present new continuum and molecular line data from the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey for the two protoclusters, G12.42+0.50 and G19.88-0.53. The 3 mm continuum maps reveal seven cores in each of the two globally contracting protoclusters. These cores satisfy the radius-mass relation and the surface mass density criteria for high-mass star formation. Similar to their natal clumps, the virial analysis of the cores suggests that they are undergoing gravitational collapse ($\rm α_{vir} << 2$). The clump to core scale fragmentation is investiga…
Fragmentation of massive dense molecular clouds is the starting point in the formation of rich clusters and massive stars. Theory and numerical simulations indicate that the population of the fragments (number, mass, diameter, separation) resulting from the gravitational collapse of such clumps is probably regulated by the balance between the magnetic field and the other competitors of self-gravity, in particular turbulence and protostellar feedback. We have observed 11 massive, dense and young star-forming clumps with the Atacama Large Millimeter Array (ALMA) in the thermal dust continuum emi…
We present the results of CO ($J=3-2$) and HCO$^+$ ($J=4-3$) mapping observations toward a nearby embedded cluster, Serpens South, using the ASTE 10 m telescope. Our CO ($J=3-2$) map reveals that many outflows are crowded in the dense cluster-forming clump that can be recognized as a HCO$^+$ clump with a size of $\sim$ 0.2 pc and mass of $\sim$ 80 M$_\odot$. The clump contains several subfragments with sizes of $\sim$ 0.05 pc. By comparing the CO ($J=3-2$) map with the 1.1 mm dust continuum image taken by AzTEC on ASTE, we find that the spatial extents of the outflow lobes are sometimes anti-c…
We present the results of high spatial resolution observations at 1.1 mm waveband, with the Submillimetre Array (SMA), towards the protocluster G10.6-0.4. The 1.1 mm continuum emission reveals seven dense cores, towards which infall motions are all detected with the red-shifted absorption dips in HCN (3--2) line. This is the first time that infall is seen towards multiple sources in a protocluster. We also identified four infrared point sources in this region, which are most likely Class 0/I protostars. Two jet-like structures are also identified from Spitzer/IRAC image. The dense core located…
The ALMA Survey of Star Formation and Evolution in Massive Protoclusters with Blue Profiles (ASSEMBLE): Core Growth, Cluster Contraction, and Primordial Mass Segregation
If star formation proceeds by thermal fragmentation and the subsequent gravitational collapse of the individual fragments, how is it possible to form fragments massive enough for O and B stars in a typical star-forming molecular cloud where the Jeans mass is about 1Msun at the typical densities (10^4 cm^-3) and temperatures (10K)? We test the hypothesis that a first generation of low-mass stars may heat the gas enough that subsequent thermal fragmentation results in fragments >=10Msun, sufficient to form B stars. We combine ATCA and SMA observations of the massive star-forming region G8.68-0.3…
The Serpens South infrared dark cloud consists of several filamentary ridges, some of which fragment into dense clumps. On the basis of CCS ($J_N=4_3-3_2$), HC$_3$N ($J=5-4$), N$_2$H$^+$ ($J=1-0$), and SiO ($J=2-1, v=0$) observations, we investigated the kinematics and chemical evolution of these filamentary ridges. We find that CCS is extremely abundant along the main filament in the protocluster clump. We emphasize that Serpens South is the first cluster-forming region where extremely-strong CCS emission is detected. The CCS-to-N$_2$H$^+$ abundance ratio is estimated to be about 0.5 toward t…
The initial stage of star formation is a complex area study because of its high density and low temperature. Under such conditions, many molecules become depleted from the gas phase by freezing out onto dust grains. However, the deuterated species could remain gaseous and are thus ideal tracers. We investigate the gas dynamics and NH$_2$D chemistry in eight massive pre/protocluster clumps. We present NH$_2$D 1$_{11}$-1$_{01}$ (at 85.926 GHz), NH$_3$ (1, 1) and (2, 2) observations in the eight clumps using the PdBI and the VLA, respectively. We find that the distribution between deuterium fract…
We study the core mass function (CMF) of the massive protocluster G286.21+0.17 with the Atacama Large Millimeter/submillimeter Array via 1.3~mm continuum emission at a resolution of 1.0\arcsec\ (2500~au). We have mapped a field of 5.3\arcmin$\times$5.3\arcmin\ centered on the protocluster clump. We measure the CMF in the central region, exploring various core detection algorithms, which give source numbers ranging from 60 to 125, depending on parameter selection. We estimate completeness corrections due to imperfect flux recovery and core identification via artificial core insertion experiment…
We study the gas kinematics and dynamics of the massive protocluster G286.21+0.17 with the Atacama Large Millimeter/submillimeter Array using spectral lines of $C^{18}O$(2-1), $N_2D^+$(3-2), $DCO^+$(3-2) and $DCN$(3-2). On the parsec clump scale, $C^{18}O$ emission appears highly filamentary around the systemic velocity. $N_2D^+$ and $DCO^+$ are more closely associated with the dust continuum. $DCN$ is strongly concentrated towards the protocluster center, where no or only weak detection is seen for $N_2D^+$ and $DCO^+$, possibly due to this region being at a relatively evolved evolutionary st…
The dense molecular clump P1 in the infrared dark cloud (IRDC) complex G28.34+0.06 harbors a massive protostellar cluster at its extreme youth. Our previous Submillimeter Array (SMA) observations revealed several jet-like CO outflows emanating from the protostars, indicative of intense accretion and potential interaction with ambient natal materials. Here we present the Expanded Very Large Array (EVLA) spectral line observations toward P1 in the NH3 (J,K) = (1,1), (2,2), (3,3) lines, as well as H2O and class I CH3OH masers. Multiple NH3 transitions reveal the heated gas widely spread in the 1 …
The structure formation of the dense interstellar material and the fragmentation of clumps into cores is a fundamental step to understand how stars and stellar clusters form. We aim to establish a statistical view of clump fragmentation at sub-parsec scales based on a large sample of massive clumps selected from the ATLASGAL survey. We used the APEX/SABOCA camera at 350 $μ$m to image clumps at a resolution of 8.$''$5. The majority of the sample consists of massive clumps that are weak or in absorption at 24 $μ$m. We resolve rich filamentary structures and identify the population of compact sou…
Massive stars, multiple stellar systems and clusters are born from the gravitational collapse of massive dense gaseous clumps, and the way these systems form strongly depends on how the parent clump fragments into cores during collapse. Numerical simulations show that magnetic fields may be the key ingredient in regulating fragmentation. Here we present ALMA observations at ~0.25'' resolution of the thermal dust continuum emission at ~278 GHz towards a turbulent, dense, and massive clump, IRAS 16061-5048c1, in a very early evolutionary stage. The ALMA image shows that the clump has fragmented …
In this work, we derive the stellar initial mass function (IMF) from the superposition of mass distributions of dense cores, generated through gravoturbulent fragmentation of unstable clumps in molecular clouds (MCs) and growing through competitive accretion. MCs are formed by the turbulent cascade in the interstellar medium at scales L from 100 down to ~0.1 pc. Their internal turbulence is essentially supersonic and creates clumps with a lognormal distribution of densities n. Our model is based on the assumption of a power-law relationship between clump mass and clump density: n~m^x, where x …
Fragmentation of a spiral arm is thought to drive the formation of giant clumps in galaxies. Using linear perturbation analysis for self-gravitating spiral arms, we derive an instability parameter and define the conditions for clump formation. We extend our analysis to multi-component systems that consist of gas and stars in an external potential. We then perform numerical simulations of isolated disc galaxies with isothermal gas, and compare the results with the prediction of our analytic model. Our model describes accurately the evolution of the spiral arms in our simulations, even when spir…
The ionization feedback from HII regions modifies the properties of high-mass starless clumps (HMSCs, of several hundred to a few thousand solar masses with a size of ~0.1-1 pc), such as temperature and turbulence, on the clump scale. The question of whether the presence of HII regions modifies the core-scale fragmentation and star formation in HMSCs remains to be explored. We aim to investigate the difference of 0.025 pc-scale fragmentation between candidate HMSCs that are strongly impacted by HII regions and less disturbed ones. We also search for evidence of mass shaping and induced star fo…
We explore how the star formation efficiency in a protocluster clump is regulated by metallicity dependent stellar winds from the newly formed massive OB stars (Mstar >5 Msol). The model describes the co-evolution of the mass function of gravitationally bound cores and of the IMF in a protocluster clump. Dense cores are generated uniformly in time at different locations in the clump, and contract over lifetimes that are a few times their free fall times. The cores collapse to form stars that power strong stellar winds whose cumulative kinetic energy evacuates the gas from the clump and quenche…
The ALMA EGO-10 Survey of Massive Protoclusters: Correlation of 1.3 mm Continuum Source Clustering with Evolutionary State
Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St Andrews（圣安德鲁斯大学物理与天文学学院）；National Radio Astronomy Observatory（国家射电天文台）；INAF-IAPS（意大利国家天体物理研究所天体物理与行星科学研究所）；University of Arizona Department of Astronomy and Steward Observatory（亚利桑那大学天文学系和斯图尔德天文台）；Department of Astronomy, University of Texas at Austin（德克萨斯大学奥斯汀分校天文学系）
(Abridged) The initial physical conditions of high-mass stars and protoclusters remain poorly characterized. To this end we present the first targeted ALMA 1.3mm continuum and spectral line survey towards high-mass starless clump candidates, selecting a sample of 12 of the most massive candidates ($400-4000\, M_\odot$) within 5 kpc. The joint 12+7m array maps have a high spatial resolution of $\sim 3000\, \mathrm{au}$ ($\sim 0.8^{\prime\prime}$) and have point source mass-completeness down to $\sim 0.3\, M_\odot$ at $6σ$ (or $1σ$ column density sensitivity of $1.1\times10^{22}\, \mathrm{cm^{-2…
(Abridged) ASHES has been designed to systematically characterize the earliest stages and to constrain theories of high-mass star formation. A total of 12 massive (>500 $M_{\odot}$), cold (<15 K), 3.6-70 $μ$m dark prestellar clump candidates, embedded in IRDCs, were carefully selected in the pilot survey to be observed with ALMA. We mosaiced each clump (~1 arcmin^2) in dust and line emission with the 12m/7m/TP arrays at 224 GHz, resulting in ~1.2" resolution (~4800 AU). As the first paper of the series, we concentrate on the dust emission to reveal the clump fragmentation. We detect 294 cores,…
Massive clumps tend to fragment into clusters of cores and condensations, some of which form high-mass stars. In this work, we study the structure of massive clumps at different scales, analyze the fragmentation process, and investigate the possibility that star formation is triggered by nearby HII regions. We present a high angular resolution study of a sample of 8 massive proto-cluster clumps. Combining infrared data, we use few-arcsecond resolution radio- and millimeter interferometric data to study their fragmentation and evolution. Our sample is unique in the sense that all the clumps hav…
We report new, $\sim$1000 AU spatial resolution observations of 225 GHz dust continuum emission towards the OB cluster-forming molecular clump G33.92+0.11. On parsec scales, this molecular clump presents a morphology with several arm-like dense gas structures surrounding the two central massive ($\gtrsim$100 $M_{\odot}$) cores. From the new, higher resolution observations, we identified 28 localized, spatially compact dust continuum emission sources, which may be candidates of young stellar objects. Only one of them is not embedded within known arm-like (or elongated) dense gas structures. The…
We present Submillimeter Array (SMA) λ= 0.88mm observations of an infrared dark cloud (IRDC) G28.34+0.06. Located in the quiescent southern part of the G28.34 cloud, the region of interest is a massive ($>10^3$\,\msun) molecular clump P1 with a luminosity of $\sim 10^3$ \lsun, where our previous SMA observations at 1.3mm have revealed a string of five dust cores of 22-64 \msun\ along the 1 pc IR-dark filament. The cores are well aligned at a position angle of 48 degrees and regularly spaced at an average projected separation of 0.16 pc. The new high-resolution, high-sensitivity 0.88\,mm image …
Migration of dense gaseous clumps that form in young protostellar disks via gravitational fragmentation is investigated to determine the likelihood of giant planet formation. High-resolution numerical hydrodynamics simulations in the thin-disk limit are employed to compute the formation and long-term evolution of a gravitationally unstable protostellar disk around a solar-mass star. We show that gaseous clumps that form in the outer regions of the disk (>100 AU) through disk fragmentation are often perturbed by other clumps or disk structures, such as spiral arms, and migrate toward the centra…
We derive a metallicity dependent relation between the surface density of the star formation rate (Sigma_{SFR}) and the gas surface density (Sigma_{g}) in a feedback regulated model of star formation in galactic disks. In this model, star formation occurs in gravitationally bound protocluster clumps embedded in larger giant molecular clouds with the protocluster clump mass function following a power law function with a slope of -2. Metallicity dependent feedback is generated by the winds of OB stars (M > 5 Msol) that form in the clumps. The quenching of star formation in clumps of decreasing m…
Fragmentation of spiral arms can drive the formation of giant clumps and induce intense star formation in disc galaxies. Based on the spiral-arm instability analysis of our Paper I, we present linear perturbation theory of dynamical instability of self-gravitating spiral arms of magnetised gas, focusing on the effect of toroidal magnetic fields. Spiral arms can be destabilised by the toroidal fields which cancel Coriolis force, i.e. magneto-Jeans instability. Our analysis can be applied to multi-component systems that consist of gas and stars. To test our analysis, we perform ideal magneto-hyd…
We present the results of N$_2$H$^+$ ($J=1-0$) observations toward Serpens South, the nearest cluster-forming, infrared dark cloud. The physical quantities are derived by fitting the hyperfine structure of N$_2$H$^+$. The Herschel and 1.1-mm continuum maps show that a pc-scale filament fragments into three clumps with radii of $0.1-0.2$ pc and masses of $40-230M_\odot$. We find that the clumps contain smaller-scale ($\sim 0.04$ pc) structures, i.e., dense cores. We identify 70 cores by applying CLUMPFIND to the N$_2$H$^+$ data cube. In the central cluster-forming clump, the excitation temperat…
We show results from the radiation hydrodynamics (RHD) simulations of tidal disruption of a star on a parabolic orbit by a supermassive black hole (SMBH) based on a three-dimensional smoothed particle hydrodynamics code with radiative transfer. We find that such a tidally disrupted star fragment and form clumps soon after its tidal disruption. The fragmentation results from the endothermic processes of ionization and dissociation that reduce the gas pressure, leading to local gravitational collapse. Radiative cooling is less effective because the stellar debris is still highly optically thick …
We describe results from semi-analytical modelling of star formation in protocluster clumps of different metallicities. In this model, gravitationally bound cores form uniformly in the clump following a prescribed core formation efficiency per unit time. After a contraction timescale which is equal to a few times their free-fall times, the cores collapse into stars and populate the IMF. Feedback from the newly formed OB stars is taken into account in the form of stellar winds. When the ratio of the effective energy of the winds to the gravitational energy of the system reaches unity, gas is re…
[Abridged] We have recently reported on the collapse and fragmentation properties of the northernmost part of this structure, located ~2.4pc north of Orion KL -- the Orion Molecular Cloud 3 (OMC 3, Takahashi et al. 2013). As part of our project to study the integral-shaped filament, we analyze the fragmentation properties of the northern OMC 1 filament. This filament is a dense structure previously identified by JCMT/SCUBA submillimeter continuum and VLA ammonia observations and shown to have fragmented into clumps. We observed OMC1 n with the Submillimeter Array (SMA) at 1.3mm and report on o…
The dynamical processes that control star formation in molecular clouds are not well understood, and in particular, it is unclear if rotation plays a major role in cloud evolution. We investigate the importance of rotation in cloud evolution by studying the kinematic structure of a spiral-shaped Galactic molecular cloud G052.24+00.74. The cloud belongs to a large filament, and is stretching over ~ 100 pc above the Galactic disk midplane. The spiral-shaped morphology of the cloud suggests that the cloud is rotating. We have analysed the kinematic structure of the cloud, and study the fragmentat…
We investigate how the removal of interstellar material by stellar feedback limits the efficiency of star formation in molecular clouds and how this determines the shape of the mass function of young star clusters. In particular, we derive relations between the power-law exponents of the mass functions of the clouds and clusters in the limiting regimes in which the feedback is energy-driven and momentum-driven, corresponding to minimum and maximum radiative losses and likely to bracket all realistic cases. We find good agreement between the predicted and observed exponents, especially for mome…
This paper summarises results from semi-analytical modelling of star formation in protocluster clumps of different metallicities. In this model, gravitationally bound cores form uniformly in the clump following a prescribed core formation efficiency per unit time. After a contraction timescale which is equal to a few times their free-fall times, the cores collapse into stars and populate the IMF. Feedback from the newly formed OB stars is taken into account in the form of stellar winds. When the ratio of the effective wind energy of the winds to the gravitational energy of the system reaches u…
We present two-dimensional hydrodynamic simulations of self-gravitating protostellar disks subject to axisymmetric infall from envelopes and irradiation from the central star, to explore disk fragmentation due to gravitational instability (GI), and the fragmented clump evolution. We assume that the disk is built gradually and smoothly by the infall, resulting in good numerical convergence. We confirm that for disks around solar-mass stars, infall at high rates at radii beyond ~50 AU leads to disk fragmentation. At lower infall rates <1e-5 Msun/yr, however, irradiation suppresses fragmentation.…
The formation process of high-mass stars (>8M$_\odot$) is poorly constrained, particularly, the effects of clump fragmentation creating multiple systems and the mechanism of mass accretion onto the cores. We study the fragmentation of dense gas clumps, and trace the circumstellar rotation and outflows by analyzing observations of the high-mass (~500M$_\odot$) star-forming region IRAS 23033+5951. Using the Northern Extended Millimeter Array (NOEMA) in three configurations and the IRAM 30-m single-dish telescope at 220GHz, we probe the gas and dust emission at an angular resolution of ~0.45arcse…
Ambipolar diffusion likely plays a pivotal role in the formation and evolution of dense cores in weakly-ionized molecular clouds. Linear analyses show that the evolutionary times and fragmentation scales are significantly greater than the hydrodynamic (Jeans) values even for clouds with mildly supercritical mass-to-flux ratio. We utilize values of fragmentation scales and growth times that correspond to typical ionization fractions within a molecular cloud, and apply to the context of the observed estimated lifetime of prestellar cores as well as the observed number of such embedded cores form…
We present $\sim10-40\,μ$m SOFIA-FORCAST images of 14 intermediate-mass protostar candidates as part of the SOFIA Massive (SOMA) Star Formation Survey. We build spectral energy distributions (SEDs), also utilizing archival Spitzer, Herschel and IRAS data. We then fit the SEDs with radiative transfer (RT) models of Zhang & Tan (2018), based on Turbulent Core Accretion theory, to estimate key protostellar properties. With the addition of these intermediate-mass sources, SOMA protostars span luminosities from $\sim10^{2}-10^{6}\:L_{\odot}$, current protostellar masses from $\sim0.5-30\:M_{\odot}$…
We use deep $8\:μm$ Spitzer-IRAC imaging of a massive Infrared Dark Cloud (IRDC) G028.37+00.07 to construct a Mid-Infrared (MIR) extinction map that probes mass surface densities up to $Σ\:\sim 1\:\rm{g~cm^{-2}}$ ($A_V\sim200\:$mag), amongst the highest values yet probed by extinction mapping. Merging with a NIR extinction map of the region, creates a high dynamic range map that reveals structures down to $A_V\sim1\:$mag. We utilize the map to: (1) Measure a cloud mass $\sim7\times10^4\:M_\odot$ within a radius of $\sim8\:$pc. $^{13}$CO kinematics indicate that the cloud is gravitationally bou…
We investigate structure of self-gravitating disks, their fragmentation and evolution of the fragments (the clumps) using both analytic approach and three-dimensional radiation hydrodynamics simulations starting from molecular cores. The simulations show that non-local radiative transfer determines disk temperature. We find the disk structure is well described by an analytical model of quasi-steady self-gravitating disk with radial radiative transfer. Because the radiative process is not local and radiation from the interstellar medium cannot be ignored, the local radiative cooling would not b…
Evading the dust fragmentation barrier with the streaming instability in protoplanetary disks
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学，巴黎西岱大学，法国原子能和替代能源委员会，法国国家科学研究中心，天体分子研究所）；American Museum of Natural History（美国自然历史博物馆）
Filamentary structures are ubiquitously seen in the interstellar medium. The concentrated molecular mass in the filaments allows fragmentation to occur in a shorter timescale than the timescale of the global collapse. Such hierarchical fragmentation may further assist the dissipation of excessive angular momentum. It is crucial to resolve the morphology and the internal velocity structures of the molecular filaments observationally. We perform 0".5-2".5 angular resolution interferometric observations toward the nearly face-on OB cluster forming region G33.92+0.11. Observations of various spect…
We report the results of our three-dimensional radiation hydrodynamics simulation of collapsing unmagnetized molecular cloud cores. We investigate the formation and evolution of the circumstellar disk and the clumps formed by disk fragmentation. Our simulation shows that disk fragmentation occurs in the early phase of circumstellar disk evolution and many clumps form. The clump can be represented by a polytrope sphere of index $n \sim 3$ and $n \gtrsim 4$ at central temperature $T_c \lesssim100$ K and $T_c \gtrsim 100$ K, respectively. We demonstrate, numerically and theoretically, that the ma…
We report results from a cosmological simulation with non-equilibrium chemistry of 21 species, including H2, HD, and LiH molecular cooling. Starting from cosmological initial conditions, we focus on the evolution of the central 1.8 Kpc region of a 3 x 10^7 Msun halo. The crossing of a few 10^6 Msun halos and the gas accretion through larger scale filaments generate a turbulent environment within this region. Due to the short cooling time caused by the non-equilibrium formation of H2, the supersonic turbulence results in a very fragmented mass distribution, where dense, gravitationally unstable…
We investigate the dynamics of gaseous clumps formed via gravitational fragmentation in young protostellar disks, focusing on the fragments that are ejected from the disk via many-body gravitational interaction. Numerical hydrodynamics simulations were employed to study the evolution of young protostellar disks formed from the collapse of rotating pre-stellar cores with mass in the 1.1-1.6 M_sun range. Protostellar disks formed in our models undergo gravitational fragmentation driven by continuing mass loading from parental collapsing cores. A few fragments can be ejected from the disk during …
Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds shows that molecular clouds exhibit a preferred length scale for collapse that depends on the mass-to-flux ratio and neutral-ion collision time within the cloud. We extend this linear analysis to the context of clustered star formation. By combining the results of the linear analysis with a realistic ionization profile for the cloud, we find that a molecular cloud may evolve through two fragmentation events in the evolution toward the formation of stars. Our model suggests that the initial fragmentati…
