THE ROLE OF CORE MASS IN CONTROLLING EVAPORATION: THE KEPLER RADIUS DISTRIBUTION AND THE KEPLER-36 DENSITY DICHOTOMY

We present the core mass function (CMF) of the massive star-forming clump G33.92 + 0.11 using 1.3 mm observations obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). With a resolution of 1000 au, this is one of the highest resolution CMF measurements to date. The CMF is corrected by flux and number incompleteness to obtain a sample that is complete for gas masses M ≳ 2.0 M ⊙. The resulting CMF is well represented by a power-law function ( dN / d log M ∝ M Γ ), whose slope is determined using two different approaches: (i) by least-squares fitting of power-law functions to the flux- and number-corrected CMF, and (ii) by comparing the observed CMF to simulated samples with similar incompleteness. We provide a prescription to quantify and correct a flattening bias affecting the slope fits in the first approach, which is caused by small-sample or edge effects when the data are represented by either classical histograms or a kernel density estimate, respectively. The resulting slopes from both approaches are in good agreement each other, with Γ = − 1.11 − 0.11 + 0.12 being our adopted value. Although this slope appears to be slightly flatter than the Salpeter slope Γ = −1.35 for the stellar initial mass function (IMF), we find from Monte Carlo simulations that the CMF in G33.92 + 0.11 is statistically indistinguishable from the Salpeter representation of the stellar IMF. Our results are consistent with the idea that the form of the IMF is inherited from the CMF, at least at high masses and when the latter is observed at high enough resolution.

Context.Among the most central open questions regarding the initial mass function (IMF) of stars is the impact of environment on the shape of the core mass function (CMF) and thus potentially on the IMF.Aims.The ALMA-IMF Large Program aims to investigate the variations in the core distributions (CMF and mass segregation) with cloud characteristics, such as the density and kinematic of the gas, as diagnostic observables of the formation process and evolution of clouds. The present study focuses on the W43-MM2&MM3 mini-starburst, whose CMF has recently been found to be top-heavy with respect to the Salpeter slope of the canonical IMF.Methods.W43-MM2&MM3 is a useful test case for environmental studies because it harbors a rich cluster that contains a statistically significant number of cores (specifically, 205 cores), which was previously characterized in Paper III. We applied a multi-scale decomposition technique to the ALMA 1.3 mm and 3 mm continuum images of W43-MM2&MM3 to define six subregions, each 0.5–1 pc in size. For each subregion we characterized the probability distribution function of the high column density gas,η-PDF, using the 1.3 mm images. Using the core catalog, we investigate correlations between the CMF and cloud and core properties, such as theη-PDF and the core mass segregation.Results.We classify the W43-MM2&MM3 subregions into different stages of evolution, from quiescent to burst to post-burst, based on the surface number density of cores, number of outflows, and ultra-compact HII presence. The high-mass end (>1M⊙) of the subregion CMFs varies from close to the Salpeter slope (quiescent) to top-heavy (burst and post-burst). Moreover, the second tail of theη-PDF varies from steep (quiescent) to flat (burst and post-burst), as observed for high-mass star-forming clouds. We find that subregions with flat secondη-PDF tails display top-heavy CMFs.Conclusions.In dynamical environments such as W43-MM2&MM3, the high-mass end of the CMF appears to be rooted in the cloud structure, which is at high column density and surrounds cores. This connection stems from the fact that cores and their immediate surroundings are both determined and shaped by the cloud formation process, the current evolutionary state of the cloud, and, more broadly, the star formation history. The CMF may evolve from Salpeter to top-heavy throughout the star formation process from the quiescent to the burst phase. This scenario raises the question of if the CMF might revert again to Salpeter as the cloud approaches the end of its star formation stage, a hypothesis that remains to be tested.

Aims: We examine the recoverability and completeness limits of the dense core mass functions (CMFs) derived for a molecular cloud using extinction data and a core identification scheme based on two-dimensional thresholding. Methods: We performed simulations where a population of artificial cores was embedded into the variable background extinction field of the Pipe nebula. We extracted the cores from the simulated extinction maps, constructed the CMFs, and compared them to the input CMFs. The simulations were repeated using a variety of extraction parameters and several core populations with differing input mass functions and differing degrees of crowding. Results: The fidelity of the observed CMF depends on the parameters selected for the core extraction algorithm for our background. More importantly, it depends on how crowded the core population is. We find that the observed CMF recovers the true CMF reliably when the mean separation of cores is larger than their mean diameter (f>1). If this condition holds, the derived CMF is accurate and complete above M > 0.8-1.5 Msun, depending on the parameters used for the core extraction. In the simulations, the best fidelity was achieved with the detection threshold of 1 or 2 times the rms-noise of the extinction data, and with the contour level spacings of 3 times the rms-noise. Choosing larger threshold and wider level spacings increases the limiting mass. The simulations show that when f>1.5, the masses of individual cores are recovered with a typical uncertainty of 25-30 %. When f=1 the uncertainty is ~60 %. In very crowded cases where f<1 the core identification algorithm is unable to recover the masses of the cores adequately. For the cores of the Pipe nebula f~2.0 and therefore the use of the method in that region is justified.

Many studies have revealed that the core mass function (CMF) in high-mass star-forming regions is top-heavy. In this work, we start from the canonical initial mass function (IMF) to inversely synthesize the observed CMFs of high-mass star formation regions, taking into account variations in multiplicity and mass conversion efficiency from core to star (ε_ core). To match the observed CMFs, cores of different masses should have varying ε_ core, with ε_ core increasing as the core mass decreases. However, the multiplicity fraction does not affect the synthesized CMFs. To accurately fit the high-mass end of the CMF, it is essential to determine whether the CMF shows a slope transition from the low-mass end to the high-mass one. If the CMF truly undergoes a slope transition but observational biases obscure it, leading to a combined fit with a shallower slope, this could artificially create a top-heavy CMF.

Observations indicate that the central portions of the Present-Day Prestellar Core Mass Function (CMF) and the Stellar Initial Mass Function (IMF) both have approximately log-normal shapes, but that the CMF is displaced to higher mass than the IMF by a factor F = 4+/-1. This has lead to suggestions that the shape of the IMF is directly inherited from the shape of the CMF - and therefore, by implication, that there is a self-similar mapping from the CMF onto the IMF. If we assume a self-similar mapping, it follows (i) that F = N0/eta, where eta is the mean fraction of a core's mass that ends up in stars, and N0 is the mean number of stars spawned by a single core; and (ii) that the stars spawned by a single core must have an approximately log-normal distribution of relative masses, with universal standard deviation sigma0. Observations can be expected to deliver ever more accurate estimates of F, but this still leaves a degeneracy between eta and N0; and sigma0 is also unconstrained by observation. Here we show that these parameters can be estimated by invoking binary statistics. Specifically, if (a) each core spawns one long-lived binary system, and (b) the probability that a star of mass M is part of this long-lived binary is proportional to M^alpha, current observations of the binary frequency as a function of primary mass and the distribution of mass ratios strongly favour eta = 1.0 +/- 0.3, N0 = 4.3 +/- 0.4, sigma0 = 0.3 +/- 0.03 and alpha = 0.9 +/- 0.6. The mapping from CMF to IMF is not necessarily self-similar - there are many possible motivations for a non self-similar mapping - but if it is not, then the shape of the IMF cannot be inherited from the CMF. Given the limited observational constraints currently available and the ability of a self-similar mapping to satisfy them, the possibility that the shape of the IMF is inherited from the CMF cannot be ruled out at this juncture.

We use a recently-developed analytic model for the ISM structure from scales of GMCs through star-forming cores to explore how the pre-stellar core mass function (CMF) and, by extrapolation, stellar initial mass function (IMF) should depend on both local and galactic properties. If the ISM is supersonically turbulent, the statistical properties of the density field follow from the turbulent velocity spectrum, and the excursion set formalism can be applied to analytically calculate the mass function of collapsing cores on the smallest scales on which they are self-gravitating (non-fragmenting). Two parameters determine the model: the disk-scale Mach number M_h (which sets the shape of the CMF), and the absolute velocity (to assign an absolute scale). For 'normal' variation in disk properties and core gas temperatures in the MW and local galaxies, there is almost no variation in the predicted high-mass behavior of the CMF/IMF. The slope is always close to Salpeter down to <1 M_sun. We predict modest variation in the sub-solar regime, mostly from variation in M_h, but within the observed scatter in sub-solar IMFs in local regions. For fixed galaxy properties, there is little variation in shape or 'upper mass limit' with parent GMC mass. However, in extreme starbursts (e.g. ULIRGs) we predict a bottom-heavy CMF. This agrees with the IMF inferred for the centers of Virgo ellipticals, believed to form in such a nuclear starburst. The CMF is bottom heavy despite the gas temperature being an order of magnitude larger, because M_h is also much larger. Larger M_h values make the 'parent' cloud mass (turbulent Jeans mass) larger, but promote fragmentation to smaller scales; this steepens the slope of the low-mass CMF and shifts the turnover mass. The model may predict a top-heavy CMF for the sub-pc disks around Sgr A*, but the relevant input parameters are uncertain.

Similarity in shape between the initial mass function (IMF) and the core mass functions (CMFs) in star-forming regions prompts the idea that the IMF originates from the CMF through a self-similar core-to-star mass mapping process. To accurately determine the shape of the CMF, we create a sample of 8431 cores with the dust continuum maps of the Cygnus X giant molecular cloud complex, and design a procedure for deriving the CMF considering the mass uncertainty, binning uncertainty, sample incompleteness, and the statistical errors. The resultant CMF coincides well with the IMF for core masses from a few M ⊙ to the highest masses of 1300 M ⊙ with a power-law of dN / dM ∝ M − 2.30 ± 0.04 , but does not present an obvious flattened turnover in the low-mass range as the IMF does. More detailed inspection reveals that the slope of the CMF steepens with increasing mass. Given the numerous high-mass star-forming activities of Cygnus X, this is in stark contrast with the existing top-heavy CMFs found in high-mass star-forming clumps. We also find that the similarity between the IMF and the mass function of cloud structures is not unique at core scales, but can be seen for cloud structures of up to several parsec scales. Finally, our SMA observations toward a subset of the cores do not present evidence for the self-similar mapping. The latter two results indicate that the shape of the IMF may not be directly inherited from the CMF.

Applying dendrogram analysis to the CARMA-NRO C18O (J = 1–0) data having an angular resolution of ∼8″, we identified 692 dense cores in the Orion Nebula Cluster region. Using this core sample, we compare the core and initial stellar mass functions in the same area to quantify the step from cores to stars. About 22% of the identified cores are gravitationally bound. The derived core mass function (CMF) for starless cores has a slope similar to Salpeter’s stellar initial mass function (IMF) for the mass range above 1 M ⊙, consistent with previous studies. Our CMF has a peak at a subsolar mass of ∼0.1 M ⊙, which is comparable to the peak mass of the IMF derived in the same area. We also find that the current star formation rate is consistent with the picture in which stars are born only from self-gravitating starless cores. However, the cores must gain additional gas from the surroundings to reproduce the current IMF (e.g., its slope and peak mass), because the core mass cannot be accreted onto the star with 100% efficiency. Thus, the mass accretion from the surroundings may play a crucial role in determining the final stellar masses of stars.

Kepler’s observations show most of the exoplanets are super-Earths. The formation of a super-Earth is generally related to the atmospheric mass loss that is crucial in the planetary structure and evolution. The shock driven by the giant impact will heat the planet, resulting in the atmosphere escape. We focus on whether self-gravity changes the efficiency of mass loss. Without self-gravity, if the impactor mass is comparable to the envelope mass, there is a significant mass-loss. The radiative-convective boundary will shift inward by self-gravity. As the temperature and envelope mass increase, the situation becomes more prominent, resulting in a heavier envelope. Therefore, the impactor mass will increase to motivate the significant mass loss, as the self-gravity is included. With the increase of envelope mass, the self-gravity is particularly important.

Context. The connection between the prestellar core mass function (CMF) and the stellar initial mass function (IMF) lies at the heart of all star formation theories, but it is inherently observationally unreachable. Aims. In this paper we aim to elucidate the earliest phases of star formation with a series of high-resolution numerical simulations that include the formation of sinks from high-density clumps. In particular, we focus on the transition from cores to sink particles within a massive molecular filament, and work towards identifying the factors that determine the shape of the CMF and the IMF. Methods. We have compared the CMF and IMF between magnetized and unmagnetized simulations, and between different resolutions. In order to study the effect of core stability, we applied different selection criteria according to the virial parameter and the mass-to-flux ratio of the cores. Results. We find that, in all models, selecting cores based on their kinematic virial parameter tends to exclude collapsing objects, because they host high velocity dispersions. Selecting only the thermally unstable magnetized cores, we observe that their mass-to-flux ratio spans almost two orders of magnitude for a given mass. We also see that, when magnetic fields are included, the CMF peaks at higher core mass values with respect to a pure hydrodynamical simulation. Nonetheless, all models produce sink mass functions with a high-mass slope consistent with Salpeter. Finally, we examined the effects of resolution and find that, in these isothermal simulations, even models with very high dynamical range fail to converge in the mass function. Conclusions. Our main conclusion is that, although the resulting CMFs and IMFs have similar slopes in all simulations, the cores have slightly different sizes and kinematical properties when a magnetic field is included, and this affects their gravitational stability. Nonetheless, a core selection based on the mass-to-flux ratio is not enough to alter the shape of the CMF, if we do not take thermal stability into account. Finally, we conclude that extreme care should be given to resolution issues when studying sink formation with an isothermal equation of state, since with each increase in resolution, fragmentation continues to smaller scales in a self-similar way.

The core mass function (CMF) of prestellar cores is essential for understanding the initial conditions of star and cluster formation. However, the universality of the CMF and its relationship to the initial mass function (IMF) remain unclear. We study the CMF in the earliest stage of high-mass star formation using 461 prestellar core candidates and 254 protostellar cores as a part of the ALMA Survey of 70 µm Dark High-mass Clumps in Early Stages (ASHES). We find that prestellar core candidates tend to have lower masses than protostellar cores. We also find that the lifetime of prestellar cores is several times longer than the freefall time, although it approaches the freefall time as the core mass increases. The CMF, including both protostellar and prestellar cores, has a power-law slope of −2.05 ± 0.04, shallower than Salpeter’s IMF slope of −2.35. Conversely, the CMF of gravitationally bound, prestellar cores has a steeper slope (−2.32 ± 0.30), indistinguishable from Salpeter’s slope. This finding is consistent with observations in both low-mass star-forming regions and high-mass protoclusters, implying a universal core formation mechanism. The protostellar CMF with a larger maximum core mass can be reproduced by the prestellar CMF when an external gas infall is considered. The inferred mass infall rate is higher than the Bondi–Hoyle–Lyttleton accretion rate and follows a shallower mass dependence (smaller power-law index), more consistent with the tidal-lobe accretion. This may contribute to the evolution of CMFs seen in later stages.

Context. One of the central questions in astrophysics is the origin of the initial mass function (IMF). It is intrinsically linked to the processes from which it originates, and hence its connection with the core mass function (CMF) must be elucidated. Aims. We aim to measure the CMF in the evolved W33-Main star-forming protocluster to compare it with CMF recently obtained in other Galactic star-forming regions, including the ones that are part of the ALMA-IMF program. Methods. We used observations from the ALMA-IMF large programme: ~2′ × 2′ maps of emission from the continuum and selected lines at 1.3 mm and 3 mm observed by the ALMA 12m only antennas. Our angular resolution was typically 1″, that is, ~2400 au at a distance of 2.4 kpc. The lines we analysed are CO (2–1), SiO (5–4), N2H+ (1–0), H41α as well as He41α blended with C41α. We built a census of dense cores in the region, and we measured the associated CMF based on a core-dependent temperature value. Results. We confirmed the ‘evolved’ status of W33-Main by identifiying three H II regions within the field, and to a lesser extent based on the number and extension of N2H+ filaments. We produced a filtered core catalogue of 94 candidates that we refined to take into account the contamination of the continuum by free-free and line emission, obtaining 80 cores with masses that range from 0.03 to 13.2 M⊙. We fitted the resulting high-mass end of the CMF with a single power law of the form N(log(M)) ∝ Mα, obtaining α = −1.44−0.22+0.16, which is slightly steeper but consistent with the Salpeter index. We categorised our cores as prestellar and protostellar, mostly based on outflow activity and hot core nature. We found the prestellar CMF to be steeper than a Salpeter-like distribution, and the protostellar CMF to be slightly top heavy. We found a higher proportion of cores within the H II regions and their surroundings than in the rest of the field. We also found that the cores’ masses were rather low (maximum mass of ~13 M⊙). Conclusions. We find that star formation in W33-Main could be compatible with a ‘clump-fed’ scenario of star formation in an evolved cloud characterised by stellar feedback in the form of H II regions, and under the influence of massive stars outside the field. Our results differ from those found in less evolved young star-forming regions in the ALMA-IMF program. Further investigations are needed to elucidate the evolution of late CMFs towards the IMF over statistically significant samples.

The origin of the so called 'detached shells' around AGB stars is not fully understood, but two common hypotheses state that these shells form either through the interaction of distinct wind phases or an eruptive mass loss associated with a He-shell flash. We present a model of the formation of detached shells around thermal pulse asymptotic giant branch (TP-AGB) stars, based on detailed modelling of mass loss and stellar evolution, leading to a combination of eruptive mass loss and wind interaction. The purpose of this paper is first of all to connect stellar evolution with wind and mass loss evolution and demonstrate its consistency with observations, but also to show how thin detached shells around TP-AGB stars can be formed. Previous attempts to link mass loss evolution with the formation of detached shells were based on approximate prescriptions for the mass loss and have not included detailed modelling of the wind formation as we do here. (abridged)

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 (2500 au). We have mapped a field of 5.′3 × 5.′3 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 experiments. For masses M ≳ 1 M ⊙, the fiducial dendrogram-identified CMF can be fit with a power law of the form dN/dlog M ∝ M −α with α ≃ 1.24 ± 0.17, slightly shallower than, but still consistent with, the index of the Salpeter stellar initial mass function of 1.35. Clumpfind-identified CMFs are significantly shallower with α ≃ 0.64 ± 0.13. While raw CMFs show a peak near 1 M ⊙, completeness-corrected CMFs are consistent with a single power law extending down to ∼0.5 M ⊙, with only a tentative indication of a shallowing of the slope around ∼1 M ⊙. We discuss the implications of these results for star and star cluster formation theories.

We reanalyse all of the archived observations of the Ophiuchus dark cloud L1688 that were carried out with the submillimetre common-user bolometer array on the James Clerk Maxwell Telescope. For the first time, we put together all the data that were taken of this cloud at different times to make a deeper map at 850 μm than has ever been published. Using this new, deeper map, we extract the pre-stellar cores from the data. We use updated values for the distance to the cloud complex, and also for the internal temperatures of the pre-stellar cores to generate an updated core mass function (CMF). This updated CMF is consistent with previous results in so far as they went, but our deeper map gives an improved completeness limit of 0.1 M⊙ (0.16 Jy), which enables us to show that a turnover exists in the low-mass regime of the CMF. The L1688 CMF shows the same form as the stellar initial mass function (IMF), and can be mapped on to the stellar IMF, showing that the IMF is determined at the pre-stellar core stage. We compare L1688 with the Orion star-forming region and find that the turnover in the L1688 CMF occurs at a mass roughly a factor of 2 lower than the CMF turnover in Orion. This suggests that the position of the CMF turnover may be a function of environment.