Alexander Men’SHchikov

An accurate characterization of filamentary structures in star-forming clouds is essential for understanding star formation. Traditional methods fit observed surface density profiles Σ( r ) with slope γ and width H using the Plummer function, assuming β = γ + 1 and h ≈ H for the volume density slope and width. These assumptions break down for shallow profiles, with the slope and width relations deviating progressively more for compact and extended filaments, respectively. We present a new fitting method that explicitly accounts for finite cylindrical geometry and establishes self-consistent empirical relationships between the parameters of Σ( r ) and those of the volume density profile ρ ( r ), characterized by slope β and width h . The method was validated on model profiles and applied to selected filaments in the California molecular cloud. The slope difference, δ ≡ β − γ , falls below unity for shallow ( β ≲ 2) and compact profiles. Moreover, h and H can differ by over an order of magnitude for extended filaments with shallow slopes. Accurate parameter recovery requires high resolvedness ℛ ≡ H/O ≳ 10 (where O is the beam width). At lower resolvedness, slopes are severely overestimated and filaments remain unresolved even when H ≫ O . The traditional Plummer function yields systematically overestimated slopes. Accurate deconvolution requires a priori knowledge of the true parameters, creating a fundamental circular problem whose only robust solution is obtaining sufficiently high angular resolution. Current far-infrared observations typically lack sufficient resolution, and some previously reported filament properties may require reinterpretation.

Aims. The gravoturbulent fragmentation of the interstellar medium is expected to create a hierarchical cascade of cloud structures, crossing the scales from core to disk. We aim to predict how the currently observed top-heavy core mass function (CMF) in the massive protocluster W43-MM1 evolves due to core subfragmentation. Methods. We used the getsf algorithm to extract sources in five ALMA images of W43-MM1 at 3 mm, with a spatial resolution ranging from 14 kau to 270 au. Then, we applied FAMILY , a graph-theory-based analysis tool, to create and characterize networks of nested sources in W43-MM1. We compared the hierarchical fragmentation cascade of W43-MM1 to those measured in the NGC 2264 protocluster and in synthetic images of an Orion-like protocluster simulated by magneto-hydrodynamical calculations. Results. Assuming self-similarity, we measured a small fractality index of F _3D = 1.19 ± 0.10 in W43-MM1, which means that, on average, a cloud structure fragments into only 1.19 fragments each time the physical scale decreases by a factor of two. In line with values measured above the core scale in the NGC 2264 and synthetic protoclusters, the W43-MM1 fractality index increases by about 30% at larger scales. We also estimate an imbalanced mass partition between siblings, with two-thirds of the mass of siblings at a given scale belonging to the dominant sibling. The mass transfer efficiency, computed from one physical scale to another, is high and corresponds to a core formation efficiency (CFE) from 2400 au cores to 200 au seeds of ∼16%. Conclusions. Based on the fractality and efficiency values measured in W43-MM1, the gravoturbulent model by Thomasson predicts that its fragmentation below ∼14 kau is not driven by turbulence but by gravity. Using these parameters and the measured mass partition, we demonstrate that the seed mass function, from which the initial mass function (IMF) emerges, has a high-mass end that remains top-heavy. Therefore, based on our current assumptions, core subfragmentation in W43-MM1, and perhaps more broadly in massive Galactic protoclusters, plays a minimal role in shaping the high-mass slope of the IMF.

The high-mass slope of the stellar initial mass function (IMF), first measured by Salpeter in 1955, appears nearly universal across star-forming environments, yet its physical origin remains unknown. Using the multiscale extraction method getsf , we measure the filament linear density function (FLDF) across seven nearby molecular clouds (140–920 pc) spanning a wide range of star-forming activity. The FLDF slope shows no systematic trend with spatial scale. Combining all clouds and scales, the composite FLDF follows a power law d N / d log Λ ∝ Λ − α with α ≈ 1.40, close to the Salpeter value of 1.35, and the same composite slope is found in every cloud despite an order-of-magnitude spread in their supercritical-filament fractions. The close similarity between the composite FLDF slope and the Salpeter value suggests a possible physical link between the hierarchical filamentary structure of the cold interstellar medium and the IMF.

We present a systematic analysis of scale-dependent properties of filamentary structures in seven nearby molecular clouds – Taurus, Ophiuchus, Perseus, Orion A, California, IC 5146, and Vela C – using the multiscale extraction method getsf . Alongside the usual surface density profiles Σ( r ), we derived volume density profiles ρ ( r ) for a large sample of filaments, providing new observational constraints on their three-dimensional structure. The half-maximum widths H and h of the surface and volume density profiles, respectively, systematically increase with the spatial scale, following power laws H˜ ∝ Y ^0.50 and h˜ ∝ Y ^0.37 , with distributions spanning ~0.01–1 pc across all scales, challenging the notion of a universal filament width of ~0.1 pc. The median volume density slopes β˜ ≈ 2.1−2.4 are systematically lower than the value β = 4 expected for an isothermal cylinder in hydrostatic equilibrium. For shallow profiles with β ≲ 1, the volume density width h falls below the surface density width H by one to two orders of magnitude, demonstrating that surface density widths overestimate the true physical extent of filaments with shallow profiles. Volume density contrasts are substantially higher than surface density contrasts ( C˜ _ρ ≈ 17−52 versus C˜ _Σ ≈ 1.1−2.7), confirming that filaments are substantially more prominent in three dimensions than their projected appearance suggests. The median linear densities of filaments increase linearly with the spatial scale, Λ˜ ≈ Y , with the fraction of supercritical filaments (Λ > 15 M _⊙ pc ⁻¹ ) increasing strongly with the scale and varying widely among clouds, from ~7% in Taurus and Ophiuchus to ~54% in Vela C, which is broadly consistent with the known star formation activity of the clouds. The statistical properties of the combined filament linear density function across all seven clouds will be presented in a subsequent paper. Measured filament widths and slopes systematically depend on the angular resolution and distance, highlighting the importance of accounting for resolution bias in comparative filament studies.

Analyzing filaments and cores in molecular clouds is key to understanding galactic star formation and its environmental dependence. This paper studies the properties and distribution of dense cores and filaments in the Ophiuchus molecular cloud, with a focus on the L1688 hub-filament system (HFS) and its star formation potential. We extracted sources and filaments from Herschel images and a 13 . ″ 5 resolution surface density map using the getsf method, identified dense cores among the extracted sources, evaluated core mass segregation, and constructed the core mass function (CMF). We derived properties of the filaments from their radial surface density profiles, constructed the filament linear density function (FLDF), and assessed the mass distribution in the L1688 HFS to estimate the core and filament formation efficiencies (CFEs, FFEs). We identified 64 protostellar, 132 prestellar, and 686 unbound cores. The CMF of the prestellar cores has a power-law exponent of −0.86, and the FLDF of the densest filaments has a similar slope of −0.97, whereas the CMF of the unbound cores is found to be −1.36. Mass segregation is prominent among the most massive cores, with only slight differences between the bound and unbound cores. The low-mass unbound cores affect the overall spatial distribution. Among the 769 well-resolved filaments, we find a median half-maximum width of 0.12 pc and a median slope of −1.4 for the filament radial profiles. Mass distribution in the L1688 hub is dominated by the filaments, and outside the hub, it is dominated by the molecular cloud background. There exists a strong correlation between FFE and CFE, which reach their respective maxima of 71% and 5% within the hub and decrease to 21% and 0.9% outside it. The results suggest that the gravitational potential in the L1688 HFS influences core clustering in its high-density regions and that the filament-dominated core formation is a key mechanism in star formation within the system.

Analyzing filaments and cores in molecular clouds is key to understanding galactic star formation and its environmental dependence. This paper studies the properties and distribution of dense cores and filaments in the Ophiuchus molecular cloud, with a focus on the L1688 hub-filament system (HFS) and its star formation potential. We extracted sources and filaments from Herschel images and a 13.5 arcsec resolution surface density map using the getsf method, identified prestellar cores among the extracted sources, evaluated core mass segregation, and constructed the core mass function (CMF). We derived properties of the filaments from their radial surface density profiles, constructed the filament linear density function (FLDF), and assessed the mass distribution in the L1688 HFS to estimate the core and filament formation efficiencies (CFE, FFE). The results suggest that the filament-dominated core formation is a key mechanism in star formation within the system.

Context. The ALMA-IMF Large Program imaged 15 massive protoclusters down to a resolution of ~2 kau scales, identifying about 10³ star-forming cores. The mass and luminosity of these cores, which are fundamental physical characteristics, are difficult to determine, a problem greatly exacerbated at the distances ≥2 kpc of ALMA-IMF protoclusters. Aims. We combined new datasets and radiative transfer modeling to characterize these cores. We estimated their mass-averaged temperature and the masses these estimates imply. For one-sixth of the sample, we measured the bolometric luminosities, implementing deblending corrections when necessary. Methods. We used spectral energy distribution (SED) analysis obtained with the point process mapping (PPMAP) Bayesian procedure, which aims to preserve the best angular resolution of the input data. We extrapolated the luminosity and dust temperature images provided by PPMAP at 2.5″ resolution to estimate those of individual cores, which were identified at higher angular resolution. To do this, we applied approximate radiative transfer relationships between the luminosity of a protostar and the temperature of its surrounding envelope and between the external heating of prestellar cores and their temperatures. Results. For the first time, we provide data-informed estimates of dust temperatures for 882 cores identified with ALMA-IMF: 17–31 K and 28–79 K (5th and 95th percentiles, up to 127 K) for the 616 prestellar and 266 protostellar cores, respectively. We also measured protostellar luminosities spanning 20–80 000 L_⊙. Conclusions. Dust temperatures previously estimated from SED-based analyses at a comparatively lower resolution validate our method. For hot cores, on the other hand, we estimated systematically lower temperatures than studies based on complex organic molecules. We established a mass-luminosity evolutionary diagram, for the first time at the core spatial resolution and for a large sample of intermediate- to high-mass protostellar cores. The ALMA-IMF data favor a scenario in which protostars accrete their mass from a larger mass reservoir than their host cores.

Context. Recent studies suggest that filamentary structures are representative of the initial conditions of star formation in molecular clouds and support a filament paradigm for star formation, potentially accounting for the origin of the stellar initial mass function (IMF). The detailed, local physical properties of molecular filaments remain poorly characterized, however. Aims. Using Herschel imaging observations of the California giant molecular cloud, we aim to further investigate the filament paradigm for low- to intermediate-mass star formation and to better understand the exact role of filaments in the origin of stellar masses. Methods. Using the multiscale, multiwavelength extraction method getsf, we identify starless cores, protostars, and filaments in the Herschel data set and separate these components from the background cloud contribution to determine accurate core and filament properties. Results. We find that filamentary structures contribute approximately 20% of the overall mass of the California cloud, while compact sources such as dense cores contribute a mere 2% of the total mass. Considering only dense gas (defined as gas with A_V,bg > 4.5–7), filaments and cores contribute ~66–73% and 10–14% of the dense gas mass, respectively. The transverse half-power diameter measured for California molecular filaments has a median undeconvolved value of 0.18 pc, consistent within a factor of 2 with the typical ~0.1 pc width of nearby filaments from the Herschel Gould Belt survey. A vast majority of identified prestellar cores (~82–90%) are located within ~0.1 pc of the spines of supercritical filamentary structures. Both the prestellar core mass function (CMF) and the distribution of filament masses per unit length or filament line mass function (FLMF) are consistent with power-law distributions at the high-mass end, ΔN/ΔlogM ∝ M^−1.4±0.2 at M > 1 M_⊙ for the CMF and ΔN/Δlog M_line ∝ M_line^−1.5±0.2 for the FLMF at M_line > 10 M_⊙ pc⁻¹, which are both consistent with the Salpeter power-law IMF. Based on these results, we propose a revised model for the origin of the CMF in filaments, whereby the global prestellar CMF in a molecular cloud arises from the integration of the CMFs generated by individual thermally supercritical filaments within the cloud. Conclusions. Our findings support the existence a tight connection between the FLMF and the CMF/IMF and suggests that filamentary structures represent a critical evolutionary step in establishing a Salpeter-like mass function.

Context. A crucial aspect in addressing the challenge of measuring the core mass function (CMF), that is pivotal for comprehending the origin of the initial mass function (IMF), lies in constraining the temperatures of the cores. Aims. We aim to measure the luminosity, mass, column density and dust temperature of star-forming regions imaged by the ALMA-IMF large program. These fields were chosen to encompass early evolutionary stages of massive protoclusters. High angular resolution mapping is required to capture the properties of protostellar and pre-stellar cores within these regions, and to effectively separate them from larger features, such as dusty filaments. Methods. We employed the point process mapping (PPMAP) technique, enabling us to perform spectral energy distribution fitting of far-infrared and submillimeter observations across the 15 ALMA-IMF fields, at an unmatched 2.5″ angular resolution. By combining the modified blackbody model with near-infrared data, we derived bolometric luminosity maps. We estimated the errors impacting values of each pixel in the temperature, column density, and luminosity maps. Subsequently, we employed the extraction algorithm getsf on the luminosity maps in order to detect luminosity peaks and measure their associated masses. Results. We obtained high-resolution constraints on the luminosity, dust temperature, and mass of protoclusters, that are in agreement with previously reported measurements made at a coarser angular resolution. We find that the luminosity-to-mass ratio correlates with the evolutionary stage of the studied regions, albeit with intra-region variability. We compiled a PPMAP source catalog of 313 luminosity peaks using getsf on the derived bolometric luminosity maps. The PPMAP source catalog provides constraints on the mass and luminosity of protostars and cores, although one source may encompass several objects. Finally, we compare the estimated luminosity-to-mass ratio of PPMAP sources with evolutionary tracks and discuss the limitations imposed by the 2.5″ beam.