arXiv subjects

Ralf S. Klessen

Publications and source records attributed to Ralf S. Klessen.

At least 127 records · Page 7Linked to original sources

arXiv2025

Machine learning the gap between real and simulated nebulae: A domain-adaptation approach to classify ionised nebulae in nearby galaxies

Classifying ionised nebulae in nearby galaxies is crucial to studying stellar feedback mechanisms and understanding the physical conditions of the interstellar medium. This classification task is generally performed by comparing observed line ratios with photoionisation simulations of different types of nebulae (HII regions, planetary nebulae, and supernova remnants). However, due to simplifying assumptions, such simulations are generally unable to fully reproduce the line ratios in observed nebulae. This discrepancy limits the performance of the classical machine-learning approach, where a model is trained on the simulated data and then used to classify real nebulae. For this study, we used a domain-adversarial neural network (DANN) to bridge the gap between photoionisation models (source domain) and observed ionised nebulae from the PHANGS-MUSE survey (target domain). The DANN is an example of a domain-adaptation algorithm, whose goal is to maximise the performance of a model trained on labelled data in the source domain on an unlabelled target domain by extracting domain-invariant features. Our results indicate a significant improvement in classification performance in the target domain when employing the DANN framework compared to a classical neural network (NN) classifier. Additionally, we investigated the impact of adding noise to the source dataset, finding that noise injection acts as a form of regularisation, further enhancing the performances of both the NN and DANN models on the observational data. The combined use of domain adaptation and noise injection improved the classification accuracy in the target domain by 23%. This study highlights the potential of domain adaptation methods in tackling the domain-shift challenge when using theoretical models to train machine-learning pipelines in astronomy.

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arXiv2025

PAH Feature Ratios Around Stellar Clusters and Associations in 19 Nearby Galaxies

We present a comparison of observed polycyclic aromatic hydrocarbon (PAH) feature ratios in 19 nearby galaxies with a grid of theoretical expectations for near- and mid-infrared dust emission. The PAH feature ratios are drawn from Cycle 1 JWST observations and are measured for 7224 stellar clusters and 29176 stellar associations for which we have robust ages and mass estimates from HST five-band photometry. Though there are galaxy-to-galaxy variations, the observed PAH feature ratios largely agree with the theoretical models, particularly those that are skewed toward more ionized and larger PAH size distributions. For each galaxy we also extract PAH feature ratios for 200 pc-wide circular regions in the diffuse interstellar medium, which serve as a non-cluster/association control sample. Compared to what we find for stellar clusters and associations, the 3.3um/7.7um and 3.3um/11.3um ratios from the diffuse interstellar medium are $\sim 0.10-0.15$ dex smaller. When the observed PAH feature ratios are compared to the radiation field hardness as probed by the [OIII]/H$β$ ratio, we find anti-correlations for nearly all galaxies in the sample. These results together suggest that the PAH feature ratios are driven by the shape intensity of the radiation field, and that the smallest PAHs -- observed via JWST F335M imaging -- are increasingly 'processed' or destroyed in regions with the most intense and hard radiation fields.

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arXiv2025

The fragmentation of molecular clouds in starburst environments

A significant amount of star formation occurs and has occurred in environments unlike the solar neighbourhood. The majority of stars formed closer to the peak of the cosmic star formation rate (z > 1.3) and a great deal of star formation presently occurs in the central molecular zone (CMZ) of the Galaxy. These environments are unified by the presence of a high interstellar radiation field (ISRF) and a high cosmic ray ionisation rate (CRIR). Numerical studies of stellar birth typically neglect this fact, and those that do not have thus far been limited in scope. In this work we present the first comprehensive analysis of hydrodynamical simulations of star formation in extreme environments where we have increased the ISRF and CRIR to values typical of the CMZ and starburst galaxies. We note changes in the fragmentation behaviour on both the core and stellar system scale, leading to top-heavy core and stellar system mass functions in high ISRF/CRIR clouds. Clouds fragment less on the core scale, producing fewer but more massive cores. Conversely, the cores fragment more intensely and produce richer clusters of stellar systems. We present a picture where high ISRF/CRIR clouds fragment less on the scale of cores and clumps, but more on the scale of stellar systems. The change in fragmentation behaviour subsequently changes the mass function of the stellar systems that form through enhanced accretion rates.

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arXiv2024

The radiative torque spin-up efficiency of ballistic dust grain aggregates

Aims. It is quintessential for the analysis of the observed dust polarization signal to understand the rotational dynamics of interstellar dust grains. Additionally, high rotation velocities may rotationally disrupt the grains, which impacts the grain-size distribution. We aim to constrain the set of parameters for an accurate description of the rotational spin-up process of ballistic dust grain aggregates driven by radiative torques (RATs). Methods. We modeled the dust grains as complex fractal aggregates grown by the ballistic aggregation of uniform spherical particles (monomers) of different sizes. A broad variation of dust materials, shapes, and sizes were studied in the presence of different radiation sources. Results. We find that the canonical parameterization for the torque efficiency overestimates the maximum angular velocity $ω_{\mathrm{RAT}}$ caused by RATs acting on ballistic grain aggregates. To resolve this problem, we propose a new parameterization that predicts $ω_{\mathrm{RAT}}$ more accurately. We find that RATs are most efficient for larger grains with a lower monomer density. Following the constant part, the parameterization has two power laws with different slopes that retain universality for all grain sizes. The maximum grain rotation does not scale linearly with radiation strength because different drag mechanisms dominate, depending on the grain material and environment. The angular velocity $ω_{\mathrm{RAT}}$ of individual single dust grains has a wide distribution and may even differ from the mean by up to two orders of magnitude. Even though ballistic aggregates have a lower RAT efficiency, strong sources of radiation (stronger than $\approx 100$ times the typical interstellar radiation field) may still produce rotation velocities high enough to cause the rotational disruption of dust grains.

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arXiv2024

Do stars still form in molecular gas within CO-dark dwarf galaxies?

In the Milky Way and other main-sequence galaxies, stars form exclusively in molecular gas, which is traced by CO emission. However, low metallicity dwarf galaxies are often `CO-dark' in the sense that CO emission is not observable even at the high resolution and sensitivities of modern observing facilities. In this work we use ultra high-resolution simulations of four low-metalicity dwarf galaxies (which resolve star formation down to the scale of star-forming cores, 0.01 pc) combined with a time-dependent treatment of the chemistry of the interstellar medium, to investigate the star formation environment in this previously hidden regime. By generating synthetic observations of our models we show that the galaxies have high to extremely high dark gas fractions (0.13 to 1.00 dependent on beam size and conditions), yet despite this form stars. However, when examined on smaller scales, we find that the stars still form in regions dominated by molecular gas, it is simply that these are far smaller than the scale of the beam (1.5"). Thus, while stars in CO-dark dwarf galaxies form in small molecular cores like larger galaxies, their cloud-scale environment is very different.

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arXiv2024

Tracing the earliest stages of star and cluster formation in 19 nearby galaxies with PHANGS-JWST and HST: compact 3.3 $μ$m PAH emitters and their relation to the optical census of star clusters

The earliest stages of star and cluster formation are hidden within dense cocoons of gas and dust, limiting their detection at optical wavelengths. With the unprecedented infrared capabilities of JWST, we can now observe dust-enshrouded star formation with $\sim$10 pc resolution out to $\sim$20 Mpc. Early findings from PHANGS-JWST suggest that 3.3 $μ$m polycyclic aromatic hydrocarbon (PAH) emission can identify star clusters in their dust-embedded phases. Here, we extend this analysis to 19 galaxies from the PHANGS-JWST Cycle 1 Treasury Survey, providing the first characterization of compact sources exhibiting 3.3$μ$m PAH emission across a diverse sample of nearby star-forming galaxies. We establish selection criteria, a median color threshold of F300M-F335M=0.67 at F335M=20, and identify of 1816 sources. These sources are predominantly located in dust lanes, spiral arms, rings, and galaxy centers, with $\sim$87% showing concentration indices similar to optically detected star clusters. Comparison with the PHANGS-HST catalogs suggests that PAH emission fades within $\sim$3 Myr. The H$α$ equivalent width of PAH emitters is 1-2.8 times higher than that of young PHANGS-HST clusters, providing evidence that PAH emitters are on average younger. Analysis of the bright portions of luminosity functions (which should not suffer from incompleteness) shows that young dusty clusters may increase the number of optically visible $\leq$ 3 Myr-old clusters in PHANGS-HST by a factor between $\sim$1.8x-8.5x.

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arXiv2024

3-D CMZ II: Hierarchical Structure Analysis of the Central Molecular Zone

The Central Molecular Zone (CMZ) is the way station at the heart of our Milky Way Galaxy, connecting gas flowing in from Galactic scales with the central nucleus. Key open questions remain about its 3-D structure, star formation properties, and role in regulating this gas inflow. In this work, we identify a hierarchy of discrete structures in the CMZ using column density maps from Paper I (Battersby et al., submitted). We calculate the physical ($N$(H$_2$), $T_{\rm{dust}}$, mass, radius) and kinematic (HNCO, HCN, and HC$_3$N moments) properties of each structure as well as their bolometric luminosities and star formation rates (SFRs). We compare these properties with regions in the Milky Way disk and external galaxies. Despite the fact that the CMZ overall is well below the Gao-Solomon dense gas star-formation relation (and in modest agreement with the Schmidt-Kennicutt relation), individual structures on the scale of molecular clouds generally follow these star-formation relations and agree well with other Milky Way and extragalactic regions. We find that individual CMZ structures require a large external pressure ($P_e$/k$_B$ $> 10^{7-9}$ K cm$^{-3}$) to be considered bound, however simple estimates suggest that most CMZ molecular-cloud-sized structures are consistent with being in pressure-bounded virial equilibriuim. We perform power-law fits to the column density probability distribution functions (N-PDFs) of the inner 100 pc, SgrB2, and the outer 100 pc of the CMZ as well as several individual molecular cloud structures and find generally steeper power-law slopes ($-9<α<-2$) compared with the literature ($-6 < α< -1$).

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arXiv2024

Subsweep: Extensions to the Sweep method for radiative transfer

We introduce the radiative transfer postprocessing code Subsweep. The code is based on the method of transport sweeps, in which the exact solution to the scattering-less radiative transfer equation is computed in a single pass through the entire computational grid. The radiative transfer module is coupled to radiation chemistry, and chemical compositions as well as temperatures of the cells are evolved according to photon fluxes computed during radiative transfer. Subsweep extends the method of transport sweeps by incorporating sub-timesteps in a hierarchy of partial sweeps of the grid. This alleviates the need for a low, global timestep and as a result Subsweep is able to drastically reduce the amount of computation required for accurate integration of the coupled radiation chemistry equations. We succesfully apply the code to a number of physical tests such as the expansion of HII regions, the formation of shadows behind dense objects, and its behavior in the presence of periodic boundary conditions.

astro-ph.IM↗

arXiv2024

A-SLOTH reveals the nature of the first stars

The first generation of stars (PopIII) are too dim to be observed directly and probably too short-lived to have survived for local observations. Hence, we rely on simulations and indirect observations to constrain the nature of the first stars. In this study, we calibrate the semi-analytical model A-SLOTH (Ancient Stars and Local Observables by Tracing Halos), designed for simulating star formation in the early Universe, using a likelihood function based on nine independent observables. These observables span Milky Way-specific and cosmologically representative variables, ensuring a comprehensive calibration process. This calibration methodology ensures that A-SLOTH provides a robust representation of the early Universe's star formation processes, aligning simulated values with observed benchmarks across a diverse set of parameters. The outcome of this calibration process is best-fit values and their uncertainties for 11 important parameters that describe star formation in the early Universe, such as the shape of the initial mass function (IMF) of PopIII stars or escape fractions of ionizing photons. Our best-fitting model has a PopIII IMF with a steeper slope, d$N$/d$M \propto M^{-1.77}$, than the log-flat models often proposed in the literature, and also relatively high minimum and maximum masses, $M_{\rm min} = 13.6$Msun and $M_{\rm max} = 197$Msun. However, we emphasize that the IMF-generating parameters are poorly constrained and, e.g., the IMF slope could vary from log-flat to Salpeter. We also provide data products, such as delay time distribution, bubble size distributions for ionizing and metal-enriched bubbles at high redshift, and correlation plots between all 11 input parameters. Our study contributes to understanding the formation of early stars through A-SLOTH and provides valuable insights into the intricate processes involved in the early Universe's star formation.

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arXiv2024

Testing kinematic distances under a realistic Galactic potential

Obtaining reliable distance estimates to gas clouds within the Milky Way is challenging in the absence of certain tracers. The kinematic distance approach has been used as an alternative, derived from the assumption of circular trajectories around the Galactic centre. Consequently, significant errors are expected in regions where gas flow deviates from purely circular motions. We aim to quantify the systematic errors that arise from the kinematic distance method in the presence of a Galactic potential that is non-axisymmetric. We investigate how these errors differ in certain regions of the Galaxy and how they relate to the underlying dynamics. We perform 2D hydrodynamical simulation of the gas disk with the moving-mesh code Arepo, adding the capability of using an external potential provided by the Agama library for galactic dynamics. We introduce a new analytic potential of the Milky Way, taking elements from existing models and adjusting parameters to match recent observational constraints. In line with results of previous studies, we report significant errors in the kinematic distance estimate for gas close to the Sun, along sight lines towards the Galactic centre and anti-centre, and associated with the Galactic bar. Kinematic distance errors are low within the spiral arms as gas resides close to local potential minima and the resulting LOS velocity is similar to what is expected for an axisymmetric potential. Interarm regions exhibit large deviations at any given Galactic radius. This is caused by the gas being sped up or slowed down as it travels into or out of spiral arms. In addition, we identify 'zones of avoidance' in the lv-diagram, where the kinematic distance method is particularly unreliable and should only be used with caution, and we find a power law relation between the kinematic distance error and the deviation of the projected LOS velocity from circular motion.

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arXiv2024

3-D CMZ III: Constraining the 3-D structure of the Central Molecular Zone via molecular line emission and absorption

The Milky Way's Central Molecular Zone (CMZ) is the largest concentration of dense molecular gas in the Galaxy, the structure of which is shaped by the complex interplay between Galactic-scale dynamics and extreme physical conditions. Understanding the 3-D geometry of this gas is crucial as it determines the locations of star formation and subsequent feedback. We present a catalogue of clouds in the CMZ using Herschel data. Using archival data from the APEX and MOPRA CMZ surveys, we measure averaged kinematic properties of the clouds at 1mm and 3mm. We use archival ATCA data of the H$_{2}$CO (1$_{1,0}$ - 1$_{1,1}$) 4.8 GHz line to search for absorption towards the clouds, and 4.85 GHz GBT C-band data to measure the radio continuum emission. We measure the absorption against the continuum to provide new constraints for the line-of-sight positions of the clouds relative to the Galactic centre, and find a highly asymmetric distribution, with most clouds residing in front of the Galactic centre. The results are compared with different orbital models, and we introduce a revised toy model of a vertically-oscillating closed elliptical orbit. We find that most models describe the PPV structure of the gas reasonably well, but find significant inconsistencies in all cases regarding the near vs. far placement of individual clouds. Our results highlight that the CMZ is likely more complex than can be captured by these simple geometric models, along with the need for new data to provide further constraints on the true 3-D structure of the CMZ.

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arXiv2024

Dynamical resonances in PHANGS galaxies

Bars are remarkable stellar structures that can transport gas toward centers and drive the secular evolution of galaxies. In this context, it is important to locate dynamical resonances associated with bars. For this study, we used ${Spitzer}$ near-infrared images as a proxy for the stellar gravitational potential and the ALMA CO(J=2-1) gas distribution from the PHANGS survey to determine the position of the main dynamical resonances associated with the bars in the PHANGS sample of 74 nearby star-forming galaxies. We used the gravitational torque method to estimate the location of the bar corotation radius ($R_{\rm CR}$), where stars and gas rotate at the same angular velocity as the bar. Of the 46 barred galaxies in PHANGS, we have successfully determined the corotation (CR) for 38 of them. The mean ratio of the $R_{\rm CR}$ to the bar radius ($R_{\rm bar}$) is $\mathcal{R} = R_{\rm CR}/R_{\rm bar} = 1.12$, with a standard deviation of $0.39$. This is consistent with the average value expected from theory and suggests that bars are predominantly fast. We also compared our results with other bar CR measurements from the literature, which employ different methods, and find good agreement ($ρ= 0.64$). Finally, using rotation curves, we have estimated other relevant resonances such as the inner Lindblad resonance (ILR) and the outer Lindblad resonance (OLR), which are often associated with rings. This work provides a useful catalog of resonances for a large sample of nearby galaxies and emphasizes the clear connection between bar dynamics and morphology.

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arXiv2024

Halo Mergers Enhance the Growth of Massive Black Hole Seeds

High redshift observations of 10$^9$ M$_\odot$ supermassive black holes (SMBHs) at $z \sim7$ and `Little Red Dots' that may host overmassive black holes at $z>4$ suggests the existence of so-called heavy seeds (>1000 M$_\odot$) in the early Universe. Recent work has suggested that the rapid assembly of halos may be the key to forming heavy seeds early enough in the Universe to match such observations without the need for extreme radiation fields or dark matter streaming velocities. We perform simulations of BH seed formation in 4 distinct idealised halo collapse scenarios; an isolated 10$^6$ M$_\odot$ minihalo, an isolated 10$^7$ M$_\odot$ atomic halo, the direct collision of two 10$^7$ M$_\odot$ halos and a fly-by collision of two 10$^7$ M$_\odot$ halos. We have shown that halo collisions create a central environment of enhanced density, inside which BH seeds can accrete at enhanced rates. For direct collisions, the gas density peaks are disrupted by the interaction, as the collisionless DM peaks pass through each other while the colliding gas is left in the center, removing the sink particle from its accretion source. When the central density peaks instead experience a fly-by interaction, the sink particle remains embedded in the dense gas and maintains enhanced accretion rates throughout the simulated period when compared to the isolated halo cases. Here the final mass of the sink particle achieved a factor of 2 greater in mass than in the isolated atomic halo case, and a factor of 3 greater than the minihalo case, reaching 10$^4$ M$_\odot$ via its 0.03 pc accretion radius. As the maximum halo mass before collapse is determined by the atomic cooling limit of a few times 10$^7$ M$_{\odot}$, the ability of halo-halo mergers to further boost accretion rates onto the central object may play a crucial role in growing SMBH seeds.

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arXiv2024

Metallicity calibrations based on auroral lines from PHANGS-MUSE data

We present a chemical analysis of selected HII regions from the PHANGS-MUSE nebular catalogue. Our intent is to empirically re-calibrate strong-line diagnostics of gas-phase metallicity, applicable across a wide range of metallicities within nearby star-forming galaxies. To ensure reliable measurements of auroral line fluxes, we carried out a new spectral fitting procedure whereby only restricted wavelength regions around the emission lines of interest are taken into account: this assures a better fit for the stellar continuum. No prior cuts to nebulae luminosity were applied to limit biases in auroral line detections. Ionic abundances of O+, O++, N+, S+, and S++ were estimated by applying the direct method. We integrated the selected PHANGS-MUSE sample with other existing auroral line catalogues, appropriately re-analysed to obtain a homogeneous dataset. This was used to derive strong-line diagnostic calibrations that span from 12+log(O/H) = 7.5 to 8.8. We investigate their dependence on the ionisation parameter and conclude that it is likely the primary cause of the significant scatter observed in these diagnostics. We apply our newly calibrated strong-line diagnostics to the total sample of HII regions from the PHANGS-MUSE nebular catalogue, and we exploit these indirect metallicity estimates to study the radial metallicity gradient within each of the 19 galaxies of the sample. We compare our results with the literature and find good agreement, validating our procedure and findings. With this paper, we release the full catalogue of auroral and nebular line fluxes for the selected HII regions from the PHANGS-MUSE nebular catalogue. This is the first catalogue of direct chemical abundance measurements carried out with PHANGS-MUSE data.

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arXiv2024

Gravitational waves from mergers of Population III binary black holes: roles played by two evolution channels

The gravitational wave (GW) signal from binary black hole (BBH) mergers is a promising probe of Population III (Pop III) stars. To fully unleash the power of the GW probe, one important step is to understand the relative importance and features of different BBH evolution channels. We model two channels, isolated binary stellar evolution (IBSE) and nuclear star cluster-dynamical hardening (NSC-DH), in one theoretical framework based on the semi-analytical code A-SLOTH, under various assumptions on Pop III initial mass function (IMF), initial binary statistics and high-$z$ nuclear star clusters (NSCs). The NSC-DH channel contributes $\sim 8-95\%$ of Pop III BBH mergers across cosmic history, with higher contributions achieved by initially wider binary stars, more top-heavy IMFs, and more abundant high-$z$ NSCs. The dimensionless stochastic GW background (SGWB) produced by Pop III BBH mergers has peak values $Ω^{\rm peak}_{\rm GW}\sim 10^{-11}-8\times 10^{-11}$ around observer-frame frequencies $ν\sim 10-100\ \rm Hz$. The Pop III contribution can be a non-negligible ($\sim 2-32\%$) component in the total SGWB at $ν\lesssim 10\ \rm Hz$. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are $\sim 6-230\ \rm yr^{-1}$ and $\sim 30-1230\ \rm yr^{-1}$ for the NSC-DH and IBSE channels, respectively. Pop III BBH mergers in NSCs are more massive than those from IBSE, so they dominate the Pop III SGWB below $20$ Hz in most cases. Besides, the detection rate of Pop III BBH mergers involving at least one intermediate-mass BH above $100\ \rm M_\odot$ by the Einstein Telescope is $\sim 0.5-200\ \rm yr^{-1}$ in NSCs but remains below $0.1\ \rm yr^{-1}$ for IBSE.

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arXiv2024

JWST MIRI and NIRCam observations of NGC 891 and its circumgalactic medium

We present new JWST observations of the nearby, prototypical edge-on, spiral galaxy NGC 891. The northern half of the disk was observed with NIRCam in its F150W and F277W filters. Absorption is clearly visible in the mid-plane of the F150W image, along with vertical dusty plumes that closely resemble the ones seen in the optical. A $\sim 10 \times 3~{\rm kpc}^2$ area of the lower circumgalactic medium (CGM) was mapped with MIRI F770W at 12 pc scales. Thanks to the sensitivity and resolution of JWST, we detect dust emission out to $\sim 4$ kpc from the disk, in the form of filaments, arcs, and super-bubbles. Some of these filaments can be traced back to regions with recent star formation activity, suggesting that feedback-driven galactic winds play an important role in regulating baryonic cycling. The presence of dust at these altitudes raises questions about the transport mechanisms at play and suggests that small dust grains are able to survive for several tens of million years after having been ejected by galactic winds in the disk-halo interface. We lay out several scenarios that could explain this emission: dust grains may be shielded in the outer layers of cool dense clouds expelled from the galaxy disk, and/or the emission comes from the mixing layers around these cool clumps where material from the hot gas is able to cool down and mix with these cool cloudlets. This first set of data and upcoming spectroscopy will be very helpful to understand the survival of dust grains in energetic environments, and their contribution to recycling baryonic material in the mid-plane of galaxies.

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arXiv2024

JWST Observations of Starbursts: Massive Star Clusters in the Central Starburst of M82

We present a near infrared (NIR) candidate star cluster catalog for the central kiloparsec of M82 based on new JWST NIRCam images. We identify star cluster candidates using the F250M filter, finding 1357 star cluster candidates with stellar masses $>10^4$ M$_\odot$. Compared to previous optical catalogs, nearly all (87%) of the candidates we identify are new. The star cluster candidates have a median intrinsic cluster radius of $\approx$1 pc and have stellar masses up to $10^6$ M$_\odot$. By comparing the color-color diagram to dust-free yggdrasil stellar population models, we estimate that the star cluster candidates have A$_{\rm V}\sim3-24$ mag, corresponding to A$_{\rm 2.5μm}\sim0.3-2.1$ mag. There is still appreciable dust extinction towards these clusters into the NIR. We measure the stellar masses of the star cluster candidates, assuming ages of 0 and 8 Myr. The slope of the resulting cluster mass function is $β=1.9\pm0.2$, in excellent agreement with studies of star clusters in other galaxies.

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arXiv2024

Gravitational collapse at low to moderate Mach numbers: The relationship between star formation efficiency and the fraction of mass in the massive object

The formation of massive objects via gravitational collapse is relevant both for explaining the origin of the first supermassive black holes and in the context of massive star formation. Here, we analyze simulations of the formation of massive objects pursued by different groups and in various environments, concerning the formation of supermassive black holes, primordial stars, as well as present-day massive stars. We focus particularly on the regime of small virial parameters, i.e., low ratios of the initial kinetic to gravitational energy, low to moderate Mach numbers, and the phase before feedback is very efficient. We compare the outcomes of collapse under different conditions using dimensionless parameters, particularly the star formation efficiency ε_*, the fraction f_* of mass in the most massive object relative to the total stellar mass, and the fraction f_{\rm tot} of mass of the most massive object as a function of the total mass. We find that in all simulations analyzed here, f_{\rm tot} increases as a function of ε_*, although the steepness of the increase depends on the environment. The relation between f_* and ε_* is found to be more complex and also strongly depends on the number of protostars present at the beginning of the simulations. We show that a collision parameter, estimated as the ratio of the system size divided by the typical collision length, allows us to approximately characterize whether collisions will be important. We analyze the statistical correlation between the dimensionless quantities using the Spearman coefficient and confirm via a machine learning analysis that good predictions of f_* can be obtained from ε_* together with a rough estimate of the collision parameter. This suggests that a good estimate of the mass of the most massive object can be obtained once the maximum efficiency for a given environment is known.

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