arXiv subjects

František Dinnbier

Publications and source records attributed to František Dinnbier.

16 recordsLinked to original sources

arXiv2024

The masses of open star clusters and their tidal tails and the stellar initial mass function

Unresolved binaries have a strong influence on the observed parameters of stellar clusters (SCs). We quantify this influence and compute the resulting mass underestimates and stellar mass function (MF). N-body simulations of realistic SCs were used to investigate the evolution of the binary population in a SC and its tidal tails. Together with an empirically gauged stellar mass-luminosity relation, the results were then used to determine how the presence of binaries changes the photometric mass and MF of the SC and its tails as deduced from observations. Tail 1 (T1), which is the tidal tail caused by gas expulsion, contains a larger fraction of binaries than both the SC and tail 2 (T2), which forms after gas expulsion. Additionally, T1 has a larger velocity dispersion. Using the luminosity of an unresolved binary, an observer would underestimate its mass. This bias sensitively depends on the companion masses due to the structure of the stellar mass-luminosity relation. Combining the effect of all binaries in the simulation, the total photometric mass of the SC is underestimated by 15%. Dark objects (black holes/neutron stars) increase the difference between the real and observed mass of the SC further. For both the SC and the tails, the observed power-law index of the MF between a stellar mass of 0.3 and 0.7 $M_\odot$ is smaller by up to 0.2 than the real one, the real initial mass function (IMF) being steeper by this amount. This difference is larger for stars with a larger velocity dispersion or binary fraction. Since the stars formed in SCs are the progenitors of the Galactic field stars, this work suggests that the binary fractions of different populations of stars in the Galactic disc will differ as a function of the velocity dispersion. The direction of this correlation is currently unclear and a complete population synthesis will be needed to investigate this effect.

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arXiv2024

On the dynamical evolution of Cepheid multiplicity in star clusters and its implications for B-star multiplicity at birth

Classical Cepheid variable stars provide a unique probe to binary evolution in intermediate-mass stars over the course of several tens to hundreds of Myr. We studied the binary and multiple properties of Cepheids, assuming that all mid-B stars form in binaries inside star clusters. The binaries were subjected both to stellar evolution and dynamical encounters with other stars in the cluster. The dynamical cluster environment results in a higher binary fraction among the Cepheids that remain in star clusters ($\approx 60$%) than among the Cepheids which have escaped to the field ($\approx 35$%). In clusters, the binary, triple, and multiple fraction decreases with increasing cluster mass. More massive clusters have binaries of shorter orbital periods than lower mass clusters and field Cepheids. Mergers are very common with $\approx 30$% of mid-B stars not evolving to Cepheids because of the interaction with their companion. Approximately $40$ % of Cepheids have merged with their companion, and the merger event impacts stellar evolution; the age of Cepheids expected from their mass can differ from the age of their host cluster. Our models predict that one in five Cepheids is the result of a merger between stars with mass below the lower mass limit for Cepheids; in clusters, these objects occur substantially later than expected from their mass. Approximately $3$ to $5$ % of all Cepheids have a compact companion ($\approx 0.15$ % of all Cepheids are accompanied by a black hole). The binary fraction derived from our simulations (42%) underestimates the observed binary Cepheid fraction by approximately a factor of 2. This suggests that the true multiplicity fraction of B-stars at birth could be substantially larger than unity and, thus, that mid-B stars may typically form in triple and higher order systems.

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arXiv2022

Do the majority of stars form as gravitationally unbound?

Some of the youngest stars (age $\lesssim 10$ Myr) are clustered, while many others are observed scattered throughout star forming regions or in complete isolation. It has been intensively debated whether the scattered or isolated stars originate in star clusters, or if they form truly isolated, which could help constrain the possibilities how massive stars are formed. We adopt the assumption that all stars form in gravitationally bound star clusters embedded in molecular cloud cores ($Γ$-$1\;$ model), which expel their natal gas, and compare the fraction of stars found in clusters with observational data. The star clusters are modelled by the code nbody6, which includes stellar and circumbinary evolution, gas expulsion, and the external gravitational field of their host galaxy. We find that small changes in the assumptions in the current theoretical model estimating the fraction, $Γ$, of stars forming in embedded clusters have a large influence on the results, and we present a counterexample as an illustration. This calls into question theoretical arguments about $Γ$ in embedded clusters, and it suggests that there is no firm theoretical ground for low $Γ$ in galaxies with lower star formation rates (SFRs). Instead, the assumption that all stars form in embedded clusters is in agreement with observational data for the youngest stars (age $\lesssim 10$ Myr). In the $Γ$-$1\;$ scenario, the observed fraction of the youngest stars in clusters increases with the SFR only weakly; the increase is caused by the presence of more massive clusters in galaxies with higher SFRs, which release fewer stars to the field in proportion to their mass. The $Γ$-$1\;$ model yields a higher fraction of stars in clusters for older stars (age between $10$ and $300$ Myr) than what is observed. This discrepancy can be caused by interactions with molecular clouds.

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arXiv2021

On the dynamical evolution of Cepheids in star clusters

We investigate the occurrence of classical (type-I) Cepheid variable stars (henceforth: Cepheids) in dynamically evolving star clusters from birth to an age of approximately 300 Myr. The clusters are modelled by the Aarseth code nbody6, and they feature a realistic stellar initial mass function and initial binary star population, single star and binary star evolution, expulsion of the primordial gas, and the tidal field of the galaxy. Our simulations provide the first detailed dynamical picture of how frequently Cepheids remain gravitationally bound to their birth clusters versus how frequently they occur in the field. They allow us to quantify the relevance of various cluster escape mechanisms and how they depend on stellar mass. Overall, the simulations agree with the empirical picture that a small fraction ($\approx 10\%$) of Cepheids reside in clusters, that cluster halo membership is relatively common, and that the majority of Cepheid hosting clusters have only a single Cepheid member. Additionally, the simulations predict that a) Cepheid progenitors are much more likely to escape from low-mass than higher-mass clusters; b) higher-mass (long-period) Cepheids are $\approx 30\%$ more likely to be found in clusters than low-mass (short-period) Cepheids; c) the clustered Cepheid fraction increases with galactocentric radius since cluster dispersal is less efficient at greater radii; d) a lower metallicity reduces the overall clustered Cepheid fraction; e) high-mass clusters are much more likely to have more than one Cepheid member at any given time, in particular at a lower metallicity. We interpret the results as outcomes of various aspects of star cluster dynamics. The comparison of predicted and observed clustered Cepheid fractions, $f_{\rm CC}$, highlights the need for additional cluster disruption mechanisms, most likely encounters with giant molecular clouds.

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arXiv2021

Estimating the ages of open star clusters from properties of their extended tidal tails

The most accurate current methods for determining the ages of open star clusters, stellar associations and stellar streams are based on isochrone fitting or the lithium depletion boundary. We propose another method for dating these objects based on the morphology of their extended tidal tails, which have been recently discovered around several open star clusters. Assuming that the early-appearing tidal tails, the so called tidal tails I, originate from the stars released from the cluster during early gas expulsion, or that they form in the same star forming region as the cluster (i.e. being coeval with the cluster), we derive the analytical formula for the tilt angle $β$ between the long axis of the tidal tail and the orbital direction for clusters or streams on circular trajectories. Since at a given Galactocentric radius, $β$ is only a function of age $t$ regardless of the initial properties of the cluster, we estimate the cluster age by inverting the analytical formula $β= β(t)$. We illustrate the method on a sample of $12$ objects, which we compiled from the literature, and we find a reasonable agreement with previous dating methods in $\approx 70$% of the cases. This can probably be improved by taking into account the eccentricity of the orbits and by revisiting the dating methods based on stellar evolution. The proposed morphological method is suitable for relatively young clusters (age $\lesssim 300$ Myr), where it provides a relative age error of the order of $10$ to $20$% for an error in the observed tilt angle of $5 ^\circ$.

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arXiv2021

Tree-based solvers for adaptive mesh refinement code FLASH -- II: radiation transport module TreeRay

The treatment of radiative transfer with multiple radiation sources is a critical challenge in simulations of star formation and the interstellar medium. In this paper we present the novel TreeRay method for solving general radiative transfer problems, based on reverse ray tracing combined with tree-based accelerated integration. We implement TreeRay in the adaptive mesh refinement code FLASH, as a module of the tree solver developed by Wünsch et al. However, the method itself is independent of the host code and can be implemented in any grid based or particle based hydrodynamics code. A key advantage of TreeRay is that its computational cost is independent of the number of sources, making it suitable for simulations with many point sources (e.g. massive star clusters) as well as simulations where diffuse emission is important. A very efficient communication and tree-walk strategy enables TreeRay to achieve almost ideal parallel scalings. TreeRay can easily be extended with sub-modules to treat radiative transfer at different wavelengths and to implement related physical processes. Here, we focus on ionising (EUV) radiation and use the On-the-Spot approximation to test the method and its parameters. The ability to set the tree solver time step independently enables the speedy calculation of radiative transfer in a multi-phase interstellar medium, where the hydrodynamic time step is typically limited by the sound speed of the hot gas produced in stellar wind bubbles or supernova remnants. We show that complicated simulations of star clusters with feedback from multiple massive stars become feasible with TreeRay.

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arXiv2021

SILCC VI -- Multi-phase ISM structure, stellar clustering, and outflows with supernovae, stellar winds, ionising radiation and cosmic rays

We present simulations of the multi-phase interstellar medium (ISM) at solar neighbourhood conditions including thermal and non-thermal ISM processes, star cluster formation, and feedback from massive stars: stellar winds, hydrogen ionising radiation computed with the novel TreeRay radiative transfer method, supernovae (SN), and the injection of cosmic rays (CR). N-body dynamics is computed with a 4th-order Hermite integrator. We systematically investigate the impact of stellar feedback on the self-gravitating ISM with magnetic fields, CR advection and diffusion and non-equilibrium chemical evolution. SN-only feedback results in strongly clustered star formation with very high star cluster masses, a bi-modal distribution of the ambient SN densities, and low volume-filling factors (VFF) of warm gas, typically inconsistent with local conditions. Early radiative feedback prevents an initial starburst, reduces star cluster masses and outflow rates. Furthermore, star formation rate surface densities of $Σ_{\dot{M}_\star} = 1.4-5.9 \times 10^{-3}$ $\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$, VFF$_\mathrm{warm} = 60-80$ per cent as well as thermal, kinetic, magnetic, and cosmic ray energy densities of the model including all feedback mechanisms agree well with observational constraints. On the short, 100 Myr, timescales investigated here, CRs only have a moderate impact on star formation and the multi-phase gas structure and result in cooler outflows, if present. Our models indicate that at low gas surface densities SN-only feedback only captures some characteristics of the star-forming ISM and outflows/inflows relevant for regulating star formation. Instead, star formation is regulated on star cluster scales by radiation and winds from massive stars in clusters, whose peak masses agree with solar neighbourhood estimates.

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arXiv2021

3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR3: its Relation to Cluster Dynamics

We analyze the 3D morphology and kinematics of 13 open clusters (OCs) located within 500 pc of the Sun, using Gaia EDR3 and kinematic data from literature. Members of OCs are identified using the unsupervised machine learning method StarGO, using 5D parameters (X, Y, Z, $μ_α\cosδ, μ_δ$). The OC sample covers an age range of 25Myr--2.65Gyr. We correct the asymmetric distance distribution due to the parallax error using Bayesian inversion. The uncertainty in the corrected distance for a cluster at 500~pc is 3.0--6.3~pc, depending on the intrinsic spatial distribution of its members. We determine the 3D morphology of the OCs in our sample and fit the spatial distribution of stars within the tidal radius in each cluster with an ellipsoid model. The shapes of the OCs are well-described with oblate spheroids (NGC2547, NGC2516, NGC2451A, NGC2451B, NGC2232), prolate spheroids (IC2602, IC4665, NGC2422, Blanco1, Coma Berenices), or triaxial ellipsoids (IC2391, NGC6633, NGC6774). The semi-major axis of the fitted ellipsoid is parallel to the Galactic plane for most clusters. Elongated filament-like substructures are detected in three young clusters (NGC2232, NGC2547, NGC2451B), while tidal-tail-like substructures (tidal tails) are found in older clusters (NGC2516, NGC6633, NGC6774, Blanco1, Coma Berenices). Most clusters may be super-virial and expanding. $N$-body models of rapid gas expulsion with an SFE of $\approx 1/3$ are consistent with clusters more massive than $250\rm M_\odot$, while clusters less massive than 250$\rm M_\odot$ tend to agree with adiabatic gas expulsion models. Only six OCs (NGC2422, NGC6633, and NGC6774, NGC2232, Blanco1, Coma Berenices) show clear signs of mass segregation.

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arXiv2020

Tidal tails of open star clusters as probes to early gas expulsion II: Predictions for Gaia

We study the formation and evolution of the tidal tail released from a young Pleiades-like star cluster, due to expulsion of primordial gas in a realistic gravitational field of the Galaxy. The tidal tails (as well as clusters) are integrated from their embedded phase for 300 Myr. We vary star formation efficiencies (SFEs) from 33% to 100% and the timescales of gas expulsion as free parameters, and provide predictions for the morphology and kinematics of the evolved tail for each of the models. The resulting tail properties are intended for comparison with anticipated Gaia observations in order to constrain the poorly understood early conditions during the gas phase and gas expulsion. The simulations are performed with the code Nbody6 including a realistic external gravitational potential of the Galaxy, and an analytical approximation for the natal gaseous potential. Assuming that the Pleiades formed with rapid gas expulsion and an SFE of $\approx 30$%, the current Pleiades are surrounded by a rich tail extending from $\approx 150$ to $\approx 350$ pc from the cluster and containing 0.7 to 2.7 times the number of stars in the present-day cluster. If the Pleiades formed with an SFE close to 100%, then the tail is shorter ($\lesssim 90$ pc) and substantially poorer, containing only $\approx 2$% of the number of present-day cluster stars. If the Pleiades formed with an SFE of $\approx 30$%, but the gas expulsion was adiabatic, the tail signatures are indistinguishable from the case of the model with 100% SFE. The model takes into account the estimated contamination due to the field stars and the Hyades-Pleiades stream, which constitutes a more limiting factor than the accuracy of the Gaia measurements.

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arXiv2020

Tidal tails of open star clusters as probes to early gas expulsion I: A semi-analytic model

Star clusters form out of the densest parts of infrared dark clouds. The emergence of massive stars expels the residual gas, which has not formed stars yet. Gas expulsion lowers the gravitational potential of the embedded cluster, unbinding many of the cluster stars. These stars then move on their own trajectories in the external gravitational field of the Galaxy, forming a tidal tail. We investigate the formation and evolution of the tidal tail forming due to expulsion of primordial gas under various scenarios of gas expulsion to provide predictions for tidal tails around dynamically evolved (age > 100 Myr) galactic star clusters, which can be possibly detected by the Gaia mission. We provide a semi-analytical model for the tail evolution. We find that tidal tails released during gas expulsion have different kinematic properties than the tails gradually forming due to evaporation. The gas expulsion tidal tail shows non-monotonic expansion with time, where longer epochs of expansion are interspersed with shorter epochs of contraction. The tail thickness and velocity dispersions strongly, but not exactly periodically, vary with time. The times of minima of tail thickness and velocity dispersions are given only by the properties of the galactic potential, and not by the properties of the cluster. The estimates provided by the (semi-)analytical model for the extent of the tail, the minima of tail thickness, and velocity dispersions are in a very good agreement with the nbody6 simulations. This implies that the semi-analytic model can be used for estimating the properties of the gas expulsion tidal tail for a cluster of a given age and orbital parameters without the necessity of performing numerical simulations. A study with a more extended parameter space of the initial conditions is performed in the follow up paper.

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arXiv2018

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.

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arXiv2018

The relative impact of photoionizing radiation and stellar winds on different environments

Photoionizing radiation and stellar winds from massive stars deposit energy and momentum into the interstellar medium (ISM). They might disperse the local ISM, change its turbulent multi-phase structure, and even regulate star formation. Ionizing radiation dominates the massive stars' energy output, but the relative effect of winds might change with stellar mass and the properties of the ambient ISM. We present simulations of the interaction of stellar winds and ionizing radiation of 12, 23, and 60 M$_{\odot}$ stars within a cold neutral (CNM, $n_{0}$ = 100 cm$^{-3}$), warm neutral (WNM, $n_{0}$ = 1, 10 cm$^{-3}$) or warm ionized (WIM, $n_{0}$ = 0.1 cm$^{-3}$) medium. The FLASH simulations adopt the novel tree-based radiation transfer algorithm TreeRay. With the On-the-Spot approximation and a temperature-dependent recombination coefficient, it is coupled to a chemical network with radiative heating and cooling. In the homogeneous CNM, the total momentum injection ranges from 1.6$\times$10$^{4}$ to 4$\times$10$^{5}$ M$_{\odot}$ km s$^{-1}$ and is always dominated by the expansion of the ionized H$_{\text{II}}$ region. In the WIM, stellar winds dominate (2$\times$10$^{2}$ to 5$\times$10$^{3}$ M$_{\odot}$ km s$^{-1}$), while the input from radiation is small ($\sim$ 10$^{2}$ M$_{\odot}$ km s$^{-1}$). The WNM ($n_{0}$ = 1 cm$^{-3}$) is a transition regime. Energetically, stellar winds couple more efficiently to the ISM ($\sim$ 0.1 percent of wind luminosity) than radiation ($<$ 0.001 percent of ionizing luminosity). For estimating the impact of massive stars, the strongly mass-dependent ratios of wind to ionizing luminosity and the properties of the ambient medium have to be considered.

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arXiv2018

Evidence for feedback and stellar-dynamically regulated bursty star cluster formation: the case of the Orion Nebula Cluster

(abridged) A scenario for the formation of multiple co-eval populations separated in age by about 1 Myr in very young clusters (VYCs, ages less than 10 Myr) and with masses in the range 600-20000 Msun is outlined. It rests upon a converging inflow of molecular gas building up a first population of pre-main sequence stars. The associated just-formed O stars ionise the inflow and suppress star formation in the embedded cluster. However, they typically eject each other out of the embedded cluster within 10^6 yr, that is before the molecular cloud filament can be ionised entirely. The inflow of molecular gas can then resume forming a second population. This sequence of events can be repeated multiply. This model is applied to the Orion Nebula Cluster (ONC), in which three well-separated pre-main sequences in the color-magnitude diagram of the cluster have recently been discovered. The mass-inflow history is constrained using this model and the number of OB stars ejected from each population are estimated for verification using Gaia data. As a consequence of the proposed model, the three runaway O star systems, AE Aur, mu Col and iota Ori, are considered as significant observational evidence for stellar-dynamical ejections of massive stars from the oldest population in the ONC.

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arXiv2018

Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths

We describe an OctTree algorithm for the MPI-parallel, adaptive mesh-refinement code {\sc FLASH}, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalisation of the Ewald method. The gravity calculation can be accelerated with the {\em adaptive block update} technique by partially re-using the solution from the previous time-step. Comparison with the {\sc Flash} internal multi-grid gravity solver shows that tree based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple APE MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the {\sc RADMC-3D} radiation transport code, with the tree solver being much faster. Our algorithm is available in the standard release of the {\sc FLASH} code in version 4.0 and later.

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arXiv2017

Nature of the Galactic centre NIR-excess sources. I. What can we learn from the continuum observations of the DSO/G2 source?

The Dusty S-cluster Object (DSO/G2) orbiting the supermassive black hole (Sgr A*) in the Galactic centre has been monitored in both near-infrared continuum and line emission. There has been a dispute about the character and the compactness of the object: interpreting it as either a gas cloud or a dust-enshrouded star. A recent analysis of polarimetry data in $K_{\rm s}$-band ($2.2\,{\rm μm}$) allows us to put further constraints on the geometry of the DSO. The purpose of this paper is to constrain the nature and the geometry of the DSO. We compare 3D radiative transfer models of the DSO with the NIR continuum data including polarimetry. In the analysis, we use basic dust continuum radiative transfer theory implemented in the 3D Monte Carlo code Hyperion. Moreover, we implement analytical results of the two-body problem mechanics and the theory of non-thermal processes. We present a composite model of the DSO -- a dust-enshrouded star that consists of a stellar source, dusty, optically thick envelope, bipolar cavities, and a bow shock. This scheme can match the NIR total as well as polarized properties of the observed spectral energy distribution (SED). The SED may be also explained in theory by a young pulsar wind nebula that typically exhibits a large linear polarization degree due to magnetospheric synchrotron emission. The analysis of NIR polarimetry data combined with the radiative transfer modelling shows that the DSO is a peculiar source of compact nature in the S cluster $(r \lesssim 0.04\,{\rm pc})$. It is most probably a young stellar object embedded in a non-spherical dusty envelope, whose components include optically thick dusty envelope, bipolar cavities, and a bow shock. Alternatively, the continuum emission could be of a non-thermal origin due to the presence of a young neutron star and its wind nebula.

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arXiv2017

Fragmentation of vertically stratified gaseous layers: monolithic or coalescence-driven collapse

We investigate, using 3D hydrodynamic simulations, the fragmentation of pressure-confined, vertically stratified, self-gravitating gaseous layers. The confining pressure is either thermal pressure acting on both surfaces, or thermal pressure acting on one surface and ram-pressure on the other. In the linear regime of fragmentation, the dispersion relation we obtain agrees well with that derived by Elmegreen & Elmegreen (1978), and consequently deviates from the dispersion relations based on the thin shell approximation (Vishniac 1983) or pressure assisted gravitational instability (Wünsch et al. 2010). In the non-linear regime, the relative importance of the confining pressure to the self-gravity is a crucial parameter controlling the qualitative course of fragmentation. When confinement of the layer is dominated by external pressure, self- gravitating condensations are delivered by a two-stage process: first the layer fragments into gravitationally bound but stable clumps, and then these clumps coalesce until they assemble enough mass to collapse. In contrast, when external pressure makes a small contribution to confinement of the layer, the layer fragments monolithically into gravitationally unstable clumps and there is no coalescence. This dichotomy persists whether the external pressure is thermal or ram. We apply these results to fragments forming in a shell swept up by an expanding H II region, and find that, unless the swept up gas is quite hot or the surrounding medium has low density, the fragments have low-mass ( ~< 3 M_Sun ), and therefore they are unlikely to spawn stars that are sufficiently massive to promote sequential self-propagating star formation.

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