Initial Virial Ratio Research Articles

Structure of the equivalent Newtonian systems in MONDN-body simulations

Aims.We investigate the core-cusp problem of the Λ cold dark matter (ΛCDM) scenario in the context of the modified Newtonian dynamics (MOND) paradigm while exploiting the concept of an equivalent Newtonian system (ENS).Methods.By means of particle-meshN-body simulations in MOND, we explored the processes of galaxy formation via cold dissipationless collapse and the merging of smaller substructures. From the end states of our simulations, we recovered the associated ENS and studied the properties of their dark matter halos. We compared the simulation results with simple analytical estimates with a family ofγ-models.Results.We find that the dark matter density of ENSs of most spherical cold collapses have a markedly cored structure, particularly for the lowest values of the initial virial ratios. End states of some simulations with initially clumpy conditions have more complex profiles, and some of their ENSs exhibit a moderate cusp, with the logarithmic density slope always shallower than one.Conclusions.In contrast to what one would expect from theoretical and numerical arguments in ΛCDM, these results seem to point towards the fact that the absence of a central DM cusp in most observed galaxies would be totally consistent in a MONDian description.

Comparison of Instabilities of Annular Perturbations on the Background of Pulsating 2D and 3D Self-Gravitating Models

The problem of gravitational instability of the observed annular (ring-like) structural perturbation modes on the background of a nonlinearly pulsating spherical model based on the well-known equilibrium Camm ball is studied. Nonstationary analogues of dispersion relations for the perturbation modes under consideration within this model are obtained. Critical diagrams of the initial virial ratio versus the model rotation parameter are constructed for each case. A comparative analysis of the increments of gravitational instability of annular perturbation modes on the background of spherical and disk-shaped nonlinearly pulsating models is also performed. An analysis of the results shows that the annular perturbation modes are predominantly more unstable in a nonstationary disk than in a spherical nonequilibrium model, regardless of the rotation parameters and the initial virial ratio of the systems. The article is partly based on a report presented at the conference “Modern Stellar Astronomy-2022” held at the Caucasian Mountain Observatory of the Sternberg Astronomical Institute of Lomonosov Moscow State University, November 8–10, 2022.

Early dynamical evolution of rotating star clusters in a tidal field

ABSTRACT In order to explore how the early internal rotational properties of star clusters are affected by the external potential of their host galaxies, we have run a suite of N-body simulations following the early dynamical evolution and violent relaxation of rotating star clusters embedded in a tidal field. Our study focuses on models for which the cluster’s rotation axis has a generic orientation relative to the torque of the tidal field. The interaction between the violent relaxation process, angular momentum of the cluster, and the external torque creates a complex kinematic structure within the cluster, most prominently a radial variation in the position of the rotation axis, along both the polar and azimuthal directions. We also examine the cluster’s velocity dispersion anisotropy and show that the projected anisotropy may be affected by the variation of the rotation axis directions within the cluster; the combination of projection effects and the complex kinematical features may result in the measurement of tangential anisotropy in the cluster’s inner regions. We also characterize the structural properties of our clusters as a function of their initial rotation and virial ratio and find that clusters may develop a triaxial morphology and a radial variation of the minor axis not necessarily aligned with the rotation axis. Finally, we examine the long-term evolution of these complex kinematic features.

The formation of binary star clusters in the Milky Way and Large Magellanic Cloud

ABSTRACT Recent observations of young embedded clumpy clusters and statistical identifications of binary star clusters have provided new insights into the formation process and subsequent dynamical evolution of star clusters. The early dynamical evolution of clumpy stellar structures provides the conditions for the origin of binary star clusters. Here, we carry out N-body simulations in order to investigate the formation of binary star clusters in the Milky Way and in the Large Magellanic Cloud (LMC). We find that binary star clusters can form from stellar aggregates with a variety of initial conditions. For a given initial virial ratio, a higher degree of initial substructure results in a higher fraction of binary star clusters. The number of binary star clusters decreases over time due to merging or dissolution of the binary system. Typically, $\sim 45{{\ \rm per\ cent}}$ of the aggregates evolve into binary/multiple clusters within t = 20 Myr in the Milky Way environment, while merely $\sim 30{{\ \rm per\ cent}}$ survives beyond t = 50 Myr, with separations ≲ 50 pc. On the other hand, in the LMC, $\sim 90{{\ \rm per\ cent}}$ of the binary/multiple clusters survive beyond t = 20 Myr and the fraction decreases to $\sim 80{{\ \rm per\ cent}}$ at t = 50 Myr, with separations ≲ 35 pc. Multiple clusters are also rapidly formed for highly substructured and expanding clusters. The additional components tend to detach and the remaining binary star cluster merges. The merging process can produce fast rotating star clusters with mostly flat rotation curves that speed up in the outskirts.

Far and extreme ultraviolet radiation fields and consequent disc destruction in star-forming regions

ABSTRACT The first stages of planet formation usually occur when the host star is still in a (relatively) dense star-forming region, where the effects of the external environment may be important for understanding the outcome of the planet formation process. In particular, star-forming regions that contain massive stars have strong far-ultraviolet (FUV) and extreme ultraviolet (EUV) radiation fields, which can induce mass-loss from protoplanetary discs due to photoevaporation. In this paper, we present a parameter-space study of the expected FUV and EUV fields in N-body simulations of star-forming regions with a range of initial conditions. We then use recently published models to determine the mass-loss due to photoevaporation from protoplanetary discs. In particular, we focus on the effects of changing the initial degree of spatial structure and initial virial ratio in the star-forming regions, as well as the initial stellar density. We find that the FUV fields in star-forming regions are much higher than in the interstellar medium, even when the regions have stellar densities as low as in the Galactic field, due to the presence of intermediate-mass, and massive, stars (>5 M⊙). These strong radiation fields lead to the destruction of the gas component in protoplanetary discs within 1 Myr, implying that gas giant planets must either form extremely rapidly (<1 Myr), or that they exclusively form in star-forming regions like Taurus, which contain no intermediate-mass or massive stars. The latter scenario is in direct tension with meteoritic evidence from the Solar system that suggests the Sun and its protoplanetary disc was born in close proximity to massive stars.

Collision between molecular clouds – I. The effect of the cloud virial ratio in head-on collisions

ABSTRACT In a series of papers, we investigate the effect of collisions between turbulent molecular clouds on their structure, evolution, and star formation activity. In this paper, we look into the role of the clouds’ initial virial ratios. Three different scenarios were examined: both clouds initially bound, one cloud bound and one unbound, and both clouds initially unbound. Models in which one or both clouds are bound generate filamentary structures aligned along the collision axis and discernible in position–position and position–velocity space. If neither cloud is bound, no filaments result. Unlike in previous simulations of collisions between smooth clouds, owing to the substructure created in the clouds by turbulence before the collisions, dissipation of kinetic energy by the collision is very inefficient and in none of our simulations is sufficient bulk kinetic energy lost to render the clouds bound. Simulations where both clouds are bound created twice as much stellar mass than the bound–unbound model, and both these scenarios produced much more stellar mass than the simulation in which both clouds are unbound. Each simulation was also compared with a control run in which the clouds do not collide. We find the bound–bound collision increases the overall star formation efficiency by a factor of approximately two relative to the control, but that the bound–unbound collision produces a much smaller increase, and the collision has very little effect on the unbound–unbound cloud collision.

Dynamical evolution of star-forming regions: III. Unbound stars and predictions for Gaia

We use $N$-body simulations to probe the early phases of the dynamical evolution of star-forming regions and focus on mass and velocity distributions of unbound stars. In this parameter space study, we vary the initial virial ratio and degree of spatial and kinematic substructure and analyse the fraction of stars that become unbound in two different mass classes (above and below 8 M$_{\odot}$). We find that the fraction of unbound stars differs depending on the initial conditions. After 10 Myr, in initially highly subvirial, substructured simulations, the high-mass and lower-mass unbound fractions are similar at $\sim$23 per cent. In initially virialised, substructured simulations, we find only $\sim$16 per cent of all high-mass stars are unbound, whereas $\sim$37 per cent of all lower-mass stars are. The velocity distributions of unbound stars only show differences for extremely different initial conditions. The distributions are dominated by large numbers of lower-mass stars becoming unbound just above the escape velocity of $\sim$3 km s$^{-1}$ with unbound high-mass stars moving faster on average than lower-mass unbound stars. We see no high-mass runaway stars (velocity > 30 km s$^{-1}$) from any of our initial conditions and only an occasional lower-mass runaway star from initially subvirial/substructured simulations. In our simulations, we find a small number of lower-mass walkaway stars (with velocity 5-30 km s$^{-1}$) from all of our initial conditions. These walkaway stars should be observable around many nearby star-forming regions with Gaia.

Phase-space structure analysis of self-gravitating collisionless spherical systems

In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code, and a N-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles ρ(r) ∝ rn, 0 ≤ n ≤ −1.5, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios η = 0.5 (“warm”) and η = 0.1 (“cool”). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well-known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady-state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phase-space distribution at the coarse grained level, and (iii) relaxation to a non-spherical state due to radial orbit instabilities for n ≤ −1 in the cool case.

Feeding supermassive black holes by collisional cascades

The processes driving gas accretion on to supermassive black holes (SMBHs) are still poorly understood. Angular momentum conservation prevents gas within $\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where viscous accretion becomes efficient. Here we present simulations of the collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have formed as a result of feedback from a previous episode of AGN activity. The gas falls towards the SMBH forming clumps and streams, which intersect, collide, and often form a disc. These collisions promote partial cancellations of angular momenta, resulting in further infall and more collisions. This continued collisional cascade generates a tail of gas with sufficiently small angular momenta and provides a viable route for gas inflow to sub-parsec scales. The efficiency of this process hardly depends on details, such as gas temperature, initial virial ratio and power spectrum of the gas distribution, as long as it is not strongly rotating. Adding star formation to this picture might explain the near-simultaneous formation of the S-stars (from tidally disrupted binaries formed in plunging gas streams) and the sub-parsec young stellar disc around Sgr A$^{\!\star}$.

The effect of the virial state of molecular clouds on the influence of feedback from massive stars

A set of Smoothed Particle Hydrodynamics simulations of the influence of photoionising radiation and stellar winds on a series of 10$^{4}$M$_{\odot}$ turbulent molecular clouds with initial virial ratios of 0.7, 1.1, 1.5, 1.9 and 2.3 and initial mean densities of 136, 1135 and 9096\,cm$^{-3}$ are presented. Reductions in star formation efficiency rates are found to be modest, in the range $30\%-50\%$ and to not vary greatly across the parameter space. In no case was star formation entirely terminated over the $\approx3$\,Myr duration of the simulations. The fractions of material unbound by feedback are in the range $20-60\%$, clouds with the lowest escape velocities being the most strongly affected.\\ Leakage of ionised gas leads to the HII regions rapidly becoming underpressured. The destructive effects of ionisation are thus largely not due to thermally--driven expansion of the HII regions, but to momentum transfer by photoevaporation of fresh material. Our simulations have similar global ionisation rates and we show that the effects of feedback upon them can be adequately modelled as a steady injection of momentum, resembling a momentum--conserving wind.

Supernova enrichment and dynamical histories of solar-type stars in clusters

We use N-body simulations of star cluster evolution to explore the hypothesis that short-lived radioactive isotopes found in meteorites, such as 26-Al, were delivered to the Sun's protoplanetary disc from a supernova at the epoch of Solar System formation. We cover a range of star cluster formation parameter space and model both clusters with primordial substructure, and those with smooth profiles. We also adopt different initial virial ratios - from cool, collapsing clusters to warm, expanding associations. In each cluster we place the same stellar population; the clusters each have 2100 stars, and contain one massive 25M_Sun star which is expected to explode as a supernova at about 6.6Myr. We determine the number of Solar (G)-type stars that are within 0.1 - 0.3pc of the 25M_Sun star at the time of the supernova, which is the distance required to enrich the protoplanetary disc with the 26-Al abundances found in meteorites. We then determine how many of these G-dwarfs are unperturbed `singletons'; stars which are never in close binaries, nor suffer sub-100au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of twenty initially identical clusters is highly stochastic, with the supernova enriching over 10 G-dwarfs in some clusters, and none at all in others. Typically only ~25 per cent of clusters contain enriched, unperturbed singletons, and usually only 1 - 2 per cluster (from a total of 96 G-dwarfs in each cluster). The initial conditions for star formation do not strongly affect the results, although a higher fraction of supervirial (expanding) clusters would contain enriched G-dwarfs if the supernova occurred earlier than 6.6Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.

Ionizing feedback from massive stars in massive clusters – III. Disruption of partially unbound clouds

We extend our previous smoothed particle hydrodynamics parameter study of the effects of photoionization from O-stars on star-forming clouds to include initially unbound clouds. We generate a set of model clouds in the mass range 104–106 M⊙ with initial virial ratios Ekin/Epot = 2.3, allow them to form stars and study the impact of the photoionizing radiation produced by the massive stars. We find that, on the 3 Myr time-scale before supernovae are expected to begin detonating, the fraction of mass expelled by ionizing feedback is a very strong function of the cloud escape velocities. High-mass clouds are largely unaffected dynamically, while low-mass clouds have large fractions of their gas reserves expelled on this time-scale. However, the fractions of stellar mass unbound are modest and significant portions of the unbound stars are so only because the clouds themselves are initially partially unbound. We find that ionization is much more able to create well-cleared bubbles in the unbound clouds, owing to their intrinsic expansion, but that the presence of such bubbles does not necessarily indicate that a given cloud has been strongly influenced by feedback. We also find, in common with the bound clouds from our earlier work, that many of the systems simulated here are highly porous to photons and supernova ejecta, and that most of them will likely survive their first supernova explosions.

Violent and mild relaxation of an isolated self-gravitating uniform and spherical cloud of particles

The collapse of an isolated, uniform and spherical cloud of self-gravitating particles represents a paradigmatic example of a relaxation process leading to the formation of a quasi-stationary state in virial equilibrium. We consider several N-body simulations of such a system, with the initial velocity dispersion as a free parameter. We show that there is a clear difference between structures formed when the initial virial ratio is b_0 =2K_0/W_0 < b_0^c ~ -1/2 and b_0> b_0^c. These two sets of initial conditions give rise respectively to a mild and violent relaxation occurring in about the same time scale: however in the latter case the system contracts by a large factor, while in the former it approximately maintains its original size. Correspondingly the resulting quasi equilibrium state is characterized by a density profile decaying at large enough distances as ~1/r^4 or with a sharp cut-off. The case b_0<b_0^c can be well described by the Lynden-Bell theory of collisionless relaxation considering the system confined in a box. On the other hand the relevant feature for b_0>b_0^c is the ejection of particles and energy, which is not captured by such a theoretical approach: for this case we introduce a simple physical model to explain the formation of the power-law density profile. This model shows that the behavior n(r) ~1/r^4 is the typical density profile that is obtained when the initial conditions are cold enough that mass and energy ejection occurs. In addition, we clarify the origin of the critical value of the initial virial ratio b_0^c.

Gravitational instability of perturbations in a background nonlinear nonstationary model of a disk-like system. II. Large-scale tesseral oscillation modes

We study the gravitational instability of large-scale tesseral perturbation modes against the background of the previously built model od a disk galaxy, nonlinearly pulsating and anisotropic in velocities. This model rests on a nonstationary generalization of the well-known equilibrium isotropic disk model due to Bisnovaty-Kogan and Zeldovich. We have obtained the corresponding nonstationary analogs of the dispersion equations for the five basic tesseral perturbation modes. The results are presented in the form of critical dependences of the initial virial ratio on the superposition parameter for different degrees of rotation. We have also carried out a comparative analysis of the instability increments for all large-scale perturbation modes.

Formation rates of star clusters in the hierarchical merging scenario

Stars form with a complex and highly structured distribution. For a smooth star cluster to form from these initial conditions, the star cluster must erase this substructure. We study how substructure is removed using N-body simulations that realistically handle two-body relaxation. In contrast to previous studies, we find that hierarchical cluster formation occurs chiefly as a result of scattering of stars out of clumps, and not through clump merging. Two-body relaxation, in particular within the body of a clump, can significantly increase the rate at which substructure is erased beyond that of clump-merging alone. Hence the relaxation time of individual clumps is a key parameter controlling the rate at which smooth, spherical star clusters can form. The initial virial ratio of the clumps is an additional key parameter controlling the formation rate of a cluster. Reducing the initial virial ratio causes a star cluster to lose its substructure more rapidly.

Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.

RADIATION FEEDBACK, FRAGMENTATION, AND THE ENVIRONMENTAL DEPENDENCE OF THE INITIAL MASS FUNCTION

The fragmentation of star-forming interstellar clouds, and the resulting stellar initial mass function (IMF), is strongly affected by the temperature structure of the collapsing gas. Since radiation feedback from embedded stars can modify this as collapse proceeds, feedback plays an important role in determining the IMF. However, the effects and importance of radiative heating are likely to depend strongly on the surface density of the collapsing clouds, which determines both their effectiveness at trapping radiation and the accretion luminosities of the stars forming within them. In this paper, we report a suite of adaptive mesh refinement radiation–hydrodynamic simulations using the ORION code in which we isolate the effect of column density on fragmentation by following the collapse of clouds of varying column density while holding the mass, initial density and velocity structure, and initial virial ratio fixed. We find that radiation does not significantly modify the overall star formation rate or efficiency, but that it suppresses fragmentation more and more as cloud surface densities increase from those typical of low-mass star-forming regions like Taurus, through the typical surface density of massive star-forming clouds in the Galaxy, up to conditions found only in super-star clusters. In regions of low surface density, fragmentation during collapse leads to the formation of small clusters rather than individual massive star systems, greatly reducing the fraction of the stellar population with masses ≳10 M☉. Our simulations have important implications for the formation of massive stars and the universality of the IMF.

Gravitational instability of perturbations in a background nonlinear nonstationary model of a disklike system. I. Sectorial modes

Using a nonstationary generalization of the Bisnovatyi-Kogan-Zel’dovich well-known isotropic model, a new model of a nonstationary self-gravitating disklike system is constructed, with an anisotropic velocity diagram. This model is formed as a linear superposition of two exact models with the same nonstationarity law. We investigate the stability of the new model under sectorial modes of perturbations up to the 10th order inclusive. The results are presented in the form of critical dependencies of the initial virial ratio on the rotation and superposition parameters. The dependences of the instability increments on the basic physical parameters of the model are presented.

One-dimensional self-gravitating sheet model and Lynden-Bell statistics

The Lynden-Bell statistics has been proposed to explain common features among galaxies, which are not in thermal equilibrium. The statistics is not successful to reproduce energy distribution in the one-dimensional self-gravitating sheet model except for initial states near the virial equilibrium. The breakdown is caused by dynamically accelerated high-energy sheets, and hence a modified statistics is examined by focusing on low-energy sheets in order to clarify validity of the basic idea of the Lynden-Bell statistics. The modification improves agreement between the theoretical and numerical energy distributions in a wide interval of the initial virial ratio.

Instabilities in a nonstationary model of self-gravitating disks. I. Bar and ring perturbation modes

The instabilities of bar and ring mode perturbations against the background of a disk oscillating nonlinearly in its own plane are examined in a disk model which is a nonstationary generalization of the well known Bisnovatyi-Kogan-Zel'dovich model. Nonstationary analogs corresponding to a dispersion relation are found for these two oscillation modes. The results of the calculations are presented in the form of critical dependences of the initial virial ratio on the degree of rotation. A comparative analysis of the growth rates of the gravitational instability for these modes is also carried out. The bar mode instability occurs if the initial total kinetic energy of the disk is no more than 10.4% of the initial potential energy. The mechanism is associated with an instability in the radial motions which is aperiodic for small values of the rotation parameter Ω < 0.1, but is otherwise oscillatory. Calculations show that a ring structure can be formed as a result of an instability in the radial motions if the initial total energy of the model is no more than 5.2% of the initial potential energy, regardless of the value of Ω.