Spherical Collapse Research Articles

A compressible 3D finite volume approach for the simulation of unsteady viscoelastic cavitating flows

We present a fully compressible, density-based finite volume solver for the simulation of 3D cavitating flows in viscoelastic Maxwell-/Oldroyd-like fluids. The upper-convected Maxwell model, the Oldroyd-B model and the linear and exponential simplified Phan-Thien Tanner models are implemented as viscoelastic constitutive equations in conservative formulation, and we identified the Truesdell rate as appropriate objective time derivative for compressible flows. Cavitation is modeled by a single-fluid homogeneous mixture equilibrium approach considering condensation and evaporation assuming volume averaged mixture quantities. The corresponding simplified quasilinear system is analyzed, and the wave speeds are calculated in order to adapt the employed four step Runge–Kutta explicit time stepping concerning the viscoelastic transport equations. We introduce a novel ghost cell boundary condition for the viscoelastic stress tensor. The approach is tested against (semi-)analytical unsteady and steady-state references and shows very good agreement. 3D simulations of the spherical vapor bubble collapse are performed for all implemented viscoelastic models and show a distinct influence compared to the Newtonian case. For the upper-convected Maxwell fluid a variation of the relaxation time exhibits its perspicuous influence on the dynamics of the collapse.

Mass assembly history of dark matter haloes in the light of H0 tension

ABSTRACT The Hubble tension may introduce a new course of action to revise the standard Lambda cold dark matter (ΛCDM) model to unravel dark energy and dark matter physics. The Hubble parameter can be reconstructed by late-time observations of the background evolution model independently. We relate the reconstructed Hubble parameter to the structure formation and large-scale structure observables in this work. We use excursion set theory to calculate the number density of dark matter haloes and the mass function of progenitors. We obtain results for both the Markov and non-Markov extensions of excursion set theory in the context of spherical and ellipsoidal collapse. We show that the number density of dark matter haloes in the reconstructed model has ∼2σ difference in comparison with the Planck 2018 ΛCDM in the mass range M ≳ 1012 M⊙. We also compare the dark matter halo progenitor mass function with the pair-galaxy statistics and their mass assembly history from observational data of the Hubble Space Telescope Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. Due to complications in distinguishing the ratio of accretion and merger in mass assembly, our result on the pair fraction is for illustration only. However, the ∼5 times more accurate observations will be promising for distinguishing the reconstructed model and the Planck 2018 ΛCDM.

A Short Review on Clustering Dark Energy

We review dark energy models that can present non-negligible fluctuations on scales smaller than Hubble radius. Both linear and nonlinear evolutions of dark energy fluctuations are discussed. The linear evolution has a well-established framework, based on linear perturbation theory in General Relativity, and is well studied and implemented in numerical codes. We highlight the main results from linear theory to explain how dark energy perturbations become important on the scales of interest for structure formation. Next, we review some attempts to understand the impact of clustering dark energy models in the nonlinear regime, usually based on generalizations of the Spherical Collapse Model. We critically discuss the proposed generalizations of the Spherical Collapse Model that can treat clustering dark energy models and their shortcomings. Proposed implementations of clustering dark energy models in halo mass functions are reviewed. We also discuss some recent numerical simulations capable of treating dark energy fluctuations. Finally, we summarize the observational predictions based on these models.

Challenging cosmic censorship in Einstein-Maxwell-scalar theory with numerically simulated gedanken experiments

We perform extensive nonlinear numerical simulations of the spherical collapse of (charged) wavepackets onto a charged black hole within Einstein-Maxwell theory and in Einstein-Maxwell-scalar theory featuring nonminimal couplings and a spontaneous scalarization mechanism. We confirm that black holes in full-fledged Einstein-Maxwell theory cannot be overcharged past extremality and no naked singularities form, in agreement with the cosmic censorship conjecture. We show that naked singularities do not form even in Einstein-Maxwell-scalar theory, although it is possible to form scalarized black holes with charge above the Reissner-Nordstr\"om bound. We argue that charge and mass extraction due to superradiance at fully nonlinear level is crucial to bound the charge-to-mass ratio of the final black hole below extremality. We also discuss some "descalarization" mechanisms for scalarized black holes induced either by superradiance or by absorption of an opposite-charged wavepacket; in all cases the final state after descalarization is a subextremal Reissner-Nordstr\"om black hole.

Excursion set peaks in energy as a model for haloes

ABSTRACT The simplest models of dark matter halo formation rely on the heuristic assumption, motivated by spherical collapse, that virialized haloes originate from initial regions that are maxima of the smoothed matter density field. Here, we replace this notion with the dynamical requirement that protohaloes be regions where the local gravitational flow converges to a point. For this purpose, we look for spheres whose acceleration at the boundary – relative to their centre of mass – points towards their geometric centre: that is, spheres with null dipole moment. We show that these configurations are minima of the energy, corresponding to the most energetically bound spheres. Therefore, we study peaks of the smoothed energy overdensity field. This significant conceptual change is technically trivial to implement: to change from density to energy one need only modify the standard top-hat smoothing filter. However, this comes with the important benefit that, for power spectra of cosmological interest, the model is no longer plagued by divergences: improving the physics mends the mathematics. In addition, the ‘excursion set’ requirement that the smoothed matter density crosses a critical value can be naturally replaced by a threshold in energy. Measurements in simulations of haloes more massive than 1013h−1M⊙ show very good agreement with a number of generic predictions of our model.

Numerical investigation of non-condensable gas effect on vapor bubble collapse

We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure, and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the cavitating liquid is a barotropic thermodynamic equilibrium model. Compressibility of all phases is considered in order to capture the shock wave of the bubble collapse. After validating the model with an analytical energy partitioning model, simulations of collapsing wall-attached bubbles with different stand-off distances are performed. The effect of the non-condensable gas on rebound and damping of the emitted shock wave is well captured.

Dynamics of dissipative self-gravitating source in Rastall gravity

The dynamics of dissipative gravitational collapse of a source is explored in Rastall gravity. The field equations are derived for the geometry and collapsing matter. The dynamical equations are formulated for the heat flux and diffusion approximation. The heat transportation equation is derived by using Müller–Israel–Stewart approach to investigate the effects of heat flux on the collapsing source. Moreover, an equation is found by combining the dynamical and heat transport equation, the consequences of this equation are discussed in detail. Furthermore, the Rastall parameter [Formula: see text] effect is analyzed for the collapse of sphere.

Dynamics near the central singularity in spherical collapse

We study the dynamics near the central singularity in spherically symmetric collapse of a massless scalar field toward Schwarzschild black hole formation. The equations of motion take different simplified forms in the early and late stages of the singularity curve. We report some fine structures of the analytic solutions and universal features for the metric functions and matter near the singularity.

Evolution of splashback boundaries and gaseous outskirts: insights from mergers of self-similar galaxy clusters

ABSTRACT A self-similar spherical collapse model predicts a dark matter (DM) splashback and accretion shock in the outskirts of galaxy clusters while missing a key ingredient of structure formation – processes associated with mergers. To fill this gap, we perform simulations of merging self-similar clusters and investigate their DM and gas evolution in an idealized cosmological context. Our simulations show that the cluster rapidly contracts during the major merger and the splashback radius rsp decreases, approaching the virial radius rvir. While in the self-similar model rsp depends on a smooth mass accretion rate parameter Γs, our simulations show that in the presence of mergers, rsp responds to the changes in the total mass accretion rate Γvir, which accounts for both mergers and smooth accretion. The scatter of the Γvir − rsp/rvir relation indicates a generally low Γs ∼ 1 in clusters in cosmological simulations. In contrast to the DM, the hot gaseous atmospheres significantly expand by the merger-accelerated (MA-) shocks formed when the runaway merger shocks overtake the outer accretion shock. After a major merger, the MA-shock radius is larger than rsp by a factor of up to ∼1.7 for Γs ≲ 1 and is ∼rsp for Γs ≳ 3. This implies that (1) mergers could easily generate the MA-shock-splashback offset measured in cosmological simulations, and (2) the smooth mass accretion rate is small in regions away from filaments where MA-shocks reside. We further discuss the shapes of the DM haloes, various shocks, and contact discontinuities formed at different epochs of the merger, and the ram-pressure stripping in cluster outskirts.

Convergent filaments contracting towards an intermediate-mass pre-stellar core

ABSTRACT Filamentary structures are closely associated with star-forming cores, but their detailed physical connections are still not clear. We studied the dense gas in OMC-3 MMS-7 region in the Orion A molecular cloud using the molecular lines observed with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Submillimeter Array (SMA). The ALMA N2H+ (1–0) emission has revealed three dense filaments intersected at the centre, coincident with the central core MMS-7, which has a mass of 3.6 M⊙. The filaments and cores are embedded in a parental clump with a total mass of 29 M⊙. The N2H+ velocity field exhibits a noticeable increasing trend along the filaments towards the central core MMS-7 with a scale of v − vlsr ≃ 1.5 km s−1 over a spatial range of ∼20 arcsec (8 × 103 au), corresponding to a gradient of $40\, {\rm km\, s^{-1}}\, {\rm pc}^{-1}$. This feature is most likely to indicate an infall motion towards the centre. The derived infall rate (8 × 10−5 M⊙ yr−1) and time-scale (3.6 × 105 yr) are much lower than that for a spherical free-fall collapse and more consistent with the contraction of the filament structures. The filaments also exhibit a possible fragmentation. But this does not seem to largely interrupt the gas structure or its contraction towards the centre. Thus, MMS-7 provides an example of filamentary inward motion directly towards a pre-stellar core. The filament contraction could be less intense but more steady than global spherical collapse, and may help generate an intermediate-mass or even high-mass star.

Muscle-ups: improved approximations of the matter field with the extended Press–Schechter formalism and Lagrangian perturbation theory

ABSTRACT Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose ‘MUltiscale Spherical Collapse Lagrangian Evolution Using Press–Schechter’ (muscle-ups), a new scheme that reproduces the results from Lagrangian perturbation theory on large scales, while improving the modelling of overdensities on small scales. In muscle-ups, we adapt the extended Press and Schechter formalism to Lagrangian algorithms of the displacement field. For regions exceeding a collapse threshold in the density smoothed at a radius R, we consider all particles within a radius R collapsed. Exploiting a multiscale smoothing of the initial density, we build a halo catalogue on the fly by optimizing the selection of halo candidates. This allows us to generate a density field with a halo mass function that matches one measured in N-body simulations. We further explicitly gather particles in each halo together in a profile, providing a numerical, Lagrangian-based implementation of the halo model. Compared to previous semi-analytical Lagrangian methods, we find that muscle-ups improves the recovery of the statistics of the density field at the level of the probability density function, the power spectrum, and the cross-correlation with the N-body result.

Position-dependent Voronoi probability distribution functions for matter and halos

We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which approximates the Lagrangian density field. For halos, the Voronoi densities contain information about the local environment of each halo. We measure the halo virial masses, the total amount of dark matter within each halo Voronoi cell, and the halo Voronoi cell volumes, and we show how halo abundances depend on these three quantities. We then study the position-dependent Voronoi density PDF, measured within finite subregions of the Universe, using separate universe simulations. We demonstrate that the spatial variation of the position-dependent PDF is due to large-scale density fluctuations, indicating that the position-dependent PDF is a biased tracer of large-scale structure. We measure this bias for the dark matter, and interpret it as the bias of regions of the Lagrangian density field that are selected based on density. For the halos, this bias can be interpreted as a form of assembly bias. We present the mapping from late-time to early-time Voronoi density for each simulation dark matter particle, which is highly stochastic. We compare the median of this stochastic map with spherical collapse calculations and discuss challenges involved in modeling the evolution of the density field on these scales.

Kepler’s Goat Herd: An exact solution to Kepler’s equation for elliptical orbits

ABSTRACT A fundamental relation in celestial mechanics is Kepler’s equation, linking an orbit’s mean anomaly to its eccentric anomaly and eccentricity. Being transcendental, the equation cannot be directly solved for eccentric anomaly by conventional treatments; much work has been devoted to approximate methods. Here, we give an explicit integral solution, utilizing methods recently applied to the ‘geometric goat problem’ and to the dynamics of spherical collapse. The solution is given as a ratio of contour integrals; these can be efficiently computed via numerical integration for arbitrary eccentricities. The method is found to be highly accurate in practice, with our C++ implementation outperforming conventional root-finding and series approaches by a factor greater than two.

The Corona Borealis supercluster: connectivity, collapse, and evolution

Context. Rich superclusters of galaxies represent dynamically active environments in which galaxies and their systems form and evolve. Aims. We study the dynamical properties and connectivity of the richest galaxy clusters in the Corona Borealis (CB) supercluster and of the whole supercluster, and analyse star formation of galaxies in them with the aim to understand the evolution of the supercluster and the galaxies within it. We compare it with the supercluster SCl A2142. Methods. We used the luminosity-density field to determine the high-density cores of the CB. We identified the richest galaxy clusters in them and studied the dynamical state of the clusters, analysed their substructure, and studied the star formation properties of galaxies in them using normal mixture modelling and the projected phase space diagram. We determined filaments in the supercluster to analyse the connectivity of clusters. To understand the possible future evolution of the CB, we compared the mass distribution in it with predictions from the spherical collapse model and analysed the gravitational acceleration field in the CB. Results. The richest clusters in the high-density cores of the CB are the Abell clusters A2065, A2061 (together with A2067), A2089, and Gr2064. At a radius R30 around each cluster (corresponding to the density contrast Δρ ≈ 30), the galaxy distribution shows a minimum. The R30 values for individual clusters lie in the range of 3 − 6 h−1 Mpc. The radii of the clusters (splashback radii) lie in the range of Rcl ≈ 2 − 3 Rvir. The projected phase space diagrams and the comparison with the spherical collapse model suggest that R30 regions have passed turnaround and are collapsing, forming infall regions around each cluster. Galaxies in the richest cluster of the CB, A2065, and in its infall region have on average younger stellar populations than other clusters and their environment. The cluster A2061 has the highest fraction of galaxies with very old stellar populations, similar to those in A2142. The number of long filaments that begin near clusters vary from one near A2089 to five near A2061. The total connectivity of these clusters (the number of infalling groups and filaments) varies from two to nine. Conclusions. During the future evolution, the clusters in the main part of the CB may merge and form one of the largest bound systems in the nearby Universe. Another part, with the cluster Gr2064, will form a separate system. Our study suggests that structures with a current characteristic density contrast Δρ ≈ 30 have passed turnaround and started to collapse at redshifts z ≈ 0.3 − 0.4. The comparison of the number and properties of the most massive collapsing supercluster cores from observations and simulations may serve as a test for cosmological models.

Axion miniclusters made easy

We use a modified version of the peak patch excursion set formalism to compute the mass and size distribution of QCD axion miniclusters from a fully non-Gaussian initial density field obtained from numerical simulations of axion string decay. We find strong agreement with $N$-body simulations at significantly lower computational cost. We employ a spherical collapse model, and provide fitting functions for the modified barrier in the radiation era. The halo mass function at $z=629$ has a power-law distribution ${M}^{\ensuremath{-}0.6}$ for masses within the range ${10}^{\ensuremath{-}15}\ensuremath{\lesssim}M\ensuremath{\lesssim}{10}^{\ensuremath{-}10}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, with all masses scaling as $({m}_{a}/50\text{ }\text{ }\ensuremath{\mu}\mathrm{eV}{)}^{\ensuremath{-}0.5}$. We construct merger trees to estimate the collapse redshift and concentration mass relation, $C(M)$, which is well described using analytical results from the initial power spectrum and linear growth. Using the calibrated analytic results to extrapolate to $z=0$, our method predicts a mean concentration $C\ensuremath{\sim}\mathcal{O}(\mathrm{few})\ifmmode\times\else\texttimes\fi{}{10}^{4}$. The low computational cost of our method makes future investigation of the statistics of rare, dense miniclusters easy to achieve.

Effects of Rastall parameter on perturbation of dark sectors of the Universe

In recent years, Rastall gravity is undergoing a considerable surge in popularity. This theory purports to be a modified gravity theory with a non-conserved energy–momentum tensor (EMT) and an unusual non-minimal coupling between matter and geometry. This work looks for the evolution of homogeneous spherical perturbations within the Universe in the context of Rastall gravity. Using the spherical Top-Hat collapse model, we seek for exact solutions in linear regime for density contrast of dark matter (DM) and dark energy (DE). We find that the Rastall parameter affects crucially the dynamics of density contrasts for DM and DE and the fate of spherical collapse is different in comparison to the case of general relativity (GR). Numerical solutions for perturbation equations in nonlinear regime reveal that DE perturbations could amplify the rate of growth of DM perturbations depending on the values of Rastall parameter.

Relation between general relativity and a class of Hořava gravity theories

Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Ho\v{r}ava, but are increasingly constrained in the infrared. At low energies, Ho\v{r}ava gravity is characterized by three dimensionless couplings, $\alpha$, $\beta$ and $\lambda$, which vanish in the general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings ($\alpha$ and $\beta$) to tiny values, but the third remains relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). Moreover, demanding that (slowly moving) black-hole solutions are regular away from the central singularity requires $\alpha$ and $\beta$ to vanish {\it exactly}. Although a canonical constraint analysis shows that the class of khronometric theories resulting from these constraints ($\alpha=\beta=0$ and $\lambda\neq0$) cannot be equivalent to General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary pulsars and gravitational-wave generation show perfect agreement with General Relativity. Here, we analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave {\it exactly} as in General Relativity, as far as {\it observational} predictions are concerned. Nevertheless, we find that spherical collapse leads to the formation of a regular {\it universal} horizon, i.e. a causal boundary for signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons. Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2 graviton of General Relativity remains strongly coupled at low energies, even on curved backgrounds. These puzzling results suggest that any further bounds on Ho\v{r}ava gravity will probably come from cosmology.

Universality of the spherical collapse with respect to the matter type: the case of a barotropic fluid with linear equation of state

We study the spherical collapse of an over-density of a barotropic fluid with linear equation of state in a cosmological background. Fully relativistic simulations are performed by using the Baumgarte-Shibata-Shapiro-Nakamura formalism jointly with the Valencia formulation of the hydrodynamics. This permits us to test the universality of the critical collapse with respect to the matter type by considering the constant equation of state parameter $\omega$ as a control parameter. We exhibit, for a fixed radial profile of the energy-density contrast, the existence of a critical value $\omega^*$ for the equation of state parameter under which the fluctuation collapses to a black hole and above which it is diluting. It is shown numerically that the mass of the formed black hole, for subcritical solutions, obeys a scaling law $M\propto |\omega - \omega^*|^\gamma$ with a critical exponent $\gamma$ independent on the matter type, revealing the universality. This universal scaling law is shown to be verified in the empty Minkoswki and de Sitter space-times. For the full matter Einstein-de Sitter universe, the universality is not observed if conformally flat sub-horizon initial conditions are used. But when super-horizon initial conditions computed from the long-wavelength approximation are used, the universality appears to be true.

Dynamical conditions and causal transport of dissipative spherical collapse in f(R, T) gravity

In this paper, we have investigated the non-adiabatic spherical gravitational collapse in the framework of the $f(R,T)$ theory of gravity with a locally anisotropic fluid that undergoes dissipation in the form of heat flux, free-streaming radiation, and shearing viscosity. The dynamical equations are analyzed in detail, both in the Newtonian and post-Newtonian regimes. Finally we couple the dynamical equations to the full causal transport equation in the context of Israel-Stewart theory of dissipative systems. This yields us a better understanding of the collapse dynamics and may be connected to various astrophysical consequences.

A Stochastic Theory of the Hierarchical Clustering. II. Halo Progenitor Mass Function and Large-scale Bias

Abstract We generalize the stochastic theory of hierarchical clustering presented in Paper I by Lapi & Danese to derive the (conditional) halo progenitor mass function and the related large-scale bias. Specifically, we present a stochastic differential equation that describes fluctuations in the mass growth of progenitor halos of given descendant mass and redshift, as driven by a multiplicative Gaussian white noise involving the power spectrum and the spherical collapse threshold of density perturbations. We demonstrate that, as cosmic time passes, the noise yields an average drift of the progenitors toward larger masses, which quantitatively renders the expectation from the standard extended Press and Schechter (EPS) theory. We solve the Fokker–Planck equation associated with the stochastic dynamics, and obtain as an exact, stationary solution, the EPS progenitor mass function. Then we introduce a modification of the stochastic equation in terms of a mass-dependent collapse threshold modulating the noise, and solve analytically the associated Fokker–Planck equation for the progenitor mass function. The latter is found to be in excellent agreement with the outcomes of N-body simulations; even more remarkably, this is achieved with the same shape of the collapse threshold used in Paper I to reproduce the halo mass function. Finally, we exploit the above results to compute the large-scale halo bias, and find it in pleasing agreement with the N-body outcomes. All in all, the present paper illustrates that the stochastic theory of hierarchical clustering introduced in Paper I can describe effectively not only halos’ abundance, but also their progenitor distribution and their correlation with the large-scale environment across cosmic times.