Spherical Infall Model Research Articles

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions – XV. Steady accretion from global collapse to core feeding in massive hub-filament system SDC335

ABSTRACT We present ALMA Band-3/7 observations towards ‘the Heart’ of a massive hub-filament system (HFS) SDC335, to investigate its fragmentation and accretion. At a resolution of ∼0.03 pc, 3 mm continuum emission resolves two massive dense cores MM1 and MM2, with $383(^{\scriptscriptstyle +234}_{\scriptscriptstyle -120})$ M⊙ (10–24 % mass of ‘the Heart’) and $74(^{\scriptscriptstyle +47}_{\scriptscriptstyle -24})$ M⊙, respectively. With a resolution down to 0.01 pc, 0.87 mm continuum emission shows MM1 further fragments into six condensations and multi-transition lines of H2CS provide temperature estimation. The relation between separation and mass of condensations at a scale of 0.01 pc favors turbulent Jeans fragmentation where the turbulence seems to be scale-free rather than scale-dependent. We use the H13CO+ J = 1 − 0 emission line to resolve the complex gas motion inside ‘the Heart’ in position-position-velocity space. We identify four major gas streams connected to large-scale filaments, inheriting the anti-clockwise spiral pattern. Along these streams, gas feeds the central massive core MM1. Assuming an inclination angle of 45(± 15)° and a H13CO+ abundance of 5(± 3) × 10−11, the total mass infall rate is estimated to be 2.40(± 0.78) × 10−3 M⊙ yr−1, numerically consistent with the accretion rates derived from the clump-scale spherical infall model and the core-scale outflows. The consistency suggests a continuous, near steady-state, and efficient accretion from global collapse, therefore ensuring core feeding. Our comprehensive study of SDC335 showcases the detailed gas kinematics in a prototypical massive infalling clump, and calls for further systematic and statistical studies in a large sample.

Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems

Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exists. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, , known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark matter halos with central cusps, ρ ∼ r −1, and outer parts, ρ ∼ r −4. Here we define a nonequilibrium functional, S D , which is maximized for DARKexp and increases monotonically during the evolution toward equilibrium of idealized collisionless systems of the extended spherical infall model. Systems that undergo more mixing more closely approach DARKexp.

Splashback Radius in a Spherical Collapse Model

It was shown several years ago that dark matter halo outskirts are characterized by very steep density profiles in a very small radial range. This feature has been interpreted as a pile-up of different particle orbits at a similar location, namely, splashback material at half an orbit after collapse. Adhikari et al. (2014) obtained the location of the splashback radius through a very simple model by calculating a dark matter shell trajectory in the secondary infall model while it crosses a growing NFW profile-shaped dark matter halo. Because they imposed a halo profile instead of calculating it from the trajectories of the shells of dark matter, they were not able to find the dark matter profile around the splashback radius. In the present paper, we use an improved spherical infall model taking into account shell crossing as well as several physical effects such as ordered and random angular momentum, dynamical friction, adiabatic contraction, etc. This allows us to determine the density profile from the inner to the outer region and to study the behavior of the outer density profile. We compare the density profiles and their logarithmic slope of with the simulation results of Diemer and Kravtsov (2014), finding a good agreement between the prediction of the model and the simulations.

Mass Accretion Rates of the HectoMAP Clusters of Galaxies

Abstract We estimate the mass accretion rate (MAR) of 321 clusters of galaxies in the HectoMAP Cluster Survey. The clusters span the redshift range 0.17–0.42 and the M 200 mass range ≈ (0.5–3.5) × 1014 M ⊙. The MAR estimate is based on the caustic technique along with a spherical infall model. Our analysis extends the measurement of MARs for 129 clusters at z < 0.3 from the Cluster Infall Regions in the Sloan Digital Sky Survey and the Hectospec Cluster Survey to redshift z ∼ 0.42. Averaging over redshift, low-mass clusters with masses near 0.7 × 1014 M ⊙ roughly accrete 3 × 104 M ⊙ yr−1; more massive clusters with masses near 2.8 × 1014 M ⊙ roughly accrete 1 × 105 M ⊙ yr−1. Low- and high-mass clusters increase their MAR by approximately 46% and 84%, respectively, as the redshift increases from z in the range 0.17–0.29 to z in the range 0.34–0.42. The MARs at fixed redshift increase with mass and MARs at fixed mass increase with redshift in agreement with the ΛCDM cosmological model for hierarchical structure formation. We consider the extension of MAR measurements to z ∼ 1.

The Diffusion Coefficient of the Splashback Mass Function as a Probe of Cosmology

Abstract We present an analytic model for the splashback mass function of dark matter halos, which is parameterized by a single coefficient and constructed in the framework of the generalized excursion set theory and the self-similar spherical infall model. The value of the single coefficient that quantifies the diffusive nature of the splashback boundary is determined at various redshifts by comparing the model with the numerical results from the Erebos N-body simulations for the Planck and the WMAP7 cosmologies. Showing that the analytic model with the best-fit coefficient provides excellent matches to the numerical results in the mass range of 5 ≤ M/(1012 h −1 M ⊙) < 103, we employ the Bayesian and Akaike Information Criterion tests to confirm that our model is most preferred by the numerical results compared to previous models at redshifts of 0.3 ≤ z ≤ 3 for both of the cosmologies. We also found that the diffusion coefficient decreases almost linearly with redshift, converging to zero at a certain threshold redshift, z c , whose value significantly differs between the Planck and WMAP7 cosmologies. Our result implies that the splashback mass function of dark matter halos at z ≥ z c is well described by a parameter-free analytic formula and that z c may have the potential to independently constrain the initial conditions of the universe.

Phase-space structure of protohalos: Vlasov versus particle-mesh

The phase-space structure of primordial dark matter halos is revisited using cosmological simulations with three sine waves and cold dark matter (CDM) initial conditions. The simulations are performed with the tessellation based Vlasov solver ColDICE and a particle-mesh (PM) N-body code. The analyses include projected density, phase-space diagrams, radial density ρ(r), and pseudo-phase space density: Q(r) = ρ(r)/σv(r)3 with σv the local velocity dispersion. Particular attention is paid to force and mass resolution. Because the phase-space sheet complexity, estimated in terms of total volume and simplex (tetrahedron) count, increases very quickly, ColDICE can follow only the early violent relaxation phase of halo formation. During the violent relaxation phase, agreement between ColDICE and PM simulations having one particle per cell or more is excellent and halos have a power-law density profile, ρ(r) ∝ r−α, α ∈ [1.5, 1.8]. This slope, measured prior to any merger, is slightly larger than in the literature. The phase-space diagrams evidence complex but coherent patterns with clear signatures of self-similarity in the sine wave simulations, while the CDM halos are somewhat scribbly. After additional mass resolution tests, the PM simulations are used to follow the next stages of evolution. The power law progressively breaks down with a convergence of the density profile to the well-known Navarro–Frenk–White universal attractor, irrespective of initial conditions, that is even in the three-sine-wave simulations. This demonstrates again that mergers do not represent a necessary condition for convergence to the dynamical attractor. Not surprisingly, the measured pseudo phase-space density is a power law Q(r) ∝ r−αQ, with αQ close to the prediction of secondary spherical infall model, αQ ≃ 1.875. However this property is also verified during the early relaxation phase, which is non-trivial.

Preprocessing among the Infalling Galaxy Population of EDisCS Clusters

Abstract We present results from a low-resolution spectroscopic survey for 21 galaxy clusters at 0.4 < z < 0.8 selected from the ESO Distant Cluster Survey. We measured spectra using the low-dispersion prism in IMACS on the Magellan Baade telescope and calculate redshifts with an accuracy of σ z = 0.007. We find 1763 galaxies that are brighter than R = 22.9 in the large-scale cluster environs. We identify the galaxies expected to be accreted by the clusters as they evolve to z = 0 using spherical infall models and find that ∼30%–70% of the z = 0 cluster population lies outside the virial radius at z ∼ 0.6. For analogous clusters at z = 0, we calculate that the ratio of galaxies that have fallen into the clusters since z ∼ 0.6 to those that were already in the core at that redshift is typically between ∼0.3 and 1.5. This wide range of ratios is due to intrinsic scatter and is not a function of velocity dispersion, so a variety of infall histories is to be expected for clusters with current velocity dispersions of 300 km s−1 ≲ σ ≲ 1200 km s−1. Within the infall regions of z ∼ 0.6 clusters, we find a larger red fraction of galaxies than in the field and greater clustering among red galaxies than blue. We interpret these findings as evidence of “preprocessing,” where galaxies in denser local environments have their star formation rates affected prior to their aggregation into massive clusters, although the possibility of backsplash galaxies complicates the interpretation.

Density distribution of the cosmological matter field

The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering, massive production of mock galaxy catalogs, and testing predictions of cosmological models. Here we make a comprehensive analysis of the dark matter PDF using a suite of 7000 N-body simulations that covers a wide range of numerical and cosmological parameters. We find that the PDF has a simple shape: it declines with density as a power-law P~rho**(-2), which is exponentially suppressed on both small and large densities. The proposed double-exponential approximation provides an accurate fit to all our N-body results for small filtering scales R< 5Mpc/h with rms density fluctuations sigma>1. In combination with the spherical infall model that works well for small fluctuations sigma<1, the PDF is now approximated with just few percent errors over the range of twelve orders of magnitude -- a remarkable example of precision cosmology. We find that at 5-10% level the PDF explicitly depends on redshift (at fixed sigma) and on cosmological density parameter Omega_m. We test different existing analytical approximations and find that the often used log-normal approximation is always 3-5 times less accurate than either the double-exponential approximation or the spherical infall model.

Dwarfs in the entourage of the Local Volume groups: flow tracers and cosmological probes

AbstractWe consider a sample of dwarf galaxies with accurate distances and velocities around 14 massive groups in the Local Volume. We combine all the data into a single synthetic group, and then determine its radius of the zero-velocity surface, separating it against the global cosmic expansion. Our estimation is derived from fitting the the spherical infall model (including effects of the cosmological constant) to the observational data.We found the optimal value of the radius to be 0.93 ± 0.02 Mpc. Assuming the Planck model parameters, it corresponds to the total mass of the synthetic group (1.6 ± 0.2) × 1012M⊙. Thus, we obtain the paradoxical result that the total mass of the synthetic group estimated on the scale of 3–4 its virial radius is only 60% of the virial mass estimate. Anyway, we conclude that wide outskirts of the nearby groups do not contain a large amount of hidden mass outside their virial radii.

Cosmic flow around local massive galaxies

Aims. We use accurate data on distances and radial velocities of galaxies around the Local Group, as well as around 14 other massive nearby groups, to estimate their radius of the zero-velocity surface, R0, which separates any group against the global cosmic expansion. Methods. Our R0 estimate was based on fitting the data to the velocity field expected from the spherical infall model, including effects of the cosmological constant. The reported uncertainties were derived by a Monte Carlo simulation. Results. Testing various assumptions about a location of the group barycentre, we found the optimal estimates of the radius to be 0.91 ± 0.05 Mpc for the Local Group, and 0.93 ± 0.02 Mpc for a synthetic group stacked from 14 other groups in the Local Volume. Under the standard Planck model parameters, these quantities correspond to the total mass of the group ~ (1.6 ± 0.2) × 1012M⊙. Thus, we are faced with the paradoxical result that the total mass estimate on the scale of R0 ≈ (3−4)Rvir is only 60% of the virial mass estimate. Anyway, we conclude that wide outskirts of the nearby groups do not contain a large amount of hidden mass outside their virial radius.

Effects of the cosmological constant on cold dark matter clusters

Context. Cold dark matter inhomogeneities are considered in a homogeneous background of matter, radiation, and the cosmological constant in a flat universe. Aims. We investigate the influence of the cosmological constant on the non-linear collapse of cold dark matter clusters. Methods. For simplicity, a spherical infall model has been used to describe the collapse of non-relativistic mass shells; besides, an average distribution of density around a cluster of galaxies has been taken. Boundary conditions are imposed by the solution of the linearized equation for the growth of matter perturbations and by the cold dark matter power spectrum. Results. For an average cluster, the radii of shells and masses enclosed by them have been obtained at their zero proper acceleration (ZA) redshifts, at their turn-around (TA) redshifts and at their virialization (VIR) redshifts. According to our results at present, the shell that reaches its turn-around point shows [r TA ]0 = 6.85 Mpc and [M TA ]0 = 6.76 × 10 14 M� . The virializing shell fulfills [r TA ]0 = 4.57 [r VIR ]0 and [M TA ]0 = 1.95 [M VIR ]0. These results differ appreciably from those derived from a model with cosmological constant equal to zero in a flat universe: [r TA ( Λ= 0)]0 = 6.62 [r VIR ( Λ= 0)]0 and [M TA ( Λ= 0)]0 = 5.26 [M VIR ( Λ= 0)]0 ;t his discrepancy could be considered as a new independent proof of the existence of dark energy. The shell with zero proper acceleration presents [r ZA ]0 = 1.59 [r TA ]0 and [M ZA ]0 = 1.63 [M TA ]0. We have found that there is a limit to the mass of the average cluster, which is able to virialize; its value is {M VIR }MAX = 8.1 × 10 14 M� . As expected, we found that shells present null proper acceleration at redshift values that are smaller than 0.755. Conclusions. We have noticed that the cosmological constant imposes an upper limit for the mass enclosed by shells, which are able to reach zero proper velocity. Hence, this mass is the maximum mass of the virialized core, {M VIR }MAX. For the average cluster addressed in this work, the value is 2.34 times the mass of the virialized core at present. Shells enclosing masses M > {M VIR }MAX achieve zero proper acceleration and speed up, moving away from the virialized core, and never reach a turn-around point. Shells with M�{ M VIR }MAX show zero proper aceleration at redshifts close to that at which the universe background acceleration is null. Finally, we have found that the relation between shell proper velocities and their radii can be adjusted by a straight line at z = 0a nd from approximately 20 up to 40 Mpc; however, this line does not intercept the origin as velocities due to the Hubble flux do.

Distortion of infall regions in redshift space-I

We show that spherical infall models (SIMs) can better describe some galaxy clusters in redshift slice space than in traditional axially-convolved projection space. This is because in SIM, the presence of transverse motion between cluster and observer, and/or shear flow about the cluster (such as rotation), causes the infall artifact to tilt, obscuring the characteristic two-trumpet profile; and some clusters resemble such tilted artifacts. We illustrate the disadvantages of applying SIM to convolved data and, as an alternative, introduce a method fitting a tilted 2D envelope to determine a 3D envelope. We also introduce a fitting algorithm and test it on toy SIM simulations as well as three clusters (Virgo, A1459, and A1066). We derive relations useful for using the tilt and width-to-length ratio of the fitted envelopes to analyze peculiar velocities. We apply them to our three clusters as a demonstration. We find that transverse motion between cluster and observer can be ruled out as sole cause of the observed tilts, and that a multi-cluster study could be a feasible way to find our infall toward Virgo cluster.

Non-linear density–velocity divergence relation from phase space dynamics

We obtain the non-linear relation between cosmological density and velocity perturbations by examining their joint dynamics in a two dimensional density-velocity divergence phase space. We restrict to spatially flat cosmologies consisting of pressureless matter and non-clustering dark energy characterized by a constant equation of state $w$. Using the spherical top-hat model, we derive the coupled equations that govern the joint evolution of the perturbations and examine the flow generated by this system. In general, the initial density and velocity are independent, but requiring that the perturbations vanish at the big bang time sets a relation between the two. This relation, which we call the `Zel'dovich curve', acts like an attracting solution for the phase space dynamics and is the desired non-linear extension of the density-velocity divergence relation. We obtain a fitting formula for the curve, which is a generalization of the formulae by Bernardeau and Bilicki & Chodorowski, and find that as in the linear regime, the explicit dependence on the dark energy parameters stays weak even in the non-linear regime. Although the result itself is somewhat expected, the new feature of this work is the interpretation of the relation in the phase space picture and the generality of the method. Finally, as an observational implication, we examine the evolution of galaxy cluster profiles using the spherical infall model for different values of $w$. We demonstrate that using only the density or the velocity information to constrain $w$ is subject to degeneracies in other parameters such as $\sigma_8$ but plotting observations onto the joint density-velocity phase space can help lift this degeneracy.

Hubble flow around Fornax cluster of galaxies

Aims. This work aims to provide a new mass estimate for the Fornax cluster and the Fornax-Eridanus complex, avoiding methods like the virial or fits of X-ray emission profile, which assume that the system is in equilibrium, probably not the case of Fornax, still in process of formation. Methods. Our mass estimate is based on the determination of the zero-velocity surface which, in the context of the spherical infall model permits an evaluation of the total mass inside such a surface. The zero-velocity surface radius R0 was estimated either by a running median procedure or by fitting the data to the velocity field expected from the spherical model, including effects of the cosmological constant. The velocity field in a region within 20 Mpc of the Fornax center was mapped using a list of 109 galaxies whose distances have an average accuracy of 0.31 mag in their distance modulus. Results. Our analysis indicates that the mass of the Fornax cluster itself inside a radius of [2.62-5.18] Mpc is [0.40-3.32] \times 10^14 Modotwhile the mass inside [3.88-5.60] Mpc, corresponding to the Fornax-Eridanus complex is [1.30-3.93] \times 10^14 M\odot.

Studying the dynamical properties of 20 nearby galaxy clusters

Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the region of 20 galaxy clusters. Using two successive iterative methods, the adaptive kernel method and the spherical infall model, we obtained 3396 galaxies as members belonging to the studied sample. The 2D projected map for the distribution of the clusters members is introduced using the 2D adaptive kernel method to get the clusters centers. The cumulative surface number density profile for each cluster is fitted well with the generalized King model. The core radii of the clusters' sample are found to vary from 0.18 Mpc $\mbox{h}^{-1}$ (A1459) to 0.47 Mpc $\mbox{h}^{-1}$ (A2670) with mean value of 0.295 Mpc $\mbox{h}^{-1}$. The infall velocity profile is determined using two different models, Yahil approximation and Praton model. Yahil approximation is matched with the distribution of galaxies only in the outskirts (infall regions) of many clusters of the sample, while it is not matched with the distribution within the inner core of the clusters. Both Yahil approximation and Praton model are matched together in the infall region for about 9 clusters in the sample but they are completely unmatched for the clusters characterized by high central density. For these cluster, Yahil approximation is not matched with the distribution of galaxies, while Praton model can describe well the infall pattern of such clusters.

On the coldness of the local Hubble flow: the role of baryons

(Abridged) Our aim is to investigate whether the presence of baryons can have any significant influence on the properties of the local Hubble flow which has proved to be "cold". We use two cosmological zoom simulations in the standard LCDM cosmology with the same set of initial conditions to study the formation of a local group-like system within a sphere of ~7 Mpc/h. The first one is a pure dark matter simulation (runDM) while a complete treatment of the physics of baryons is introduced in the second one (runB). We found that galaxies identified in runB and their corresponding dark matter haloes in runDM have very similar spatial distributions and dynamical properties on large scales. Then, when analyzing the velocity field and the deviation from a pure Hubble flow in both simulations, namely when computing the dispersion of peculiar velocities of galaxies \sigma*(R) and those of their corresponding dark matter haloes in runDM, we found no particular differences for distances R=1 to 8 Mpc from the local group mass center. The results indicate that the "true" \sigma*(R) values can be estimated from the pure dark matter simulation with a mean error of 3 km/s when dark matter haloes are selected with maximum circular velocities of Vc$\ge$30 km/s, corresponding to a population of dark matter haloes in runB that host galaxies. By investigating the properties of the Hubble flow at distances R~0.7 to 3 Mpc, we also found that the estimation of the total mass enclosed at the radius of the zero-velocity surface R0, using the spherical infall model adapted to LCDM, can be underestimated by at least 50%.

Mass estimation in the outer non-equilibrium region of galaxy clusters

We discuss a new criterion to estimate the mass in the outer, non-equilibrium region of galaxy clusters, where the galaxy dynamics is dominated by an overall infall motion towards the cluster centre. In the framework of the spherical infall model the local mean velocity of the infalling galaxies at every radius provides information about the integrated matter overdensity $\delta$. Thus, a well-defined value of the overdensity $\delta_t$ is expected at the turnaround radius $r_t$, i.e. the radius where the Hubble flow balances the infall motion. Within this scenario, we analysed the kinematical properties of a large catalogue of simulated clusters, using both dark matter particles and member galaxies as tracer of the infall motion. We also compared the simulation with analytical calculation performed in the spherical infall approximation, to analyze the dependence of the results on cosmology in spatially flat universe. If we normalize cluster mass profiles by means of the turnaround mass $M_t$ (i.e. the mass within $r_t$), they are consistent with an exponential profile in the whole non-equilibrium region ($0.5\la r/r_t\la 2$). Turnaround radii are proportional to virialization radii ($r_t\simeq 3.5 r_v$), while turnaround masses are proportional to virialization masses, i.e. $M_t\simeq 1.7 M_v$, where $M_v$ is the mass within $r_v$. Actually, the mass evaluated within the turnaround radius is a more exhaustive evaluation of the total mass of the cluster. These results can be applied to the analysis of observed clusters.

Evolution of the fine-structure constant in the non-linear regime

We study the evolution of the fine-structure constant,α, induced by non-linear density perturbations in the context of the simplest class ofquintessence models with a non-minimal coupling to the electromagnetic field, in which thegauge kinetic function is Taylor-expanded up to linear order. We show that the resultsobtained using the spherical infall model for an infinite wavelength inhomogeneity areinconsistent with the results of a local linearized gravity study and we argue infavour of the second approach. We also discuss recent claims that the value ofα inside virialized regions could be significantly different from the background one on thebasis of these findings.

Understanding the Equilibrium Structure of CDM Halos

N-body simulations find a universal structure for the halos which result from the nonlinear growth of Gaussian-random-noise density fluctuations in the CDM universe. This talk summarized our attempts to derive and explain this universal structure by analytical approximation and simplified models. As an example, we show here that a 1D spherical infall model involving a fluid approximation derived from the Boltzmann equation can explain not only the halo density profile but its phase-space density profile, as well.

Mass determination of groups of galaxies: Effects of the cosmological constant

The spherical infall model first developed by Lemaıˆtre and Tolman was modified in order to include the effects of a dark energy term. The resulting velocity–distance relation was evaluated numerically. This equation, when fitted to actual data, permits the simultaneous evaluation of the central mass and of the Hubble parameter. Application of this relation to the Local Group, when the dark energy is modeled by a cosmological constant, yields a total mass for the M31-Milky Way pair of (2.5±0.7)×1012M⊙, a Hubble parameter H0=74±4kms−1Mpc−1 and a 1-D velocity dispersion for the flow of about 39kms−1. The zero-velocity and the marginally bound surfaces of the Local Group are at about 1.0 and 2.3Mpc, respectively, from the center of mass. A similar analysis for the Virgo cluster yields a mass of (1.10±0.12)×1015M⊙ and H0=65±9kms−1Mpc−1. The zero-velocity is located at a distance of 8.6±0.8Mpc from the center of the cluster. The predicted peculiar velocity of the Local Group towards Virgo is about 190kms−1, in agreement with other estimates. Slightly lower masses are derived if the dark energy is represented by a fluid with an equation of state P=wϵ with w=−2/3.