Velocity Dispersion Of Particles Research Articles

Primordial Black Hole–Neutron Star Merger Rate in Modified Gravity

In this work, we investigate the merger rate of primordial black hole–neutron star (PBH-NS) binaries in two widely studied modified gravity (MG) models: Hu–Sawicki f(R) gravity and the normal branch of Dvali–Gabadadze–Porrati gravity. In our analysis, we take into account the effects of MG on the halo properties, including halo mass function, halo concentration parameter, halo density profile, and velocity dispersion of dark matter particles. We find that these MG models, due to their stronger gravitational field induced by an effective fifth force, predict enhanced merger rates compared to general relativity. This enhancement is found to be redshift-dependent and sensitive to model parameters and PBH mass and fraction. Assuming a PBH mass range of 5–50 M ⊙, we compare the predicted merger rate of PBH-NS binaries with those inferred from LIGO–Virgo–KAGRA observations of gravitational waves (GWs). We find that the merger rates obtained from MG models will be consistent with the GW observations if the abundance of PBHs is relatively large, with the exact amount depending on the MG model and its parameter values, as well as PBH mass. We also establish upper limits on the abundance of PBHs in these MG frameworks while comparing them with the existing non-GW constraints, which can potentially impose even more stringent constraints.

Low-velocity impact experiments of porous ice balls simulating Saturn's ring particles: Porosity dependence of restitution coefficients and the mechanism of inelastic collision

We investigated the porosity dependence of the restitution coefficient (ε) of porous ice balls with porosities of 49.6%, 53.8%, and 60.8% colliding with granite, ice and porous ice plates at a low impact velocity (vi = 0.93–96.9 cm s−1) and temperature of −13.8 °C. The relationship between the impact velocity and the restitution coefficient was divided into two regions by the critical velocity vc: In the quasi-elastic region (vi≤vc), the restitution coefficient had a constant value of εqe regardless of the impact velocity and could be explained by using Dilley's viscous dissipation model. In the inelastic region (vi≥vc), the restitution coefficient decreased with the impact velocity and could be explained by using the improved Andrews' plastic deformation model. We then determined the porosity dependence of the εqe and vc empirically for collisions between the porous ice ball and the porous ice plate from our results. Then we extrapolated the porosity dependence of the restitution coefficient by substituting the calculated εqe and vc for the porosity of 10 to 70%. The restitution coefficient was found to decrease with increasing porosity of the porous ice, and to be strongly dependent on the porosity of the porous ice. Considering the energy budget in the steady-state dense ring system which is controlled by the restitution coefficient of the ring particles, the velocity dispersion of the ring particles was estimated to be ∼10−2 mm s−1 to cm s−1 for the ring particles with the porosity from 45% to 70% and < 10–90 cm s−1 for those with the porosity <45%.

Halo heating from fluctuating gas in a model dwarf

ABSTRACTThe cold dark matter (CDM) structure formation scenario faces challenges on (sub)galactic scales, central among them being the ‘cusp-core’ problem. A known remedy, driving CDM out of Galactic Centres, invokes interactions with baryons, through fluctuations in the gravitational potential arising from feedback or orbiting clumps of gas or stars. Here, we interpret core formation in a hydrodynamic simulation in terms of a theoretical formulation, which may be considered a generalization of Chandrasekhar’s theory of two body relaxation to the case when the density fluctuations do not arise from white noise; it presents a simple characterization of the effects of complex hydrodynamics and ‘subgrid physics’. The power spectrum of gaseous fluctuations is found to follow a power law over a range of scales, appropriate for a fully turbulent compressible medium. The potential fluctuations leading to core formation are nearly normally distributed, which allows for the energy transfer leading to core formation to be described as a standard diffusion process, initially increasing the velocity dispersion of test particles as in Chandrasekhar’s theory. We calculate the energy transfer from the fluctuating gas to the halo and find it consistent with theoretical expectations. We also examine how the initial kinetic energy input to halo particles is redistributed to form a core. The temporal mass decrease inside the forming core may be fit by an exponential form; a simple prescription based on our model associates the characteristic time-scale with an energy relaxation time. We compare the resulting theoretical density distribution with that in the simulation.

The impact of spurious collisional heating on the morphological evolution of simulated galactic discs

ABSTRACT We use a suite of idealized N-body simulations to study the impact of spurious heating of star particles by dark matter (DM) particles on the kinematics and morphology of simulated galactic discs. We find that spurious collisional heating leads to a systematic increase of the azimuthal velocity dispersion (σϕ) of stellar particles and a corresponding decrease in their mean azimuthal velocities ($\overline{v}_\phi$). The rate of heating is dictated primarily by the number of DM halo particles (or equivalently, by the DM particle mass at fixed halo mass) and by radial gradients in the local DM density along the disc; it is largely insensitive to the stellar particle mass. Galaxies within haloes resolved with fewer than ≈106 DM particles are particularly susceptible to spurious morphological evolution, irrespective of the total halo mass (with even more particles required to prevent heating of the galactic centre). Collisional heating transforms galactic discs from flattened structures into rounder spheroidal systems, causing them to lose rotational support in the process. It also affects the locations of galaxies in standard scaling relations that link their various properties: at fixed stellar mass, it increases the sizes of galaxies, and reduces their mean stellar rotation velocities and specific angular momenta. Our results urge caution when extrapolating simulated galaxy scaling relations to low masses where spurious collisional effects can bias their normalization, slope, and scatter.

Planetesimal Dynamics in the Presence of a Giant Planet. II. Dependence on Planet Mass and Eccentricity

The presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and “accretion-friendly” locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect of a Jupiter-like planet on an external planetesimal disk, we generalize our findings to extrasolar planetary systems by varying the planet parameters. In particular, we focus on the dependence of the planetesimal relative velocities on the mass and eccentricity of the existing planet. We found that the velocity dispersion of identical-mass particles increases monotonically with increasing planet mass. Meanwhile, the dependence of the relative velocity between different-mass planetesimals on their mass ratio becomes weaker as the planet mass increases. While the relative velocities generally increase with increasing planet eccentricity, the velocity dispersion of lower-mass particles (m ≲ 1018 g) is almost independent of planet eccentricity owing to their strong coupling to gas. We find that the erosion limits are met for a wider range of parameters (planet mass/eccentricity, planetesimal mass ratio) when the planetesimal size decreases. Our results could provide some clues for the formation of Saturn’s core, as well as the architecture of some exoplanetary systems with multiple cold giant planets.

Coevolution of Brightest Cluster Galaxies and Their Host Clusters in IllustrisTNG

We use IllustrisTNG simulations to explore the dynamic scaling relation between massive clusters and their—central—brightest cluster galaxies (BCGs). The IllustrisTNG-300 simulation we use includes 280 massive clusters from the z = 0 snapshot with M 200 > 1014 M ⊙, enabling a robust statistical analysis. We derive the line-of-sight velocity dispersion of the stellar particles of the BCGs (σ *,BCG), analogous to the observed BCG stellar velocity dispersion. We also compute the subhalo velocity dispersion to measure the cluster velocity dispersion (σ cl). Both σ *,BCG and σ cl are proportional to the cluster halo mass, but the slopes differ slightly. Thus, like the observed relation, σ *,BCG/σ cl declines as a function of σ cl, but the scatter is large. We explore the redshift evolution of the σ *,BCG − σ cl scaling relation for z ≲ 1 in a way that can be compared directly with observations. The scaling relation has a similar slope at high redshift, but the scatter increases because of the large scatter in σ *,BCG. The simulations imply that high-redshift BCGs are dynamically more complex than their low-redshift counterparts.

Powder-flow behavior and process mechanism in laser directed energy deposition based on determined restitution coefficient from inverse modeling

In order to clarify the transportation mechanism of particles in continuous coaxial powder feeding (CCPF) process, a trial-and-matching method is developed to quantify the restitution coefficient which is used to describe the inelastic collision between the particle and the nozzle wall. The consistency of the outlet velocity and the spatial concentration distribution of particles between the experimental statistic and the numerical calculation shows that the restitution coefficient of 0.9 can be used to measure the inelastic collision behavior between particles and the nozzle wall. Employing the determined restitution coefficient, a semi-quantitative method based on optical diagnostic and quantitative analysis derived from numerical calculation are proposed to study the powder-gas flow transport characteristics from single-layer to multi-layer jet flow. It is found that the outer shielding gas flow (OSGF) has a great influence on the multi-layer jet flow field, and it is most conducive to powder focusing at the OSGF of 20 L/min. The velocity distribution of CGF determined by the inner structure of CCPFN and the inelastic collision between the particle and the wall are the two mutually coupled factors that determine the outlet velocity of particles. Frequent inelastic collisions and the decrease of the CGF velocity lead to velocity dispersion and trajectory fluctuation of particles. When the inlet velocity of particles is 1.33 m/s, the outlet velocity ranged from 0.4 m/s to 0.9 m/s. This paper aims to provide a general method to determine the restitution coefficient and offer a comprehensive understanding of transportation mechanism of power particles both inside continuous coaxial powder feeding nozzle (CCPFN) and multi-layer jet zone between substrate and the CCPFN outlet.

Simulating the Cosmic Neutrino Background Using Collisionless Hydrodynamics

The cosmic neutrino background is an important component of the Universe that is difficult to include in cosmological simulations due to the extremely large velocity dispersion of neutrino particles. We develop a new approach to simulate cosmic neutrinos that decomposes the Fermi-Dirac phase space into shells of constant speed and then evolves those shells using hydrodynamic equations. These collisionless hydrodynamic equations are chosen to match linear theory, free particle evolution and allow for superposition. We implement this method into the information-optimized cosmological $N$-body code CUBE and demonstrate that neutrino perturbations can be accurately resolved to at least $k\sim1 h/$Mpc. This technique allows for neutrino memory requirements to be decreased by up to $\sim 10^3$ compared to traditional $N$-body methods.

The Nature of Fractal Relief of Fractured Metal Samples after Dynamic Loading

Experimental and theoretical results demonstrating that the fractal nature of a surface periphery destroyed under the impact of dynamic loading can be attributed to velocity dispersion of particles (elementary deformation carriers) at various scale and structure levels of deformation and fracture are presented.

Gravitational Instability in the Dust Layer of a Protoplanetary Disk with Interaction between the Layer and the Surrounding Gas

We consider gravitational instability of the dust layer in the midplane of a protoplanetary disk with turbulence and shear stresses between the gas in the disk and that in the dust layer. We solve a linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation. We take into account the gas drag of solid particles (dust aggregates), turbulent diffusion and the velocity dispersion of particles, and the perturbation of the azimuthal velocity of gas in the layer upon the transfer of angular momentum from solid particles to it and from this gas to the surrounding gas in the disk. We obtain and solve the dispersion equation for the layer with the ratio of surface densities of the dust phase and gas being well above unity. The following parameters of gravitational instability in the dust layer are calculated: the critical surface density of solid matter and the Stokes number of particles corresponding to the onset of instability, the wavelength range in which instability occurs, and the rate of its growth as a function of the perturbation wavelength in the circumsolar disk at radial distances of 1 and 10 AU. We show that at 10 AU, the maximum instability growth rate increases due to the transfer of angular momentum of gas in the layer to gas outside it, a new maximum emerges at a longer wavelength, a long-wavelength instability “tail” forms, and the critical surface density initiating instability decreases relative to that determined without the transfer of angular momentum to gas outside the layer. None of these effects are observed at 1 AU, since instability in this region probably develops faster than the transfer of angular momentum to the surrounding gаs of a protoplanetary disk occurs.

Velocity Segregation and Systematic Biases in Velocity Dispersion Estimates with the SPT-GMOS Spectroscopic Survey

Abstract The velocity distribution of galaxies in clusters is not universal; rather, galaxies are segregated according to their spectral type and relative luminosity. We examine the velocity distributions of different populations of galaxies within 89 Sunyaev Zel’dovich (SZ) selected galaxy clusters spanning . Our sample is primarily draw from the SPT-GMOS spectroscopic survey, supplemented by additional published spectroscopy, resulting in a final spectroscopic sample of 4148 galaxy spectra—2868 cluster members. The velocity dispersion of star-forming cluster galaxies is 17 ± 4% greater than that of passive cluster galaxies, and the velocity dispersion of bright ( ) cluster galaxies is 11 ± 4% lower than the velocity dispersion of our total member population. We find good agreement with simulations regarding the shape of the relationship between the measured velocity dispersion and the fraction of passive versus star-forming galaxies used to measure it, but we find a small offset between this relationship as measured in data and simulations, which suggests that our dispersions are systematically low by as much as 3% relative to simulations. We argue that this offset could be interpreted as a measurement of the effective velocity bias that describes the ratio of our observed velocity dispersions and the intrinsic velocity dispersion of dark matter particles in a published simulation result. Measuring velocity bias in this way suggests that large spectroscopic surveys can improve dispersion-based mass-observable scaling relations for cosmology even in the face of velocity biases, by quantifying and ultimately calibrating them out.

THE SCALING OF STELLAR MASS AND CENTRAL STELLAR VELOCITY DISPERSION FOR QUIESCENT GALAXIES AT z &lt; 0.7

ABSTRACT We examine the relation between stellar mass and central stellar velocity dispersion—the M * σ relation—for massive quiescent galaxies at z &lt; 0.7. We measure the local relation from the Sloan Digital Sky Survey and the intermediate redshift relation from the Smithsonian Hectospec Lensing Survey. Both samples are highly complete (&gt;85%) and we consistently measure the stellar mass and velocity dispersion for the two samples. The M * σ relation and its scatter are independent of redshift with for M * ≳ 1010.3 M ⊙. The measured slope of the M * σ relation is the same as the scaling between the total halo mass and the dark matter halo velocity dispersion obtained by N-body simulations. This consistency suggests that massive quiescent galaxies are virialized systems, where the central dark matter concentration is either a constant or negligible fraction of the stellar mass. The relation between the total galaxy mass (stellar + dark matter) and the central stellar velocity dispersion is consistent with the observed relation between the total mass of a galaxy cluster and the velocity dispersion of the cluster members. This result suggests that the central stellar velocity dispersion is directly proportional to the velocity dispersion of the dark matter halo. Thus, the central stellar velocity dispersion is a fundamental, directly observable property of galaxies, which may robustly connect galaxies to dark matter halos in N-body simulations. To interpret the results further in the context of ΛCDM, it would be useful to analyze the relationship between the velocity dispersion of stellar particles and the velocity dispersion characterizing their dark matter halos in high-resolution cosmological hydrodynamic simulations.

Dynamics of Centaur Chariklo and evolution of its rings

It follows from observations that the asteroid Chariklo has two outer rings. The purpose of this paper is constructing the equilibrium model of asteroid and developing the kinetic mechanism of evolution of its rings. We have specified for Chariklo the density \(\rho_{0} \approx 2.71~\mbox{g}/\mbox{cm}^{3}\), the mass \(M_{0} \approx 8.817 \times 10^{21}~\mbox{g}\), and the average radius \(R_{0} \approx 128.16~\mbox{km}\). Its rings are modeled by circular gravitating tori consisting of the small rock-ice particles that orbit the asteroid. The method does not imply the presence of hidden satellites close to the asteroid, and the equilibrium of the rings is determined by the small velocity dispersion and gravity of particles. The problem of expansion of the internal torus gravitational potential in series in powers of its geometrical parameter is solved. This enables the gravitational energy of Chariklo’s rings to be found and to express their masses in terms of the mass of the asteroid \(M_{0}\). We calculated the mass of the inner ring to be \(M_{r1} \approx 9.8 \times 10^{18}~\mbox{g}\), and its relation to the mass of the asteroid is \(\frac{M_{r1}}{M_{0}} \approx 0.001\); similarly, for the outer ring \(M_{r2} \approx 10^{18}~\mbox{g}\), and \(\frac{M_{r2}}{M_{0}} \approx 0.0001\). The mass ratio \(\frac{M_{r1}}{M_{r2}} \approx 10\) is typical for satellites of other asteroids and dwarf planets. The velocity dispersion of particles in rings \(\upsilon_{1} \approx 1~\mbox{m}/\mbox{s}\) and \(\upsilon_{2} \approx 45~\mbox{cm}/\mbox{s}\) is no greater than \(1 \div 2~\%\) of its rotational velocity \(\upsilon_{rot} \approx 40~\mbox{m}/\mbox{s}\). The particle of medium radius \(r_{p} = 25~\mbox{cm}\) has the mean free path \(\lambda \approx 7~\mbox{m}\), and its diffusion time from center line on the surface of the torus is \(\frac{T'_{1}}{T_{rot1}} \approx 13\) and \(\frac{T'_{2}}{T_{rot2}} \approx 5\). The dissipation rate equation for Chariklo’s rings is derived. From this equation a surprising result follows: the time of energy dissipation (the time of evolution of rings) is only \(T_{d1} \approx 10^{3} \div 10^{4}~\mbox{years}\), which by astronomical measures is a very short time scale. We adduce the arguments supporting the idea that these rings in near future can become Chariklo’s satellites, and that the transformation of the rings into satellites energetically is favored.

Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer

Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed.

Dark matter velocity dispersion effects on CMB and matter power spectra

Effects of velocity dispersion of dark matter particles on the CMB TT power spectrum and on the matter linear power spectrum are investigated using a modified CAMB code. Cold dark matter originated from thermal equilibrium processes does not produce appreciable effects but this is not the case if particles have a non-thermal origin. A cut-off in the matter power spectrum at small scales, similar to that produced by warm dark matter or that produced in the late forming dark matter scenario, appears as a consequence of velocity dispersion effects, which act as a pressure perturbation.

FLUX ENHANCEMENT OF SLOW-MOVING PARTICLES BY SUN OR JUPITER: CAN THEY BE DETECTED ON EARTH?

Slow-moving particles capable of interacting solely with gravity might be detected on Earth as a result of the gravitational lensing induced focusing action of the Sun. The deflection experienced by these particles are inversely proportional to the square of their velocities and as a result their focal lengths will be shorter. We investigate the velocity dispersion of these slow-moving particles, originating from distant point-like sources, for imposing upper and lower bounds on the velocities of such particles in order for them to be focused onto Earth. We find that fluxes of such slow-moving and non-interacting particles must have speeds between ~0.01 and ~0.14 times the speed of light, $c$. Particles with speeds less than ~0.01 c will undergo way too much deflection to be focused, although such individual particles could be detected. At the caustics, the magnification factor could be as high as ~10E+6. We impose lensing constraints on the mass of these particles in order for them to be detected with large flux enhancements to be greater than E-9 eV. An approximate mass density profile for Jupiter is used to constrain particle velocities for lensing by Jupiter. We show that Jupiter could potentially focus particles with speeds as low as ~0.001c, which the Sun cannot. As a special case, the perfect alignment of the planet Jupiter with the Sun is also considered.

THE LONGITUDINAL PROPERTIES OF A SOLAR ENERGETIC PARTICLE EVENT INVESTIGATED USING MODERN SOLAR IMAGING

We use combined high-cadence, high-resolution, and multi-point imaging by the Solar-Terrestrial Relations Observatory (STEREO) and the Solar and Heliospheric Observatory to investigate the hour-long eruption of a fast and wide coronal mass ejection (CME) on 2011 March 21 when the twin STEREO spacecraft were located beyond the solar limbs. We analyze the relation between the eruption of the CME, the evolution of an Extreme Ultraviolet (EUV) wave, and the onset of a solar energetic particle (SEP) event measured in situ by the STEREO and near-Earth orbiting spacecraft. Combined ultraviolet and white-light images of the lower corona reveal that in an initial CME lateral phase, the EUV disturbance tracks the laterally expanding flanks of the CME, both moving parallel to the solar surface with speeds of approx 450 km/s. When the lateral expansion of the ejecta ceases, the EUV disturbance carries on propagating parallel to the solar surface but devolves rapidly into a less coherent structure. Multi-point tracking of the CME leading edge and the effects of the launched compression waves (e.g., pushed streamers) give anti-sunward speeds that initially exceed 900 km/s at all measured position angles. We combine our analysis of ultraviolet and white-light images with a comprehensive study of the velocity dispersion of energetic particles measured in situ by particle detectors located at STEREO-A (STA) and first Lagrange point (L1), to demonstrate that the delayed solar particle release times at STA and L1 are consistent with the time required (30-40 minutes) for the CME to perturb the corona over a wide range of longitudes. This study finds an association between the longitudinal extent of the perturbed corona (in EUV and white light) and the longitudinal extent of the SEP event in the heliosphere.

PLANETESIMAL FORMATION AT THE BOUNDARY BETWEEN STEADY SUPER/SUB-KEPLERIAN FLOW CREATED BY INHOMOGENEOUS GROWTH OF MAGNETOROTATIONAL INSTABILITY

We have studied formation of planetesimals at a radial pressure bump in a protoplanetary disk created by radially inhomogeneous magnetorotational instability (MRI), through three-dimensional resistive MHD simulations including dust particles. In our previous papers, we showed that the inhomogeneous MRI developing in non-uniform structure of magnetic field or magnetic resistivity can transform the local gas flow in the disk to a quasi-steady state with local rigid rotation that is no more unstable against the MRI. Since the outer part of the rigid rotation is super-Keplerian flow, a quasi-static pressure bump is created and dust concentration is expected there. In this paper, we perform simulations of the same systems, adding dust particles that suffer gas drag and modulate gas flow via the back-reaction of the gas drag (dust drag). We use O(10^7) super-particles, each of which represents many dust particles with sizes of centimeter to meter. We have found that the dust drag suppresses turbulent motion to decrease the velocity dispersion of the dust particles while it broadens the dust concentrated regions to limit peaky dust concentration, compared with the simulation without the dust drag. We found that reduction in the velocity dispersion) is dominated over the suppression in particle concentration. For meter-size particles with the friction time ~1/Omega, where Omega is Keplerian frequency, the gravitational instability of the dust particles that may lead to planetesimal formation is expected. For such a situation, we further introduced the self-gravity of dust particles to the simulation to demonstrate that several gravitationally bound clumps are actually formed. Through analytical arguments, we found that the planetesimal formation from meter-sized dust particles can be possible at ~5AU, if dust spatial density is a few times larger than that in the minimum mass solar nebula.

How to generate a significant effective temperature for cold dark matter, from first principles

I show how to reintroduce velocity dispersion into perturbation theory (PT) calculations of structure in the Universe, i.e., how to go beyond the pressureless fluid approximation, starting from first principles. This addresses a possible deficiency in uses of PT to compute clustering on the weakly non-linear scales that will be critical for probing dark energy. Specifically, I show how to derive a non-negligible value for the (initially tiny) velocity dispersion of dark matter particles, ⟨δν2⟩ , where δν is the deviation of particle velocities from the local bulk flow. The calculation is essentially a renormalization of the homogeneous (zeroorder) dispersion by fluctuations 1st order in the initial power spectrum. For power law power spectra with n > −3, the small-scale fluctuations diverge and significant dispersion can be generated from an arbitrarily small starting value — the dispersion level is set by an equilibrium between fluctuations generating more dispersion and dispersion suppressing fluctuations. For an n = −1.4 power law normalized to match the present non-linear scale, the dispersion would be ∼ 100kms−1. This n corresponds roughly to the slope on the non-linear scale in the real ΛCDM Universe, but ΛCDM contains much less initial small-scale power — not enough to bootstrap the small starting dispersion up to a significant value within linear theory (viewed very broadly, structure formation has actually taken place rather suddenly and recently, in spite of the usual ``hierarchical'' description). Thenext order PT calculation drives the ΛCDM dispersion up into balance with growing structure, and should eventually account for dispersion effects seen recently in simulations (I have not yet carried out that calculation).

Astrophysical limitations to the identification of dark matter: Indirect neutrino signalsvis-à-visdirect detection recoil rates

A convincing identification of dark matter (DM) particles can probably be achieved only through a combined analysis of different detections strategies, which provides an effective way of removing degeneracies in the parameter space of DM models. In practice, however, this program is made complicated by the fact that different strategies depend on different physical quantities, or on the same quantities but in a different way, making the treatment of systematic errors rather tricky. We discuss here the uncertainties on the recoil rate in direct-detection experiments and on the muon rate induced by neutrinos from dark matter annihilations in the Sun, and we show that, contrarily to the local DM density or overall cross section scale, irreducible astrophysical uncertainties affect the two rates in a different fashion, therefore limiting our ability to reconstruct the parameters of the dark matter particles. By varying within their respective errors astrophysical parameters such as the escape velocity and the velocity dispersion of dark matter particles, we show that the uncertainty on the relative strength of the neutrino and direct-detection signal is as large as a factor of 2 for typical values of the parameters, but can be even larger in some circumstances.