Peculiar Velocity Distribution Research Articles

Kinematical Evolution of the Pairwise Velocity Field of Galaxies

It has been a long-standing cosmological issue to explain why the statistical distribution of the radial pairwise peculiar velocity of galaxies has an exponential shape rather than the Gaussian, as suggested by observations and explicitly shown by results of N-body simulations. Previous explanations on the exponential distribution are based on highly nonlinear dynamics of galactic systems (R < 1h–1 Mpc). That is, the exponential feature appears as a result of superposition of Gaussian velocity distributions in clumps with various velocity dispersions. Hence although this model is suitable to account for a symmetric exponential distribution with vanishing mean net relative velocity, a more elaborate treatment is necessary in order to reproduce an asymmetric exponential distribution with its peak at a negative relative velocity as observed in numerical simulations.

Reconstruction Analysis of Galaxy Redshift Surveys: A Hybrid Reconstruction Method

In reconstruction analysis of galaxy redshift surveys, one works backwards from the observed galaxy distribution to the primordial density field in the same region, then evolves the primordial fluctuations forward in time with an N-body code. This incorporates assumptions about the cosmological parameters, the properties of primordial fluctuations, and the biasing relation between galaxies and mass. These can be tested by comparing the reconstruction to the observed galaxy distribution, and to peculiar velocity data. This paper presents a hybrid reconstruction method that combines the `Gaussianization'' technique of Weinberg(1992) with the dynamical schemes of Nusser & Dekel(1992) and Gramann(1993). We test the method on N-body simulations and on N-body mock catalogs that mimic the depth and geometry of the Point Source Catalog Redshift Survey and the Optical Redshift Survey. This method is more accurate than Gaussianization or dynamical reconstruction alone. Matching the observed morphology of clustering can limit the bias factor b, independent of Omega. Matching the cluster velocity dispersions and z-space distortions of the correlation function xi(s,mu) constrains the parameter beta=Omega^{0.6}/b. Relative to linear or quasi-linear approximations, a fully non-linear reconstruction makes more accurate predictions of xi(s,mu) for a given beta, thus reducing the systematic biases of beta measurements and offering further scope for breaking the degeneracy between Omega and b. It also circumvents the cosmic variance noise that limits conventional analyses of xi(s,mu). It can also improve the determination of Omega and b from joint analyses of redshift & peculiar velocity surveys as it predicts the fully non-linear peculiar velocity distribution at each point in z-space.

Expansions for nearly Gaussian distributions

Various types of expansions in series of Cheby shev-Hermite polynomials currently used in astrophysics for weakly non-normal distributions are compared, namely the Gram-Charlier, Gauss-Hermite and Edgeworth expansions. It is shown that the Gram-Charlier series is most suspect because of its poor convergence properties. The Gauss-Hermite expansion is better but it has no intrinsic measure of accuracy. The best results are achieved with the asymptotic Edgeworth expansion. We draw attention to the form of this expansion found by Petrov for arbitrary order of the asymptotic parameter and present a simple algorithm realizing Petrov's prescription for the Edgeworth expansion. The results are illustrated by examples similar to the problems arising when fitting spectral line profiles of galaxies, supernovae, or other stars, and for the case of approximating the probability distribution of peculiar velocities in the cosmic string model of structure formation.

Evolution of the Pairwise Peculiar Velocity Distribution Function in Lagrangian Perturbation Theory

The statistical distribution of the radial pairwise peculiar velocity of galaxies is known to have an exponential form as implied by observations and explicitly shown in N-body simulations. Here we calculate its statistical distribution function using a Lagrangian perturbation theory assuming that the primordial density fluctuations are Gaussian distributed. We show that the exponential distribution is realized as a transient phenomenon on megaparsec scales in the standard cold-dark-matter model.

The Pairwise Velocity Distribution of Galaxies in the Las Campanas Redshift Survey

We present a novel measurement of the pairwise peculiar velocity distribution function of galaxies on scales r<3200 km s-1 in the Las Campanas Redshift Survey. The distribution is well described by a scale-independent exponential with a width τ, where σ12 = √2τ=363 km s-1. The signal is very stable. Results from the northern and southern sets of slices agree within ±13 km s-1, and the fluctuations among the six individual survey slices vary as ±44 km s-1. The distribution was determined using a Fourier-space deconvolution of the redshift-space distortions in the correlation function. This technique is insensitive to the effect of rich clusters in the survey and recovers the entire distribution function rather than just its second moment. Taken together with the large effective volume of the survey, 6.0 × 106 h-1 Mpc3, we believe this to be a definitive result for r-band-selected galaxies with absolute magnitudes -18.5 < Mr < -22.5 and z < 0.2.

The distribution of pairwise peculiar velocities in the non-linear regime

The distribution of pairwise, relative peculiar velocities, $f(u;r)$, on small nonlinear scales, $r$, is derived from the Press--Schechter approach. This derivation assumes that Press--Schechter clumps are virialized and isothermal. The virialized assumption requires that the circular velocity, $V_c \propto M^{1/3}$, where $M$ denotes the mass of the clump. The isothermal assumption means that the circular velocity is independent of radius. Further, it is assumed that the velocity distribution within a clump is Maxwellian, that the pairwise relative velocity distribution is isotropic, and that on nonlinear scales clump-clump motions are unimportant when calculating the distribution of velocity differences. Comparison with $N$-body simulations shows that, on small nonlinear scales, all these assumptions are accurate. For most power spectra of interest, the resulting line of sight, pairwise, relative velocity distribution, $f(u_{\rm r})$, is well approximated by an exponential, rather than a Gaussian distribution. This simple Press--Schechter model is also able to provide a natural explanation for the observed, non-Maxwellian shape of $f(v)$, the distribution of peculiar velocities.

The Observed Distribution Function of Peculiar Velocities of Galaxies

We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in detail the effects of uncertainties in sampling and in distance measures on the estimated distribution function. The observed distribution function is consistent with an earlier prediction of gravitational clustering, over the entire range of peculiar velocities, from field galaxies to rich clusters, on scales up to 50 Mpc (H=100). In the simplest consistent model, most of the inhomogeneous mass of the Universe is in galaxies or their halos. We estimate the ``Mach Number'' for the bulk flow within 50 Mpc (H=100) from us to be approximately 0.8, which includes the effect of high-dispersion galaxies in clusters.

Destruction of the Galactic Globular Cluster System

We investigate the dynamical evolution of the Galactic globular cluster system in considerably greater detail than has been done hitherto, finding that destruction rates are significantly larger than given by previous estimates. The general scheme (but not the detailed implementation) follows Aguilar, Hut, & Ostriker. For the evolution of individual clusters, we use a Fokker-Planck code including the most important physical processes governing the evolution: two-body relaxation, tidal truncation of clusters, compressive gravitational shocks while clusters pass through the Galactic disk, and tidal shocks due to passage close to the bulge. Gravitational shocks are treated comprehensively, using a recent result by Kundi? & Ostriker that the ?E2 shock-induced relaxation term, driving an additional dispersion of energies, is generally more important than the usual energy shift term ?E. Various functional forms of the correction factor are adopted to allow for the adiabatic conservation of stellar actions in a presence of transient gravitational perturbation. We use a recent compilation of the globular cluster positional and structural parameters, and a collection of radial velocity measurements. Two transverse to the line-of-sight velocity components were assigned randomly according to the two kinematic models for the cluster system (following the method of Aguilar, Hut, & Ostriker): one with an isotropic peculiar velocity distribution, corresponding to the present-day cluster population, and the other with the radially preferred peculiar velocities, similar to those of the stellar halo. We use the Ostriker & Caldwell and the Bahcall, Schmidt, & Soneira models for our Galaxy. For each cluster in our sample, we calculated its orbits over a Hubble time, starting from the present observed positions and assumed velocities. Medians of the resulting set of peri- and apogalactic distances and velocities are used then as an input for the Fokker-Planck code. Evolution of the cluster is followed up to its total dissolution due to a coherent action of all of the destruction mechanisms. The rate of destruction is then obtained as a median over all the cluster sample, in accord with Aguilar, Hut, & Ostriker. We find that the total destruction rate is much larger than that given by Aguilar, Hut, & Ostriker with more than half of the present clusters (52%-58% for the Ostriker & Caldwell model, and 75%-86% for the Bahcall, Schmidt, & Soneira model) destroyed in the next Hubble time. Alternatively put, the typical time to destruction is comparable to the typical age, a result that would follow from (but is not required by) an initially power law distribution of destruction times. We discuss some implications for a past history of the globular cluster system and the initial distribution of the destruction times, raising the possibility that the current population is but a very small fraction of the initial population with the remnants of the destroyed clusters constituting presently a large fraction of the spheroid (bulge + halo) stellar population.

Unresolved Wind-driven Shells and the Supersonic Velocity Dispersion in Giant H II Regions

The presence of giant shells or loops in giant H II regions is clear witness to the mechanical energy input from massive stars. Here we evaluate the impact that winds may have on the structure of giant nebulae and on their supersonic velocity dispersion. We follow the recent suggestion of Chu and Kennicutt to see whether a combination of a large number of unresolved wind-driven shells caused by massive stars could produce the integrated broad Gaussian profiles typical of giant H II regions. <P />The results, accounting for a wide range of energies, densities, and velocities or ages of the expanding shells, show that supersonic Gaussian profiles may arise only from a collection of unresolved wind-driven shells if the shells present a peculiar velocity distribution which implies a strongly peaked age distribution leading to an awkward star formation history. On the other hand, a uniform distribution of ages produces profiles with a flat-topped core defined by the terminal shell velocity and a steep decay as ν<SUP>-6</SUP>, up to the largest detectable shell speed. Thus, supersonic profiles can arise only if the final speed of the unresolved shells is supersonic. This implies an equally supersonic random speed of motions in the ionized gas disrupting the shells before they slow down to subsonic speeds. It also implies a mechanism, independent of the shells caused by massive stars, responsible for the supersonic stirring of the background medium. These facts, together with the conditions for shells to remain unresolved by present-day devices (energies, final speeds, and ages), indicate that the winds may be produced by low-mass stars. In the latter case, if the sources move supersonically in the gravitational potential of the whole system, they could stir the gas, with their cometary bow shocks, to a velocity dispersion σ<SUB>gas</SUB> σ<SUB>stars</SUB>, causing a supersonic local random speed of motions within the system.

Statistics of peculiar velocities from cosmic strings

We calculate the probability distribution of a single component of peculiar velocities due to cosmic strings, smoothed over regions with a radius of several $h^{-1}$ Mpc. The probability distribution is shown to be Gaussian to good accuracy, in agreement with the distribution of peculiar velocities deduced from the 1.9 Jy IRAS redshift survey. Using the normalization of parameters of the cosmic string model from CMB measurements, we show that the rms values for peculiar velocities inferred from IRAS are consistent with the cosmic string model provided that long strings have some small-scale structure.

The motions of clusters and group of galaxies

The distributions of peculiar velocities of rich clusters and of groups of galaxies are investigated for different cosmological models and are compared with observations. Four cosmological models are studied: standard cold dark matter (CDM) ({OMEGA} = 1); low-density CDM ({OMEGA} = 0.3); hot dark matter (HDM) ({OMEGA} = 1); and primeval baryonic isocurvature (PBI) ({OMEGA} = 0.3). All models are normalized to the microwave background fluctuations observed by COBE. We find that rich clusters of galaxies exhibit a Maxwellian distribution of peculiar velocities in all models, as expected from a Gaussian initial density field. The clusters appear to be fundamental and efficient tracers of the large-scale velocity field. The cluster three-dimensional velocity distribution typically peaks at v ~ 600 km s^-1^ and extends to high cluster velocities of v ~ 2000 km s^-1^. The low-density CDM model exhibits somewhat lower velocities: it peaks at ~400 km s^-1^ and extends to ~1200 km s^-1^. Approximately 10% (~1% for low-density CDM) of all model rich clusters move with high peculiar velocities of v &gt;= 10^3^ km s^-1^. The highest velocity clusters frequently originate in dense superclusters. The model velocity distributions of rich clusters are compared with the model velocity distributions of small groups of galaxies, and of the total matter. The group velocity distribution is, in general, similar to the velocity distribution of the rich clusters. The matter velocity distribution is similar to that of the rich clusters for the {OMEGA} = 0.3 models; these models exhibit Maxwellian velocity distributions for clusters, for groups, and for matter that are all similar to one another. The mass distribution in the {OMEGA} = 1 models, however, exhibits a longer tail of high velocities than do the clusters. This high-velocity tail originates mostly from the high velocities that exist within rich clusters. The model velocity distributions of groups and clusters of galaxies are compared with observations. The data exhibit a larger high-velocity tail, to v_r_ &gt;= 2000 km s^-1^, than is seen in the model simulations (except for HDM). Because of the large observational uncertainties, however, the data are consistent at a ~1-3 σ level with the model predictions and with a Gaussian initial density field. Accurate observations of cluster peculiar velocities, especially at the high- velocity tail, should provide powerful constraints on the cosmological models.

Probing the large-scale velocity field with clusters of galaxies

What is the role of clusters of galaxies in probing the large-scale velocity field of the universe? We investigate the distribution of peculiar velocities of clusters of galaxies in the popular low-density ($\Omega=0.3$) flat Cold-Dark-Matter (CDM) cosmological model, which best fits many large-scale structure observations. An $\Omega=1$ CDM model is also studied for comparison. We find that clusters of galaxies are efficient tracers of the large-scale velocity field. The clusters exhibit a Maxwellian distribution of peculiar velocities, as expected from Gaussian initial density fluctuations. The cluster 3-D velocity distribution for the $\Omega=0.3$ model peaks at $v \sim 400$ km s$^{-1}$, and extends to high velocities of $v \sim 1200$ km s$^{-1}$. The rms peculiar velocity of the clusters is $440$ km s$^{-1}$. Approximately 10\% of all model clusters move with high peculiar velocities of $v \ge 700$ km s$^{-1}$. The observed velocity distribution of clusters of galaxies is compared with the predictions from cosmological models. The observed data exhibit a larger velocity tail than seen in the model simulations; however, due to the large observational uncertainties, the data are consistent at a $\sim 3\sigma$ level with the model predictions, and with a Gaussian initial density field. The large peculiar velocities reported for some clusters of galaxies ($v \geq 3000$ km s$^{-1}$) are likely to be overestimated, if the current model is viable.

Large-Scale Peculiar Velocity Field Due to Infinitely Long Cosmic Strings

view Abstract Citations (9) References (26) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Large-Scale Peculiar Velocity Field Due to Infinitely Long Cosmic Strings Hara, Tetsuya ; Maehoenen, Petri ; Miyoshi, Shigeru Abstract We investigate the large-scale peculiar velocity field of dark matter due to the wakes formed by infinitely long cosmic strings. The peculiar velocity due to such strings, which passed through at the stage 1 + ζi is solved analytically for one-dimensional case, including the contribution of the background radiation density. The three dimensional large-scale peculiar velocities will be the vector sum of such velocities, and the root mean square (rms) peculiar velocities can be estimated. The large peculiar velocity of the Local Group (≃600 km s-1) and the distribution of peculiar velocities for nearby 20 clusters of galaxies can be explained by adopting the parameter Gμβγ(n)1/2 (4 ± 1) × 10-6, where μ and β are the line density and the velocity of a cosmic string in units of c = 1 and γ = (1 - β2)-1/2. The parameter n denotes the number of infinitely long cosmic strings per horizon passed through in each e-time expansion of the universe. Publication: The Astrophysical Journal Pub Date: October 1993 DOI: 10.1086/173176 Bibcode: 1993ApJ...415..445H Keywords: COSMOLOGY: THEORY; COSMOLOGY: DARK MATTER; COSMIC STRINGS; GALAXIES: DISTANCES AND REDSHIFTS; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS | data products SIMBAD (1)

Point-axial mass distribution in the external Galactic Bulge

The main purpose in this work is to present some analytical results about the spatial distribution of the stars in the Galactic Bulge. These results have been obtained by considering that the stellar system verifies the collisionless Boltzman equation and the ellipsoidal hypothesis (non-axisymmetrical) for the distribution of peculiar velocities of the stars.

Distribution of peculiar velocities from cosmic strings

The peculiar velocities due to multiple cosmic string impulses is found to have a normal distribution whose mean and standard deviation can be written in terms of the string network evolution parameters. It appears that the observed peculiar velocities may be accounted for in the scenario although there may be a problem with the scaling of peculiar velocities with the size of the region. Some uncertainties in the predictions are discussed.

The distribution of cD galaxy peculiar velocities

A modified version of a cluster evolution computer code first described in Richstone and Malumuth (1983) and Malumuth and Richstone (1984) to investigate the distributon of cD galaxy peculiar velocities and positions relative to the center, for a sample of cDs formed through mergers in a virialized cluster. This distribution is compared to an observed distribution of 19 cD galaxies to test whether cD galaxies with large peculiar velocities could have been formed in virialized clusters. At the time of their formation the cD galaxies have a distribution of peculiar velocities similar to that of the observed cD galaxies. By the end of the simulations the cD galaxies were dragged to the center of the cluster by dynamical friction, and the distribution of peculiar velocities is inconsistent with the observed distribution. The typical cD galaxy has nine mergers and is 5 solar luminosities. This is in comparison with the observed luminosity of Morgan poor clusters of 7 solar luminosities.

Large scale peculiar velocities of galaxies

We have calculated in detail the distribution of large scale peculiar velocities on assuming gaussian primordial mass perturbation and spherical symmetry, instead of the linear perturbaton approximation and window function used in usual fluid models. Calculation was made for several model universes dominated by various kinds of matter. The expected values of the peculiar velocities was found to decrease with increasing distance scale, in agreement with the conventional fluid and cosmic string models. For all acceptable parameter values our model is unable to explain the observed high peculiar velocity on a scale of 60 h −1 Mpc (Dressler et al. 1987). A reasonable explanation for the discrepancy is that there may be a region of huge mass concentration at a distance above 60 h −1 Mpc away from the Local Group.

The diffusion of stars through phase space

An orbit-averaged Fokker-Planck equation has been derived to study the secular evolution of stellar systems with regular orbits and the heating of stellar disks. It is shown that a population of stars with an initially Maxwellian peculiar-velocity distribution will remain Maxwellian as it diffuses through orbit space only if: (1) a second-order diffusion tensor is proportional to epicycle energy; and (2) the population's velocity dispersion grows as the square root of time. Scattering by ephemeral spiral waves is able to account for the observed kinematics of the solar neighborhood only if the waves have wavelengths in excess of 9 kpc and constantly drifting pattern speeds.

Density peaks and large scale velocities

The velocity dispersion of density extrema is calculated for a general fluctuation spectrum and is shown to be-smaller than for randomly selected points for most spectra by a factor 2/(n+3), where |δ k |2 =k n . This is valid for the peculiar velocity distribution of clusters of galaxies as well. Our location near the Virgo cluster changes the interpretation of the large scale velocity field measurements. The results imply that “biased” galaxy formation with cold dark matter has even more serious difficulties than previously suggested by Vittorio and Silk [1].

Which kind of spiral structure can fit the observed gradient of vertex deviation?

We analyse the distribution of peculiar velocities of stars within 200 pc of the Sun in terms of space variations of the velocity ellipsoid.