arXiv subjects

Richard Watkins

Publications and source records attributed to Richard Watkins.

At least 37 records · Page 2Linked to original sources

arXiv2011

A Slight Excess of Large Scale Power from Moments of the Peculiar Velocity Field

The peculiar motions of galaxies can be used to infer the distribution of matter in the Universe. It has recently been shown that measurements of the peculiar velocity field indicates an anomalously high bulk flow of galaxies in our local volume. In this paper we find the implications of the high bulk flow for the power spectrum of density fluctuations. We find that analyzing only the dipole moment of the velocity field yields an average power spectrum amplitude which is indeed much higher than the LCDM value. However, by also including shear and octupole moments of the velocity field, and marginalizing over possible values for the growth rate, an average power spectrum amplitude which is consistent with LCDM is recovered. We attempt to infer the shape of the matter power spectrum from moments of the velocity field, and find a slight excess of power on scales ~ h-1 Gpc.

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arXiv2010

Cosmic Flows on 100 Mpc/h Scales: Standardized Minimum Variance Bulk Flow, Shear and Octupole Moments

The low order moments, such as the bulk flow and shear, of the large scale peculiar velocity field are sensitive probes of the matter density fluctuations on very large scales. In practice, however, peculiar velocity surveys are usually sparse and noisy, which can lead to the aliasing of small scale power into what is meant to be a probe of the largest scales. Previously, we developed an optimal ``minimum variance'' (MV) weighting scheme, designed to overcome this problem by minimizing the difference between the measured bulk flow (BF) and that which would be measured by an ideal survey. Here we extend this MV analysis to include the shear and octupole moments, which are designed to have almost no correlations between them so that they are virtually orthogonal. We apply this MV analysis to a compilation of all major peculiar velocity surveys, consisting of 4536 measurements. Our estimate of the BF on scales of ~ 100 Mpc/h has a magnitude of |v|= 416 +/- 78 km/s towards Galactic l = 282 degree +/- 11 degree and b = 6 degree +/- 6 degree. This result is in disagreement with LCDM with WMAP5 cosmological parameters at a high confidence level, but is in good agreement with our previous MV result without an orthogonality constraint, showing that the shear and octupole moments did not contaminate the previous BF measurement. The shear and octupole moments are consistent with WMAP5 power spectrum, although the measurement noise is larger for these moments than for the BF. The relatively low shear moments suggest that the sources responsible for the BF are at large distances.

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arXiv2008

Consistently Large Cosmic Flows on Scales of 100 Mpc/h: a Challenge for the Standard LCDM Cosmology

Peculiar velocity surveys have non-uniform spatial distributions of tracers, so that the bulk flow estimated from them does not correspond to that of a simple volume such as a sphere. Thus bulk flow estimates are generally not strictly comparable between surveys, even those whose effective depths are similar. In addition, the sparseness of typical surveys can lead to aliasing of small scale power into what is meant to be a probe of the largest scales. Here we introduce a new method of calculating bulk flow moments where velocities are weighted to give an optimal estimate of the bulk flow of an idealized survey, with the variance of the difference between the estimate and the actual flow being minimized. These "minimum variance" estimates can be designed to estimate the bulk flow on a particular scale with minimal sensitivity to small scale power, and are comparable between surveys. We compile all major peculiar velocity surveys and apply this new method to them. We find that most surveys we studied are highly consistent with each other. Taken together the data suggest that the bulk flow within a Gaussian window of radius 50 Mpc/h is 407 km/s toward l=287 and b=8. The large-scale bulk motion is consistent with predictions from the local density field. This indicates that there are significant density fluctuations on very large scales. A flow of this amplitude on such a large scale is not expected in the WMAP5-normalized LCDM cosmology, for which the predicted one-dimensional r.m.s. velocity is ~110 km/s. The large amplitude of the observed bulk flow favors the upper values of the WMAP5 error-ellipse, but even the point at the top of the WMAP5 95% confidence ellipse predicts a bulk flow which is too low compared to that observed at >98% confidence level.

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arXiv2008

Bulk Flow and Shear Moments of the SFI++ Survey

We find the nine bulk--flow and shear moments from the SFI++ survey, as well as for subsamples of group and field galaxies. We constrain the velocity power spectrum shape parameter $Γ$ in linear theory using these moments. A likelihood function for $Γ$ was found after marginalizing over the power spectrum amplitude $σ_8Ω_m^{0.6}$ using constraints obtained from comparisons between redshift surveys and peculiar velocity data. We have estimated the velocity noise $σ_*$ from the data since without it our results may be biased. We also performed a statistical analysis of the difference between the field and group catalogues and found that the results from each reflect the same underlying large scale flows. We found that we can constrain the power spectrum shape parameter to be $Γ=0.15^{+0.18}_{-0.08}$ for the groups catalogue and $Γ=0.09^{+0.04}_{-0.04}$ for the field galaxy catalogue in fair agreement with the value from WMAP.

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arXiv2008

Cosmic Flows on 100 Mpc/h scales

To study galactic motions on the largest available scales, we require bulk flow moments whose window functions have as narrow a peak as possible and having as small an amplitude as possible outside the peak. Typically the moments found using the maximum likelihood estimate weights do not meet these criteria. We present a new method for calculating weights for moments that essentially allow us to "design" the moment's window function, subject, of course, to the distribution and uncertainties of the available data.

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arXiv2007

Current Status Of Velocity Field Surveys: A Consistency Check

We present an analysis comparing the bulk--flow measurements for six recent peculiar velocity surveys, namely, ENEAR, SFI, RFGC, SBF and the Mark III singles and group catalogs. We study whether the direction of the bulk--flow estimates are consistent with each other and construct the full three dimensional bulk--flow vectors for each survey. We show that although the surveys differ in their geometry, galaxy morphologies, distance measures and measurement errors, their bulk flow vectors are expected to be highly correlated and in fact show impressive agreement in all cases. We found a combined weighted mean bulk motion of 330 km s$^{-1}$ $\pm 101$ km s$^{-1}$ toward $l= 234^{\degree}\pm 11^{\degree}$ and $b=12^{\degree}\pm 9^{\degree}$ in a sphere with an effective depth of $\sim4000$ km s$^{-1}$.

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arXiv2007

Power Spectrum Shape from Peculiar Velocity Data

We constrain the velocity power spectrum shape parameter $Γ$ in linear theory using the nine bulk-flow and shear moments estimated from four recent peculiar velocity surveys. For each survey, a likelihood function for $Γ$ was found after marginalizing over the power spectrum amplitude $σ_8Ω_m^{0.6}$ using constraints obtained from comparisons between redshift surveys and peculiar velocity data. In order to maximize the accuracy of our analyses, the velocity noise $σ_*$ was estimated directly for each survey. A statistical analysis of the differences between the values of the moments estimated from different surveys showed consistency with theoretical predictions, suggesting that all the surveys investigated reflect the same large scale flows. The peculiar velocity surveys were combined into a composite survey yielding the constraint $Γ=0.13^{+0.09}_{-0.05}$. This value is lower than, but consistent with, values obtained using redshift surveys and CMB data.

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arXiv2003

Optimal Moments for Velocity Fields Analysis

We describe a new method of overcoming problems inherent in peculiar velocity surveys by using data compression as a filter with which to separate large-scale, linear flows from small-scale noise that biases the results systematically. We demonstrate the effectiveness of our method using realistic catalogs of galaxy velocities drawn from N--body simulations. Our tests show that a likelihood analysis of simulated catalogs that uses all of the information contained in the peculiar velocities results in a bias in the estimation of the power spectrum shape parameter $Γ$ and amplitude $β$, and that our method of analysis effectively removes this bias. We expect that this new method will cause peculiar velocity surveys to re--emerge as a useful tool to determine cosmological parameters.

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arXiv2003

Optimal Moments for the Analysis of Peculiar Velocity Surveys II: Testing

Analyses of peculiar velocity surveys face several challenges, including low signal--to--noise in individual velocity measurements and the presence of small--scale, nonlinear flows. This is the second in a series of papers in which we describe a new method of overcoming these problems by using data compression as a filter with which to separate large--scale, linear flows from small--scale noise that can bias results. We demonstrate the effectiveness of our method using realistic catalogs of galaxy velocities drawn from N--body simulations. Our tests show that a likelihood analysis of simulated catalogs that uses all of the information contained in the peculiar velocities results in a bias in the estimation of the power spectrum shape parameter $Γ$ and amplitude $β$, and that our method of analysis effectively removes this bias. We expect that this new method will cause peculiar velocity surveys to re--emerge as a useful tool to determine cosmological parameters.

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arXiv2001

Optimal Moments for the Analysis of Peculiar Velocity Surveys

We present a new method for the analysis of peculiar velocity surveys which removes contributions to velocities from small scale, nonlinear velocity modes while retaining information about large scale motions. Our method utilizes Karhunen--Loève methods of data compression to construct a set of moments out of the velocities which are minimally sensitive to small scale power. The set of moments are then used in a likelihood analysis. We develop criteria for the selection of moments, as well as a statistic to quantify the overall sensitivity of a set of moments to small scale power. Although we discuss our method in the context of peculiar velocity surveys, it may also prove useful in other situations where data filtering is required.

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arXiv1997

A New Approach to Probing Large Scale Power with Peculiar Velocities

We propose a new strategy to probe the power spectrum on large scales using galaxy peculiar velocities. We explore the properties of surveys that cover only two small fields in opposing directions on the sky. Surveys of this type have several advantages over those that attempt to cover the entire sky; in particular, by concentrating galaxies in narrow cones these surveys are able to achieve the density needed to measure several moments of the velocity field with only a modest number of objects, even for surveys designed to probe scales $\gtwid 100$\hmpc. We construct mock surveys with this geometry and analyze them in terms of the three moments to which they are most sensitive. We calculate window functions for these moments and construct a $χ^2$ statistic which can be used to put constraints on the power spectrum. In order to explore the sensitivity of these surveys, we calculate the expectation values of the moments and their associated measurement noise as a function of the survey parameters such as density and depth and for several popular models of structure formation. In addition, we have studied how well these kind of surveys can distinguish between different power spectra and found that, for the same number of objects, cone surveys are as good or better than full-sky surveys in distinguishing between popular cosmological models. We find that a survey with $200-300$ galaxy peculiar velocities with distance errors of 15% in two cones with opening angle of $\sim 10^\circ$ could put significant constraints on the power spectrum on scales of $100-300$\hmpc, where few other constraints exist.

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arXiv1997

The RMS Peculiar Velocity of Clusters

We study the rms peculiar velocity of clusters as a convenient statistic to put constraints on cosmological models. This statistic is easy to compute theoretically given a model for the power spectrum; we show that with some assumptions it can be directly related to the quantity $Ω_0^{0.6}σ_8$. We develop a likelihood method for estimating the rms peculiar velocity of clusters from line-of-sight velocity measurements and their associated errors. We apply our method to two samples of cluster peculiar velocities; a new sample known as the SCI sample and a subsample of the Mark III catalog. Although these two samples initially give results which are inconsistent, we show that they can be put into good agreement by the removal, particularly from the Mark III sample, of a set of clusters with multiple mass concentrations, cluster membership ambiguities, or excessive obscuration, properties which may have introduced unaccounted for errors into measurements of their peculiar velocities. Once these clusters are removed from the samples, they both favor a relatively low value for the 1-D rms peculiar velocity of clusters $σ_v= 265^{+106}_{-75}{km s}^{-1}$ (at 90% confidence), leading to the constraint $Ω_0^{0.6}σ_8= 0.44^{+0.19}_{-0.13}$, consistent with cluster abundance studies but inconsistent with $Ω_0=1$ CDM normalized to COBE at the 99.7% confidence level.

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arXiv1996

Linear Graviational Instability of Filamentary and Sheet-like Molecular Clouds with Magnetic Fields

We study the linear evolution of small perturbations in self-gravitating fluid systems with magnetic fields. We consider wave-like perturbations to nonuniform filamentary and sheet-like hydrostatic equilibria in the presence of a uniform parallel magnetic field. Motivated by observations of molecular clouds that suggest substantial nonthermal (turbulent) pressure, we adopt equations of state that are softer than isothermal. We numerically determine the dispersion relation and the form of the perturbations in the regime of instability. The form of the dispersion relation is the same for all equations of state considered, for all magnetic field strengths, and for both geometries examined. We demonstrate the existence of a fastest growing mode for the system and study how its characteristics depend on the amount of turbulence and the strength of the magnetic field. Generally, turbulence tends to increase the rate and the length scale of fragmentation. While tending to slow the fragmentation, the magnetic field has little effect on the fragmentation length scale until reaching some threshold, above which the length scale decreases significantly. Finally, we discuss the implications of these results for star formation in molecular clouds.

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arXiv1995

Interpreting New Data on Large Scale Bulk Flows

We study the implications of a recent estimate of the bulk flow of a sample of galaxies containing supernovae type Ia by Riess, Press, and Kirshner. We find that their results are quite consistent with power spectra from several currently popular models of structure formation, but that the sample is as yet too sparse to put significant constraints on the power spectrum. We compare this new result with that of Lauer and Postman, with which there is apparent disagreement. We find that for the power spectra we consider, the difference in window functions between the two samples used for the measurements results in a low level of expected correlation between the estimated bulk flows. We calculate a $χ^2$ for the two measurements taken together and find that their lack of agreement tends to disfavor spectra with excessive power on large scales, but not at a level sufficient to rule them out. A sample consisting of other SN type Ia's found in the Asiago catalog is used to study how the sensitivity of the method used by RPK will improve with increasing sample size. We conclude that the local group motion should be able to be determined with a sample of $\sim 100$ SN Ia light curve shapes.

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arXiv1995

Wave Motions In Molecular Clouds: Results in Two Dimensions

We study the linear evolution of small perturbations in self-gravitating fluid systems in two spatial dimensions; we consider both cylindrical and cartesian (i.e., slab) geometries. The treatment is general, but the application is to molecular clouds. We consider a class of equations of state which heuristically take into account the presence of turbulence; in particular, we consider equations of state which are {\it softer} than isothermal. We take the unperturbed cloud configuration to be in hydrostatic equilibrium. We find a class of wave solutions which propagate along a pressure supported cylinder (or slab) and have finite (trapped) spatial distributions in the direction perpendicular to the direction of propagation. Our results indicate that the dispersion relations for these two dimensional waves have similar forms for the two geometries considered here. Both cases possess a regime of instability and a fastest growing mode. We also find the (perpendicular) form of the perturbations for a wide range of wavelengths. Finally, we discuss the implications of our results for star formation and molecular clouds. The mass scales set by instabilities in both molecular cloud filaments and sheets are generally much larger than the masses of stars. However, these instabilities can determine the length scales for the initial conditions for protostellar collapse.

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arXiv1995

Vortices In Circumstellar Disks

We discuss the physics of vortices in the circumstellar disks associated with young stellar objects. We elucidate the basic physical properties of these localized storm systems. In particular, we consider point vortices, linear vortices, the effects of self-gravity, magnetic fields, and nonlinear aspects of the problem. We find that these vortices can exist in many different forms in the disks of young stellar objects and may play a role in the formation of binary companions and/or giant planets. Vortices may enhance giant planet formation via gravitational instability by allowing dust grains (heavy elements) to settle to the center on a short timescale; the gravitational instability itself is also enhanced because the vortices also create a larger local surface density in the disk. In addition, vortices can enhance energy dissipation in disks and thereby affect disk accretion. Finally, we consider the possibility that vortices of this type exist in molecular clouds and in the disk of the galaxy itself. On all of these size scales, vortices can produce long-lived structures which may correspond to observed structures in these systems.

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arXiv1993

Theoretical Expectations for Bulk Flows in Large Scale Surveys

We calculate the theoretical expectation for the bulk motion of a large scale survey of the type recently carried out by Lauer and Postman. Included are the effects of survey geometry, errors in the distance measurements, clustering properties of the sample, and different assumed power spectra. We consider the power spectrum calculated from the IRAS--QDOT survey, as well as spectra from hot $+$ cold and standard cold dark matter models. We find that sparse sampling and clustering can lead to an unexpectedly large bulk flow, even in a very deep survey. Our results suggest that the expected bulk motion is inconsistent with that reported by Lauer and Postman at the $90-94\%$ confidence level.

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arXiv1993

General Analytic Results for Nonlinear Waves and Solitons in Molecular Clouds

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a ``charge density'' $q(ρ)$; this quantity replaces the density on the right hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This ``no-charge'' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We then apply these results to study nonlinear waves in Jeans-type theories, Yukawa theories, and a pseudo-two-dimensional treatment. We study the allowed types of wave behavior for all of these models. Finally, we discuss the implications of this work for molecular cloud structure.

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