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--Lo\`eve 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.Comment: 25 Pages, 3 figures. Submitted to Ap

Flows on scales of 150 Mpc?

We investigate the reality of large-scale streaming on scales of up to 150 Mpc using the peculiar motions of galaxies in three directions. New R-band CCD photometry and spectroscopy for elliptical galaxies is used. The Fundamental Plane distance indicator is calibrated using the Coma cluster and an inhomogeneous Malmquist bias correction is applied. A linear bulk-flow model is fitted to the peculiar velocities in the sample regions and the results do not reflect the bulk flow observed by Lauer and Postman (LP). Accounting for the difference in geometry between the galaxy distribution in the three regions and the LP clustersconfirms the disagreement; assuming a low-density CDM power spectrum, we find that the observed bulk flow of the galaxies in our sample excludes the LP bulk flow at the 99.8% confidence level.Comment: 16 pages, 1 figur

The dependence of solar wind burst size on burst duration and its invariance across solar cycles 23 and 24

Time series of solar wind variables are “bursty” in nature. Bursts, or excursions, in the time series of solar wind parameters are associated with various transient structures in the solar wind plasma, and are often the drivers of increased space weather activity in Earth's magnetosphere. We define bursts by setting a threshold value of the time series and identifying how often, and for how long, it is exceeded. This allows us to study how the statistical distributions and scaling properties of burst parameters vary over solar cycles 23 and 24. We find the distributions of burst duration and integrated burst size vary over the solar cycle, and between the equivalent phases of consecutive cycles. However, there exists a single power law scaling relation between burst size and duration, with a joint area‐duration scaling exponent α that is independent of the solar cycle. This provides a solar cycle invariant constraint between possible sizes and durations of solar wind bursts that can occur

Using the <i>aa</i> index over the last 14 solar cycles to characterize extreme geomagnetic activity

Geomagnetic indices are routinely used to characterize space weather event intensity. The DST index is well resolved, but is only available over 5 solar cycles. The aa index extends over 14 cycles but is highly discretized with poorly resolved extremes. We parameterize extreme aa activity by the annual averaged top few % of observed values, show these are exponentially distributed and they track annual DST index minima. This gives a 14 cycle average of ~ 4% chance of at least one great (DST nT) storm and ~ 28% chance of at least one severe (DST nT) storm per year. At least one DST=‐809 [‐663,‐955] nT event in a given year would be a 1:151 year event. Carrington event estimate DST ~ ‐850 nT is within the same distribution as other extreme activity seen in aa since 1868 so that its likelihood can be deduced from that of more moderate events. Events with DST ≲ ‐1000 nT are in a distinct class, requiring special conditions

Hubble flow variance and the cosmic rest frame

We characterize the radial and angular variance of the Hubble flow in the COMPOSITE sample of 4534 galaxies, on scales in which much of the flow is in the nonlinear regime. With no cosmological assumptions other than the existence of a suitably averaged linear Hubble law, we find with decisive Bayesian evidence (ln B >> 5) that the Hubble constant averaged in independent spherical radial shells is closer to its asymptotic value when referred to the rest frame of the Local Group, rather than the standard rest frame of the Cosmic Microwave Background. An exception occurs for radial shells in the range 40/h-60/h Mpc. Angular averages reveal a dipole structure in the Hubble flow, whose amplitude changes markedly over the range 32/h-62/h Mpc. Whereas the LG frame dipole is initially constant and then decreases significantly, the CMB frame dipole initially decreases but then increases. The map of angular Hubble flow variation in the LG rest frame is found to coincide with that of the residual CMB temperature dipole, with correlation coefficient -0.92. These results are difficult to reconcile with the standard kinematic interpretation of the motion of the Local Group in response to the clustering dipole, but are consistent with a foreground non-kinematic anisotropy in the distance-redshift relation of 0.5% on scales up to 65/h Mpc. Effectively, the differential expansion of space produced by nearby nonlinear structures of local voids and denser walls and filaments cannot be reduced to a local boost. This hypothesis suggests a reinterpretation of bulk flows, which may potentially impact on calibration of supernovae distances, anomalies associated with large angles in the CMB anisotropy spectrum, and the dark flow inferred from the kinematic Sunyaev-Zel'dovich effect. It is consistent with recent studies that find evidence for a non-kinematic dipole in the distribution of distant radio sources.Comment: 37 pages, 9 tables, 13 figures; v2 adds extensive new analysis (including additional subsections, tables, figures); v3 adds a Monte Carlo analysis (with additional table, figure) which further tightens the statistical robustness of the dipole results; v4 adds further clarifications, small corrections, references and discussion of Planck satellite results; v5 typos fixed, matches published versio

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 $\chi^2$ 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.Comment: 15 pages, 3 figures, Some revisions and different figure. Accepted for publication at ApJ letter