Proper Motions Of VLBI Lenses, Inertial Frames and The Evolution of Peculiar Velocities

Precise determinations of the image positions in quad gravitational lenses using VLBI can be used to measure the transverse velocity of the lens galaxy and the observer. The typical proper motions are $\mu$as yr$^{-1}$, so the time scale to measure the motion is ten years. By measuring the dipole of the proper motions in an ensemble of lenses we can set limits on the deviation of the inertial frame defined by the lenses from that defined by the CMB dipole and estimate the Hubble constant. The residual proper motions after subtracting the dipole probe the evolution of peculiar velocities with redshift and can be used to estimate the density parameter $\Omega_0$. For $N$ lenses, VLBI measurement accuracies of $\sigma_\theta$, and a baseline of $T$ years, we estimate that the 2$\sigma$ limit on the rms peculiar velocity of the lens galaxies is 3100 (\sigma_\theta/10\mu\{as})({yrs}/T)/N^{1/2} \kms, and that the time required for the 2--$\sigma$ limit to reach the level of the local rms peculiar velocity $v_{0,rms}$ is approximately 10 N^{-1/2} (v_{0,rms}/600\kms)(\sigma_\theta/10\mu as) years. For a ten year baseline and $N=10$ lenses we expect the 1$\sigma$ limit on the misalignment with the CMB dipole to be $\Delta \theta=20^{\circ}$ or equivalently to obtain an upper limit of $\Delta H_0 /H_0 < 0.34$.Comment: 23 pages, figures included uuencoded gzipped ps-file, submitted to the ApJ. One correction made from the original versio

Do Spirals and Ellipticals Trace the Same Velocity Field?

We test the hypothesis that the velocity field derived from Tully-Fisher measurements of spiral galaxies, and that derived independently from Dn-sigma measurements of ellipticals and S0s, are noisy versions of the same underlying velocity field. The radial velocity fields are derived using tensor Gaussian smoothing of radius 1200 km/s. They are compared at grid points near which the sampling by both types of galaxies is proper. This requirement defines a volume of ~(50 Mpc/h)^3, containing ~10 independent subvolumes, mostly limited by the available ellipticals. The two fields are compared using a correlation statistic, whose distribution is determined via Monte-Carlo simulations. We find that the data is consistent with the hypothesis, at the 10% level. We demonstrate that the failure to reject the correlation is not just a result of the errors being big, by using the same method to rule out complete independence between the fields at the 99.8% level. The zero points of the two distance indicators are matched by maximizing the correlation between the two velocity fields. There is a marginal hint that the ellipticals tend to stream slower than the spirals by ~8%. The correlation reinforced here is consistent with the common working hypotheses that (a) the derived large-scale velocity field is real, (b) it has a gravitational origin, and (c) the large-scale velocities of spirals and ellipticals are hardly biased relative to each other. On the other hand, it does not rule out any alternative to gravity where objects of all types obtain similar large-scale velocities.Comment: 16 pages, compressed and uuencoded PostScript 0.6Mbyte, (Also anonymous ftp venus.huji.ac.il pub/dekel/es/es.ps.Z of 0.43Mbyte

Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used to determine the fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained Realizations (CR) are then used to sample the statistical scatter about the WF mean field. The WF/CR method is applied as a demonstration to the Mark III data with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed structures are consistent with those extracted by the POTENT method. A comparison with the structures in the distribution of IRAS 1.2Jy galaxies yields a general agreement. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of +/-8000 km/s centered on the Local Group. The divergent component is very similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ. Postscript version of the figures can be obtained by anonymous ftp from: ftp://alf.huji.ac.il/pub/saleem

POTENT Reconstruction from Mark III Velocities

We present an improved POTENT method for reconstructing the velocity and mass density fields from radial peculiar velocities, test it with mock catalogs, and apply it to the Mark III Catalog. Method improvments: (a) inhomogeneous Malmquist bias is reduced by grouping and corrected in forward or inverse analyses of inferred distances, (b) the smoothing into a radial velocity field is optimized to reduce window and sampling biases, (c) the density is derived from the velocity using an improved nonlinear approximation, and (d) the computational errors are made negligible. The method is tested and optimized using mock catalogs based on an N-body simulation that mimics our cosmological neighborhood, and the remaining errors are evaluated quantitatively. The Mark III catalog, with ~3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 Mpc/h out to ~60 Mpc/h. We present maps of the 3D velocity and mass-density fields and the corresponding errors. The typical systematic and random errors in the density fluctuations inside 40 Mpc/h are \pm 0.13 and \pm 0.18. The recovered mass distribution resembles in its gross features the galaxy distribution in redshift surveys and the mass distribution in a similar POTENT analysis of a complementary velocity catalog (SFI), including the Great Attractor, Perseus-Pisces, and the void in between. The reconstruction inside ~40 Mpc/h is not affected much by a revised calibration of the distance indicators (VM2, tailored to match the velocities from the IRAS 1.2Jy redshift survey). The bulk velocity within the sphere of radius 50 Mpc/h about the Local Group is V_50=370 \pm 110 km/s (including systematic errors), and is shown to be mostly generated by external mass fluctuations. With the VM2 calibration, V_50 is reduced to 305 \pm 110 km/s.Comment: 60 pages, LaTeX, 3 tables and 27 figures incorporated (may print the most crucial figures only, by commenting out one line in the LaTex source

Is the Lambda CDM Model Consistent with Observations of Large-Scale Structure?

The claim that large-scale structure data independently prefers the Lambda Cold Dark Matter model is a myth. However, an updated compilation of large-scale structure observations cannot rule out Lambda CDM at 95% confidence. We explore the possibility of improving the model by adding Hot Dark Matter but the fit becomes worse; this allows us to set limits on the neutrino mass.Comment: To appear in Proceedings of "Sources and Detection of Dark Matter/Energy in the Universe", ed. D. B. Cline. 6 pages, including 2 color figure

The Magnetic Power Spectrum in Faraday Rotation Screens

The autocorrelation function and similarly the Fourier-power spectrum of a rotation measure (RM) map of an extended background radio source can be used to measure components of the magnetic autocorrelation and power-spectrum tensor within a foreground Faraday screen. It is possible to reconstruct the full non-helical part of this tensor in the case of an isotropic magnetic field distribution statistics. The helical part is only accessible with additional information; e.g. the knowledge that the fields are force-free. The magnetic field strength, energy spectrum and autocorrelation length l_B can be obtained from the non-helical part alone. We demonstrate that l_B can differ substantially from l_RM, the observationally easily accessible autocorrelation length of an RM map. In typical astrophysical situation l_RM > l_B. Any RM study, which does not take this distinction into account, likely underestimates the magnetic field strength. For power-law magnetic power spectra, and for patchy magnetic field configurations the central RM autocorrelation function is shown to have characteristic asymptotic shapes. Ways to constrain the volume filling factor of a patchy field distribution are discussed. We discuss strategies to analyse observational data, taking into account - with the help of a window function - the limited extent of the polarised radio source, the spatial distribution of the electron density and average magnetic energy density in the screen, and allowing for noise reducing data weighting. We briefly discuss the effects of possible observational artefacts, and strategies to avoid them.Comment: 15 pages, 4 figures, accepted by Astronomy & Astrophysic