@MISC{Strauss96thelarge-scale, author = {Michael A. Strauss}, title = {The Large-Scale Velocity Field}, year = {1996} }

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Abstract

are proportional to their observed recession velocities, at least at low redshifts: cz = H0r. (1) However, this is not exactly correct. Galaxies have peculiar velocities above and beyond the Hubble flow indicated by Eq. (1). We denote the peculiar velocity v(r) at every point in space; the observed redshift in the rest frame of the Local Group is then: cz = H0r + ˆr · (v(r) − v(0)) , (2) where the peculiar velocity of the Local Group itself is v(0), and ˆr is the unit vector to the galaxy in question. In practice, we will measure distances in units of km s −1, which means that H0 ≡ 1, and the uncertainties in the value of H0 discussed by Freedman and Tammann in this volume are not an issue. Thus measurements of redshifts cz, and of redshift-independent distances via standard candles, yield estimates of the radial component of the velocity field. What does the resulting velocity field tell us? On scales large enough that the rms density fluctuations are small, the equations of gravitational instability can be linearized, yielding a direct proportionality between the divergence of the velocity field and the density field at late times [33], [34]: This equation is easily translated to Fourier space: ∇ · v(r) = −Ω 0.6 δ(r). (3)