Using eigenmode expansion of the Mark III and SFI surveys of cosmological radial velocities, a goodness-of-fit analysis is applied on a mode-by-mode basis. This differential analysis complements the Bayesian maximum likelihood analysis that finds the most probable model given the data. Analyzing the surveys with their corresponding most likely models from the CMB-like family of models, as well as with the currently popular ACDM model, reveals a systematic inconsistency of the data with these "best" models. There is a systematic trend of the cumulative χ2 to increase with the mode number (where the modes are sorted by decreasing order of the eigenvalues). This corresponds to a decrease of the χ2 with the variance associated with a mode and hence with its effective scale. It follows that the differential analysis finds that on small (large) scales the global analysis of all the modes "puts" less (more) power than actually required by the data. This observed trend might indicate one of the following: (1) the theoretical model (i.e., power spectrum) or the error model (or both) have an excess of power on large scales, (2) velocity bias, or (3) the velocity data suffers from systematic errors that have not yet been corrected.
Bibliographical noteFunding Information:
We have benefited from many interesting discussions with Avishai Dekel, Zafrir Kolatt, Ofer Lahav, Lior Silverman, Simon White, and Idit Zehavi. The hospitality of the Racah Institute of Physics and the Max-Planck-Institut für Astrophy-sik is gratefully acknowledged. This research has been partially supported by a Binational Science Foundation grant (94-00185) and an Israel Science Foundation grant (103/98).
© 2000 The American Astronomical Society.
- Cosmology: observations
- Cosmology: theory
- Galaxies: distances and redshifts
- Large-scale structure of universe
- Methods: statistical