### Abstract

We have computed the power spectrum of galaxy clustering, P(k), for a flux-limited redshift survey of 5304 galaxies detected by the Infrared Astronomical Satellite (IRAS), using a window function which minimizes the aliasing due to the sample boundaries. We use Monte Carlo realizations of the data sample drawn from an N-body simulation of a cold dark matter (CDM) universe to check our methods and to derive error estimates for the IRAS power spectrum. The derived IRAS P(k) appears consistent with the known two-point correlation function of IRAS galaxies on scales ∼20 h^{-1} Mpc extrapolated out to large spatial scales (2π/k ≲ 100 h^{-1} Mpc) and is characterized by a power law, P(k) ∝ k^{n}, with n ∼ -1.4. On larger scales, the IRAS power spectrum begins to flatten, but we see no significant evidence for a turnover out to the largest scales we measure, ∼180 h^{-1} Mpc. We compare the IRAS power spectrum qualitatively with a variety of theoretical models. The shape of the IRAS power spectrum is not well matched by the standard CDM model (Ωh = 0.5); models with more large-scale power such as CDM with Ωh = 0.2 or CDM seeded with textures provide a better fit to the IRAS power spectrum. We perform a detailed quantitative comparison between standard CDM and the data using N-body simulations to map out the error distribution of P(k) on large scales. We find that the variance in the measured power on the largest scales is dominated by the poor sampling of Fourier modes with wavelengths comparable to the size of the sample, rather than by dilute sampling statistics. Consequently, in order to determine the validity of the standard CDM model on large scales, one must analyze many independent realizations of the CDM power spectrum. The analysis of repeated sampling of a single realization results in a significant underestimation of the variance in the CDM power which can lead to incorrect conclusions regarding the statistical significance of an observed power spectrum. The large sky coverage of our survey and our choice of window function leads to the orthogonality of different modes. We use this fact, in addition to the assumption of linear biasing, to derive the probability that the standard CDM model can produce power of comparable amplitude to that measured in the IRAS sample on large scales. On scales between 36 h^{-1} Mpc and 180 h^{-1} Mpc, consistency of the CDM model with the IRAS data constrains the linear biasing parameter, b (IRAS to dark matter), to be b < 1.5 at the 95% confidence level and b < 2 at the 99% confidence level. On large scales the CDM model is in good agreement with the IRAS P(k) if IRAS galaxies are unbiased tracers of the mass distribution (b = 1). However, if the linear biasing model were to extend to smaller scales, it would lead to excessive power.

Original language | English (US) |
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Pages (from-to) | 42-57 |

Number of pages | 16 |

Journal | Astrophysical Journal |

Volume | 402 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1993 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Cosmology: theory
- Dark matter
- Galaxies: clustering
- Galaxies: distances and redshifts
- Infrared: galaxies

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## Cite this

*Astrophysical Journal*,

*402*(1), 42-57. https://doi.org/10.1086/172110