The Intermittent Behavior and Hierarchical Clustering of the Cosmic Mass Field

The hierarchical clustering model of the cosmic mass field is examined in the context of intermittency. We show that the mass field satisfying the correlation hierarchy ξn ≃ Qn(ξ2)n-1 is intermittent if κ < d, where d is the dimension of the field and κ is the power-law index of the nonlinear power spectrum in the discrete wavelet transform (DWT) representation. We also find that a field with singular clustering can be described by hierarchical clustering models with scale-dependent coefficients Qn and that this scale dependence is completely determined by the intermittent exponent and κ. Moreover, the singular exponents of a field can be calculated by the asymptotic behavior of Qn when n is large. Applying this result to the transmitted flux of HS 1700 Lyα forests, we find that the underlying mass field of the Lyα forests is significantly intermittent. On physical scales less than about 2.0 h-1 Mpc, the observed intermittent behavior is qualitatively different from the prediction of the hierarchical clustering with constant Qn. The observations, however, do show the existence of an asymptotic value for the singular exponents. Therefore, the mass field can be described by the hierarchical clustering model with scale-dependent Qn. The singular exponent indicates that the cosmic mass field at redshift ~2 is weakly singular at least on physical scales as small as 10 h-1 kpc.