2001ApJ...555...74F

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 ξ_n≃Q_n(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 Q_n 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 Q_n 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 Q_n. 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 Q_n. 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.