We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the Secondary Infall (SI) model. The novelties are: i) we deal with triaxial virialised objects; ii) their seeds in the linear regime are peaks endowed with {\it unconvolved} spherically averaged density profiles according to the peak formalism; iii) the initial peculiar velocities are taken into account; and iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurately checked by comparing analytical predictions on such a growth with the results of numerical simulation. We show that the spherically averaged density profile of virialised objects can be inferred with no need to specify their shape. The {\it typical} spherically averaged halo density profile is inferred, down to arbitrarily small radii, from the power-spectrum of density perturbations. The predicted profile in the $\Lambda$CDM cosmology is approximately described by an Einasto profile, meaning that it does not have a cusp but rather a core, where the inner slope slowly converges to zero. Down to one hundredth the total radius, the profile has the right NFW and Einasto forms, being close to the latter down to a radius of about four orders of magnitude less. The inner consistency of the model implies that the density profiles of haloes harbour no information on their past aggregation history. This would explain why major mergers do not alter the typical density profile of virialised objects formed by SI and do not invalidate the peak formalism based on such a formation.Comment: 14 pages, 7 figures. Published in MNRA

In a recent paper, Salvador-Solé et al. have derived the typical inner structure of dark matter haloes from that of peaks in the initial random Gaussian density field, determined by the power spectrum of density perturbations characterizing the hierarchical cosmology under consideration. In this paper, we extend this formalism to the typical kinematics and triaxial shape of haloes. Specifically, we establish the link between such halo properties and the power spectrum of density perturbations through the typical shape of peaks. The trends of the predicted typical halo shape, pseudo-phase-space density and anisotropy profiles are in good agreement with the results of numerical simulations. Our model sheds light on the origin of the power-law-like pseudo-phase-space density profile for virialized haloes.Key words: methods: analytic -galaxies: haloes -cosmology: theory -dark matter. I N T RO D U C T I O NVirialized haloes in N-body simulations of cold dark matter (CDM) cosmologies show a wide variety of ellipsoidal shapes. On the contrary, their structural and kinematic properties are remarkably similar from one object to another. They are little sensitive not only to the mass, redshift, environment and even specific cosmology, but also to their individual shape. Only their scaling shows a mild dependence on some of these properties. As shown by gravohydrodynanic simulations, baryons introduce a larger scatter in the properties of haloes at their central region. However, in this paper, we will concentrate on pure dark matter haloes and we will not deal with such secondary baryonic effects.The typical spherically averaged halo density profile, ρ (r), is well fitted, down to about one-hundredth the virial radius, by the so-called NFW profile (Navarro, Frenk & White 1997) as well as by the Einasto (1965) profile, which gives slightly better fits down to smaller radii (Navarro et al. 2004;Merritt et al. 2005Merritt et al. , 2006Stadel et al. 2009;Navarro et al 2010). The velocity dispersion profile, σ (r), is reasonably well fitted by the solution of the Jeans equation for spherically symmetric isotropic systems with null value at infinity (Cole & Lacey 1996;Merritt et al. 2006). More remarkably, Taylor & Navarro (2001) showed that the pseudo-phase-space density profile is very nearly a pure power law, (1), σ (r) is the velocity dispersion over the whole spherical shell with r, so the variance coincides with the spherical average of the local value at points with r, σ 2 (r) = σ 2 loc (r). Finally, Hansen & Moore (2006) found that the velocity anisotropy profile β(r) behaves linearly with the logarithmic derivative of the density,with a and b, respectively, equal to about −0.2 and 0.8 (Hansen & Stadel 2006; see also Ludlow et al. 2011 for an alternative expression), although with a substantial scatter this time.The origin of all these trends is certainly related with the way dark matter clusters. In hierarchical cosmologies, haloes grow through continuous mergers with notably different dynamic effects accordin...

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