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by theoretical considerations and N- body simulations of dark matter haloes. In particular, one should not use the same β profile as in equation (1), since there is little reason to assume that the dark matter ...
of Hernandez & Bertschinger. Owing to the Kepler solver, these methods treat close two - body interactions correctly, while close three- body encounters contribute to the truncation error at second order and above ...
})=2.39 \, \mathrm{Mpc}$| is 1.56 × 1015M⊙. 3.2 Virial theorem The implementation of the virial theorem is based on that of Limber & Mathews (1960) and Heisler, Tremaine & Bahcall (1985). In the case where ...
the spherical collapse and virial theorem . The density profile for each halo is stored using 20 logarithmically spaced bins that reach out to |$2 \,\mathrm{ \mathit{ h}}^{-1}\,{\rm Mpc}$|. We compute ...
slide Euler equation support terms as a function of fractional virial radius for our three samples (L* haloes- aqua, group haloes- orange, clusters- magenta). Median values are shown in thick lines and 25 ...
polymers [23, 24] or graphene [25], the low-energy fermion excitation spectrum is effectively described by a (quasi)relativistic Dirac equation rather than by a Schrödinger equation . Such a similarity ...
inferred through equation (1) (blue), and best-fitting profiles (red) for two randomly selected ideal haloes. Errors on the inferred profile are obtained through 100 bootstrap resamples of the full parent ...
, from two different calculations, and are then injected into the Fokker–Planck equation . When the DF is allowed to change self-consistently, one obtains an integrodifferential equation describing ...
*} (19) i.e. |$\mathcal {P}_{w_{\rm los}}$| coincides with the positive |$r_\parallel$| branch of |$\mathcal {P}_{w_\parallel }$|. Substituting in equation (4) and breaking the integral into two parts ...
}(\boldsymbol {a})]_{i} = \sigma ^2(\boldsymbol {a}_{i}, \boldsymbol {a})$|. These two equations are the principal results of GPE. The estimator, |$\hat{r}$|, is the sum of two terms. The first ...
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