The Confluent System Formalism. I. The Mass Function of Objects in the Peak Model

Manrique, Alberto; Salvador-Solé, E.

doi:10.1086/176364

Cited by 38 publications

(49 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, such analytical extensions of pinocchio would not be as powerful as the full analysis. Besides, analytical formalisms based on peaks (Manrique & Salvador Solé 1995; Hanami 1999) are manageable only when linear theory is used. We therefore regard methods like pinocchio , which are based on an actual realization of the linear density field, as a good compromise between performing a simulation and getting only statistical information from a PS‐like approximation.…”

Section: Discussionmentioning

confidence: 99%

“…Extensions of the PS approach to the non‐linear regime were attempted by many authors (Cavaliere, Colafrancesco & Menci 1992; Monaco 1995, 1997a,b; Cavaliere, Menci & Tozzi 1996; Audit, Teyssier & Alimi 1997; Lee & Shandarin 1998; Sheth & Tormen 1999, 2002; Sheth, Mo & Tormen 2001). Alternative approaches assumed objects to form at the peaks of the linear density field (Peacock & Heavens 1985; Bardeen et al 1986; Manrique & Salvador‐Solé 1995; Bond & Myers 1996a,b; Hanami 2001), or applied the Zel'dovich approximation to smoothed initial conditions (truncated Zel'dovich approximation –Coles, Melott & Shandarin 1993; Borgani, Coles & Moscardini 1994), or used the second‐order LPT solution for the density field (Scoccimarro & Sheth 2002), or joined linear theory predictions with Monte Carlo methods such as the block model (Cole & Kaiser 1988) and merging cell model (Rodrigues & Thomas 1996; Nagashima & Gouda 1998; Lanzoni, Mamon & Guiderdoni 2000).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The pinocchio algorithm: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field

Monaco

Theuns

Taffoni

2002

Monthly Notices of the Royal Astronomical Society

199

211

View full text Add to dashboard Cite

pinocchio (PINpointing Orbit‐Crossing Collapsed HIerarchical Objects) is a new algorithm proposed recently by Monaco et al. (Paper I) for identifying dark matter haloes in a given numerical realization of the linear density field in a hierarchical universe. Mass elements are assumed to have collapsed after undergoing orbit crossing, as computed using perturbation theory. It is shown that Lagrangian perturbation theory, and in particular its ellipsoidal truncation, is able to predict accurately the collapse, in the orbit‐crossing sense, of generic mass elements. Collapsed points are grouped into haloes using an algorithm that mimics the hierarchical growth of structure through accretion and mergers. Some points that have undergone orbit crossing are assigned to the network of filaments and sheets that connects the haloes; it is demonstrated that this network resembles closely that found in N‐body simulations. The code generates a catalogue of dark matter haloes with known mass, position, velocity, merging history and angular momentum. It is shown that the predictions of the code are very accurate when compared with the results of large N‐body simulations that cover a range of cosmological models, box sizes and numerical resolutions. The mass function is recovered with an accuracy of better than 10 per cent in number density for haloes with at least 30–50 particles. A similar accuracy is reached in the estimate of the correlation length r0. The good agreement is still valid on the object‐by‐object level, with 70–100 per cent of the objects with more than 50 particles in the simulations also identified by our algorithm. For these objects the masses are recovered with an error of 20–40 per cent, and positions and velocities with a root mean square error of ∼1–2 Mpc (0.5–2 grid lengths) and ∼100 km s−1, respectively. The recovery of the angular momentum of haloes is considerably noisier, and accuracy at the statistical level is achieved only by introducing free parameters. The algorithm requires negligible computer time as compared with performing a numerical N‐body simulation.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The pinocchio algorithm: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field

Monaco

Theuns

Taffoni

2002

Monthly Notices of the Royal Astronomical Society

199

211

View full text Add to dashboard Cite

show abstract

“…To further improve the agreement with the simulated mass function, one shall ensure that a peak of height sc on a smoothing scale R S is not embedded in a region of height sc on any larger smoothing scale. Carefully accounting for clouds in clouds in the peak formalism is a nontrivial problem even though, in a first approximation, we may simply enforce that the height of the peak be less than sc on scale R S þ dR S [132,133]. Figure 1 of [80] demonstrates that this substantially improves the agreement with the measured halo abundances at * 3 but underestimates the counts at & 2.…”

Section: E Scale Dependence Across the Acoustic Peakmentioning

confidence: 99%

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

2010

View full text Add to dashboard Cite

Models of galaxy and halo clustering commonly assume that the tracers can be treated as a continuous field locally biased with respect to the underlying mass distribution. In the peak model pioneered by Bardeen et al. (1986), one considers instead density maxima of the initial, Gaussian mass density field as an approximation to the formation site of virialized objects. In this paper, the peak model is extended in two ways to improve its predictive accuracy. Firstly, we derive the two-point correlation function of initial density peaks up to second order and demonstrate that a peak-background split approach can be applied to obtain the k-independent and k-dependent peak bias factors at all orders. Secondly, we explore the gravitational evolution of the peak correlation function within the Zel'dovich approximation. We show that the local (Lagrangian) bias approach emerges as a special case of the peak model, in which all bias parameters are scale-independent and there is no statistical velocity bias. We apply our formulae to study how the Lagrangian peak biasing, the diffusion due to large scale flows and the mode-coupling due to nonlocal interactions affect the scale dependence of bias from small separations up to the baryon acoustic oscillation (BAO) scale. For 2σ density peaks collapsing at z = 0.3, our model predicts a ∼5% residual scale-dependent bias around the acoustic scale that arises mostly from first-order Lagrangian peak biasing (as opposed to second-order gravity mode-coupling). We also search for a scale dependence of bias in the large scale auto-correlation of massive halos extracted from a very large N-body simulation provided by the MICE collaboration. For halos with mass M 10 14 M⊙/h, our measurements demonstrate a scale-dependent bias across the BAO feature which is very well reproduced by a prediction based on the peak model.

show abstract

“…However, the complicated non-Gaussian character of the F process can considerably complicate the calculations with respect to the linear theory case. In particular, an analytical approach based on the peaks of the F process (such as the confluent formalism of Manrique & Salvador-Solé (1995)) is essentially hopeless: an analytical description of the peaks of a random field can be obtained only for Gaussian or closely related fields (see Adler 1981), or for asymptotically high peaks (Catelan, Lucchin & Matarrese 1988). On the other hand, the simpler excursion set approach requires knowledge of only the 1-point PDF of the F process, which has been obtained above.…”

Section: Discussionmentioning

confidence: 99%

“…Then, since the normalization of the MF is fixed by the excursion sets approach, a procedure like that proposed by Appel & Jones (1990) and by Manrique & Salvador-Solé (1995; could be used to fragment the collapsed medium. This would be an interesting fusion of the excursion set and peak approaches, but, given the complexity of the F process, it would be best addressed though the Monte Carlo simulations of the kind presented in §3.3.2.…”

Section: From Resolution To Massmentioning

confidence: 99%

On the Cosmological Mass Function

Monaco

1997

Generation of Cosmological Large-Scale Structure

View full text Add to dashboard Cite

This thesis aims to review the cosmological mass function problem, both from the theoretical and the observational point of view, and to present a new mass function theory, based on realistic approximations for the dynamics of gravitational collapse. Chapter 1 gives a general introduction on gravitational dynamics in cosmological models. Chapter 2 gives a complete review of the mass function theory. Chapters 3 and 4 present the "dynamical" mass function theory, based on truncated Lagrangian dynamics and on the excursion set approach. Chapter 5 reviews the observational state-of-the-art and the main applications of the mass function theories described before. Finally, Chapter 6 gives conclusions and future prospects.

show abstract

The Confluent System Formalism. I. The Mass Function of Objects in the Peak Model

Cited by 38 publications

References 12 publications

The pinocchio algorithm: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field

The pinocchio algorithm: pinpointing orbit-crossing collapsed hierarchical objects in a linear density field

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

On the Cosmological Mass Function

Contact Info

Product

Resources

About