# A high precision semi-analytic mass function

## Abstract

In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the ΛCDM paradigm, we find that our MF is in agreement at the 3% level to Klypin's Bolshoi simulation, in the mass range M {sub vir} = 5 × 10{sup 9} h {sup −1} M {sub ⊙}–−5 × 10{sup 14} h {sup −1} M {sub ⊙} and redshift range 0 ∼< z ∼< 10. For z = 0 we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3% in the mass range 10{sup 12}–10{sup 16} h {sup −1} M {sub ⊙}. Moreover, we discuss our MF validity for different cosmologies.

- Authors:

- Dipartimento di Fisica e Astronomia, University of Catania, Viale Andrea Doria 6, I-95125 Catania (Italy)
- Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL (United Kingdom)
- Instituto de Física Teorica, Universidade Estadual de São Paulo (IFT-UNESP), Rua Dr. Bento Teobaldo Ferraz 271, Bloco 2—Barra Funda, 01140-070 São Paulo, SP Brazil (Brazil)

- Publication Date:

- OSTI Identifier:
- 22679974

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; ANALYTIC FUNCTIONS; ANGULAR MOMENTUM; COMPARATIVE EVALUATIONS; COSMOLOGICAL CONSTANT; COSMOLOGY; DIFFUSION BARRIERS; FUNCTIONS; INTERACTIONS; MASS; RED SHIFT; SIMULATION

### Citation Formats

```
Del Popolo, Antonino, Pace, Francesco, and Le Delliou, Morgan, E-mail: adelpopolo@oact.inaf.it, E-mail: francesco.pace@manchester.ac.uk, E-mail: delliou@ift.unesp.br.
```*A high precision semi-analytic mass function*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/032.

```
Del Popolo, Antonino, Pace, Francesco, & Le Delliou, Morgan, E-mail: adelpopolo@oact.inaf.it, E-mail: francesco.pace@manchester.ac.uk, E-mail: delliou@ift.unesp.br.
```*A high precision semi-analytic mass function*. United States. doi:10.1088/1475-7516/2017/03/032.

```
Del Popolo, Antonino, Pace, Francesco, and Le Delliou, Morgan, E-mail: adelpopolo@oact.inaf.it, E-mail: francesco.pace@manchester.ac.uk, E-mail: delliou@ift.unesp.br. Wed .
"A high precision semi-analytic mass function". United States.
doi:10.1088/1475-7516/2017/03/032.
```

```
@article{osti_22679974,
```

title = {A high precision semi-analytic mass function},

author = {Del Popolo, Antonino and Pace, Francesco and Le Delliou, Morgan, E-mail: adelpopolo@oact.inaf.it, E-mail: francesco.pace@manchester.ac.uk, E-mail: delliou@ift.unesp.br},

abstractNote = {In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the ΛCDM paradigm, we find that our MF is in agreement at the 3% level to Klypin's Bolshoi simulation, in the mass range M {sub vir} = 5 × 10{sup 9} h {sup −1} M {sub ⊙}–−5 × 10{sup 14} h {sup −1} M {sub ⊙} and redshift range 0 ∼< z ∼< 10. For z = 0 we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3% in the mass range 10{sup 12}–10{sup 16} h {sup −1} M {sub ⊙}. Moreover, we discuss our MF validity for different cosmologies.},

doi = {10.1088/1475-7516/2017/03/032},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}