### Abstract

We explore the dependence of the subhalo mass function on the spectral index n of the linear matter power spectrum using scale-free Einstein-de Sitter simulations with n = -1 and -2.5. We carefully consider finite volume effects that may call into question previous simulations of n < -2 power spectra. Subhaloes are found using a 6D friends-of-friends algorithm in all haloes originating from high-σ peaks. For n = -1, we find that the cumulative subhalo mass function is independent of the parameters used in the subhalo finding algorithm and is consistent with the subhalo mass function found in Λ cold dark matter (ΛCDM) simulations. In particular, the subhalo mass function is well fit by a power-law with an index of α = -0.9, that is the mass function has roughly equal mass in subhaloes per logarithmic interval in subhalo mass. Conversely, for n = -2.5, the algorithm parameters affect the subhalo mass function since subhaloes are more triaxial with less well-defined boundaries. We find that the index α is generally larger with α ≳ -0.75. We infer that although the subhalo mass function appears to be independent of n so long as n ≳ -2, it begins to flatten as n → -3. Thus, the common practice of using α ≈ -1.0 may greatly overestimate the number of subhaloes at the smallest scales in the CDM hierarchy.

Original language | English (US) |
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Pages (from-to) | 1950-1962 |

Number of pages | 13 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 395 |

Issue number | 4 |

DOIs | |

State | Published - Jun 1 2009 |

### Keywords

- Dark matter
- Galaxies: haloes
- Methods: N-body simulations
- Methods: numerical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Monthly Notices of the Royal Astronomical Society*,

*395*(4), 1950-1962. https://doi.org/10.1111/j.1365-2966.2009.14707.x