How empty is an empty loss cone?

Amir Weissbein*, Re'em Sari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We consider two-body relaxation in a spherical system with a loss cone. Considering two-dimensional angular momentum space, we focus on 'empty loss cone' systems, where the typical scattering during a dynamical time jd is smaller than the size of the loss cone jlc. As a result, the occupation number within the loss cone is significantly smaller than outside. Classical diffusive treatment of this regime predict exponentially small occupation number deep in the loss cone. We revisit this classical derivation of occupancy distribution of objects in the empty loss cone regime. We emphasize the role of the rare large scatterings and show that the occupancy does not decay exponentially within the loss cone, but it is rather flat, with a typical value ∼[(jd/jlc)]2ln −2(jlc/jmin ) compared to the occupation in circular angular momentum (where jmin is the smallest possible scattering). Implication are that although the loss cone for tidal break of Giants or binaries is typically empty, tidal events that occur significantly inside the loss cone (β ≿ 2) are almost as common as those with β = 1, where β is the ratio between the tidal radius and the periastron. The probability for event with penetration factor >β decreases only as β−1 rather than exponentially. This effect has no influence on events characterized by full loss cone, such as tidal disruption event of ∼1 m☉ main-sequence star.

Original languageAmerican English
Pages (from-to)1760-1768
Number of pages9
JournalMonthly Notices of the Royal Astronomical Society
Issue number2
StatePublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 The Authors


  • Galaxies: kinematics and dynamics
  • Galaxies: nuclei


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