TY - JOUR

T1 - Weak annihilation cusp inside the dark matter spike about a black hole

AU - Shapiro, Stuart L.

AU - Shelton, Jessie

N1 - Funding Information:
It is a pleasure to thank B. Fields for helpful discussions. This paper was supported in part by NSF Grant No.PHY-1300903 and NASA Grant No.NN13AH44G at the University of Illinois at Urbana-Champaign.
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/6/7

Y1 - 2016/6/7

N2 - We reinvestigate the effect of annihilations on the distribution of collisionless dark matter (DM) in a spherical density spike around a massive black hole. We first construct a very simple, pedagogic, analytic model for an isotropic phase space distribution function that accounts for annihilation and reproduces the "weak cusp" found by Vasiliev for DM deep within the spike and away from its boundaries. The DM density in the cusp varies as r-1/2 for s-wave annihilation, where r is the distance from the central black hole, and is not a flat "plateau" profile. We then extend this model by incorporating a loss cone that accounts for the capture of DM particles by the hole. The loss cone is implemented by a boundary condition that removes capture orbits, resulting in an anisotropic distribution function. Finally, we evolve an initial spike distribution function by integrating the Boltzmann equation to show how the weak cusp grows and its density decreases with time. We treat two cases, one for s-wave and the other for p-wave DM annihilation, adopting parameters characteristic of the Milky Way nuclear core and typical WIMP models for DM. The cusp density profile for p-wave annihilation is weaker, varying like ∼r-0.34, but is still not a flat plateau.

AB - We reinvestigate the effect of annihilations on the distribution of collisionless dark matter (DM) in a spherical density spike around a massive black hole. We first construct a very simple, pedagogic, analytic model for an isotropic phase space distribution function that accounts for annihilation and reproduces the "weak cusp" found by Vasiliev for DM deep within the spike and away from its boundaries. The DM density in the cusp varies as r-1/2 for s-wave annihilation, where r is the distance from the central black hole, and is not a flat "plateau" profile. We then extend this model by incorporating a loss cone that accounts for the capture of DM particles by the hole. The loss cone is implemented by a boundary condition that removes capture orbits, resulting in an anisotropic distribution function. Finally, we evolve an initial spike distribution function by integrating the Boltzmann equation to show how the weak cusp grows and its density decreases with time. We treat two cases, one for s-wave and the other for p-wave DM annihilation, adopting parameters characteristic of the Milky Way nuclear core and typical WIMP models for DM. The cusp density profile for p-wave annihilation is weaker, varying like ∼r-0.34, but is still not a flat plateau.

UR - http://www.scopus.com/inward/record.url?scp=84974588979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974588979&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.93.123510

DO - 10.1103/PhysRevD.93.123510

M3 - Article

C2 - 29881789

AN - SCOPUS:84974588979

VL - 93

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 12

M1 - 123510

ER -