testing the black hole no-hair theorem at the galactic center · (merritt, kupi, cmw) central black...
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Testing the Black Hole No-Hair Theorem at the Galactic Center
Clifford Will
University of Florida & Institut d’Astrophysique de Paris
Gravasco Seminar, 5 November 2013
Testing the Black Hole No-Hair Theorem at the Galactic Center
Gravasco Seminar, 5 November 2013
Counting hair on SgrA*
Perturbing effects of other stars
Perturbing effects of dark matter
Post-Newtonian effects and N-body
dynamics
Testing the no-hair theorem at the galactic center:
no-hair theorems:
{M, J}; Q = -J2/M
precession of orbit planes
@ 10 mas/yr
e ~ 0.9, a ~ 0.2 mpc (500 Rs)
future IR adaptive optics
telescopes (GRAVITY, Keck)
disturbing effects of other
stars & dark matter
CMW, Astrophys. J. Lett 674, L25 (2008)
Effect of other stars/BH in the central mpc
•10 stars (1Mo) & 11 BH (10Mo)
within 4 mpc
• 100 realizations
• isotropic, mass segregated
• J/M2 = 1
Numerical N-body simulations: D. Merritt, T. Alexander, S. Mikkola, & CMW, PRD 81, 062002 (2010) Analytic orbit perturbation theory: L. Sadeghian & CMW, CQG 28, 225029 (2011)
Dark matter around black holes: The Gondolo-Silk paper
initial DM distribution
let black hole grow
adiabatically
f(E, L) unchanged
E = E(E’, L’), L = L(E’, L’) holding
adiabatic invariants fixed
Newtonian analysis, but with
L cutoff at 4MBH
r ~ ∫f(E’,L’)dE’ L’ dL’
Gondolo & Silk, PRL 83, 1719 (1999)
Dark matter around black holes: A fully relativistic analysis
Schwarzschild limit:
Sadeghian, Ferrer & CMW (PRD 88, 063522, 2013)
Example: the Hernquist profile
• Approximates features of more realistic models such as NFW close to the center
• f(E) is an analytic function • M = 2πr0a3 = 1012 MSUN , a = 20 kpc
Example: the Hernquist profile
S2 no-hair target star
Mass inside 4 mpc ≈ 103 MSUN (1 MSUN)
Future work:
Incorporate more realistic profiles (NFW),
self-gravity
Implement Kerr geometry
o Phase space volume more complex
o Capture criterion more complex
o Will be circulation & non-sphericity even for
f(E,L)
A quadrupole conundrum
D. Merritt, T. Alexander, S. Mikkola, & CMW, PRD 84, 044024 (2011)
A quadrupole conundrum
Lagrange planetary equations:
A quadrupole conundrum
Over one orbit:
Over a pericenter precession timescale:
But
Final result:
Post-Newtonian cross-terms in other contexts?
N-body simulations with central black hole (Merritt, Kupi, CMW)
Central black hole in various galactic potentials (Merritt, Vasiliev)
Hierarchical triples (CMW)
PN Cross terms may be important when integrating over many relativistic precession timescales (CMW, in preparation)
Hierarchical triple (Kozai) systems
When GR pericenter precession dominates:
m3
m2
m1
Testing the Black Hole No-Hair Theorem at the Galactic Center
Gravasco Seminar, 5 November 2013
Counting hair on SgrA*
Perturbing effects of other stars
Perturbing effects of dark matter
Post-Newtonian effects and N-body
dynamics