Accretion wake of recoiled black holes Roya Mohayaee CNRS, Institut d’Astrophysique de Paris Jacques Colin Observatoire de la Côte d’Azur, Nice Joe Silk University of Oxford astro-ph/ J-P Lasota conference, Wroclaw 2007

Galaxy (black hole) mergers BHs at the centre of many galaxies Galaxy mergers BH mergers Emission of gravitational waves formation of a new central BH HST : colliding galaxies in Canis Major NGC 2207 –IC 2163

Black hole & dark matter Adiabatic accretion: f final (E final,L final ) = f initial (E initial,L initial ) Initially :  initial ~ r - 

Black hole & dark matter (Young 1980, Gondolo & Silk 1999) Without BH :  initial ~ r -  With BH :  final ~ r -(9-2  )/(4-  )

Absolute luminosity (L) of BH in  -rays  +   L = luminosity factor x ∫  2 dV  /s luminosity factor = [ N  /m  2 ] c 4 /cm 3 /s/Gev 2 For M31: Fornasa et al 2007

Galaxy (black hole) mergers BHs at the centre of many galaxies Galaxy mergers BH mergers Emission of gravitational waves If isotropic formation of a new central BH HST : colliding galaxies in Canis Major NGC 2207 –IC 2163

Galaxy (black hole) mergers BHs at the centre of many galaxies Galaxy mergers BH mergers Emission of gravitational waves Ejection of the BH From the galaxy If isotropicIf anisotropic formation of a new central BH HST : colliding galaxies in Canis Major NGC 2207 –IC 2163

Ejection of a black hole during galaxies mergers

Spin=zero X=0.38

Ejection of a black hole during galaxies mergers spin ≠ 0 recoil velocity 4000 km/s Campanelli et al 2007

Orbit of an ejected BH Virial radius V~0 low  high v high 

Density profile of the accretion wake Cold medium >Bondi-Hoyle accretion (1944) Two-body problem +mass conservation V   r  (q) dq  (x) dx=  (q) dq

Density profile of the accretion wake  Analytic solution for stationary BHs :  (r)~ 1/√r hot medium (e.g. Maxwellian velocity distribution) > Danby & Camm (1957) V Jean’s theorem numerical solution for density

Wake density : radius of influence

Wake density : hot versus cold medium  Hot environment

Wake density : hot versus cold medium   Hot environmentCold environment

Constant density contours : large 

Constant density contours : reducing 

Wake density contours Wake density contours, small 

Highest density at the apapsis passage Virial radius V~0 low  high v high 

Time to reach the apapsis Initial velocity of BH / escape velocity

Absolute luminosity of a recoiled BH in  -rays L(M,z) = [ N  /m  2 ] ∫  2 dV  /s L= (1+z) 4 (M/M o ) R 2 cutoff  /s L BH / L host galaxy

Diffused  -ray background

BH Mass function Press & Schechter (1974) Density peaks in initially random gaussian field collapse to form ‘‘galaxies’’ Number density of galaxies of mass M at redsift z N(M,z)

Diffused  -ray background  =H 0 ∫∫  t(M,z) L(M,z) N(M,z) dM dr(z) Time the BH spends at apapsis (1+z) 4 (M/Mo) R 2 cutofff  /s Press-Schechter mass function

Time spent at apapsis  =H 0 ∫∫  t(M,z) L(M,z) N(M,z) dM dr(z)

 >  cm -2 s -1 sr -1 Future Prospects: Confronting the observations

HESS, VERITAS MAGIC GLAST EGRET  cm -2 s -1 sr -1  >  cm -2 s -1 sr -1