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R.D. Viollier University of Cape Town Observational facts: Earliest quasar SDSS J114816.64 +525 150.3 has redshift z = 6.42 corresponding to receding velocity v/c = 0.96. Quasar light was emitted at te = 0.85 Gyr and is observed today at to = 13.7 Gyr after the Big Bang (WMAP-3). Simplest interpretation: Quasar is temporarily (Δt < 30 Myr) powered by isotropic accretion of baryonic matter onto a supermassive black hole of mass M = 3×109 M☼, radiating at the Eddington luminosity gravitational force on protons dominates Fgrav (r ) GM (r )m p r σT - Thomson cross section of the electron 8 T 3 LE (r ) T 4 r 2 c 2 mp proton mass 2 radiational force on electrons dominates Frad M(r) - mass enclosed within r LE(r) - nett luminosity crossing r outwards e2 0.665 1024 cm 2 2 me c local neutrality of plasma implies Fgrav(r) = Frad(r) or Eddington luminosity differential equation dM BH 1 M LE 1 M M BH 1 L 2 L M BH dt M c M tE tE T c 450.5 Myr 4 Gmp M tE 50.1 Myr 1 M L εM = 0.1 is the standard efficiency εL = L/LE = 1 for the Eddington limit Eddington time characteristic time solution M BH (t ) M BH (0) e t M BH (0) 2 t t2 mass doubling time Answer: 1 210 ~ 103 230 ~ 109 t E ln30 2 mass 34 Myr doubling times L t = 30 × 35 Myr = 1.05 Gyr M with t2 ln 2 1 M for the formation of supermassive black holes massive star ~ 25 M⊙ stellar mass BH ~ 3 M⊙ SN explosion accretion of baryonic matter supermassive BH ~ 3×109 M⊙ HOWEVER: Compare this tform > 1.437 • the massive star can only form Gyr to the observed times of te ~ 0.85 Gyr after zreion ~ 11 or treion ~ 0.365 Gyr this scenario does not work! reionization molecular hydrogen initial BH mass should be MBH(0) = 1.4×105 M☼ instead of MBH(0) = 3 M☼ population III stars? allowing super-Eddington accretion with e.g. εL = 2 instead of εL = 1 non-spherical accretion? lowering the efficiency from εM = 0.1 to εM = 0.05 (dark matter has εM = 0!) X X √ P. Minkowski, Phys. Lett. B67 (1977) 421: add 3 right-handed (or sterile) neutrinos invention of the seesaw mechanism renormalizable Lagrangean which generates Dirac and Majorana masses for all neutrinos LMSM LSM ~ MI c N Iiγ N I FαI Lα N I Φ N I N I h.c. 2 LSM: Lagrangean of the Standard Model ~ Φi = εij Φj*: Higgs doublet Lα (α=e,μ,τ): lepton doublet NI (I=1,2,3): sterile neutrino singlet kinetic energy Yukawa terms terms coupling Majorana mass MD = FαI ‹Ф›exp terms MI In comparison with the SM, the νMSM has 18 new parameters: 18 new parameters of νMSM 3 Majorana masses of NI 15 Yukawa couplings in leptonic sector 3 Dirac masses 6 mixing angles 6 CP-violating phases these parameters can be chosen such as to be consistent with the solar, atmospheric, reactor and accelerator neutrino experiments the baryon asymmetry comes out correctly the Majorana masses are below the weak interaction symmetry breaking scale the lowest mass right-handed (or sterile) neutrino has a mass of O(10 keV) and is quasi-stable: it could be the dark matter particle unstable, observable at accelerators M. Shaposhnikov arxiv: 0706.1894v1 [hep-ph] 13.06.2007 quasi-stable dark matter particle, observable through its radioactive decay to fix our ideas, we assume production process: scattering that the lightest sterile of active neutrinos out of neutrino νs has equilibrium Majorana mass • m = 15 mixing: resonant or non-resonant ≡ vacuum L. Wolfenstein (1978) keV/c2 Mixing angle of νs with νe • ϑ = 10-6.5 Lepton asymmetry • L(νe) = (n(νe) – n(͞νe))/n(γ) = 10-2 production process is number densities of νe, ͞νe, γ necessarily linked with decay • n(νe), n(͞νe), n(γ) process! νs’s produced at T ~ 328 (mc2/15 keV)1/3 MeV/K with Ωs= 0.24 through resonant and non-resonant scattering of active neutrinos ~ 22 min after Big Bang, the νs’s are non-relativistic νs’s dominate the expansion of the universe ~ 79 kyr after Big Bang degenerate νs-balls form between 650 Myr and 840 Myr mass contained within the free-streaming length at matter-radiation equality at 79 kyr is resonant production, cold non-resonant production, warm since part of the neutrinos may be ejected, the minimal mass that may collapse is perhaps Mmin ~ 106 M☼ . the maximal mass that a self-gravitating degenerate neutrino ball can support is the Oppenheimer-Volkoff limit Planck mass m-dependent for the formation of supermassive black holes supermassive νs-ball 650 Myr < t < 840 Myr M.C. Richter, G.B. Tupper, R.D. Viollier JCAP 0612 (2006) 015; astro-ph/0611552 attraction of H2-cloud to center of νs-ball massive star M ~ 25 M⊙ stellar mass BH M ~ 3 M⊙ supermassive BH through accretion of νs-ball antihierarchical formation of quasars and active galactic nuclei Bernoulli’s equation for a Bernoulli’s equation is now Here, v(x) fulfils the Lane-Emden steady-state flow • u(r): • vF(r): • φ(r): • rH: flow velocity of infalling degenerate sterile neutrino fluid Fermi velocity gravitational potential radius of the halo the flow is trans-sonic, i.e. equation Total mass enclosed within a radius r = bx is Solutions of the Lane-Emden equation with constant mass M = MC + MH = 2.714 M⊙ mass accretion rate into a sphere, containing a mass MC within a radius rC from the centre is μ = MC /M with universal time scale and shut-off parameter, defined as rC = bxC is now the radius at which the escape velocity is c M.C. Richter, G.B. Tupper, R.D. Viollier JCAP 0612 (2006) 015; astro-ph/0611552 4 main characteristics of the symbiotic scenario: no Eddington limit for νs-ball formation and accretion onto BH matter densities in νs-balls much larger than any form of baryonic matter of the same total mass νs-balls have for m ~15 keV/c2 the same mass range as supermassive BH different escape velocities from the center of the νs-balls may explain antihierarchical formation of quasars