THE SEARCH FOR PRIMORDIAL BLACK HOLES - INDICO-FNAL (Indico)
THE SEARCH FOR PRIMORDIAL BLACK HOLES JANE H MACGIBBON UNIVERSITY OF NORTH FLORIDA Cosmic Frontier Workshop SLAC March 6 - 8 2013
COLLABORATORS T. N. Ukwatta (MSU), D. Stump (MSU), J. T. Linnemann (MSU), K. Tollefson (MSU), E. Hawkes (MSU), U. Abeysekara (MSU), G. Sinnis (LANL), W. C. Parke (GWU), K. S. Dhuga (GWU), A. Eskandarian (GWU), N. Gehrels (NASA GSFC), L. Maximon (UVI), D. C. Morris (GWU/NASA GSFC), B.J. Carr (QMW), D.N. Page (UAlberta) Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
SIR ISAAC NEWTON Gravity FG GMm r2 Escape Velocity 2GM vG r ALBERT EINSTEIN General Theory of Relativity G g 8 G 4 T c Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
BLACK HOLES IN 4D SPACE-TIME Schwarzschild Metric in General Relativity where Extensions: Kerr Metric for rotating black hole Reissner-Nordström Metric for charged black hole Kerr-Newman Metric for charged rotating black hole 2GM BH , Black Hole Mass M BH rs 2 c M BH 1 So Density inside Black Hole 3 rs M BH 2 Schwarzschild Radius Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
BLACK HOLES IN THE UNIVERSE SUPERMASSIVE BLACK HOLES Galactic Centers of most spiral and elliptical galaxies and all AGN MBH 1038 – 1043 g 105 – 1010 solar masses rs 10 -3 - 103 AU Our Galaxy M87
BLACK HOLES IN THE UNIVERSE INTERMEDIATE MASS BLACK HOLES? Possibly formed in Star Clusters (Young Starburst Clusters and Old Globular Clusters) MBH 1037 g rs 103 km M82 Xray Starburst Cluster
BLACK HOLES IN THE UNIVERSE STELLAR MASS BLACK HOLES Stellar collapse supernova of stars greater than 20 solar masses (detect by X-rays or Gammarays from accretion disk in binary star system) MBH 1034 – 1035 g rs 10 - 102 km CYGNUS X-1
BLACK HOLES IN THE UNIVERSE PRIMORDIAL BLACK HOLES (PBHs)? Black Holes Formed in the Early Universe MBH 10 -5 – 1043 g rs 10 -33 cm - 103 AU Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
PBH FORMATION MECHANISMS Collapse of Overdense Regions - Primordial Density Inhomogeneities - many Inflation models (eg blue, peaked or ‘running index’ spectrum) - Epoch of Low Pressure (soft equation of state) - Cosmological Phase Transitions Colliding Bubbles of Broken Symmetry Oscillating Cosmic Strings Collapse of Domain Walls Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
PBH FORMATION PBH mass cosmic horizon (or Hubble) mass at time of formation (or smaller) t 15 M H (t ) 10 23 g 10 s Most formation scenarios give narrow PBH spectrum Scale-Invariant Density Perturbations would give extensive PBH spectrum dn 1 2 , radiation era 2 M i / M * M * PBH crit 2 dM i Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
STEPHEN HAWKING Gravitational Temperature TBH 1 M BH Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
BLACK HOLE THERMODYNAMICS HAWKING TEMPERATURE: kTBH M BH c3 1.06 13 GeV 8 GM BH 10 g Solar Mass BH TBH 10 -7 K MBH 10 25 g TBH 3 K CMB HAWKING RADIATION FLUX: d NS snl dt dE n,l 2 2 2s E n e 1 exp / 2 c 1 Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
BLACK HOLE THERMODYNAMICS ABSORPTION PROBABILITY Geometric Optics Limit s M BH , E snl n ,l 27G 2 M BH 2 E 2 2 6 c 4 4 4 16G M BH E , M , E 64G M BH E s 0 M BH , E s 1 BH 4 12 2 6 3 c c 6 6 6 2 2 2 2G M BH E M , E 256G M BH E , s 2 BH s 1/2 M BH , E 6 18 2 6 45 c c 2 2 2 Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
DIRECT HAWKING RADIATION Source: Page, Elster, Simkins
DIRECT HAWKING RADIATION Flux of Directly Emitted Species peaks at: Spin-0 Es 0 2.81TBH Spin-1/2 Es 1/2 4.02TBH Spin-1 Es 1 5.77TBH Flux integrated over E, per degree of freedom: dN/dt α TBH α 1/MBH Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
STANDARD PICTURE (MacGibbon-Webber) BH should directly evaporate those particles which appear non-composite compared to wavelength of the radiated energy (or equivalently BH size) at given TBH As TBH increases: BH directly emits photons gravitons neutrinoes electrons muons pions Once TBH ΛQCD: quarks and gluons, not direct pions) which shower and hadronize into astrophysically stable γ , ν, p, pbar, e-, e Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
HAWKING RADIATION Source: MacGibbon and Webber (1990)
HAWKING RADIATION TBH 0.3 – 100 GeV Total Instantaneous flux 1.6 0.1 N pp 23 T 2.1( 0.4) 10 GeV T Ne 2.0( 0.6) 10 GeV sec 1 sec 1 T Ee 2.9( 0.5) 10 1 GeV 1.6 0.1 T N 2.2( 0.7) 1024 GeV sec 1 1.6 0.1 N 24 T 5.6( 1.7) 10 GeV 0.8 0.1 T E pp 5.2( 0.5) 10 1 GeV 1.6 0.1 24 Average Energy sec 1 T E 3.4( 0.5) 10 1 GeV GeV 0.5 0.1 0.5 0.1 T E 2.4( 0.5) 10 GeV 1 GeV GeV 0.5 0.1 GeV Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
PBH CONSEQUENCES Dark Matter - MBH 10 15 g PBHs are CDM candidates - should cluster in galactic haloes - may enhance clustering of other Dark Matter eg WIMPs (Ultra Compact Massive Halos) - do expired PBHs leave a Planck mass relic? Large PBHs - may influence large scale structure development, seed SMBHs, cosmic x-rays from accretion disks Radiation - direct limits from extragalactic γ background and galactic γ, e , e-, p-bar backgrounds - burst searches - limits on 10 9 – 1043 g PBHs from PNS, CMB anisotrophies - may contribute to entropy, baryogenesis, reionization of Universe in earlier epochs; annihilation lines Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
MOTIVATION FOR PBH SEARCHES Observation of PBHs - Proof of amalgamation of classical gravity and thermodynamics (classical as well as quantum); insight into quantum gravity - Direct window on particle physics at higher energies than can ever be achieved by accelerators on Earth (including other DM candidates) - Information on conditions in the Early Universe Non-observation of PBHs - Information on conditions in the Early Universe - Constrain amplitude and spectral index of initial density perturbations, reheating, etc Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
Astrophysical Spectra from Uniformly Distributed PBHs with dn/dMi α Mi-2.5 Source: MacGibbon and Carr (1991)
ASTROPHYSICAL SPECTRA GAMMA RAY EXTRAGALACTIC BACKGROUND (Carr & MacGibbon 1998): PBH 5.1 1.3 x10 9 h 2 IF PBHS CLUSTER IN GALACTIC HALO: 1 5 2 h Local density enhancement local 5x10 h 0.1 Galactic Halo Gamma Ray Background (Wright 1996) Antiprotons, Positrons Antimatter interactions, Microlensing Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
ANTIPROTONS Barrau et al (2002)
PBH LIMITS Constraints on β fraction of regions of mass M which collapse 2 ( M ) ( M ) exp 2 PBH R 1 z 2 ( M ) where ε fractional overdensity of formation regions Carr et al (2010)
PBH BURSTS dM BH 2 25 1 5 x 10 M / g f M g s MASS LOSS RATE: BH BH dt BLACK HOLE LIFETIME: evap 6.24x10 M f M i -27 3 i 1 s where f(Mi) counts total directly emitted species f s 3/2 0.020 f s 0 0.267 f s 1/2 0.147, uncharged f s 1 0.060 f s 2 0.007 f s 1/2 0.142, electric charge e Mass of PBH whose lifetime equals age of Universe (MacGibbon, Carr & Page 2008): M 5.00 0.04 10 gm 14 Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
PBH Bursts dn PBHs Expiring Today: M BH 2 , dM BH M BH M * Number Expiring: N 10 local pc yr 7 -3 -1 where ηlocal is local clustering factor Remaining lifetime for given TBH: Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
PBH Bursts Fermi LAT Energy Range: 20 MeV – 300 GeV Source: MacGibbon and Webber (1990)
Ukwatta et al
Ukwatta et al
PBH Burst Rate Upper Limits
SEARCHING FOR PBH BURSTS working on predicting spectra, sensitivity and analysizing GRB events for Fermi LAT, Milagro and HAWC HAWC ideal for improving PBH search because of large FoV, energy range and high duty cycle Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
CAN A CHROMOSPHERE BE FORMED IN BLACK HOLE DECAYS? Heckler Model A.F.Heckler PRD 55, 480 (1997); A.F.Heckler PRL 78, 3430 (1997) QED/QCD bremsstrahlung and pair-production interactions between Hawking-radiated particles form photosphere/chromosphere Other 4D Photosphere/Chromosphere Models Belyanin et al Bugaev et al D. Cline and Hong Kapusta and Daghigh Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
HECKLER MODEL Number Density at radius r from BH of e- directly Hawking radiated by BH n r 10 4 where k G c 1 0 M BH r 2 Two-body QED bremsstrahlung cross-section in BH center-of-mass frame 8 3 2E brem Plasma mass correction me 2 ln m 'e me m pm 2 Total Number of Scatterings N R rmax R rmin rBH me 2 for e e e e where m pm 2 4 n r N r 1 dr 3 where r n r brem vrel and n r r 2 Eav n0 r QED Photosphere above TBH 45 GeV. Similarly QCD brem 8 s 3 2 E ln 2 mq mq Chromosphere above TBH ΛQCD
IS THE HECKLER MODEL CORRECT? Two-body bremsstrahlung cross-section brem d brem 1 8 3 2 E d 2 ln E0 d me me E Average momentum exchanged is me in centerof-momentum (CM) frame particles must be within 1/ me of each other to interact Average angle between final on-shell electron and outgoing photon in CM frame is φav me / 2E Average energy of final on-shell electron and outgoing photon in CM frame is Ee ω E / 2 Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
IS THE HECKLER MODEL CORRECT? assumes BH is center-of-momentum frame for most pairs of emitted charged particles BUT two particles moving in similar direction will not interact near BH (because their center-of-momentum frame is highly Lorentz-boosted) get ‘Exclusion cone’ around each emitted particle once particle is a distance d from BH the transverse distance to the nearest particle it can interact with is xT d particles must be within 1/me of BH to interact
IS THE HECKLER MODEL CORRECT? For radial emission r n r bremvrel is not correct must be replaced by radial description 1 particles are Hawking emitted near BH so particles do not travelling in from minus , past the BH and each other, then out to plus BUT bremsstrahlung cross-section assumes interacting particles travel in from minus interaction cross-section is decreased Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
IS THE HECKLER MODEL CORRECT? Causality Constraint Two particles must be in casual contact to interact BUT negligible fraction of Hawking emitted particles are in causal contact with each other Time between subsequent Hawking emissions is Δte 200 / Epeak For causal contact within 1 / me of BH require Δte Δtc 1 / γ me where γ Epeak / me Δtc Δte for almost all emitted particles
IS THE HECKLER MODEL CORRECT? Scale for Completion of Interaction Heckler assumed distance required for formation of final on-shell electron and outgoing photon is dform 1 / me in CM frame BUT average angle between final on-shell electron and photon is φav me / 2E so dform E / me2 in CM frame Electron must travel dform E / me2 before it can undergo next on-shell interaction Any multiple interactions of electron within 1 / me of BH are off-shell interactions and so strongly suppressed by LPM effect
QCD CHROMOSPHERE? when TBH ΛQCD the causality constraint (Δte 20 / Epeak ) and LPM suppression in any (rare) multiple scatterings also prevent QCD chromosphere formation for 4D BHs BUT could a QCD chromosphere form when TBH ΛQCD? Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
QCD CHROMOSPHERE WHEN TBH ΛQCD? Hawking emission of particle is damped (lower flux and greater Δt between emissions) near rest mass threshold (eg ΛQCD) low multiplicity per jet near ΛQCD Δt between consecutive Hawking emissions increases around ΛQCD causality constraint is stronger when BH goes from directly emitting π to directly emitting quarks and gluons the initial quarks and gluons are relativistic (not slow)
QCD CHROMOSPHERE WHEN TBH ΛQCD? number of final hadronized states is limited by available energy (E ΛQCD per Hawking emitted particle) qm conservation laws emitted particle produces mainly π ( and only a couple of π) around ΛQCD and soft gluon bremsstrahlung is insignificant (because lowest colourless state from g is π) TBH ΛQCD 4D BH can NOT form quark-gluon plasma (No analogy to RHIC’s 200 GeV per nucleon, gluonsaturated, high baryon/antibaryon asymmetry) Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
OTHER PHOTOSPHERE/ CHROMOSPHERE MODELS Kapusta and Daghigh – assumes plasma thermalized by QED and QCD bremsstrahlung and pair-production of Heckler model Belyanin et al – ‘collisionless’ QED plasma – omits Lorentz factors no self-induced MHD photosphere but strong ambient magnetic field may induce (weak) photosphere Bugaev et al – ‘Stretched Horizon’ Tpl region just outside horizon neglects LPM suppression (and thermalization scales) D. Cline and Hong – Hagedorn-type emission of remaining BH mass into exponentially growing number of states at TBH ΛQCD state occupancy should be determined by available energy E ΛQCD model would require direct coupling of BH mass to Hagedorn states (but TBH increases as 1/MBH 2)
BREMSSTRAHLUNG EFFECTS (Page, Carr and MacGibbon 2008) Inner Bremsstrahlung 2-vertex Bremsstrahlung 3-vertex Bremsstrahlung
INNER BREMSSTRAHLUNG Number flux of inner bremsstrahlung photons radiated by charged particles of mass m and γav 4.20TBH / m emitted by BH with spectrum dN/dt: d 2 Nb 2 dN ln 2 av 1 dtd dt Nearly flat power spectrum up to ω E – m cut-off Total power in inner bremsstrahlung photons radiated by charged particles emitted by BH with power dE/dt: dEb 2 dE ln 2 av 1 dt dt Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
INNER BREMSSTRAHLUNG Total power in inner bremsstrahlung photons radiated by charged particle emitted by BH with power dE/dt: dEb 2 dE ln 2 av 1 dt dt Compare with power in direct photons: dEd dt 4 0.3364 x 10 M BH For MBH 5x1014 g BH, 2 At low 0, d 2 Eb d 2 Ed dtd 8 3 2 M 3 4 1.73 x 10 19 s 1 dtd inner bremsstrahlung photons dominate the directly Hawking emitted photons below 57 MeV Jane H MacGibbon “The Search for Primordial Black Holes” Cosmic Frontier Workshop SLAC March 6 – 8 2013
LET’S GO SEARCH FOR PBHs! And Black Hole Thermodynamics!
BLACK HOLES IN 4D SPACE-TIME Schwarzschild Metric in General Relativity where Extensions: Kerr Metric for rotating black hole . 2 BH s GM c M BH 32 BH 1 s BH M rM Uvv Jane H MacGibbon "The Search for Primordial Black Holes" Cosmic Frontier Workshop SLAC March 6 - 8 2013 . BLACK HOLES IN THE UNIVERSE SUPERMASSIVE BLACK HOLES Galactic .
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