t.n. ukwatta et al "fermi sensitivity to pbh bursts" mg12 paris july 12 - 18 2009...
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T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
SENSITIVITY OF THE FERMI DETECTORS TO GAMMA-RAY BURSTS FROM EVAPORATING
PRIMORDIAL BLACK HOLES (PBHs)
T. N. Ukwatta, Jane H. MacGibbon, W. C. Parke, K. S. Dhuga, A. Eskandarian, N. Gehrels, L. Maximon, D. C. Morris and Stephen Rhodes
JANE H MACGIBBONUNIVERSITY OF NORTH FLORIDA
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
BLACK HOLES IN THE UNIVERSE
GALACTIC CENTERS: Supermassive BHs
M ~ 1038 – 1043 g rs ~ 10 -3 - 103 AU
INTERMEDIATE MASS BLACK HOLES?:
M ~ 1037 g rs ~ 103 km
STELLAR COLLAPSE:
M ~ 1034 – 1035 g rs ~ 10 - 102 km
PRIMORDIAL BLACK HOLES?:
M ~ 10 -5 – 1043 g rs ~ 10 -33 cm - 103 AU
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PRIMORDIAL BLACK HOLES
FORMATION MECHANISMS
Collapse of Overdense Regions
- Primordial Density Inhomogeneities
- Inflation, Soft Equation of State, Cosmological Phase Transitions
Colliding Bubbles of Broken Symmetry
Oscillating Cosmic Strings
Collapse of Domain Walls
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PBH FORMATION
BH mass up to ~ cosmic horizon mass at formation
If form from Scale-Invariant Density Perturbations
1523
( ) 10 g10 sH
tM t
2* *2 /i PBH crit
i
dnM M M
dM
1, radiation era
2
PBH LIMITS
Constraints on β = fraction of regions of mass M which collapse
Graph: Carr (2005)
1PBH R z
PBH LIMITS
Constraints on ε = fractional overdensity of formation regions
Graph: Carr (2005)
2
2( ) ~ ( )exp
2 ( )M M
M
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
BLACK HOLE THERMODYNAMICS
HAWKING TEMPERATURE:
Solar Mass BH TBH ~ 10 -7 K MBH ~ 10 25 g TBH ~ 3 K CMB
HAWKING RADIATION FLUX:
3
131.06 GeV
8 10BH
BHBH
MckT
GM g
12
2
,
exp 1 2 / 2
sS snl
n l
d N E n e
dt dE c
HAWKING RADIATION
Sources: Page, Elster, Simkins
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
TOTAL BLACK HOLE EMISSION
MASS LOSS RATE:
BLACK HOLE LIFETIME:
Mass of PBH whose lifetime equals age of Universe (MacGibbon, Carr & Page 2008):
gm 1004.000.5 14M
s x1024.6 1327- iievap MfM
225 15 x 10 / g g sBHBH BH
dMM f M
dt
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
STANDARD PICTURE
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:
BH directly emits quarks and gluons (not direct pions) which shower and hadronize into astrophysically stable γ , ν, p, pbar, e-, e+
BH EMISSION SPECTRA
Source: MacGibbon and Webber (1990)
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
BH EMISSION SPECTRA
Photosphere/Chromosphere Models (due to interactions between emitted particles)
eg Heckler, Cline and Hong, Kapusta and Daghigh, Belyanin et al, Bugaev et al
MacGibbon, Carr and Page 2008:
None of the photosphere/chromosphere models work because they neglect the requirement that the emitted particles must be in causal contact to interact and neglect LPM effects in any multiple scatterings; Also no quark-gluon plasma when TBH ~ ΛQCD
BH EMISSION SPECTRA
Source: MacGibbon and Webber (1990)
Astrophysical Spectra from Uniformly Distributed PBHs with dn/dMi α Mi
-2.5
Source: MacGibbon and Carr (1991)
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
ASTROPHYSICAL SPECTRA
GAMMA RAY EXTRAGALACTIC BACKGROUND (Carr & MacGibbon 1998):
IF PBHS CLUSTER IN GALACTIC HALO:
Local density enhancement
Galactic Halo Gamma Ray Background (Wright 1996)
Antiprotons, Positrons
Antimatter interactions, Microlensing
9 25.1 1.3 x10PBH h
125
local 1.010x5
hh
ANTIPROTONS
Barrau et al (2002)
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
ASTROPHYSICAL SPECTRA
CAN BURSTS FROM INDIVIDUAL BLACK HOLES AT THE END OF THEIR LIFE BE DETECTED?
Greater detection probability if number density of PBHs is locally enhanced
WHAT WOULD PBH BURST SIGNAL LOOK LIKE?
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PBH Bursts
PBHs Expiring Today:
(independent of formation spectrum)
Number Expiring:
Remaining lifetime for given TBH:
-1-3local
7 yr pc 10 N
2*, BH BH
BH
dnM M M
dM
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PBH as Seen by Ideal Detector
Photon Flux from BH:
Photon flux per unit area reaching Earth from
BH at distance d:
If detector of effective area Aeff requires X
photons over time t to register burst, need
i.e. BH must be closer thanBH effF A t X1/20.8 1/22
2
2.6 10 pc
TeV m 1 mineffBH
AT td
X
1.629 11.4 10 s
TeVBH BH
dN T
dt
2
/
4BH
BH
dN dtF
d
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PBH as Seen by Ideal Detector
What TBH maximizes chance of detection?
Take maximum t to be remaining BH lifetime
τevap. Then BH will be detected by ideal detector
if it is closer than distance d:
Detectability is maximized for lowest TBH BH visible above background and/or by using longest detector exposure time
1/20.7
2
0.03 pc
TeV meffBH
ATd
X
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
PBH as Seen by Ideal Detector
For detector of angular resolution Ω to resolve
BH above background Fγ :
Take EGRET background:
Then BH will be resolved above background by
ideal detector if it is closer than distance d:
BH eff effF A F A
2.46 2 1 1 11.0 x 10 cm GeV s sr
1 GeV
dF E
dE
0.81/2 0.7
0.04 pcsr 1 GeV TeV
BHTEd
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
Comparison of Detectors
To detect, BH must be closer than:
Scanned volume where ωA is detector
acceptance angle (field of view). To resolve above background,
BH must be closer than:
Number that may be Expiring Today:
Air Shower Detectors: large Aeff but small ωA , large Ω,
background-limited
Fermi: smaller Aeff ~ 0.8 m2 but large ωA , small Ω ~ 1°, good
time resolution, lower energy threshold, background-free
3
sr 3A
BH
dV
-1-3local
7 yr pc 10 N
0.81/2 0.7
0.04 pcsr 1 GeV TeV
BHTEd
1/20.7
2
0.03 pc
TeV meffBH
ATd
X
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
FERMI Gamma-Ray Space Telescope
• launched June 2008
• detectors:
Gamma-ray Burst Monitor (GBM)
Large Area Telescope (LAT)
PBH Bursts
Source: MacGibbon and Webber (1990)
Fermi LAT Energy Range: 20 MeV – 300 GeV
T.N. Ukwatta et al "Fermi Sensitivity to PBH Bursts" MG12 Paris July 12 - 18 2009
Detecting BH Bursts with LAT
Spectral Lag Method:
• Compare light curve in two energy bands
• Does not need many counts because not reconstructing full spectrum
• BH burst will show positive to negative evolution
with increasing energy (TBH increases with time as
BH loses mass and )
0.513 10 GeV
GeVBHT
E