Reciprocity relationships for gravitational-wave interferometers
Search for ~10 17 g Primordial Black Holes with Space-based Gravitational Wave Interferometers
description
Transcript of Search for ~10 17 g Primordial Black Holes with Space-based Gravitational Wave Interferometers
Search for ~1017g Primordial Black Holes with Space-based Gravitational
Wave Interferometers
Asantha Cooray (Caltech)
Based on Seto & Cooray, PRL,
astro-ph/0405216
IDM 2004, Edinburgh
Constraints on PBH dark matter
• M<1015g: gamma ray background
(Hawking radiation)
• M>1026g: lensing, Globular clusters, etc
• Between 1016g-1026g– Too small for observable as
trophysical effects!!
– Local halo density upto 10-2Msunpc-2
Ω~0.3
Lensing, Dymanical,
Otherconstraints
∝Ω
m1/
2
gamma-ray Background
Page-Hawking boundMean Density < 2x104 PBH pc-3
Carr et al. 1994
Current constraints on PBH abundance
If PBHs cluster in Milky-way with a clumping factor of 5x105, the observed Galactic gamma-ray flux is consistent with expectation for evaporating holes below the Hawking mass limit (Cline 1998)
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μ−
No Observational Limits
Search for PBHs with 1016g-1026g
• Difficult to constrain their presence – Small size, no coupling to matter
• Only gravitational interaction is relevant Either direct or indirect, such as femto gravitational lensing of high-z GRBs, but not galactic micro-lensing • For direct detection, gravitational perturbation rate is
very small considering the PBH abundance and flux.– Increase collecting area -> Million-km scale detectors
– Required specification of detectors?
– Role of laser interferometers?
Space Interferometers (Gravitational-Wave Detectors)
First opportunity: LISA (Laser Interferometer space antenna, ~2012)
Large-area gravitational detectors in space
Space Interferometers (Gravitational-Wave Detectors)
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h ≡ΔL
L~ 10−21
Typical gravitational-waveamplitude (say binary Neutronstar at 1 Mpc):
LISA monitors path length variations of two arms to a pico-meter accuracy
(but, not the absolute length of a single arm)L~five million kilometers
Fly-by PBH pulse
• M●: PBH mass
• R: distance of the closest approach
• V: velocity of PBHR
PBHM●
Acc
eler
atio
n of
the
test
mas
s to
war
ds th
e P
BH
t
Time scale: R/V
Amplitude: G M● /R2
Acceleration of the test mass towards the PBH
t=0
Test mass of interferometer
V
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a(t) =GM•R
R2 + (Vt)2[ ]
3 / 2
Perturbation and detector’s signal
• Direct deformation– R (closest approach) < L (arm-length)
• Tidal deformation– R > L
PBH
L1 L2
R
PBHL1 L2
R
L1~L2~L
Tidal-Suppression factor
Detector can measure the difference of two arm-lengths: δL1- δL2
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d2
dt 2δL1 −δL2( ) ~ a(t)
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d2
dt 2δL1 −δL2( ) ~ a(t) ×
L
R
Signal-to-Noise ratio of the pulse• Signal dominates at low freqs.
– Proof-mass noise ap is important
– We assume ap(f)=const for simplicity
( more later)• LISA: ap ~3x10-15m/s2/Hz1/2 down to 10-4Hz
• SNR with matched filtering– R < L
– R > L (relevant for most cases including LISA)
Hereafter we use this expression
f
h
Opt
ical
-pat
h no
ise
(fini
te p
ath-
leng
th)
Proof-mass noise
(Quantum/thermal noise
in detectors etc)
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SNR2 = dfa( f )2
ap2
0
∞
∫
€
SNR2 =3π
32
(GM• )2
VR3ap2
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SNR2 =3π
32
(GM•L)2
VR5ap2
Detector-noise curve
Observation of the fly-by pulse• The maximum distance Rmax for given detection thres
hold (e.g. SNR=5)
• Typical event frequency [1/time scale]
• Event rate
velocity of PBHs relative to the Earth estimated from Galaxy rotation curve
p
p
Or, typically, ~5 hours
From Yr. 2000 specifications: < 1 event in 10 years
Things to Note• The combination (ap/L) determines the detector sensitivity to gr
avitational waves at the low frequency end– Prospects for PBH search can be easily compared for various upcomin
g detectors
• ap=const is a very rough assumption– LISA’s proof mass noise
• ap=3x10-15m2/sec2/Hz1/2 down to ~10-4Hz
• But worse, at lower frequencies
f
h
∝ap/L
Prospects for future missions• We probably cannot detect PBH events
with LISA other than a first constraint, but
• Future missions (GREAT, BBO, DECIGO,…) discussed mainly for a detection of the weak stochastic GW background from inflation:– With ap=const to very low frequency, they ha
ve adequate sensitivity to PBHs.
– However, the proof mass noise must be controlled down to 10-5Hz with intermediate frequency missions such as the Big-Bang Observer (BBO).
– Proposed GREAT-low mission provides the best constraint (or detections)!!!
Cornish et al. 2002
Seto et al. 2001
GREAT-intermediateGREAT-low
Local halo PBH density detectable with various detectors in 10yrs
Current constraints
10-4Hz
10-5Hz
10-6Hz
10-7Hz
Characteristic frequency
Transition at L=R
Event-rate > 100 yr-1
Relative to LISA (2000 parameters): arm length/proof-mass noise/ # of
detectors
Issues• Stochastic GW background at very low frequency
– An obstacle for PBH fly-by search?• GW background form Super Massive Black Hole binaries at f<10-5Hz (m
agnitude is highly unknown)• Sagnac (different data combinations of the interferometer) method might
be an effective way to reduce the GW binary signal
(Tinto et al. 2000)
• Other optimal approaches? (Adams & Bloom 2004: Fourier-space power-spectrum of the data stream)
• Distinguish pulses by PBHs, asteroids, comets– Solar-system objects: dominated by larger sizes/masses
– Optical identification/orbit may be known a priori
• M● (mass), R (distance), V (velocity) degeneracy of PBH events– Only two parameter combinations can be obtained from a
fly-by event • Time scale R/V
• Amplitude M● /R2
– Multiple systems to determine V?
Issues -continued-
t
t
(distance-mass or distance-sizedegeneracy exists for all gravitationaldetections. e.g., lensing)
Summary• Generally, it is difficult to verify PBH dark matter w
ith mass ~1017g. Small size, no interactions. No observational limits, so-far.
• A space laser interferometer might be the only tool to detect them.– LISA may not have enough sensitivity (must wait on fin
al specifications).– Future missions have adequate sensitivity (For BBO, pro
of-mass noise must be controlled adequately at the low frequency end. GREAT low-frequency mission is close to an optimal detector for the PBH search out of all future missions so far).