1. Search for ~1017g Primordial Black Holes with Space-based Gravitational Wave Interferometers
Asantha Cooray (Caltech)
Based on Seto & Cooray, PRL,
astro-ph/
IDM 2004, Edinburgh

2. Constraints on PBH dark matter
Current constraints
on PBH abundance
Lensing,
Dymanical,
Other
constraints
M<1015g: gamma ray background
(Hawking radiation)
M>1026g: lensing, Globular clusters, etc
Between 1016g-1026g
Too small for observable astrophysical effects!!
Local halo density upto Msunpc-2
Ω～0.3
∝Ωm1/2
gamma-ray
Background
Page-Hawking bound
Mean Density < 2x104 PBH pc-3
Carr et al. 1994
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)
No Observational Limits

3. 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?

4. Space Interferometers (Gravitational-Wave Detectors)
Large-area gravitational
detectors in space
First opportunity:
LISA (Laser Interferometer
space antenna, ~2012)

5. Space Interferometers (Gravitational-Wave Detectors)
Typical gravitational-wave
amplitude (say binary Neutron
star 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

6. Fly-by PBH pulse R t=0 Acceleration of the test mass towards the PBH t
M●: PBH mass
R: distance of the closest approach
V: velocity of PBH
Test mass of interferometer R M●
PBH
t=0 V
Acceleration of the test mass
towards the PBH
Amplitude: G M● /R2
Acceleration of the test mass towards the PBH
Time scale: R/V t

7. Perturbation and detector’s signal
Detector can measure the difference of two arm-lengths: δL1- δL2
Direct deformation
R (closest approach) < L (arm-length) L1 L2
PBH R
Tidal deformation
R > L
L1~L2~L L1 L2
PBH R
Tidal-Suppression factor

8. 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)
Optical-path noise
(finite path-length)
Proof-mass noise
(Quantum/thermal noise
in detectors etc) f
Detector-noise
curve
Hereafter we use this expression

9. Observation of the fly-by pulse
The maximum distance Rmax for given detection threshold (e.g. SNR=5)
Typical event frequency [1/time scale]
Event rate p
velocity of PBHs relative to the Earth estimated from Galaxy rotation curve p
Or, typically, ~5 hours
From Yr specifications: < 1 event in 10 years

10. Things to Note
The combination (ap/L) determines the detector sensitivity to gravitational waves at the low frequency end
Prospects for PBH search can be easily compared for various upcoming 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 h
∝ap/L f

11. 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 have 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)!!!
Seto et al. 2001
GREAT-low
GREAT-intermediate
Cornish et al. 2002

12. Local halo PBH density detectable with various detectors in 10yrs
Transition at L=R
10-4Hz
10-5Hz
Current constraints
10-6Hz
10-7Hz
Characteristic frequency
Relative to LISA (2000 parameters): arm length/proof-mass noise/ # of detectors
Event-rate > 100 yr-1

13. 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 (magnitude 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)

14. Issues -continued- 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?
(distance-mass or distance-size
degeneracy exists for all gravitational
detections. e.g., lensing) t t

15. Summary
Generally, it is difficult to verify PBH dark matter with 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 final specifications).
Future missions have adequate sensitivity (For BBO, proof-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).