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)

€

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)

€

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

€

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

€

d2

dt 2δL1 −δL2( ) ~ a(t)

€

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)

€

SNR2 = dfa( f )2

ap2

0

∞

∫

€

SNR2 =3π

32

(GM• )2

VR3ap2

€

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).