Search for ~10 17 g Primordial Black Holes with Space-based Gravitational Wave Interferometers

1. 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

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 10-2Msunpc-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. M●: PBH mass R: distance of the closest approach V: velocity of PBH Fly-by PBH pulse 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 h Optical-path noise (finite path-length) Proof-mass noise (Quantum/thermal noise in detectors etc) • 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) f Detector-noise curve Hereafter we use this expression

9. Observation of the fly-by pulse p • The maximum distance Rmax for given detection threshold (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 Or, typically, ~5 hours From Yr. 2000 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 Seto et al. 2001 • 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)!!! 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).