Observational Prospects
Detecting spin memory across the gravitational wave spectrum
Measurement Strategy
The accumulated spin observable is defined as:
$$\Sigma(u_f) = \int_{-\infty}^{u_f} h_{\times,B}(u)\,du$$
After the wave train passes, $\Sigma$ saturates to a permanent non-zero constant.
Matched Filtering SNR
$$\mathrm{SNR}^2 = 4\int_0^\infty \frac{|\tilde{h}_{\rm spin}(f)|^2}{S_n(f)}\,df \propto 4\,|\Delta J|^2 \int_0^{f_{\rm ISCO}} \frac{df}{f^2\,S_n(f)}$$
The $1/f^2$ weighting means spin memory SNR is dominated by the low-frequency noise floor.
Detector Landscape
| Detector | Band | Displacement Memory | Spin Memory |
|---|---|---|---|
| LIGO/Virgo O4 | 10–1000 Hz | Marginal (stacking) | Not accessible |
| Einstein Telescope | 2–10,000 Hz | Detectable (BBH) | Marginal (stacking) |
| LISA | $10^{-4}$–1 Hz | SMBBH & EMRI | Promising (SMBBH) |
| Pulsar Timing Arrays | nHz | Background | Background $\Delta J$ |
Optimal Sources
1. Supermassive BBH mergers: $M\sim 10^8\,M_\odot$, LISA primary target. Spin memory strain $\sim 10^{-16}$ at $D_L = 1\,\text{Gpc}$.
2. Extreme mass-ratio inspirals: $10^5$ orbits, cumulative spin memory builds coherently.
3. Precessing binaries: Spin–orbit coupling enhances B-mode memory.
4. Core-collapse supernovae: Detection would directly measure proto-NS angular momentum.
Open Questions
- Precise post-Newtonian waveform templates for B-mode spin memory signal
- Disentangling spin memory from frame-dragging effects in EMRI signals
- Role of spin memory in the black-hole information paradox (Hawking–Perry–Strominger soft-hair proposal)
- Extension to higher memory orders: sub-subleading soft theorems