Individual Nanohertz Sources and Memory

An individual nanohertz source is resolvable when its coherent angular, phase, and spectral structure is distinguishable from the common background and from pulsar noise. A burst with gravitational-wave memory has a different signature: a persistent strain change produces a ramp-like timing residual after the wavefront passes Earth. The NANOGrav 15-year analyses discussed here set source- and sky-dependent limits and examine candidates, but establish neither a compelling individual binary nor a memory event. This is a release-specific assessment with evidence cutoff 2026-08-18.

Helpful background. Earth Terms, Pulsar Terms, and Antenna Response supplies the deterministic response. Common-Spectrum and Correlated-Process Inference defines the background alternative.

Nearly continuous supermassive binaries

For a circular binary evolving slowly over the observing span, define the leading strain scale by

$$h_0 =\frac{2(G\mathcal M_z)^{5/3}(\pi f)^{2/3}}{D_L}, \qquad \mathcal M_z=(1+z)\mathcal M.$$

Here $f$ is the observed gravitational-wave frequency, twice the orbital frequency. This PTA amplitude convention puts $h_+=h_0(1+\cos^2\iota)\cos\Phi$ and $h_\times=2h_0\cos\iota\sin\Phi$, up to the chosen phase and polarization orientation. A convention placing $(1+\cos^2\iota)/2$ in $h_+$ uses an amplitude twice as large. The Earth term is coherent across the array. Each pulsar term has a distance-dependent phase and samples the binary at an earlier epoch; if evolution is appreciable, it can have a different frequency.

A resolvable signal need not have the largest strain at every pulsar. It must improve a coherent array likelihood with the predicted antenna pattern and survive a model containing an unresolved background. A feature dominated by one pulsar or coincident with its binary period is a noise or timing-model warning.

The background and a single source can be confused. A finite background is made from discrete binaries and can be non-Gaussian or anisotropic; a loud member may appear as both excess power and a deterministic candidate. Joint models avoid forcing all power into one category.

Gravitational-wave memory

A merger or other burst can produce a net transverse strain change $\Delta h_{ij}^{\rm TT}$. For an Earth-term wavefront arriving at $t_0$, the fractional frequency shift acquires a step,

$$z_a(t)=B_a\,\Theta(t-t_0),$$

so the timing residual contains a ramp,

$$r_a(t)=B_a(t-t_0)\Theta(t-t_0),$$

up to components absorbed by the timing fit. With the redshift sign fixed on the response page, $B_a=\sum_A F_a^A\Delta h_A$. Its sign can differ between pulsars, so a coherent memory burst does not require every ramp to slope upward. The approximation keeps only the Earth term over the observed span; the delayed pulsar term supplies a second step if the wavefront reaches the corresponding emission event within the data window.

A clock step, ephemeris disturbance, backend change, pulsar glitch, or unmodeled red event can mimic part of this morphology. The coherent tensor sky pattern and common epoch distinguish an Earth-term memory burst. A pulsar-term burst occurs at a different apparent epoch for each pulsar and is usually searched separately.

Timing-model spin parameters absorb slow ramps, especially near dataset boundaries. Sensitivity therefore depends strongly on burst epoch and array baseline.

Current results and competing interpretations

The NANOGrav 15-year continuous-wave analysis found no compelling individual supermassive-black-hole binary after accounting for a common background. Candidate-like features were weakened by including Hellings–Downs correlations or traced largely to one pulsar and astrophysical-prior tension Agazie et al. 2023, §§3–5.

The NANOGrav 15-year memory search likewise reports no significant memory evidence and provides epoch- and sky-dependent upper limits Agazie et al. 2025, §§3–5.

Evidence line	Supported result	Interpretation limit
Coherent searches find no compelling individual binary	Strain limits constrain declared circular-binary models	Eccentric, evolving, or environmentally driven sources need separate models
Background modeling weakens low-frequency candidates	Unresolved common power can mimic a deterministic source	A future loud source may coexist with the background
One high-frequency feature is pulsar dominated	Single-pulsar systematics are a credible explanation	It is not an array-coherent detection
Memory searches are null	Limits constrain common-epoch tensor ramps	Boundary absorption and source orientation shape sensitivity

Forecasts or new geometric statistics published by the cutoff are methods until validated on an accepted data release; they do not supersede these observational results.

Conditions for a resolved claim

A convincing individual source should have:

1. array-coherent evidence over a background-plus-noise model;
2. a stable sky pattern and frequency under ephemeris, pulsar-noise, and Fourier-basis variations;
3. no one-pulsar or one-backend dominance;
4. Earth- and, when claimed, pulsar-term phase treatment with distance uncertainty;
5. calibrated trials over sky, frequency, and source evolution;
6. real-cadence injection recovery and parameter coverage;
7. a plausible but not mandatory host association consistent with distance and mass.

A memory claim replaces periodic phase coherence with a common epoch, tensor angular pattern, ramp sign/amplitude relation, and stability against timing-model and instrumental steps.

Reproduction and review

Pin the public PTA files, timing/noise solutions, ephemeris, background covariance, binary or memory waveform, priors, sky/frequency grid, pulsar-distance treatment, sampler, and evidence estimator. Run noise/background-only false-alarm ensembles and source injections across sky, frequency, eccentricity/evolution or memory epoch. Report detection efficiency rather than only posterior upper limits.

Review after a new PTA/IPTA release, a public candidate with independent confirmation, corrected single-pulsar noise, or a method validated to separate discrete-source and background correlations in real data.

Exercises

1. Strain scaling. At fixed redshifted chirp mass and distance, how does $h_0$ change if frequency doubles?

Solution

Since $h_0\propto f^{2/3}$,

$$\frac{h_0(2f)}{h_0(f)}=2^{2/3}\approx1.59.$$

This assumes a circular slowly evolving source; residence time and population abundance change in the opposite direction for a background calculation.

2. A late memory burst. Why is a memory event arriving very near the end of the dataset difficult to measure?

Solution

Only a short piece of the post-burst ramp is observed, making its slope covariant with timing-model and noise terms. There are also fewer post-event TOAs across pulsars. Injection-calibrated limits therefore worsen near temporal boundaries.

References

• Agazie, Gabriella, et al. “The NANOGrav 15-Year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries.” Astrophysical Journal Letters 951 (2023): L50. Open PDF.
• Agazie, Gabriella, et al. “The NANOGrav 15-Year Data Set: Search for Gravitational-Wave Memory.” arXiv:2502.18599 (2025). Open PDF.

Further reading

• Burke-Spolaor, Sarah, et al. “The Astrophysics of Nanohertz Gravitational Waves.” Astronomy and Astrophysics Review 27 (2019): 5. DOI. Open PDF.
• Mingarelli, Chiara M. F., Bjorn Larsen, Ellis Eisenberg, Qinyuan Zheng, and Forrest Hutchison. “Fingerprints of Individual Supermassive Black Hole Binaries in Pulsar Timing Arrays.” arXiv:2603.05722 (2026). Open PDF.