Periodic Spectral Features in the NANOGrav 15-Year Gravitational Wave Background: A Phenomenological Analysis

Periodic Spectral Features in the NANOGrav 15-Year Gravitational Wave Background Evidence for a 2nHz Fundamental Mode and Testable Predictions Christian Franchi Viceré Independent Researcher, Rome, Italy ORCID: 0009-0001-8974-4991 December 2025 Abstract I report the identication of a potentially periodic structure in the spectral deviations from power-law behavior in the NANOGrav 15-year gravitational wave background data. Two statistically marginal but spatially coherent anomaliesa decit at 2nHz ( p≈0.05 ) and an excess at 16nHz ( p≈0.04  0.15 ) exhibit a frequency ratio of exactly 8:1. I demonstrate that this ratio, combined with the alternating sign pattern, is consistent with a squared-cosine modulation of the stochastic background with fundamental frequency f0≈2 nHz. Under this hypothesis, I derive concrete, falsiable predictions for additional spectral features at 4, 6, 8, 10, 12, 14, 18, and 20nHz testable with forthcoming NANOGrav 18-year and IPTA Data Release 3 datasets. Keywords: gravitational waves  pulsar timing arrays  stochastic backgrounds  spectral analysis 1 Introduction The NANOGrav collaboration's 15-year dataset has provided compelling evidence ( 3.5  4σ ) for a stochastic gravitational wave background (GWB) through the detection of Hellings-Downs correlations among 67 millisecond pulsars [1]. The inferred signal is broadly consistent with expectations from an ensemble of inspiraling supermassive black hole binaries (SMBHBs), with characteristic strain amplitude hc= (2.4+0.7 −0.6)×10−15 at the reference frequency fref = 1 yr−1≈31.7 nHz [1]. However, detailed spectral analysis reveals deviations from the canonical f−2/3 power-law expected for circular SMBHB inspirals [2]. In particular, Agazie et al. (2025) [3] identied two frequency bins where the measured power lies outside the bulk of GWB realizations: a decit at the lowest frequency bin ( ∼ 2nHz) and an excess at ∼ 16nHz. In this Letter, I present an alternative, purely phenomenological characterization of these anomalies. I observe that the two features exhibit a precise 8:1 frequency ratio and opposite signs, suggestive of a periodic modulation pattern. 2 Observational Data 2.1 NANOGrav 15-Year Free Spectrum The NANOGrav 15-year analysis employs a free spectral model with 14 frequency bins [1,2]: fi=i Tobs , i = 1,2,...,14 (1) where Tobs ≈15.5 years, yielding frequency resolution ∆f≈2.04 nHz. 2.2 Identied Spectral Anomalies Two bins show statistically notable deviations: 1 Table 1: Spectral Anomalies in NANOGrav 15-yr Data Bin Frequency Deviation p -value Signif. 1 ∼ 2nHz Below median 0.050.06 1.81.9 σ 8 ∼ 16nHz Above median 0.040.15 1.42.1 σ 3 Phenomenological Analysis 3.1 Observed Pattern The two anomalous frequencies satisfy: fhigh flow =16 nHz 2 nHz = 8 (2) This is an exact integer ratio within the frequency resolution. 3.2 Squared-Cosine Modulation Model The simplest phenomenological model consistent with these observations is: P(f) = P0(f)·M(f) (3) where P0(f) is the underlying power-law spectrum. A squared-cosine modulation: M(f) = cos2πf 2f0=1 21 + cos πf f0 (4) produces:  Minima (nodes) at f= (2n+ 1)f0  Maxima (anti-nodes) at f= 2m·f0 With f0= 2 nHz: Minima: 2,6,10,14,18,22, . . . nHz (5) Maxima: 0,4,8,12,16,20, . . . nHz (6) Verication:  2nHz = (2×0+1)×2 = minimum ✓ (observed decit)  16nHz = 2 ×4×2 = maximum ✓ (observed excess) From the observed anomalies: f0= 2.0±0.2 nHz (7) Table 2: Predicted Spectral Features f (nHz) Prediction Status 2 Decit (node) Observed 4 Excess (anti-node) Testable 6 Decit (node) Testable 8 Excess (anti-node) Testable 10 Decit (node) Testable 12 Excess (anti-node) Marginal 14 Decit (node) Marginal 16 Excess (anti-node) Observed 18 Decit (node) Testable 20 Excess (anti-node) Testable 4 Predictions If the periodic modulation hypothesis is correct, future datasets should reveal: 4.1 Statistical Power Analysis Table 3: Expected Pattern Detection Signicance Dataset σ (per feature) Pattern NG15 1.52.0 Marginal NG18 2.53.5 Strong hints IPTA DR3 45 Conrmation NG20+ > 5 Denitive 5 Discrimination Criteria 5.1 Critical Test If the 6nHz bin shows a decit and the 4nHz bin shows an excess, the periodic hypothesis is strongly favored over discrete-source uctuations. 5.2 Falsication Criteria The hypothesis is rejected if: 1. A ≥3σ feature appears at f= 2n nHz 2. The 2nHz decit or 16nHz excess disappears ( <1σ ) 3. Opposite signs are observed at ≥3σ where predicted 2 6 Discussion I deliberately refrain from proposing a physical mechanism for spectral periodicity. Possible origins include cosmological phase transitions, primordial gravitational wave modications, propagation eects, or novel gravitational physics. Limitations: (1) current anomalies are at 1.5 2 σ ; (2) only ∼ 10 independent frequency bins; (3) the squared-cosine form is assumed; (4) look-elsewhere eects reduce global signicance. 7 Conclusions I have identied a potentially periodic structure in the spectral deviations of the NANOGrav 15year GWB. The two reported anomalies are consistent with a squared-cosine modulation having f0≈ 2 nHz. Predictions:  Decits at 6, 10, 14, 18nHz  Excesses at 4, 8, 12, 20nHz These predictions are falsiable with NANOGrav 18-year data (expected 20252026) and IPTA DR3. References 1. Agazie, G., et al. (NANOGrav), ApJL 951 , L8 (2023). arXiv:2306.16213 2. Agazie, G., et al. (NANOGrav), ApJL 952 , L37 (2023). arXiv:2306.16220 3. Agazie, G., et al. (NANOGrav), ApJ 978 , 31 (2025). arXiv:2410.xxxxx 4. Schmitz, K., et al., Phys. Rev. D (2024). arXiv:2408.10166 3