Choralis: Hellings–Downs Curve
Relativity & Gravity arc, page 39 of 193. Back to The Pixelated Physics Universe
Who they are
Choralis conducts a ring of pulsar singers. A gravitational-wave background makes their timing sway together, in one particular pattern.
Choralis is a character of the Relativity & Gravity arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A background of gravitational waves nudges the arrival times of pulses from millisecond pulsars. In general relativity, how strongly two pulsars' timing wobbles agree depends only on their angle on the sky. The curve starts at ½, crosses zero near 49° and 122°, dips to about −0.15 near 82°, and ends at ¼ at 180°. R. W. Hellings and G. S. Downs derived it in 1983; in June 2023 NANOGrav (67 pulsars, 15 years) reported evidence for the background with this correlation.
$$ \begin{gathered} \Gamma(\theta) = \frac{1}{2} - \frac{x}{4} + \frac{3}{2}\,x\ln x, \qquad x = \frac{1-\cos\theta}{2} \\ \Gamma_{\min} \approx -0.15 \text{ near } 82^{\circ}; \quad \Gamma = 0 \text{ near } 49^{\circ},\ 122^{\circ}; \quad \Gamma(180^{\circ}) = \tfrac{1}{4} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\Gamma(\theta)$ | correlation between two distinct pulsars' timing residuals (Γ → ½ as θ → 0) | 1 |
| $\theta$ | angle between the two pulsars on the sky | rad |
| $x$ | (1 − cos θ)/2 | 1 |
Honest caveat: Evidence at about 3–4σ, not yet a 5σ detection, and the source is not settled.
Status: part of this topic is unsolved, unconfirmed or debated. The text above says which part; treat it as an open question, not settled fact.
Sources
- Hellings & Downs (1983) Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, Astrophys. J. 265, L39
- Agazie et al. (NANOGrav) (2023) The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951, L8
Crossovers
Choralis meets Graviton Whisper (Quantum Gravity / Force Carrier). Choralis listens to pulsar timing for a gravitational-wave background. Graviton Whisper reminds her that these are classical waves. Whether they are made of gravitons is a separate question that no detector can yet test.
Choralis meets Kilonova (GW170817 Neutron Star Merger). Kilonova was one loud merger in LIGO and Virgo's band. Choralis hunts a quiet hum at nanohertz frequencies from many sources, perhaps supermassive black-hole binaries. The evidence for that hum is still short of 5σ.
Choralis meets Fermia (Fermi Paradox). Fermia listens to the sky for signals and hears nothing. Choralis listens to pulsars for a gravitational-wave hum and finds evidence, though not yet at 5σ. Patience and statistics decide what counts as a detection.
Wear the lore
Concept keywords: Hellings–Downs Curve, Choralis, Relativity & Gravity, physics lore, Pixelated Physics