• Choralis Hellings–Downs Curve pixel-art physics T-shirt, white tee, front view

IndexRelatività e cosmoTee

Choralis

The Hellings–Downs Curve Physics

\[\Gamma(\theta) = \frac{1}{2} - \frac{x}{4} + \frac{3}{2}\,x\ln x, \qquad x = \frac{1-\cos\theta}{2}\]
$29.99 USD
$29.99 USD
In offerta Esaurito
Size
Color

Size guide S–5XL · inches

Choralis conducts a ring of pulsar singers. A gravitational-wave background makes their timing sway together, in one particular pattern.

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°.

Γ(θ) = ½ − x/4 + (3/2) x ln x, x = (1 − cos θ)/2

  • Γ(θ): correlation between two pulsars' timing residuals (dimensionless)
  • θ: angle between the pulsars on the sky (rad)
  • x: (1 − cos θ)/2 (dimensionless)

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.

Honest caveat: Evidence at about 3–4σ, not yet a 5σ detection, and the source is not settled.

On the shirt

Front: Choralis, the pixel-art character, with the title. Back: the Hellings–Downs formula, what it means, its key points, the NANOGrav 2023 result and both papers. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Per avere un'idea: la taglia M è larga 20 in (50.80 cm), circa 3.143 × 1034 lunghezze di Planck (lP = 1.616255 × 10−35 m). Un metro a nastro fa prima.

Measurements in inches, ±1.5 in tolerance.

ShippingBy destination

Shipping calculated at checkout by destination. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

I conduct a ring of pulsar singers. A background of gravitational waves makes their timing sway together, in one particular pattern.

Millisecond pulsars tick with astonishing regularity. A sea of gravitational waves passing through the galaxy nudges the arrival times of their pulses. In general relativity, how strongly two pulsars' timing wobbles agree depends only on their angle on the sky: Ron Hellings and George Downs worked out the curve in 1983. It starts at ½, crosses zero near 49°, dips to about −0.15 near 82°, crosses zero again near 122°, and ends at ¼ at 180°.

In June 2023 NANOGrav, timing 67 pulsars for 15 years, reported evidence for a background with this correlation. Evidence at about 3 to 4σ, not yet a 5σ detection, and what makes the background is not settled.

Equations

\[\Gamma(\theta) = \frac{1}{2} - \frac{x}{4} + \frac{3}{2}\,x\ln x, \qquad x = \frac{1-\cos\theta}{2}\]
\[\Gamma_{\min} \approx -0.15 \text{ near } 82^{\circ}; \quad \Gamma = 0 \text{ near } 49^{\circ},\ 122^{\circ}; \quad \Gamma(180^{\circ}) = \tfrac{1}{4}\]
SymbolMeaningUnit
\(\Gamma(\theta)\) correlation between two distinct pulsars' timing residuals (Γ → ½ as θ → 0) \(\mathrm{1}\)
\(\theta\) angle between the two pulsars on the sky \(\mathrm{rad}\)
\(x\) (1 − cos θ)/2 \(\mathrm{1}\)

Sources

  1. Hellings & Downs (1983) Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, Astrophys. J. 265, L39
  2. Agazie et al. (NANOGrav) (2023) The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951, L8

Field notes

Visualizza tutto
1 3
Visualizza tutto