{"product_id":"choralis-the-hellings-downs-curve-physics-t-shirt","title":"Choralis – The Hellings–Downs Curve Physics T-Shirt","description":"\u003cp\u003eChoralis conducts a ring of pulsar singers. A gravitational-wave background makes their timing sway together, in one particular pattern.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eA 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°.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΓ(θ) = ½ − x\/4 + (3\/2) x ln x,   x = (1 − cos θ)\/2\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eΓ(θ): correlation between two pulsars' timing residuals (dimensionless)\u003c\/li\u003e\n\u003cli\u003eθ: angle between the pulsars on the sky (rad)\u003c\/li\u003e\n\u003cli\u003ex: (1 − cos θ)\/2 (dimensionless)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eR. 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.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Evidence at about 3–4σ, not yet a 5σ detection, and the source is not settled.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: 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.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936690966631,"sku":"25475472780727101769","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936690999399,"sku":"22017318955936724704","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936691032167,"sku":"16755889901828180927","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936691064935,"sku":"11693310005516094293","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936691097703,"sku":"25096591608652714136","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936691130471,"sku":"73936307298839243892","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936691163239,"sku":"34320260466614032809","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936691196007,"sku":"16673899769306367751","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936691228775,"sku":"24228843327127818462","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936691261543,"sku":"30366782056827581236","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936691294311,"sku":"89132610646162202168","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936691327079,"sku":"73068747103822669160","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936691359847,"sku":"32779700232701026893","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936691392615,"sku":"18977743772389713831","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936691425383,"sku":"10746307457356994657","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936691458151,"sku":"18463356799615707385","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/hellings-downs_front_16_white.png?v=1793595932","url":"https:\/\/pixelatedphysics.com\/pl\/products\/choralis-the-hellings-downs-curve-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}