Gamma-Ray Burst Prompt Correlations

<div>Direct fit of <svg height="14.5368pt" id="M749" style="vertical-align:-5.300651pt" version="1.1" viewbox="-0.0498162 -9.23615 89.3104 14.5368" width="89.3104pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path></g><g transform="matrix(.013,0,0,-0.013,3.289,0)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g121-109"></path></g><g transform="matrix(.013,0,0,-0.013,9.919,0)"><path d="M463 437C426 431 375 425 327 422C297 440 264 449 231 449H230C153 449 51 396 51 283C51 215 94 168 139 149C123 129 91 103 51 88C50 78 53 60 62 46C75 25 100 2 136 -9C112 -28 73 -59 53 -79C38 -94 29 -113 29 -135C30 -192 91 -257 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This is shown here for two independent data sets for which the luminosities are derived by two independent methods. The first data set consists of 20 bursts with spectroscopically measured redshifts (the open circles). The second one is for 84 bursts (whose binned values are shown as filled diamonds, and the horizontal bars are the bin widths) whose luminosity (and then redshift) were determined with the spectral lag and variability light curve parameters. Both data sets show a highly significant and similar power law relations. (Figure after Schaefer [<a href="/journals/aa/2018/4969503/#B215">203</a>]; see Figure <svg height="8.55521pt" id="M750" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 6.36303 8.55521" width="6.36303pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g></svg> therein. @ AAS. Reproduced with permission.)</div>

Advances in Astronomy

Gamma-Ray Burst Prompt Correlations

Figure 10