Asymmetric Velocity Distributions from Halo Density Profiles in the Eddington Approach

<div>The asymmetry parameter <svg height="12.6917pt" id="M147" style="vertical-align:-3.40337pt" version="1.1" viewbox="-0.0498162 -9.28833 58.7729 12.6917" width="58.7729pt" 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="M563 583C563 664 501 710 433 710C381 710 334 692 285 648C212 582 178 506 149 350L74 -56C49 -190 36 -222 24 -226L30 -257C52 -256 95 -247 121 -229C131 -222 134 -206 165 -21L219 303C254 510 296 665 397 665C447 665 481 626 481 572C481 512 446 457 390 420C367 405 351 400 323 397L302 349C398 338 466 285 466 197C466 117 419 45 306 45C268 45 224 59 198 74L186 50C197 20 228 -14 274 -14C318 -14 359 3 401 26C478 68 554 144 554 225C554 322 493 367 412 396C490 446 563 500 563 583Z" id="g50-224"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,11.308,0)"><path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" 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vert-adv-y="427"></glyph.data></g></svg> as a function of <svg height="12.2611pt" id="M148" style="vertical-align:-2.5552pt" version="1.1" viewbox="-0.0498162 -9.7059 6.089 12.2611" width="6.089pt" 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="M435 683C435 695 433 700 417 700C380 700 311 676 267 649C217 655 198 677 198 698C198 713 202 725 205 731L185 739C156 728 122 706 122 679C122 646 165 618 221 611C170 578 115 533 115 461C115 416 145 377 177 365C103 329 24 261 24 163C24 72 81 34 155 14C181 7 201 3 222 -1C284 -14 298 -34 298 -59C298 -97 254 -151 235 -171L262 -194C285 -179 378 -110 378 -28C378 14 343 58 273 70C248 74 219 80 190 89C140 104 109 134 109 190C109 259 165 325 225 350C251 343 285 340 318 340C334 340 376 381 376 403C376 416 372 420 355 420C323 420 284 410 258 403C221 409 194 444 194 490C194 540 236 586 274 608C317 608 364 613 388 623C408 631 435 653 435 683Z" id="g50-236"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="459" vert-adv-y="459"></glyph.data></g></svg> for values of <svg height="10.0558pt" id="M149" style="vertical-align:-1.72002pt" version="1.1" viewbox="-0.0498162 -8.33578 186.858 10.0558" width="186.858pt" 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="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.36,0)"><path 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Advances in High Energy Physics

fig2

Figure 2

Figure 2: Asymmetric Velocity Distributions from Halo Density Profiles in the Eddington Approach 