Elliptic flow from two- and four-particle correlations in Au + Au collisions at sqrt(sNN) = 130 GeV
C. Adler et al., Phys. Rev. C 66, 034904 (2002)


Fig.2 : Correlation between the event plane angles

Errors are statistical
nch/nmax correlation between the event plane angles determined from pairs of subevents partitioned randomly (circles) correlation between the event plane angles determined from pairs of subevents partitioned by pseudorapidity (squares) correlation between the event plane angles determined from pairs of subevents partitioned by charge (crosses)
0.06 0.1122 +- 0.0028 0.0936 +- 0.0033 0.1183 +- 0.0033
0.17 0.2851 +- 0.0037 0.2544 +- 0.0045 0.2940 +- 0.0044
0.25 0.3835 +- 0.0040 0.3555 +- 0.0048 0.3924 +- 0.0047
0.36 0.4212 +- 0.0044 0.4024 +- 0.0053 0.4315 +- 0.0052
0.47 0.4027 +- 0.0046 0.4007 +- 0.0055 0.4350 +- 0.0054
0.58 0.3524 +- 0.0052 0.3560 +- 0.0061 0.3919 +- 0.0060
0.70 0.2603 +- 0.0060 0.2941 +- 0.0069 0.3132 +- 0.0069
0.84 0.1564 +- 0.0058 0.1787 +- 0.0064 0.1985 +- 0.0064

Fig. 3. The event plane resolution for full events as a function of centrality

Errors are statistical
nch/nmax The event plane resolution for full events, using randomly partitioned subevents with with pt weight (circles) The event plane resolution for full events, using randomly partitioned subevents without pt weight (triangles)
0.06 0.457 +- 0.005 0.405 +- 0.007
0.17 0.687 +- 0.004 0.600 +- 0.006
0.25 0.769 +- 0.003 0.690 +- 0.005
0.36 0.795 +- 0.003 0.726 +- 0.005
0.47 0.783 +- 0.002 0.727 +- 0.005
0.58 0.746 +- 0.004 0.680 +- 0.006
0.70 0.662 +- 0.006 0.604 +- 0.009
0.84 0.531 +- 0.009 0.465 +- 0.012

Fig. 4. Elliptic flow from event plane method as a function of centrality

Errors are statistical
nch/nmax Elliptic flow signal v2 from study of the correlation between particle pairs consisting of randomly chosen particles (circles) Elliptic flow signal v2 from study of the correlation between particle pairs consisting of opposite sign of charge (crosses) Elliptic flow signal v2 from study of the correlation between particle pairs consisting of the same sign of charge (triangles) Elliptic flow signal v2 from study of the correlation between particle pairs consisting of opposite sign of pseudorapidity (squares)
0.06 0.0690 +- 0.0011 0.0712 +- 0.0014 0.0671 +- 0.0013 0.0746 +- 0.0016
0.17 0.0677 +- 0.0006 0.0720 +- 0.0007 0.0665 +- 0.0007 0.0705 +- 0.0008
0.25 0.0648 +- 0.0004 0.0692 +- 0.0006 0.0643 +- 0.0005 0.0663 +- 0.0006
0.36 0.0590 +- 0.0004 0.0625 +- 0.0005 0.0593 +- 0.0005 0.0599 +- 0.0005
0.47 0.0503 +- 0.0004 0.0541 +- 0.0005 0.0493 +- 0.0005 0.0513 +- 0.0004
0.58 0.0406 +- 0.0004 0.0448 +- 0.0005 0.0406 +- 0.0005 0.0420 +- 0.0005
0.70 0.0304 +- 0.0005 0.0342 +- 0.0005 0.0280 +- 0.0005 0.0307 +- 0.0005
0.84 0.0197 +- 0.0005 0.0232 +- 0.0006 0.0162 +- 0.0005 0.0202 +- 0.0005

Fig. 5. Compare pt weight v2 with unit weight v2

Errors are statistical
nch/nmax v2 versus from the conventional method with pt weight (circles) v2 versus from the conventional method with unit weight. ratio of statistical error on v2 with pt weighting divided by the same with unit weighting.
0.06 0.0690 +- 0.00112 0.0687 +- 0.00161 0.69
0.17 0.0677 +- 0.00057 0.0705 +- 0.00091 0.63
0.25 0.0648 +- 0.00043 0.0653 +- 0.00065 0.66
0.36 0.0590 +- 0.00039 0.0604 +- 0.00057 0.68
0.47 0.0503 +- 0.00036 0.0511 +- 0.00052 0.70
0.58 0.0406 +- 0.00038 0.0417 +- 0.00056 0.67
0.70 0.0304 +- 0.00046 0.0323 +- 0.00066 0.70
0.84 0.0197 +- 0.00050 0.0215 +- 0.00074 0.68

Fig. 6. Compare event plane method and scalar product method

Errors are statistical
nch/nmax v2 versus from the event plane method (circles) v2 versus from the scalar product method (triangles) ratio of statistical error on v2 for the scalar product method divided by the same for the event plane method.
0.06 0.06822 +- 0.00167 0.07287 +- 0.00112 0.67
0.17 0.06849 +- 0.00086 0.07127 +- 0.00065 0.76
0.25 0.06428 +- 0.00061 0.06794 +- 0.00050 0.81
0.36 0.05886 +- 0.00055 0.06153 +- 0.00045 0.82
0.47 0.05111 +- 0.00049 0.05348 +- 0.00041 0.83
0.58 0.04148 +- 0.00051 0.04354 +- 0.00041 0.80
0.70 0.03177 +- 0.00057 0.03312 +- 0.00044 0.77
0.84 0.02000 +- 0.00061 0.02104 +- 0.00043 0.71

Fig.8: Elliptic flow as determined from the fits to the q distributions in different centrality bins.

Errors are statistical. pt range for q is 0.1 - 2 GeV/c, eta range for q is -1.3 - 1.3. The circles are from the standard method with random subevents. For the squares, all the centralities were fit separately. For the triangles, centrality bins 2 to 8 were fit with the same value of the non-flow parameter.
nch/nmax v2 from standard method v2 from seperately fitting of q distribution v2 from fitting of q distribution with the same nonflow par.
0.06 0.0690 +- 0.0011
0.17 0.0677 +- 0.0006 0.0536 +- 0.0025 0.0533 +- 0.0006
0.25 0.0648 +- 0.0004 0.0534 +- 0.0014 0.0558 +- 0.0005
0.36 0.0590 +- 0.0004 0.0516 +- 0.0009 0.0524 +- 0.0005
0.47 0.0503 +- 0.0004 0.0437 +- 0.0010 0.0456 +- 0.0005
0.58 0.0406 +- 0.0004 0.0357 +- 0.0010 0.0351 +- 0.0006
0.70 0.0304 +- 0.0005 0.0253 +- 0.0019 0.0250 +- 0.0008
0.84 0.0197 +- 0.0005 0.0147 +- 0.0045 0.0109 +- 0.0015

Fig.13: Measured elliptic flow versus centrality for Au + Au collisions at sqrt(sNN) = 130 GeV.

The circles show the conventional v2 with estimated systematic uncertainty due to non-flow, the stars show the 4th-order cumulant v2 from the generating function, the crosses show the conventional v2 from quarter-events, and the squares show the 4th-order cumulant v2 from the four-subevent method. Errors are statistical except that of v2 from the conventional method.
nch/nmax conventional v2 conventional v2 from quater events 4-th order cumulant v2 from the genetating function 4-th order cumulant v2 from the four-subevent method
0.06 0.0690 + 0.0011 - 0.0370 0.0615 +- 0.0032 0.0516 +- 0.0115
0.17 0.0677 + 0.0006 - 0.0101 0.0598 +- 0.0026 0.0550 +- 0.0028 0.0515 + 0.0034 - 0.0043
0.25 0.0648 + 0.0004 - 0.0076 0.0638 +- 0.0029 0.0530 +- 0.0014 0.0547 + 0.0010 - 0.0011
0.36 0.0590 + 0.0004 - 0.0051 0.0539 +- 0.0025 0.0512 +- 0.0012 0.0517 + 0.0008 - 0.0009
0.47 0.0503 + 0.0004 - 0.0044 0.0459 +- 0.0025 0.0431 +- 0.0010 0.0437 + 0.0007 - 0.0008
0.58 0.0406 + 0.0004 - 0.0044 0.0318 +- 0.0026 0.0347 +- 0.0015 0.0327 + 0.0011 - 0.0012
0.70 0.0304 + 0.0005 - 0.0047 0.0167 +- 0.0020 0.0231 +- 0.0021 0.0227 + 0.0016 - 0.0020
0.84 0.0197 + 0.0005 - 0.0050 0.0081 +- 0.0039 0.0057 +- 0.0146 0.0097 + 0.0050 - 0.0097

Fig. 14 Reconstructed v2 versus pseudorapidity from the conventional method (circles), from the second-order cumulant method (triangles), and from the fourth-order cumulant method(stars), in eight centrality bins.

pt range for the plot is 0.1 - 8 GeV/c. Errors are statistical.
centrality pseudorapidity v2 from stand event plane method v2 from 2nd order cumulant method v2 from 4th order cumulant method
53%-77% -1.15 0.0628 +- 0.0029 0.0595 +- 0.0033 0.0319 +- 0.0448
-0.90 0.0681 +- 0.0027 0.0653 +- 0.0030 0.0570 +- 0.0375
-0.70 0.0661 +- 0.0026 0.0661 +- 0.0029 0.0424 +- 0.0385
-0.50 0.0696 +- 0.0027 0.0673 +- 0.0029 0.0204 +- 0.0386
-0.30 0.0758 +- 0.0027 0.0725 +- 0.0030 0.0045 +- 0.0396
-0.10 0.0825 +- 0.0027 0.0788 +- 0.0030 0.0920 +- 0.0415
0.10 0.0755 +- 0.0027 0.0773 +- 0.0030 0.0902 +- 0.0402
0.30 0.0761 +- 0.0027 0.0739 +- 0.0030 0.0860 +- 0.0383
0.50 0.0731 +- 0.0026 0.0735 +- 0.0029 0.0635 +- 0.0384
0.70 0.0630 +- 0.0026 0.0589 +- 0.0029 0.0462 +- 0.0375
0.90 0.0579 +- 0.0028 0.0587 +- 0.0030 0.0192 +- 0.0380
1.15 0.0536 +- 0.0030 0.0541 +- 0.0034 0.0830 +- 0.0472
41%-53% -1.15 0.0607 +- 0.0017 0.0620 +- 0.0020 0.0623 +- 0.0106
-0.90 0.0652 +- 0.0016 0.0684 +- 0.0019 0.0630 +- 0.0096
-0.70 0.0683 +- 0.0015 0.0705 +- 0.0018 0.0514 +- 0.0092
-0.50 0.0686 +- 0.0015 0.0701 +- 0.0018 0.0524 +- 0.0093
-0.30 0.0698 +- 0.0015 0.0743 +- 0.0018 0.0654 +- 0.0095
-0.10 0.0698 +- 0.0016 0.0720 +- 0.0018 0.0576 +- 0.0096
0.10 0.0733 +- 0.0016 0.0742 +- 0.0018 0.0616 +- 0.0096
0.30 0.0731 +- 0.0015 0.0768 +- 0.0018 0.0585 +- 0.0095
0.50 0.0715 +- 0.0015 0.0741 +- 0.0018 0.0529 +- 0.0094
0.70 0.0663 +- 0.0015 0.0671 +- 0.0018 0.0545 +- 0.0092
0.90 0.0621 +- 0.0016 0.0643 +- 0.0019 0.0403 +- 0.0097
1.15 0.0608 +- 0.0018 0.0630 +- 0.0021 0.0509 +- 0.0111
31%-41% -1.15 0.0586 +- 0.0013 0.0607 +- 0.0016 0.0430 +- 0.0056
-0.90 0.0612 +- 0.0012 0.0644 +- 0.0015 0.0463 +- 0.0049
-0.70 0.0637 +- 0.0012 0.0670 +- 0.0014 0.0573 +- 0.0046
-0.50 0.0660 +- 0.0012 0.0694 +- 0.0014 0.0505 +- 0.0047
-0.30 0.0696 +- 0.0012 0.0736 +- 0.0014 0.0574 +- 0.0048
-0.10 0.0687 +- 0.0012 0.0737 +- 0.0014 0.0582 +- 0.0048
0.10 0.0685 +- 0.0012 0.0720 +- 0.0014 0.0563 +- 0.0048
0.30 0.0668 +- 0.0012 0.0696 +- 0.0014 0.0575 +- 0.0048
0.50 0.0662 +- 0.0012 0.0674 +- 0.0014 0.0634 +- 0.0047
0.70 0.0638 +- 0.0012 0.0661 +- 0.0014 0.0552 +- 0.0046
0.90 0.0615 +- 0.0012 0.0639 +- 0.0015 0.0458 +- 0.0049
1.15 0.0600 +- 0.0014 0.0622 +- 0.0017 0.0538 +- 0.0054
24%-31% -1.15 0.0542 +- 0.0013 0.0568 +- 0.0015 0.0483 +- 0.0046
-0.90 0.0568 +- 0.0012 0.0591 +- 0.0014 0.0522 +- 0.0041
-0.70 0.0604 +- 0.0011 0.0631 +- 0.0013 0.0492 +- 0.0038
-0.50 0.0623 +- 0.0011 0.0654 +- 0.0013 0.0558 +- 0.0039
-0.30 0.0598 +- 0.0011 0.0630 +- 0.0013 0.0540 +- 0.0039
-0.10 0.0616 +- 0.0011 0.0632 +- 0.0013 0.0533 +- 0.0040
0.10 0.0621 +- 0.0011 0.0633 +- 0.0013 0.0469 +- 0.0039
0.30 0.0612 +- 0.0011 0.0638 +- 0.0013 0.0554 +- 0.0039
0.50 0.0626 +- 0.0011 0.0665 +- 0.0013 0.0614 +- 0.0038
0.70 0.0563 +- 0.0011 0.0584 +- 0.0013 0.0511 +- 0.0038
0.90 0.0551 +- 0.0012 0.0574 +- 0.0014 0.0532 +- 0.0041
1.15 0.0524 +- 0.0013 0.0575 +- 0.0015 0.0444 +- 0.0045
16%-24% -1.15 0.0463 +- 0.0012 0.0482 +- 0.0014 0.0371 +- 0.0040
-0.90 0.0488 +- 0.0011 0.0524 +- 0.0013 0.0415 +- 0.0036
-0.70 0.0509 +- 0.0010 0.0545 +- 0.0012 0.0479 +- 0.0033
-0.50 0.0521 +- 0.0010 0.0559 +- 0.0012 0.0461 +- 0.0034
-0.30 0.0513 +- 0.0010 0.0544 +- 0.0012 0.0423 +- 0.0034
-0.10 0.0527 +- 0.0010 0.0552 +- 0.0012 0.0472 +- 0.0034
0.10 0.0512 +- 0.0010 0.0558 +- 0.0012 0.0460 +- 0.0034
0.30 0.0511 +- 0.0010 0.0549 +- 0.0012 0.0419 +- 0.0034
0.50 0.0514 +- 0.0010 0.0538 +- 0.0012 0.0444 +- 0.0033
0.70 0.0507 +- 0.0010 0.0532 +- 0.0012 0.0438 +- 0.0033
0.90 0.0486 +- 0.0011 0.0506 +- 0.0013 0.0425 +- 0.0035
1.15 0.0457 +- 0.0012 0.0472 +- 0.0014 0.0424 +- 0.0040
10%-16% -1.15 0.0377 +- 0.0012 0.0402 +- 0.0014 0.0449 +- 0.0058
-0.90 0.0401 +- 0.0011 0.0413 +- 0.0013 0.0460 +- 0.0051
-0.70 0.0407 +- 0.0010 0.0430 +- 0.0012 0.0362 +- 0.0051
-0.50 0.0434 +- 0.0010 0.0457 +- 0.0012 0.0341 +- 0.0051
-0.30 0.0411 +- 0.0010 0.0451 +- 0.0012 0.0292 +- 0.0053
-0.10 0.0422 +- 0.0010 0.0463 +- 0.0012 0.0370 +- 0.0053
0.10 0.0415 +- 0.0010 0.0445 +- 0.0012 0.0318 +- 0.0053
0.30 0.0403 +- 0.0010 0.0429 +- 0.0012 0.0265 +- 0.0052
0.50 0.0409 +- 0.0010 0.0440 +- 0.0012 0.0286 +- 0.0051
0.70 0.0411 +- 0.0010 0.0435 +- 0.0012 0.0371 +- 0.0051
0.90 0.0393 +- 0.0011 0.0422 +- 0.0013 0.0351 +- 0.0055
1.15 0.0371 +- 0.0012 0.0387 +- 0.0015 0.0454 +- 0.0067
5%-10% -1.15 0.0298 +- 0.0014 0.0344 +- 0.0015 0.0144 +- 0.0081
-0.90 0.0302 +- 0.0013 0.0332 +- 0.0014 0.0233 +- 0.0073
-0.70 0.0319 +- 0.0012 0.0337 +- 0.0013 0.0305 +- 0.0068
-0.50 0.0301 +- 0.0012 0.0344 +- 0.0013 0.0310 +- 0.0069
-0.30 0.0302 +- 0.0012 0.0322 +- 0.0013 0.0173 +- 0.0071
-0.10 0.0325 +- 0.0012 0.0336 +- 0.0013 0.0283 +- 0.0072
0.10 0.0319 +- 0.0012 0.0325 +- 0.0013 0.0190 +- 0.0072
0.30 0.0290 +- 0.0012 0.0338 +- 0.0013 0.0178 +- 0.0071
0.50 0.0312 +- 0.0012 0.0328 +- 0.0013 0.0182 +- 0.0069
0.70 0.0305 +- 0.0012 0.0323 +- 0.0013 0.0327 +- 0.0069
0.90 0.0270 +- 0.0013 0.0279 +- 0.0014 0.0302 +- 0.0075
1.15 0.0294 +- 0.0015 0.0312 +- 0.0016 0.0193 +- 0.0088
0%-5% -1.15 0.0209 +- 0.0015 0.0220 +- 0.0016 0.0716 +- 0.0553
-0.90 0.0194 +- 0.0014 0.0206 +- 0.0014 -0.0156 +- 0.0500
-0.70 0.0203 +- 0.0012 0.0205 +- 0.0013 0.1035 +- 0.0470
-0.50 0.0195 +- 0.0013 0.0207 +- 0.0013 -0.0460 +- 0.0483
-0.30 0.0223 +- 0.0013 0.0248 +- 0.0013 0.0298 +- 0.0493
-0.10 0.0201 +- 0.0013 0.0215 +- 0.0013 0.0636 +- 0.0502
0.10 0.0207 +- 0.0013 0.0224 +- 0.0013 0.0163 +- 0.0495
0.30 0.0194 +- 0.0013 0.0184 +- 0.0013 0.0200 +- 0.0487
0.50 0.0192 +- 0.0013 0.0194 +- 0.0013 -0.0186 +- 0.0478
0.70 0.0192 +- 0.0012 0.0211 +- 0.0013 -0.0379 +- 0.0476
0.90 0.0175 +- 0.0014 0.0192 +- 0.0014 -0.0129 +- 0.0525
1.15 0.0174 +- 0.0016 0.0200 +- 0.0016 -0.1400 +- 0.0635

Fig. 15. Reconstructed v2 versus pt from the conventional method(circles), from the second-order cumulant method(triangles), and from the fourth-order cumualnt method (stars), in eight centrality bins.

Eta range for the plot is -1.3-1.3. Errors are statistical.
centrality pt (GeV/c) v2 from stand event plane method v2 from 2nd order cumulant method v2 from 4th order cumulant method
53%-77% 0.15 0.0184 + 0.0022 - 0.0022 0.0186 + 0.0024 - 0.0024 0.0375 + 0.0315 - 0.0315
0.30 0.0377 + 0.0013 - 0.0013 0.0357 + 0.0015 - 0.0015 0.0355 + 0.0195 - 0.0195
0.50 0.0678 + 0.0017 - 0.0017 0.0670 + 0.0018 - 0.0018 0.0439 + 0.0241 - 0.0241
0.70 0.0979 + 0.0022 - 0.0022 0.0975 + 0.0024 - 0.0024 0.0474 + 0.0318 - 0.0318
0.90 0.1222 + 0.0029 - 0.0029 0.1212 + 0.0032 - 0.0032 0.1002 + 0.0433 - 0.0433
1.10 0.1495 + 0.0039 - 0.0039 0.1413 + 0.0043 - 0.0043 0.1094 + 0.0572 - 0.0572
1.30 0.1673 + 0.0052 - 0.0052 0.1662 + 0.0057 - 0.0057 0.0792 + 0.0741 - 0.0741
1.50 0.1902 + 0.0068 - 0.0068 0.1829 + 0.0075 - 0.0075 0.1166 + 0.1057 - 0.1057
1.70 0.2059 + 0.0089 - 0.0089 0.1944 + 0.0099 - 0.0099 0.3321 + 0.1432 - 0.1432
1.90 0.2354 + 0.0116 - 0.0116 0.2354 + 0.0128 - 0.0128 0.1208 + 0.1668 - 0.1668
2.17 0.2308 + 0.0118 - 0.0118 0.2372 + 0.0133 - 0.0133 0.3320 + 0.2269 - 0.2269
2.58 0.2612 + 0.0196 - 0.0196 0.2559 + 0.0225 - 0.0225 0.1045 + 0.3273 - 0.3273
2.98 0.2783 + 0.0307 - 0.0307 0.2542 + 0.0354 - 0.0354 0.5404 + 0.5334 - 0.5334
3.38 0.3047 + 0.0461 - 0.0461 0.3683 + 0.0551 - 0.0551 -2.0703 + 1.6467 - 1.6467
41%-53% 0.15 0.0172 + 0.0013 - 0.0013 0.0177 + 0.0015 - 0.0015 0.0099 + 0.0081 - 0.0081
0.30 0.0359 + 0.0008 - 0.0008 0.0367 + 0.0009 - 0.0009 0.0351 + 0.0047 - 0.0047
0.50 0.0653 + 0.0010 - 0.0010 0.0675 + 0.0011 - 0.0011 0.0482 + 0.0059 - 0.0059
0.70 0.0910 + 0.0012 - 0.0012 0.0936 + 0.0015 - 0.0015 0.0804 + 0.0077 - 0.0077
0.90 0.1171 + 0.0016 - 0.0016 0.1219 + 0.0019 - 0.0019 0.0962 + 0.0101 - 0.0101
1.10 0.1380 + 0.0021 - 0.0021 0.1415 + 0.0025 - 0.0025 0.1020 + 0.0133 - 0.0133
1.30 0.1583 + 0.0028 - 0.0028 0.1690 + 0.0033 - 0.0033 0.1241 + 0.0177 - 0.0177
1.50 0.1752 + 0.0036 - 0.0036 0.1775 + 0.0043 - 0.0043 0.1529 + 0.0231 - 0.0231
1.70 0.1911 + 0.0047 - 0.0047 0.2015 + 0.0056 - 0.0056 0.1713 + 0.0310 - 0.0310
1.90 0.2056 + 0.0060 - 0.0060 0.2135 + 0.0072 - 0.0072 0.1633 + 0.0395 - 0.0395
2.17 0.2163 + 0.0062 - 0.0062 0.2372 + 0.0075 - 0.0075 0.1205 + 0.0438 - 0.0438
2.58 0.2379 + 0.0101 - 0.0101 0.2728 + 0.0121 - 0.0121 0.2011 + 0.0654 - 0.0654
2.98 0.2409 + 0.0160 - 0.0160 0.2299 + 0.0194 - 0.0194 0.1821 + 0.1088 - 0.1088
3.38 0.2549 + 0.0248 - 0.0248 0.2566 + 0.0295 - 0.0295 0.3712 + 0.1451 - 0.1451
31%-41% 0.15 0.0149 + 0.0011 - 0.0011 0.0150 + 0.0012 - 0.0012 0.0026 + 0.0041 - 0.0041
0.30 0.0335 + 0.0006 - 0.0006 0.0350 + 0.0007 - 0.0007 0.0270 + 0.0024 - 0.0024
0.50 0.0610 + 0.0007 - 0.0007 0.0638 + 0.0009 - 0.0009 0.0495 + 0.0030 - 0.0030
0.70 0.0862 + 0.0010 - 0.0010 0.0910 + 0.0011 - 0.0011 0.0715 + 0.0038 - 0.0038
0.90 0.1105 + 0.0012 - 0.0012 0.1150 + 0.0015 - 0.0015 0.0990 + 0.0049 - 0.0049
1.10 0.1295 + 0.0016 - 0.0016 0.1345 + 0.0019 - 0.0019 0.1146 + 0.0064 - 0.0064
1.30 0.1460 + 0.0021 - 0.0021 0.1534 + 0.0025 - 0.0025 0.1421 + 0.0084 - 0.0084
1.50 0.1669 + 0.0027 - 0.0027 0.1772 + 0.0032 - 0.0032 0.1442 + 0.0110 - 0.0110
1.70 0.1805 + 0.0035 - 0.0035 0.1901 + 0.0042 - 0.0042 0.1780 + 0.0143 - 0.0143
1.90 0.1896 + 0.0046 - 0.0046 0.1940 + 0.0055 - 0.0055 0.1597 + 0.0190 - 0.0190
2.17 0.2017 + 0.0046 - 0.0046 0.2155 + 0.0056 - 0.0056 0.1676 + 0.0200 - 0.0200
2.58 0.2143 + 0.0076 - 0.0076 0.2198 + 0.0092 - 0.0092 0.1779 + 0.0314 - 0.0314
2.98 0.2134 + 0.0124 - 0.0124 0.2114 + 0.0150 - 0.0150 0.1399 + 0.0533 - 0.0533
3.38 0.2322 + 0.0195 - 0.0195 0.2470 + 0.0237 - 0.0237 0.2142 + 0.0985 - 0.0985
24%-31% 0.15 0.0118 + 0.0010 - 0.0010 0.0133 + 0.0012 - 0.0012 0.0132 + 0.0035 - 0.0035
0.30 0.0297 + 0.0006 - 0.0006 0.0306 + 0.0007 - 0.0007 0.0266 + 0.0020 - 0.0020
0.50 0.0553 + 0.0007 - 0.0007 0.0574 + 0.0008 - 0.0008 0.0496 + 0.0024 - 0.0024
0.70 0.0773 + 0.0009 - 0.0009 0.0808 + 0.0010 - 0.0010 0.0673 + 0.0031 - 0.0031
0.90 0.1002 + 0.0011 - 0.0011 0.1041 + 0.0013 - 0.0013 0.0897 + 0.0040 - 0.0040
1.10 0.1142 + 0.0015 - 0.0015 0.1200 + 0.0017 - 0.0017 0.1006 + 0.0053 - 0.0053
1.30 0.1328 + 0.0019 - 0.0019 0.1411 + 0.0022 - 0.0022 0.1067 + 0.0069 - 0.0069
1.50 0.1503 + 0.0025 - 0.0025 0.1586 + 0.0029 - 0.0029 0.1398 + 0.0088 - 0.0088
1.70 0.1644 + 0.0032 - 0.0032 0.1719 + 0.0038 - 0.0038 0.1373 + 0.0116 - 0.0116
1.90 0.1730 + 0.0041 - 0.0041 0.1825 + 0.0049 - 0.0049 0.1305 + 0.0156 - 0.0156
2.17 0.1833 + 0.0042 - 0.0042 0.1960 + 0.0051 - 0.0051 0.1871 + 0.0161 - 0.0161
2.58 0.1964 + 0.0069 - 0.0069 0.2083 + 0.0082 - 0.0082 0.1376 + 0.0273 - 0.0273
2.98 0.2077 + 0.0112 - 0.0112 0.2110 + 0.0135 - 0.0135 0.1412 + 0.0445 - 0.0445
3.38 0.2025 + 0.0178 - 0.0178 0.2090 + 0.0218 - 0.0218 0.1998 + 0.0617 - 0.0617
16%-24% 0.15 0.0106 + 0.0009 - 0.0009 0.0126 + 0.0011 - 0.0011 0.0047 + 0.0031 - 0.0031
0.30 0.0247 + 0.0005 - 0.0005 0.0264 + 0.0006 - 0.0006 0.0228 + 0.0018 - 0.0018
0.50 0.0460 + 0.0006 - 0.0006 0.0488 + 0.0008 - 0.0008 0.0423 + 0.0021 - 0.0021
0.70 0.0649 + 0.0008 - 0.0008 0.0693 + 0.0010 - 0.0010 0.0573 + 0.0027 - 0.0027
0.90 0.0827 + 0.0010 - 0.0010 0.0873 + 0.0012 - 0.0012 0.0679 + 0.0035 - 0.0035
1.10 0.0998 + 0.0013 - 0.0013 0.1017 + 0.0016 - 0.0016 0.0869 + 0.0045 - 0.0045
1.30 0.1163 + 0.0017 - 0.0017 0.1224 + 0.0020 - 0.0020 0.1085 + 0.0058 - 0.0058
1.50 0.1254 + 0.0022 - 0.0022 0.1308 + 0.0026 - 0.0026 0.1055 + 0.0075 - 0.0075
1.70 0.1409 + 0.0029 - 0.0029 0.1464 + 0.0034 - 0.0034 0.1186 + 0.0098 - 0.0098
1.90 0.1507 + 0.0037 - 0.0037 0.1622 + 0.0044 - 0.0044 0.1263 + 0.0129 - 0.0129
2.17 0.1584 + 0.0038 - 0.0038 0.1666 + 0.0046 - 0.0046 0.1118 + 0.0130 - 0.0130
2.58 0.1774 + 0.0064 - 0.0064 0.1957 + 0.0076 - 0.0076 0.1312 + 0.0215 - 0.0215
2.98 0.1812 + 0.0103 - 0.0103 0.1889 + 0.0124 - 0.0124 0.1206 + 0.0371 - 0.0371
3.38 0.1858 + 0.0165 - 0.0165 0.2091 + 0.0198 - 0.0198 0.1821 + 0.0538 - 0.0538
10%-16% 0.15 0.0080 + 0.0010 - 0.0010 0.0087 + 0.0011 - 0.0011 0.0100 + 0.0048 - 0.0048
0.30 0.0195 + 0.0005 - 0.0005 0.0206 + 0.0006 - 0.0006 0.0188 + 0.0027 - 0.0027
0.50 0.0360 + 0.0006 - 0.0006 0.0379 + 0.0008 - 0.0008 0.0305 + 0.0032 - 0.0032
0.70 0.0525 + 0.0008 - 0.0008 0.0553 + 0.0010 - 0.0010 0.0467 + 0.0041 - 0.0041
0.90 0.0667 + 0.0011 - 0.0011 0.0710 + 0.0012 - 0.0012 0.0543 + 0.0054 - 0.0054
1.10 0.0825 + 0.0014 - 0.0014 0.0888 + 0.0016 - 0.0016 0.0721 + 0.0068 - 0.0068
1.30 0.0956 + 0.0017 - 0.0017 0.1042 + 0.0020 - 0.0020 0.0745 + 0.0090 - 0.0090
1.50 0.1075 + 0.0022 - 0.0022 0.1165 + 0.0026 - 0.0026 0.0959 + 0.0114 - 0.0114
1.70 0.1106 + 0.0029 - 0.0029 0.1207 + 0.0034 - 0.0034 0.0842 + 0.0152 - 0.0152
1.90 0.1191 + 0.0038 - 0.0038 0.1308 + 0.0045 - 0.0045 0.0904 + 0.0188 - 0.0188
2.17 0.1325 + 0.0039 - 0.0039 0.1424 + 0.0046 - 0.0046 0.1095 + 0.0195 - 0.0195
2.58 0.1432 + 0.0065 - 0.0065 0.1581 + 0.0077 - 0.0077 0.1251 + 0.0334 - 0.0334
2.98 0.1450 + 0.0108 - 0.0108 0.1748 + 0.0126 - 0.0126 0.1605 + 0.0521 - 0.0521
3.38 0.1480 + 0.0165 - 0.0165 0.1562 + 0.0195 - 0.0195 0.1328 + 0.0896 - 0.0896
5%-10% 0.15 0.0043 + 0.0011 - 0.0011 0.0055 + 0.0012 - 0.0012 -0.0055 + 0.0066 - 0.0066
0.30 0.0138 + 0.0006 - 0.0006 0.0143 + 0.0007 - 0.0007 0.0118 + 0.0037 - 0.0037
0.50 0.0272 + 0.0008 - 0.0008 0.0286 + 0.0008 - 0.0008 0.0250 + 0.0044 - 0.0044
0.70 0.0405 + 0.0010 - 0.0010 0.0450 + 0.0010 - 0.0010 0.0291 + 0.0056 - 0.0056
0.90 0.0503 + 0.0012 - 0.0012 0.0536 + 0.0013 - 0.0013 0.0368 + 0.0071 - 0.0071
1.10 0.0616 + 0.0016 - 0.0016 0.0671 + 0.0017 - 0.0017 0.0407 + 0.0093 - 0.0093
1.30 0.0682 + 0.0020 - 0.0020 0.0749 + 0.0022 - 0.0022 0.0765 + 0.0119 - 0.0119
1.50 0.0751 + 0.0026 - 0.0026 0.0832 + 0.0029 - 0.0029 0.0663 + 0.0153 - 0.0153
1.70 0.0918 + 0.0034 - 0.0034 0.0971 + 0.0038 - 0.0038 0.0893 + 0.0204 - 0.0204
1.90 0.0975 + 0.0044 - 0.0044 0.1038 + 0.0049 - 0.0049 0.0118 + 0.0262 - 0.0262
2.17 0.1013 + 0.0046 - 0.0046 0.1068 + 0.0050 - 0.0050 0.1133 + 0.0271 - 0.0271
2.58 0.1192 + 0.0077 - 0.0077 0.1243 + 0.0085 - 0.0085 0.1071 + 0.0450 - 0.0450
2.98 0.1152 + 0.0126 - 0.0126 0.1363 + 0.0140 - 0.0140 0.0280 + 0.0766 - 0.0766
3.38 0.1003 + 0.0199 - 0.0199 0.1097 + 0.0219 - 0.0219 -0.1174 + 0.1151 - 0.1151
0%-5% 0.15 0.0028 + 0.0012 - 0.0012 0.0013 + 0.0012 - 0.0012 0.0202 + 0.0459 - 0.0459
0.30 0.0084 + 0.0007 - 0.0007 0.0083 + 0.0007 - 0.0007 -0.0145 + 0.0259 - 0.0259
0.50 0.0173 + 0.0008 - 0.0008 0.0188 + 0.0008 - 0.0008 0.0500 + 0.0306 - 0.0306
0.70 0.0262 + 0.0010 - 0.0010 0.0279 + 0.0010 - 0.0010 -0.0648 + 0.0385 - 0.0385
0.90 0.0342 + 0.0013 - 0.0013 0.0373 + 0.0013 - 0.0013 0.0501 + 0.0496 - 0.0496
1.10 0.0405 + 0.0017 - 0.0017 0.0431 + 0.0017 - 0.0017 -0.0269 + 0.0635 - 0.0635
1.30 0.0453 + 0.0022 - 0.0022 0.0469 + 0.0022 - 0.0022 0.1161 + 0.0822 - 0.0822
1.50 0.0478 + 0.0028 - 0.0028 0.0557 + 0.0029 - 0.0029 -0.1199 + 0.1051 - 0.1051
1.70 0.0571 + 0.0036 - 0.0036 0.0590 + 0.0037 - 0.0037 0.2266 + 0.1394 - 0.1394
1.90 0.0663 + 0.0047 - 0.0047 0.0728 + 0.0049 - 0.0049 -0.1165 + 0.1833 - 0.1833
2.17 0.0700 + 0.0049 - 0.0049 0.0781 + 0.0050 - 0.0050 0.0096 + 0.1888 - 0.1888
2.58 0.0696 + 0.0083 - 0.0083 0.0805 + 0.0086 - 0.0086 0.0173 + 0.3273 - 0.3273
2.98 0.0809 + 0.0136 - 0.0136 0.0925 + 0.0140 - 0.0140 -0.3531 + 0.5173 - 0.5173
3.38 0.0688 + 0.0218 - 0.0218 0.0825 + 0.0228 - 0.0228 0.4447 + 0.8089 - 0.8089

Fig. 16. Elliptic flow versus pseudorapidity from the conventional method(circles), from the 2nd order cumulant method(triangles), from the 4th order cumulant method(stars), and from the quarter events(crosses), averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

pt range for the plot is 0.1-8GeV/c. Errors are statistical.
pseudorapidity v2 from stand event plane method v2 from 2nd order cumulant method v2 from 4th order cumulant method v2 from quater events
-1.15 0.0463 +- 0.0005 0.0489 +- 0.0006 0.0399 +- 0.0026 0.0456 +- 0.0019
-0.90 0.0483 +- 0.0005 0.0510 +- 0.0006 0.0436 +- 0.0024 0.0392 +- 0.0017
-0.70 0.0503 +- 0.0005 0.0529 +- 0.0005 0.0440 +- 0.0023 0.0464 +- 0.0016
-0.50 0.0514 +- 0.0005 0.0545 +- 0.0005 0.0435 +- 0.0023 0.0479 +- 0.0016
-0.30 0.0511 +- 0.0005 0.0544 +- 0.0006 0.0412 +- 0.0023 0.0454 +- 0.0016
-0.10 0.0522 +- 0.0005 0.0549 +- 0.0006 0.0451 +- 0.0023 0.0425 +- 0.0017
0.10 0.0522 +- 0.0005 0.0545 +- 0.0006 0.0412 +- 0.0023 0.0477 +- 0.0020
0.30 0.0509 +- 0.0005 0.0542 +- 0.0006 0.0403 +- 0.0023 0.0459 +- 0.0020
0.50 0.0514 +- 0.0005 0.0539 +- 0.0005 0.0424 +- 0.0023 0.0428 +- 0.0020
0.70 0.0493 +- 0.0005 0.0513 +- 0.0005 0.0442 +- 0.0023 0.0461 +- 0.0019
0.90 0.0470 +- 0.0005 0.0491 +- 0.0006 0.0406 +- 0.0024 0.0428 +- 0.0021
1.15 0.0460 +- 0.0006 0.0483 +- 0.0007 0.0416 +- 0.0028 0.0452 +- 0.0023

Fig. 17. Elliptic flow versus transverse momentum from the conventional method(circles), from the 2nd order cumulant method (triangles), from 4th order cumulant method (stars), and from quarter events (crosses), averaged over allcentralities from bin 2-7, as defined in Figs. 14 and 15.

Eta range for the plot is -1.3 - 1.3. Errors are statistical.
pt (GeV/c) v2 from stand event plane method v2 from 2nd order cumulant method v2 from 4th order cumulant method v2 from quater events
0.15 0.0106 + 0.0004 - 0.0004 0.0116 + 0.0005 - 0.0005 0.0055 + 0.0021 - 0.0021 0.0105 + 0.0016 - 0.0016
0.30 0.0250 + 0.0002 - 0.0002 0.0260 + 0.0003 - 0.0003 0.0226 + 0.0012 - 0.0012 0.0310 + 0.0009 - 0.0009
0.50 0.0461 + 0.0003 - 0.0003 0.0482 + 0.0003 - 0.0003 0.0393 + 0.0014 - 0.0014 0.0393 + 0.0011 - 0.0011
0.70 0.0653 + 0.0004 - 0.0004 0.0690 + 0.0004 - 0.0004 0.0555 + 0.0018 - 0.0018 0.0508 + 0.0014 - 0.0014
0.90 0.0831 + 0.0005 - 0.0005 0.0872 + 0.0006 - 0.0006 0.0695 + 0.0024 - 0.0024 0.0651 + 0.0018 - 0.0018
1.10 0.0987 + 0.0006 - 0.0006 0.1034 + 0.0007 - 0.0007 0.0819 + 0.0031 - 0.0031 0.0829 + 0.0024 - 0.0024
1.30 0.1131 + 0.0008 - 0.0008 0.1206 + 0.0009 - 0.0009 0.1007 + 0.0040 - 0.0040 0.0965 + 0.0031 - 0.0031
1.50 0.1259 + 0.0010 - 0.0010 0.1332 + 0.0012 - 0.0012 0.1107 + 0.0052 - 0.0052 0.1106 + 0.0040 - 0.0040
1.70 0.1385 + 0.0014 - 0.0014 0.1461 + 0.0016 - 0.0016 0.1215 + 0.0069 - 0.0069 0.1301 + 0.0052 - 0.0052
1.90 0.1474 + 0.0018 - 0.0018 0.1559 + 0.0021 - 0.0021 0.1038 + 0.0088 - 0.0088 0.1346 + 0.0068 - 0.0068
2.17 0.1570 + 0.0018 - 0.0018 0.1675 + 0.0021 - 0.0021 0.1323 + 0.0092 - 0.0092 0.1352 + 0.0070 - 0.0070
2.58 0.1732 + 0.0030 - 0.0030 0.1868 + 0.0035 - 0.0035 0.1396 + 0.0150 - 0.0150 0.1424 + 0.0116 - 0.0116
2.98 0.1762 + 0.0049 - 0.0049 0.1868 + 0.0058 - 0.0058 0.1228 + 0.0250 - 0.0250 0.1637 + 0.0188 - 0.0188
3.38 0.1784 + 0.0077 - 0.0077 0.1893 + 0.0091 - 0.0091 0.1414 + 0.0384 - 0.0384 0.1893 + 0.0295 - 0.0295
4.03 0.1658 + 0.0089 - 0.0089 0.1763 + 0.0104 - 0.0104 0.1192 + 0.0478 - 0.0478 0.1317 + 0.0337 - 0.0337

Fig. 18. The ratio of v2 from the 4th order cumulant divided by v2, from the conventional method as a function of pt, averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

Eta range for the plot is -1.3 - 1.3. Errors are statistical.
pt (GeV/c) ratio of v2
0.15 0.52 + 0.20 - 0.20
0.30 0.90 + 0.05 - 0.05
0.50 0.85 + 0.03 - 0.03
0.70 0.85 + 0.03 - 0.03
0.90 0.84 + 0.03 - 0.03
1.10 0.83 + 0.03 - 0.03
1.30 0.89 + 0.04 - 0.04
1.50 0.88 + 0.04 - 0.04
1.70 0.88 + 0.05 - 0.05
1.90 0.70 + 0.06 - 0.06
2.17 0.84 + 0.06 - 0.06
2.58 0.81 + 0.09 - 0.09
2.98 0.70 + 0.14 - 0.14
3.38 0.79 + 0.22 - 0.22
4.03 0.72 + 0.29 - 0.29

Fig. 19. The ratio of v2 from quarter events divided by the conventional v2 as a function of pt. In both cases, event planes were constructed from low-pt ( less than 0.5GeV/c) particles. The data are averaged over all centralities from bin 2-7, as defined in Figs. 14 and 15.

Eta range for the plot is -1.3 - 1.3. Errors are statistical.
pt (GeV/c) ratio of v2
0.15 0.65 + 0.11 - 0.11
0.30 1.07 + 0.04 - 0.04
0.50 0.88 + 0.03 - 0.03
0.70 0.83 + 0.03 - 0.03
0.90 0.83 + 0.03 - 0.03
1.10 0.88 + 0.03 - 0.03
1.30 0.91 + 0.03 - 0.03
1.50 0.90 + 0.04 - 0.04
1.70 0.93 + 0.04 - 0.04
1.90 0.95 + 0.05 - 0.05
2.17 0.92 + 0.05 - 0.05
2.60 0.90 + 0.08 - 0.08
3.00 0.91 + 0.12 - 0.12
3.40 1.19 + 0.22 - 0.22
4.05 0.97 + 0.28 - 0.28

Fig. 22. v2/ε as a function of charged particle density in Au + Au collisions.

Data are from E877 at the AGS (squares), NA49 at the SPS (circles), and STAR at RHIC (stars). The AGS and SPS data have been obtained by conventional flow analysis. The STAR measurements are at sqrt(sNN) = 130 GeV, and correspond to the final corrected elliptic flow based on 4th-order cumulants (integrated over pt 0.1-2 GeV/c, eta -1.3-1.3, corrected for the b fluctuation), and we assume dN/dy = 1.15 dN/d&eta. The horizontal shaded bands indicate the hydrodynamic limits for different beam energies. The hydro band range for Sqrt(SNN) = 130 GeV is 0.19 - 0.21, and for Sqrt(SNN) = 17 GeV is 0.22 - 0.235.
1/S dN/dy (fm -2) v2/&eps
STAR 6.36 0.12 +- 0.03
13.60 0.13 +- 0.01
16.27 0.14 +- 0.00
19.37 0.16 +- 0.00
21.43 0.17 +- 0.00
22.72 0.18 +- 0.01
23.71 0.18 +- 0.02
24.85 0.21 +- 0.25
E877 4.12 0.03 +- 0.01
6.08 0.07 +- 0.01
7.51 0.09 +- 0.01
8.35 0.09 +- 0.03
NA49
14.48 0.14 +- 0.01
13.26 0.11 +- 0.01
11.54 0.11 +- 0.00
9.61 0.10 +- 0.00
7.67 0.09 +- 0.01

James Dunlop
Last modified: Mon Sep 30 15:54:16 EDT 2002