Dear colleague, We have written up a paper entitled "Precision formula for the relativistic corrections to the kinematical Sunyaev-Zeldovich effect for clusters of galaxies" and uploaded on astro-ph/0507466. We hope our results would be of some use for the upcoming projects for the precision Sunyaev-Zeldovich effect observations. We would most like to welcome your comments on our paper. We have constructed a subroutine that reproduces the results of the present work. We are herewith sending it to you for your use. With my best wishes, Naoki Itoh Department of Physics Sophia University 7-1, Kioi-cho, Chiyoda-ku, Tokyo, 102-8554, Japan Email: n_itoh@sophia.ac.jp Telephone: 81 (0)3 3238 3431 Fax: 81 (0)3 3238 3341 ******************************************************************** Implicit Real*8 (A-H, O-Z) DMASS = 511.0D0 Te = 10.D0 TH = Te/DMASS CO = 1.D0 BETA = 1.D0/300.D0 DO 10 X = 1.D0/10.D0, 15.D0, 1.D0/10.D0 SZKIN = SZK(TH,X,CO,BETA) SZTH = SZT(TH,X) Write(6, 100) X, SZTH, SZKIN 100 FORMAT(1H , 3(D12.5, 2X)) 10 CONTINUE STOP END ******************************************************************** C===================================================================C C C The function SZT returns the spectral intensity Delta I/y C of the thermal SZ effect as a function of (TH, X). C C The function SZK returns the spectral intensity Delta I/y C of the kinematic SZ effect as a function of (TH, X, CO, BETA). C C Inputs: C TH = kB Te/mc**2 (real*8) C X = hbar w/kB T (real*8) C BETA = v/c (real*8) C CO = cosine(theta_gamma) (real*8) C C Applicable region for TH , X , BETA and CO C 0.0 <= TH <= 0.05 C 0.0 <= X <= 15.0 C 0.0 <= BETA <= 1.0/300.0 C -1.0 <= CO <= 1.0 C Output: C Delta I/y (real*8) C C Remarks: y in this routine is tau (optical depth) in the C standard notation C v is the peculiar velocity of the cluster C c is the velocity of light C theta_gamma is the angle between the directions of C the peculiar velocity of cluster and the initial photon C momentum (positive z-direction) C C Created by Y. Suda (July, 2005) C C===================================================================C REAL FUNCTION SZT*8(TH, X) real*8 X,XX,S2,Y0,Y1,Y2,Y3,Y4,C1,C2,C3,D0,D1,D2,D3,FFF2 real*8 TH,CO,BETA,FFF1 XX = X*(EXP(+X) + 1.D0)/(EXP(+X) - 1.D0) S2 = 4.D0*X**2/(EXP(+X)+EXP(-X)-2.D0) Y0 = -4.D0 + XX Y1 = -10.D0 + 47.D0/2.D0*XX - 42.D0/5.D0*XX**2 * + 7.D0/10.D0*XX**3 * + 7.D0/5.D0*S2*(-3.D0 + XX) Y2 = -15.D0/2.D0 + 1023.D0/8.D0*XX * - 868.D0/5.D0*XX**2 + 329.D0/5.D0*XX**3 * - 44.D0/5.D0*XX**4 + 11.D0/30.D0*XX**5 * + S2 /30.D0*(-2604.D0 + 3948.D0*XX - 1452.D0*XX**2 * + 143.D0*XX**3) * + S2**2/60.D0*( -528.D0 + 187.D0*XX) Y3 = +15.D0/2.D0 + 2505.D0/8.D0*XX * - 7098.D0/5.D0*XX**2 + 14253.D0/10.D0*XX**3 * - 18594.D0/35.D0*XX**4 + 12059.D0/140.D0*XX**5 * - 128.D0/21.D0*XX**6 + 16.D0/105.D0*XX**7 * + S2*(-7098.D0/10.D0 + 14253.D0/5.D0*XX * - 102267.D0/35.D0*XX**2 + 156767.D0/140.D0*XX**3 * - 1216.D0/7.D0*XX**4 + 64.D0/7.D0*XX**5) * + S2**2*(-18594.D0/35.D0 + 205003.D0/280.D0*XX * - 1920.D0/7.D0*XX**2 + 1024.D0/35.D0*XX**3) * + S2**3*(-544.D0/21.D0 + 992.D0/105.D0*XX) Y4 = -135.D0/32.D0 + 30375.D0/128.D0*XX * - 62391.D0/10.D0*XX**2 + 614727.D0/40.D0*XX**3 * - 124389.D0/10.D0*XX**4 + 355703.D0/80.D0*XX**5 * - 16568.D0/21.D0*XX**6 + 7516.D0/105.D0*XX**7 * - 22.D0/7.D0*XX**8 + 11.D0/210.D0*XX**9 * + S2**4*(-682.D0/7.D0 + 7601.D0/210.D0*XX) * + S2**3*(-70414.D0/21.D0 + 465992.D0/105.D0*XX * - 11792.D0/7.D0*XX**2 + 19778.D0/105.D0*XX**3) * + S2**2*(-124389.D0/10.D0 + 6046951.D0/160.D0*XX * - 248520.D0/7.D0*XX**2 + 481024.D0/35.D0*XX**3 * - 15972.D0/7.D0*XX**4 + 18689.D0/140.D0*XX**5) * + S2 *(-62391.D0/20.D0 + 614727.D0/20.D0*XX * - 1368279.D0/20.D0*XX**2 + 4624139.D0/80.D0*XX**3 * - 157396.D0/7.D0*XX**4 + 30064.D0/ 7.D0*XX**5 * - 2717.D0/7.D0*XX**6 + 2761.D0/210.D0*XX**7) FFF1 = X**3/(EXP(+X)-1.D0) FFF2 = X*EXP(+X)/(EXP(+X) - 1.D0) SZT=FFF1*(TH * FFF2 * (Y0 + TH*Y1 + TH**2*Y2 + TH**3*Y3 +TH**4*Y4) *) END REAL FUNCTION SZK*8(TH, X, CO, BETA) real*8 X,XX,S2,Y0,Y1,Y2,Y3,Y4,C1,C2,C3,D0,D1,D2,D3,FFF2 real*8 TH,CO,BETA,FFF1 XX = X*(EXP(+X) + 1.D0)/(EXP(+X) - 1.D0) S2 = 4.D0*X**2/(EXP(+X)+EXP(-X)-2.D0) Y0 = -4.D0 + XX Y1 = -10.D0 + 47.D0/2.D0*XX - 42.D0/5.D0*XX**2 * + 7.D0/10.D0*XX**3 * + 7.D0/5.D0*S2*(-3.D0 + XX) Y2 = -15.D0/2.D0 + 1023.D0/8.D0*XX * - 868.D0/5.D0*XX**2 + 329.D0/5.D0*XX**3 * - 44.D0/5.D0*XX**4 + 11.D0/30.D0*XX**5 * + S2 /30.D0*(-2604.D0 + 3948.D0*XX - 1452.D0*XX**2 * + 143.D0*XX**3) * + S2**2/60.D0*( -528.D0 + 187.D0*XX) Y3 = +15.D0/2.D0 + 2505.D0/8.D0*XX * - 7098.D0/5.D0*XX**2 + 14253.D0/10.D0*XX**3 * - 18594.D0/35.D0*XX**4 + 12059.D0/140.D0*XX**5 * - 128.D0/21.D0*XX**6 + 16.D0/105.D0*XX**7 * + S2*(-7098.D0/10.D0 + 14253.D0/5.D0*XX * - 102267.D0/35.D0*XX**2 + 156767.D0/140.D0*XX**3 * - 1216.D0/7.D0*XX**4 + 64.D0/7.D0*XX**5) * + S2**2*(-18594.D0/35.D0 + 205003.D0/280.D0*XX * - 1920.D0/7.D0*XX**2 + 1024.D0/35.D0*XX**3) * + S2**3*(-544.D0/21.D0 + 992.D0/105.D0*XX) Y4 = -135.D0/32.D0 + 30375.D0/128.D0*XX * - 62391.D0/10.D0*XX**2 + 614727.D0/40.D0*XX**3 * - 124389.D0/10.D0*XX**4 + 355703.D0/80.D0*XX**5 * - 16568.D0/21.D0*XX**6 + 7516.D0/105.D0*XX**7 * - 22.D0/7.D0*XX**8 + 11.D0/210.D0*XX**9 * + S2**4*(-682.D0/7.D0 + 7601.D0/210.D0*XX) * + S2**3*(-70414.D0/21.D0 + 465992.D0/105.D0*XX * - 11792.D0/7.D0*XX**2 + 19778.D0/105.D0*XX**3) * + S2**2*(-124389.D0/10.D0 + 6046951.D0/160.D0*XX * - 248520.D0/7.D0*XX**2 + 481024.D0/35.D0*XX**3 * - 15972.D0/7.D0*XX**4 + 18689.D0/140.D0*XX**5) * + S2 *(-62391.D0/20.D0 + 614727.D0/20.D0*XX * - 1368279.D0/20.D0*XX**2 + 4624139.D0/80.D0*XX**3 * - 157396.D0/7.D0*XX**4 + 30064.D0/ 7.D0*XX**5 * - 2717.D0/7.D0*XX**6 + 2761.D0/210.D0*XX**7) C1=10.D0 + (7.D0*S2)/10.D0 - (47.D0*XX)/5.D0 + * (7.D0*XX**2)/5.D0 C2=25.D0 + (11.D0*S2**2)/10.D0 - (1117.D0*XX)/10.D0 + * (847.D0*XX**2)/10.D0 - (183.D0*XX**3)/10.D0 + * (11.D0*XX**4)/10.D0 + S2*(847.D0/20.D0 - (183.D0*XX)/5.D0 + * (121.D0*XX**2)/20.D0) C3=75.D0/4.D0 + (272.D0*S2**3)/105.D0 - (21873.D0*XX)/40.D0 + * (49161.D0*XX**2)/40.D0 - (27519.D0*XX**3)/35.D0 + * (6684.D0*XX**4)/35.D0 - (3917.D0*XX**5)/210.D0 + * (64.D0*XX**6)/105.D0 + S2**2*(6684.D0/35.D0 - * (66589.D0*XX)/420.D0 + (192.D0*XX**2)/7.D0) + * S2*(49161.D0/80.D0 - (55038.D0*XX)/35.D0 + * (36762.D0*XX**2)/35.D0 - (50921.D0*XX**3)/210.D0 + * (608.D0*XX**4)/35.D0) C4=-75.D0/4.D0 + (341.D0*S2**4)/42.D0 - (10443.D0*XX)/8.D0 + * (359079.D0*XX**2)/40.D0 - (938811.D0*XX**3)/70.D0 + * (261714.D0*XX**4)/35.D0 - (263259.D0*XX**5)/140.D0 + * (4772.D0*XX**6)/21.D0 - (1336.D0*XX**7)/105.D0 + * (11.D0*XX**8)/42.D0 + S2**3*(20281.D0/21.D0 - * (82832.D0*XX)/105.D0 + (2948.D0*XX**2)/21.D0) + * S2**2*(261714.D0/35.D0 - (4475403.D0*XX)/280.D0 + * (71580.D0*XX**2)/7.D0 - (85504.D0*XX**3)/35.D0 + * (1331.D0*XX**4)/7.D0) + S2*(359079.D0/80.D0 - * (938811.D0*XX)/35.D0 + (1439427.D0*XX**2)/35.D0 - * (3422367.D0*XX**3)/140.D0 + (45334.D0*XX**4)/7.D0 - * (5344.D0*XX**5)/7.D0 + (2717.D0*XX**6)/84.D0) D0=-2.D0/3.D0 + (11.D0*XX)/30.D0 D1=-4.D0 + 12.D0*XX - 6.D0*XX**2 + (19.D0*XX**3)/30.D0 + * S2*(-3.D0 + (19.D0*XX)/15.D0) D2=-10.D0 + (542.D0*XX)/5.D0 - (843.D0*XX**2)/5.D0 + * (10603.D0*XX**3)/140.D0 - (409.D0*XX**4)/35.D0 + * (23.D0*XX**5)/42.D0 + * S2**2*(-409.D0/35.D0 + (391.D0*XX)/84.D0) + * S2*(-843.D0/10.D0 + (10603.D0*XX)/70.D0 - * (4499.D0*XX**2)/70.D0 + (299.D0*XX**3)/42.D0) D3=-15.D0/2.D0 + (4929.D0*XX)/10.D0 - (39777.D0*XX**2)/20.D0 + * (1199897.D0*XX**3)/560.D0 - (4392.D0*XX**4)/5.D0 + * (16364.D0*XX**5)/105.D0 - (3764.D0*XX**6)/315.D0 + * (101.D0*XX**7)/315.D0 + * S2**3*(-15997.D0/315.D0 + (6262.D0*XX)/315.D0) + * S2**2*(-4392.D0/5.D0 + (139094.D0*XX)/105.D0 - * (3764.D0*XX**2)/7.D0 + (6464.D0*XX**3)/105.D0) + * S2*(-39777.D0/40.D0 + (1199897.D0*XX)/280.D0 - * (24156.D0*XX**2)/5.D0 + (212732.D0*XX**3)/105.D0 - * (35758.D0*XX**4)/105.D0 + (404.D0*XX**5)/21.D0) FFF1 = X**3/(EXP(+X)-1.D0) FFF2 = X*EXP(+X)/(EXP(+X) - 1.D0) SZK =FFF1*( * FFF2 * BETA**2 * (1.D0*Y0/3.D0 * + TH * (5.D0*Y0/6.D0 + 2.D0*Y1/3.D0) * + TH**2 * (5.D0*Y0/8.D0 + 3.D0*Y1/2.D0 + Y2) * + TH**3 *(-5.D0*Y0/8.D0 + 5.D0*Y1/4.D0 + 5.D0*Y2/2.D0 * + 4.D0*Y3/3.D0)) * + FFF2 * BETA * CO * (1.D0 + TH*C1 + TH**2*C2 + TH**3*C3 * + TH**4*C4) * + FFF2 * BETA**2 * (3.D0*CO**2-1.D0)/2.D0 * (D0 + TH*D1 * + TH**2*D2 + TH**3*D3)) END