"!$#%&'())*,+.-0/21-3.456%&'78 9))8

:<; =?>A@CB6>ADE>9FAGEHI<D2JLKM@NPORQ0I0STGU>"VW@

:9;E:<; XYNPHNP@C@CGU>AVZQANPDE>[H8GUSTGUNP@

\ P-](^&' 71_A]-%a`]_8 3_`b1b%&0cd1b-?%ef70L)bgih8 4c5j7%e^&70k/ld1bm n#"^&1b%eo1_A0p7<1b0kqr7sp0%e` ^&%a^&t#'c/21c(1-8%e^0-<1uv1c/2w_01%&0--%e18r_Pxy4z|7|<rq97w_`1u%&/~1b7|-%eT` q.70#1%e]q7s%e`4of7k#<1b#"zwp+c~+jwccc6c+rt2z2ocb0R_8 \ %e^er4p(16R8l/21-7<1b

p_"$21o 1l1' \ 4p__0^&w''-(7<1bl1t^&y-d^&%e.bqqE1%em1-|-%e18yP1u'81^1b%e?0_^&1 #A%1^e^e 7P0%e'Y%e]'0# [_A_`--0%&b [%eq#A%&_^e [/w7y77L1_#0%&^e%&c%&]70L_mx?7R/ ^&1'-0%&#0^18cT/21-^&'~/21C`^&'7 A1w%&'78|_Aoy$#A-¡n-0!P%e¢£|70 q`-f#<1y¤%&4

c%&'7k#1c C1c/l#Ay'1b(cbqc¥0R(/l_01%&-f/w%e7~1'1%e#Ay'1b#7¦ct1bv1v70-¦37¡C))u%ev7§^e#A4¡z|7%e#"'1#7¨7<1k1¡b©b%&v7^&^&%ed1u%&0'?^e /2(#%e <10-f1ªu%ev7C110 <10-3'%a`1-%e#A%&q2R«ª0'#Ao%&^&^e%&1bt©m))04kz|7Ly$#A0L%&cqU7L#"'1(c/ldªª7010-¬©870 M#"%e`^e 4¡z|7d1-%&1^.`^e$%e qU­7Y#^&1b7<1b_A¨C1b-¦_8 \ %&\ 1C2(1v®9 ¯qr7L(#00%e'Y-%a`$%e%e[ 10-¬_8 ]? $^aq [7k/l%e'78-¬C1¡`b1^ek_A%&0'° ª8k®mn4²±ub4£

pbk71btc³0RY%eo1¡TugihL(1'%a-'81^1T$ f1-¡7_`1u%&<1^M^e%&%eR/ %e´¶µ b©gih?d1b'%e-b 1-n#"%&1^&^a dbo7ov1^y$#"%&cq«70·

¸+r¯.z|o¸¹~+.z~5º+r+r»c!$zWc~+¼cp¸ccºc+rt2z2½ \ o+¾czwwt¯2z|+r¹~s+¿_8 +.-0/w%&np0__^&R8v1®bw7o1-%&1^"`^&P%a%e2qU|b©'81^&1u$%&2/w%e7,®mR/w-%ev1bp1b-n0|7L70tqU

ÀÁ¡à °¨Ä AÅ9Æ °ÈÇ %&wÅk9Æ °¿É %&wÆ R

/w7 Â %ec7LPÊ%&8t^1u%&0'Y`^e$%e 3-%&v10L%&1^&%eC1b`^&P%e f-%&v10L^1C/t /w7%e^&3 ÄfËvÇËvÉ o1L7m%e_0%e¬q27(^1b%&]70(1-%1b^`^e$%e 4p_0_^&qU0-]1(^&0%&n#A-%e'(d^1%eq«)®mY±bR/~1b-¡'81b^1y%&t$-%&1bÌ Á ËoÍ Á C«04 \ P--%&1b%ec'%a`Lª)«Y®Pd±bR/21- Ì Á R) ËcÍ Á ]l17%e^¤ z1((1kÎ!$1-<1' <R8y bc70%&M#1.bq<720.7<1(1%&0-kÏm%a~v1_^e4MM%&'027R/w70`^&P%a%e¯-qU70l%etq07'81^1T$ ÀÐ Ä 9Å9Æ °kÇ %&Å9Æ °É %&wÆby #^e-6ÑÒÓ9-%&v104¹2$70?`b1^&0bq ÂÔÁ b))(®md±bR± \ #A-0%a`-¡_8 f__^e%e§R(%ekv7Y$?^1' m_A17%&l-%&v12/lckv7Y$?(1^&^Õ4My7^& 07%&l-%&R` 7<1u

-%ev1bmp'81^&1u$%&p7<1C`%e¡`^&P%a%&w##A%&<1^[7%&-%&v10p%&w7?q(P-(^&' 4

(P-]%&^e' [p0__^&b¢£ Â %&c-0- W1-C1^e^&-¡7 0ÒE4!$%e%e%&wbC1^e^e 1L18C A_0p-C1bc17ks%e`'^e- <?#A#^&tC1b^&^%e|7p_0_^&o#<1b14

Vel

ocity

[km

/sec

]

Distance [Mpc]

0

500

1000

0 1 2

M%e'4~4 p_0_^&b¢£w-<1b1%&R8$4

z|7%eL`^e$%e ¦<^&-[ ÀÈÁ Ã 2717` %&#A18##" ¨71b%ekqU %ev71'-¦_8 ¬1n%e70110^1u%&¬?1bv1b%&]ql7P-%&<1u Pn4YzW371R`Y1^1b%&3v7<1b'-%e3qU»-0%&0'Y1YP-%&<1ut1bqUd1u%&f%&pC1^e^&-¡1&Ò !"#$&Ò 4z|7%&(#7%e­0-bv1b%&t1b0-§70(%&'%e]%&t_8`P%&0 M_00tn7&%"ybq

Vel

ocity

[km

/sec

]

Distance [Mpc]

0

10000

20000

30000

0 100 200 300 400 500

M%e'4r$4 c%&v1ÑÒÓ9-7%eq wqU|zr P#"1!$

1^1b%&2%&-~7o_`b1b%ew(1-c_8 1|n1L'1^1uP /w%e7n#A%e%e Ã^1b%e`Yo10-]1(`^&P%a À¬Á à ^1u%e`Y4c /l^e-¡C1#A%a%&.^1b%e`|?70^a` Ã$Á ÃrÐ Ã 1b-(`^&P%a%er^1b%e`|7^e` À$Á À|Ð À 4¹20

À Á ÃcÐ ÃÁ RÃÐ Ã Á Ã ¤(1|3'81b^1uP /l^e-3o701?__^et^1C/7<1b|/l?-04

z|7m`f70'7/l??1^&^['1^1u$%e~-%&0'qU 7%e|-$p0w(17<1u/l?1%&708qM70#1%e[4pc_`¡18 n7'81^&1uP /20^&-f?y01^e 701b(70%&'4z|7P07p__0^&L^1C/ -$tt-y<(18qUc7Ls%e`4d7tqUqU70?-%e1`^&P%a ^1C/¥-(-k1%&Ïm8pqU|7?y$#<1%&3#<1b2qUy01#^e%e70o118o`^e$%e ÀnÁ À Ã t1YÏm<1-01b%&k^&1R/ ÀnÁÃ Ã 1b%&#70%&-

ª

1^1b%&4

]1y<1b^&%e ?<0-p7<1bc'1^1u$%ew7<1C`k#A^&%&1w`^e$%e%&w%e¡1--0%e%e(7k__^e`^&P%a $/w%a71k(1'%a-0pq))k®md±b4r-02L11b^a (|7o__^eo^1C/t 00-_Pxlq"v18l.C1b^&%&_01b1_^&2^&%&%e%&71bC1_"w_0`-1br-%ev1bl^&1'0'73L7p0__^&t`^&P%a %&j))®md±b42zr P#"1L#AR`1bk1t` _%e'78C 91-1bq p11^&%e_1b%&_<1b-fn7%ep-0C1C n#A-[ "7 n7<1C`?` 3(1^&^-%&#"%ef%ef1b_^e0(1'%a-b4|w%& .oÎo%&70?R82<-f7<1bp^e#"t%ef1Lbq`^&P%e%&w(-0%&1$-0^&%¤ ^&' ÀÁ Ð °¡Í <%e Á ) )0C)]) £))ª8c/w7%&^e|7p__0^&^1C/,#-%e Á $4z|7mw7p0__^&t^&1R/7<11'P$-7%&C1b^[_<1%&1-%&~/l^e^a¤-3_0`b1b%e<1^e^e 4

z|7t1y<1b^"`b1^&0q7op0__^&v18 ~%e~^&2/l^e^-y(%e-d%&0c%a~Ïm%&~70C1(mpqM1_^&0t-%&v1%&1-3bq-%ev1bt1u%&4z|7?w^&%&®b^a Y1b'tR/¥%& Á º«d®md±bR± \ #"qU 7kc!$zo .uxo37k-0%&11^&YÕ<-(1 aÓ& "))0 Ap#0 ª0 9©mw1-]$,ª ²L®Pd±bR± \ #"?qU \ ¹1%&#8 -%&4w56/w%&^e^-%e0c(18 /~1C PoqrC1%e' ^&1bp%e370k0b4](18 n(^e'%eC1^[^e7v1%e3`b1^&0bq %&|qE1y-30p%e'7v1u%& Á $R))L%&70?v1-1-3%eq¯®md±bR± \ #A4rz|7m|%aqW1'81^&1uP (71|1k__^e`^&P%e (qrTb))®mY±ub 0%a2-0%&1c%&cR\ #A4

5j7%e^&%atql®mY±bC± \ #AY1(0^e 3-§qU 7%&0%eo/l^e-§_A0- 4.z|7?8`%en%&|%e(#0^&

Á R))o®mY±uC± \ #A ÁC)!.d±b

ª )«88«#"¦R) %$ Á ª ²&"6R) (' Á

²«c P Õª

:<;*)[; +YFAN

07|_`b1_0^&oÏm<18%a Y%eY7os%e`t%&27t1'obqW7c^e-|7%e'~%e%e4z|71_1%eC1^e^e 7t/~1C P-f1b'|qU~` n^e-7%e'4.z|70<1-n_"®mR/wf1b(#^e%&|7?0bqM70p -0%1'1 d-y%&o701'bqr1v1^e4~z|7^&%&%e dqM71xp^eC1C`P%&'L70(1%enÏmUd1b%&Ïm0% Á \ !$zt|`b1%&^e%&®b,.- /$ 7od1b%&dÏm?^&%eqUy%e(|`b1%e~^e%&®b102- 43 -5, 4376 $ 4z|70%&~C10~7<1b|1YR)98 -0%&1on'^&_0^1c^&'%e`1RT)8 t%e7L-%e`-¦1b'4c%&v10on'^&_0^1^ep1bo-y(%e-qU 7td1'%e-2q[ P1bv1 910-71c/l(-0% %"8/21R Po%&(1b7%&o1_0^e0k(1'0%e0-4tsp%e'Y70v1u%&%eC1^W#<11^&^&1unqC1b_8 ][ P1?v1b'%e`o1f1'?qU7^e-c'^e_^&1|^epqwR«:º(o P "/w7%e^&%e'(7k[ P1t1%&7 \ Õ¯1' \ 1'^&^&1%&o2^&-<~1pv10-<1-0'%e`1b31b'tq~C© c $4sp%&'n7;Ac||t!]_`b1b%&0oq20C1_m ¡_A-0/21qUt1^&%e_1b70d1%e]ÏP0(q'^e_^&1~^e'%a` < ©c $?Õ27<1_AT cd1Ïm o<1¡Î=t1R«0 <#[ >©8©0 84.z|7o'^e_^&1l^&|--3(c%&pkqUn $Lr/w%e^&^9v1®b0 Á R ²?j@ ²c PqU~7%&|7$-4

©

z|7-¬v7%&ÏmqUo-y(%e%&0'31b'tq2^&^&1c#A#^&1b%eo%&c3^e$®3qUc7^e-/w70%ew-0/21q45j7%e-$/~1`~1wqU-LqU v1./w%e7%&0%e%&1^0(1^&.71d1b_"$« ?7l5ºc2qU 1uq l1_A0|)%&^&^e%&? C1b4lcqU- P5ºcx|'~$^&1-3qE1%&84|z|7m7^&-5ºcp/w%&^e^_"t70^&1p^&0(%e1-fP^&5ºc4wz|717071-L<-[ 9q4~R/2y` A71b##"1|(_A17<1#n-0'?%e7t^&0(%e%a qUy%efq./w70%e-0/21` #"-%&0'dd1]1'?qr1_A0?Lc P4!$%&0?71-%e®1 <1-7o1|%eY7o-%e®qU-1uq ~7o7<1^ek1w1b-'^&_0^1^e 70%&~C1071b7k1'q7ks%e`%&p1bp^&1Tdc P [1b-¡~/w%&^e^[v1®b#0 Á T4 ² ²(o P4c¹21-1b¡Uq[s~o aÓ& P))8$ 1b#79±)8b)8)«8'%e`R ² n) oo PqUM71'|q97|/w7%e-0/21qM#"#^1u%&%&Y70'^&_0^1~^& \ ©4ct#%eqE1^&^"%&7%e|(y7P-%&~7t#70(qM Pv1^e%C1u%&n%en/w70%e-0/21qP0^&%¤425j70f7?81^¯#A1u?'y^eR/ 0'7[ 970m^e%.1b1b'7^e`t%&81Y'0^1c^&1b%&4oc7%&7<1##A 75ºco(1%&3qUo1^&'%&o1b10$-n(#A1bt1-n^&%&0%a 4q |7t7C1bq^&%&-0%e<1b%eY%&|1-%&1b-1C/~1C $70p5º P^e1#%e-^e 4Mz|7m27/w%&^e^<<1b01^e^e _Ac1(-'%&7p^&%&0%a qUy%eq5ºcpC10-]_8 n Pv1b^&%1b%e[4~5j7%e^&o70_A`P%&-0k%&w7<1up7^e-5ºc7<1C`[¢ yv1-n( P1^&% 7ty$#A-¡^e%&%e (qM1^&%e-%eq P%&0'5º³%ew^e d^e%&'78^a d_A^eR/70_`-¡-0'4

z|77%&-d/21R (170o1'pq[70osp%a`o%ekC17o1'q7v7(%eC1^^e84?z|70%&c7$-]^e%&p]1b-%&81b%a`?%&b#A/w%a7]^e'Y7<1b^eq^e%e`4oc%&p` ]C1 (1®L1#%&LC1(8tql7%e(?%&01Pv®f^&%&-0%e<-[ 1-¬_8 1##0^e P%&'Y7%&v7%eÏP0(Pv®Pp37k+r17f1¡^e-c1'?q.ª04 «do P%&wqU-4w¹20c$v®m7<1bqE1^e^0q.7®m [%a "1k^&-4z|7k^e^&-(y%e?%ep/l^e^-%e-10-¡7<11]1'?q©4 b©c P4oo%eckv7]-%aÊ(^ep'yt11'?qU7s%e`L1o1d/w7^& %&0k07<1w(11$-0^[qU|70?v1|qUd1b%&70%& 1-qUw^&^&1|m^e $87%& P%&^&-4<ty01#^&b W71b%&nq (' !vw (' !c%&t^&t7<1¬7<1u#-%e-6_8 ¬m^e Pm7%&C1b^&0^1b%& 21b-(' ! w3%e(1-%&1%e`b4 z|7f-0%a`-j1R`1'¡1b'3bqc73^e8(%& £ª ²Lc P4r%&'L71b|7t^&8%e7!$^&1w!P P E%&o7 (' ! w (' ! ow1b%eC1b]^e 3_Ak(10-%ef7!P^1c!P Pd/2L(1-0%eqU(^a _"y/2¬71b'kqr70sp0%e` 0 1b-d70cqU(1b%eq7!P^12!P Pn 070 0 Á C©¨ªc P4 \ P-^&~%e8/w%e7Y7 \ ¹º1b%&#8 d7<1C`?1` <1R/1'q1' 0 Á Rª ) ²c P _00~70%&~%eÏm%et(P-^i-#"-m4

z|7Y-0%&%&^e?#$-0 0 kC1¦_Ad0-¦¡-%e%&%&<1uL1'3(^e'%eC1^$-^&4.zM1®m%e' 0 Á Rª ,) (c P?U70 \ ¹º`b1^&0R~1- Á $?,ª ²®mY±uC± \ #A <70%&#$-0%&

0 Á0

«o P Á ) £,) £)8 E©8

:<;[; WB]K.NPOdH>V"SR@

5j7%e^&%a2$®/l®Pq¯0#Ac%&pC1b7-07%aq |q¯'81b^1u$%&2%ed7R8)0¢ %e/21ckv7]1%eY#7b'1#7n7­1-f(170%&(1'%a-c10-¡#"%e%&04p%&#A18o_`b1_0^&L%&c7LP0k_"tq2?_%e'78c7<1§1'%e`<$¬#At%at^e%&-1'^&4Mz|7%&l%&20(1^&^a k--¦rl¦ $/w7¦%el70^&%e(%a%e'<$" 1b-½%el70mk_Aq[_Pxy#"l1-%&1(_0%&'7m.71~4#%&%&#^e¦r.%&r1oqUy%&(q-%&y%&1|/l^&^[1<$"4r3#1%& qU|_%&'78|'81^&1u$%& $7t%&w1k` #(%e8w81u%&3%e70c0^&^&1b%e%&' P®P0T/wn1l7%&'^& 10-YR/~1b-1#^&1p%&l7c®m d®mR/w31b70o#A'81^1b%e#^&1b4.z|7%&|^&1'2C1^eo81b%e%&2®P0T/w31~7t$1^!$0#"^e4

pR/l` 1d^e$®P?1b?qE1%&81b-6qE1%em'81^&1u$%& 7dmk_Aq|'81^&1u$%&?#A1-%1b¡'o^1'p1-]^&1' 1-1^e(kv7(0%eqU 17®8 4?<p#0%&C1b^_`1u%&c7-0%&¡7 \ %e^&®8 f561C ¡C1b1Z q21R`%&-1/w7^e ¡1dqU/'81^&1u$%&o1[ _00t7%eo&%"%eot§%&¡70%e0qU1b-]_`b1b%eoqU»70c!y$#A%&8C4.z|7mw%e2%&lC1b<1b_^&k#A^1b71b27tsp%a`o%e&Ò ! " 2^1'pC1^e %e7mk_A?8q~qE1b%&8'1^1u$%e1(1##0C$%&(1b^e ¡7(1d%&§1^e^.-%&%&00%e-7 qr1C`%&-<104w#%&C1w701b(%&31^&^-0%&%&4 \ 1b7(1b%eC1^e^e %&#%ec(1w%&#70%&0-bv1b%&4

z|7Y^&#Adbq|7Ym_"8 ^& ^&~ %ek107k_`1b_^&(ÏP18%e 4¡q70dk_A%e'38- 1%aqU^e f-%&%&_0-¬7'70#<1 M7<1¦_0`P%&'¡1<$6^&%e(%at©f%e(^&R/l/w%&^&^1^e^&R/ 0d¡Y_Pxy/w%&d1qE11C/~1C 4¹l0k70%&`^&%ec«(%&^1' "d7^&#"?q.7?08%& Ð ^&w«9^&2© Á¶Ð ª$4o__^e_`-]7<1b7kk8qU^&^&R/l-n7%ep^&1R/ 1b7/2^&^¤ A%&0-%&1b%e'7<1b7'81^1T0%e_A -¿70¡$1^!$#A^ed_00d/w%a7%eÈC1v7,bq706R))%&0v7È^&#"f1-¿^&-#7b'1#7%et#^1bw/2?%eqU^e (-%&%e_0-f%e3#<14|z|7%ep%e(#^e%&~7<1bw7ks%e`%e# $ 8Ò]^1'C1^e4&1c7'%-]%&^e®%&cbo#<11u-%emC1½1-®m%e (%e^&®9 <1(70('psp%a`?%&wp#<11b-¡%&8'%&|/w%e73-% %"8p##A%e4\ 1b7(1b%&C1b^&^e 7('w(1|%e#07%&c0-|1^1b%&04

p%&w#"%e_^&_A?%e#%ec/w%e70p_"%&'7' 9_070%&#8 /w%&^e^[7^e-37^&-1bt|/l(#A%em4z|7mc170q#"^&1|P-%&<1uo'1#7n#<1#Aw%&|%e3#%&%&#^ec%&#%e1-¡%am _0%ep%&p7'04z|7k%e-%1bw¡1d'^&_AoqU 13%&b#%&#<1b310-7p731-f!$$7#"^& <_0wbp^&/w74

o%ec1^eY#A%&_^ed_"k70('c_00t%&b#%&b4t!Pv1b-<1-]Ïm<1'%e-¡'1b#7#<1#A%&t%e§#%&%&#^eL7'0t_$%a?%e?0%&b#%&L%eL70(1qU0?#qU--%ey%e4 #<1b¦^e%&®1n_%ev®/21^e^%et7'0?_0??%&#%&b4p7<1b1#<1b7<1bw%e|%&#%&c10-n7tw(c#A%&8w%e|1%e^e 70('4

M%e'4ª04 z|7L_%ev®3/21^&^¡7^eq o%eo17'0c_0tbt%&b#%&?#<1b[ [/w7%&^e70#<1bn7t%e'78w%&|%e#%eLÕ1b_"$|7t8w_00(70('4

:9;¯; =kX¨Rb© %&1tζ5j%e^&3qU0-1]y$tq1-%&(%ek%ef7_0%&'d7018<11b

¹2^&^.¯1_4kz|7%eoy$0%&k/~1tÏP0%e`b1^&8oª ³ 4[z|7%eo(1c7<1b1_^1bv®P_AP-0 /w%e7 Á ª /2^&-¡#0P-?7?1k18pqr%eb4¼_0^1v®m_A$-0 n%ec1¡_Pxyc7<1u1__0o1^&^7k1b-%1b%&71bc7%ap%eC 1-¡71o1d18c(#A1b04 %1boÎ 5j%&^&/l_`P%&'©nt Á (Y [1-]%aq.71-%&1b%e3/lk^e 31Y_^&1v®m_"P-0 "7]%e/l^&-qU^e^&R/ 7 .^1bv®Y1b-%1b%&^&1C/

Á ´ c Á y$#W Ð ¤

qU1b^&^rqUÏm%e/w%e7 1¡0v1bm4¬p %&?7%&8%e ¦bq|7®m ¦%&¦0%eq'm±b ±uC±b± p5±b ±bv± b 0±b4cp<1^&^a 7%e_^&1v®m_"P-0 31-%&1b%e/~1p<]1u71LR))L%&v7n^e#A?0-n<-37ty$#<10%&fq7?sp%a`?%&7tqUqr0%e1b%e¡q.7k%&8^&^1bpy 81'1b-%&1^~ %&8Y%a<ty$%a-]v1b4oz|7%e/21§%& Rª_$?7L^e%&'0%e1b%e]#A1u(1u Á 4 (»qw4 ª /~1t%&--¬%e'%a<C184pq R© [(18 ¡'#tC1-]7L_%&'780tqr7L®8 1bd18 n-% %8p/~1C`^&'70 0^&%&<1b%&'L%e \ 1b7 aÓ.R0 "$T$ $Ry 9/w7%&v7¡<0- Á ²«<¿) )))8&³qUw)$4²k dk( /~1C`^&'7[4

z|7%ek_^1bv®P_AP-0 61-%&1b%e¬/21k#0-0%&-¨_8 t1R/ 1-¦7%e-8L^e#71-p(1YqU 70%&l7 (qU270cqU(1b%edbq1^e^A7ov7(%eC1^[^&(m|-%&'L1k-t7b#7<1bC1^e %e77%& qW7?sp%a`b42p^&#7Î p(1¦R©8«2#-%&y1(#A1b0ql L4"¹207%ep70 3bq.7qU(1b%enqr^e8qU 8LqE1b%&^&-3d(1®kv7¡q18 m7%e'71R`P%e27<1Y7^&%e¶_"C1c7t1ckv1_0^&cm^&%A/w%e71b(%e/l%e'78|q?

0

100

200

300

400

0 5 10 15 20

Inte

nsity

[MJy

/sr]

ν [1/cm]

2 1 0.67 0.5Wavelength [mm]

FIRAS data with 400σ errorbars2.725 K Blackbody

M%e'4©4 \ ¹!$#" \ 10-3_8 nMc!Y¡|o¹~+|4

«04z|7m70%e`c1--%a%&bq[#0lr0l%&r##A-Y1u7 Á '81b#[4¹2C10qW7%e2qE1%e^& $7o#-%e%eqM1k#A1uoq¯7sp0%e`t/21w|1®3%&^e d8%&^1bq W %1tÎ 5j%e^&f7<1-¡qU-¡70k_^1bv®P_AP-0 n1-%&1b%e[4p¼'#1b r%&]^&-¡_8 c%&v®b?/21'%&'(y ndC17?1-0%1b%&/w7¡7y 3/l$#"-¡_8 W %1μ5j%&^e4~5j7]c%ev®?v1b-f70%&#ux7k1®-1(-m(-¡#`P%&0yqU1-]7L^e 3#%&cC1b8qr7(#A1b0qr70®8 ¡7<1ut7<1-_"¬#_^e%&7-/21 µ b) _8 3c%&v®?7%&^eq4~p-f7%&#<1#A/~1p#_^e%&7-3%&371`^&q70 #TÒ yÑ 71b7<1-31b(R/t¢ ~</l®A4

z|7? \ ¹~¶Õ2%& \ %&R/~1C`?¹~1v®m'-31-%1u%&9%e|%&-0%&_^a d%e#%e4.+M$#0qUp1(-%e#"^&o¸-d7!$0[¢£p(b%&3^1u%e`(7U^&%e®o7Y ÄfËvÇËvÉ |(%&n__^e¢ w0y 7o(#A1bo%&|18pt#<1w#"%&^e^&%ed1b|7t®m 4

«

M%e'4$4 q 081 \ ¹6®m 4) Á /w7%a u©: Á _^1bv®A4 \ %e--^& 81M7<1-_8 f©))b¾k 9#A^eoR`-[ 7R/w%&'Y-0%&#A^&1- \ %&^e®m 561C 4p%e'78~817<1b-]_m 0 £8u¾ 0/w%e7(0#"^& $-%&#A^eo1- \ %&^e®8 d561R YR`-[4

:<;[; GEB6NGÕDUI0STGU>AV

cÏP0(q.71-<1b-%&8#1b%e¡q.7-7%aq o%&p7<1bp7-01b%&0ql^&%e'780`o7^&-_A%eC1-]/w76^&P®m%&0'1bt7%e'7]-7%aq t_Px4Lz|7%&o7<1bo_"0<-n%&701#^&oq0t7%&'73-7%eq 0#"R`b1tqU¸o^e-7<1_A|1b-37?!$#A0T`b12(^e' .uxyL¤b))0 A1u#79±b)0R)©8ª«8~1p7R/w]%&3M%e'?04|z|7/w%&-07fqE1y³%&70k1b%&q.70-1b%efbq.7?_`--1C fY1(%&1^¯-1R 3-1b%e[4z|7kyv7qE1y|-nLC1^e%&_1bp7tzr $#A1_%&'78%ew'%e`_8 Á ° y4rqM7t#"#^1u%&qqE1kÑÒÓ¯^&R/¼-0C1C -Pttv71'/w%e7]-7%aq t0#Ay Á ° y4kp , ÔE^eC1p¸q.1b_^e0o`b1^eq|L70ko^&-07<1_A aÓ9-<1bv1L%&w7R/w]1-7<1|7tPÊ%e8

Á ) £«8 ° $ ' Õ , %&c_t1'81%e0^&%&%&f7k-<1uv10 1b-f701%&8 3%&f7y$#A8o/21`b1^e<1b-¡%&'(7k71^eq1#^&t_A$b1#f(y7P-[4t2^eC1^e 70%&%&p#"qUy^a f%e8/w%e7(7c¹2%e'¹21'#0-0%&%&(q Á ° 10-fpv1b-<1-Y-`P%&1b%el1R/21C LqU 70%&-^&%e'78|#-%e%eq Á ° 4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.7

1

1.5

2.0

2.5

Redshift z

Wid

th fa

ctor

w

M%e'4L04 z|7%&k-%e^1b%& U1b%&q2_`-§-1u%&30(%e<1^-1u%&§1u Á )8ÑÒÓ-70%eq wqU|7%e'7-7%aq #AR`1b4

R)

)[; =?>A@CB6>ADE>9FAGEHI<DOuGÕVWH8GMDUN

¹2C17? \ ¹~ %e|%&b#%&b 1-%&%e#0%&o1bwc7<1/l(#A%em|%&#^&%e7'%a 01-d1®m%&'72#A%&1d`P%&y/º7<1b~7o+r17%&l|%e1#"%1b^#^&1c%ed70 /ltoL#k^&'1b7t(^&'%eC1^A#%&%&#^e

!" #!%$&')(*,+- .!0/

!$%eo'81b^1u$%&~1o-0%&'qUC1bv7nb7 071R`1'o-%a q¯7ts%e`o/w%&^e^_A-1%e'Y/w%e7f%e(b 9^&c70%&'Y^e%&®b7L!PC1-0 ¡!P1bkP-^/ly21 _00c%aC¢ 43¤4rz|7%ew(1~71bw/27<1C`tL_A1yqU^¯1_A0w7R/ /lt-?70('%e 456t7<1C`#A%eq f1Y(%e?%&10-]v1u7<1bc7sp0%e`%&70('c^e n]^&%&7'7#1%e(t/w%e7f18o%&o%e(b4z|70%&0-c^&%e®%ep81-%ep0q7?ycbq#A%1^.^&1b%a`$%a /w70%&v76v1bt7<1ut-% %"8_`(R`P%&'1-% %8t`^&P%a%&c/w%&^e^-%e1'1b_"$/w7y7y`m1k%&k0^ev1b04oT/l` M1f_`o1R`^e%&'1ut)04ak^1b%e`w?0/l^e-d-%e1'w`Yp1b_"$7pp__0^&^1C/t m%&07w/2^&-(_^e7%eq q#]ª)0 )))d®mY±u]%e-kqr7®8 ¯1b--07%aq o'C1b7<1ª)0 £)))Y®md±b7L7t%&-Lq7L®m 4dz|7mt/2C1b§-y<(1n#"%&1^^&1tq2_` M®mR/w61(R`P%&'_0` W/w7¡1b^&^ML7(p0__^&L^&1R/³qUo'81b^1uP ]-7%eq %e%eo%&#^&kqUn45j7f/21®1v7¡(R`P%&'_`(-%&07?^e$1^-%a 65Y1bc1%e(o/w7f70C1-f1'oq¯7sp0%e`%e0 77'0%e d(1~7<1b|70%&75d%e|1kqUy%&n^e (q0|1b--$w-#A0-f70^e$1b%eYqW70_`4

[; Nm>AB6N8SRO

z|7L%&#^e%&C1u%&wqr72(^&'%eC1^ .%e%e#^&1-]7L__^e^1C/ 1_v18%&1^¤47?-%&v10_"y/2¡/lY'81^&1u$%& 1- ´ 1b%e( 0|_A 0y4|z|70%&-%&v1?71p_AC1-]_m 3(R`P%&'_`1^&^W1b%e(04oc-%ev1bo1?^1'0'7¡(7^&%e'78w1C`^¯%&t_"p%&#"v1bm 7%ep-0%&1kc_AC1-f_8 3`1^M(R`P%&0'_`c0'd0p1^e'70/21C _"y/2 ³1- ´ 4~<wy01#^e 70?#<1u7qU ¥ ´%&'78_" ´ 4wf_`c3'81^&1uP 1¡C17-%&v10 0_8 ]-%e'3011-<1bo#^&L1bo%e( 0 Á 0 Ð 0

¯10-¬%e`P%e'7Lv70f1bo%&

0 Á 0 ° 0 4.z|7t-%e1o%e~qU-n%&' Á

0 Ð 0P k1w%&1^e^[1b-<14qM

%e?7?_`o¼%&p P%&0'(d(170-%ev1bb [7?/20^&-¡7<1C`kY%e70'70?%e(b <w^e0-¡0#^em%&m<1^e^e (/w%e73C1v73#^eP--3(7v7Y1_Ak%&-8%e-f/w%a7f7kc10%e%&4p1(%e(%&8`b1^ 0w 0 ° 0 C1v7]q.7(1^e^[_0%&8`b1^&'T/wwf ° 02%&w%e%e%e%1^A`b1^&b4lz|7mqU18 #<1%ebq'81^&1u$%&70-0%&1'R/wp_8 1qE1y ° 0~`¡%eq¯7t-%&v1 %&|Ïm%at^1b'b4.z|7P07Ïm<1u%&

ÀLÁ 0 Á ¤

/w7%ev7]%&w7__^e^&1R/ %ep01^e n0`]/w7¡7k-0%&1o1^&1'7<1 1-

70%&#^e%&-`^&P%a%ep1?^1'|71f70#A-]q.^e%&'78C4|z|70%&%ec1ÏmLq7?/21C -%ev1b10-n%&w1-0<-f%e37('w(^&'%e $/w7%ev7¡1%&8/w%e77^&PC1b^&^e %e%1b^P-%&<1u|bq1(R`P%&'L_0`p0^e dqU|(1^&^[-0%&14

qU^l0Ïmq|7__^eY^1C/¶%&7<1u 0y /w7%ev7¨-#A-0670`b1%&1_^e 81d_AwqE1-d%&81o%e(~`b1%1_^e|#<1 0r1-(1$0-Y#<1 Ä /w7%ev7d-#"-70#1%&|q_Pxp_$p0w7o%e(

0 Á 0 Ä Õ«

/w7 0w%&p7k%&1^&qE1c10-1##^e%&w(7/w70^&sp%a`b /w7%&^e Ä %ep7 uÑ &Ò _A/l 10- ´ 4kc_8`P%&^e 31k^e%&#^a n1^&^¯70 Ä ¢£o_8 6R)1--%a`$%e- 02_m fR)k10-n'~7c1b(3¢£ L1k8`8%&k$Y70c1^&oq7o1^&pqE12%e--[45§/w%e^&^A<1b^&^e ( 0 Á c/w7 0 |%&27o081'cq¯7tsp%a`b4lcqW71b(1w7<1b01^&^1u%&|-tP-<1C Y/w%e^&^[_A? %_m ?#1%&n©L%e^&^e%&dT/t _0w7%&|%e|L(1^e^/2t%e'o%eC4

z|7w('T/|7qE1w ° 0-%e-d1^e%&MC1b(_A~/w%a1 0 ° 0 0y4z|7qUt7p0__^&ov18pC1n_"c/w%e31

Á 0 Õ

sp0^& - g <7?!PC1-0 3!mv1bP-^Õ 07t`b1^&0oqM7p__0^&t0v1bm/w%&^e^[v7<10'/w%a7%e(b4z|7mt#"#^&o1^&^%e~7p__0^&t#<11(y4

T

[;E:9; XYNPDEI0SRGE>AV K.NmSNPNPV I<V 0

q7__^e`^e$%e%e À¬Á 0|C13_"^1b'w7<1 </l#_<1_^a 7^&-n

7t#A%&1^[^1u%e`P%e%ecc#0#^&~qUk0^1qU|-7%eq

Á ° Á ° À

Ц
R)8

5j7<1bnv7%eÏP0¦C1º/26§%&C1b- ¢£3'¿_<1bv®j¿03%e3q_` ´ 4§t1^1uP ´ %e^e%&'781u%e( 0 Á 0 ¼1-¨/~1C`^&'7 4rz|7%&|C1v7p_`1u|%&:0 Á 0 ° 0 ~

° a4rz|7%e|-%&v10o%&|d1b^&^

/l?1t7o<-1##0C$%&(1b%e Á ° À Á ° 0 2Á ° ¨ 0 Ð 0 2 T

¹2070p%&'78r%&-0p%ex 08 0 24.z|7p11'8C1(_"p1##0^&%&-?7R/ 7<1u Á 0 08 T

M%e<1^&^a L/2'|L'81^1T$ ³1b|%e(10 Á 0 91b-C1/w%a

° Á 0 0

0 0

0m 0 Á

0 0 Á

0 02 Rª8

z|7%e?qUk^1^a ¬1##^e%&370d-70%eq ?q|(R`P%&0'f_`L1¦_8 6(R`P%&0'_`4Lt%&t1b^e/21R Po#A%&_^e7<1C`(1#<17%e#¬1C`^&%e'1b À

Á ) «Y0^&%&'7m-<1C

1C/~1C ]qU»7(!$^1b!P P %eo^e%&'78c -<1C /w7%&v7/2$-1R 3/w%e761-70%eq q ° Á ª`37'7 0 0 ~ 4

¹2C1q7t^1u%&7%e#_"y/2¡-7%eq 1b- 010-37 0 </2q 3#"1®q70%&'w7<1b##"%&0'd1bp1L'%e`n-7%aq %&C1b-3q1bp1'%e`n%&4rz|7%ep%e8`%&m_"C1070-7%eq %e|_`b1_^et1-n1^&^a Y7<11'C1bw%p7t1uwq#78 P%eC1^¯#$4

[;*)[; N8SROuGEH8@

3t1^¯w^1u%e`P%a (%a|%&|%e(#Av182LC1b^&%71b|P-%&<1uw1blxw-¡1|<1b(qU|y`84~p yÑ %e~71<1b^&'LqM1#A%emw%e#<1y¤%&4.5§tC1n<1t1n`8t!" <t ! M "/lC1'%a`k%ao1Y<1b(k0%&0'©C1b^M`b1%&1_^& A $#0%&C1b^&^e #" Ë%$AË 10-04¹2$o/21v7<10'k_A/l¬-% %8o P(obqrP-%e<1b 1-¬t³'%e`c7k^&qU01 1qU(1b%e4f#<1%&^1 "¥-y<t1 ! w7<1bp%&0-¡d-y%&?(11_^e-%ev1bo1-n%&%&8`b1^&wqU P-%e<1b?-% %4c<y01#^e A%&f#0^1?+.^e%&-1'(y 07t(y%eo%&

Á &" ° $ C©m

Rª

O

PP’

P’

M%e'4.$4 ruxy%eY-Yd1®bc1'1b#7%&pd1b#(qU 1?#7cm1(%&0<0%e#^&14

5§1/w%ec7%ew1

Á " ° &" $o° $ &" ° $ T

/w%e7 ÁÁ 1- wÁcÁ )04.z|7%&l/2%&-0y 0Ò! %&~1^&^e-d7t(y%&4MqW 1qUL1b-31b-37%eq -nP-0%&<1b

" Á ° "p Ð $ %& $ Á Í.° "%& ° $ R8

70 2Á &" ° $ /w70%&v77<1.7w1(~qU 1+.Ïm]C©my4z|7m10^1u%&.1-bv1b%&1 &Ò !"#$&Ò Ò2qr+.^e%&-1n' 4w¹20p7p$-%e<1bo1qU(1b%&w-v7<10'70tqUbq7t(y%e4r<|1b(#^e %e#"^&1~$-%&1b

Á Ã ° Ã T

_0w7%&|%&o%e^&^-0%e_"p+.^&%e-C1n#^&1o'(y 4.z|7t%&

Á ° %& R«8

%&-0% %"^e 6^&%e'78^a ¬qU +.Ïm¥T?_00%e-%&_A(16Ò "# ! W' 6/w70%&v7Z%&P+.^e%&-1[4¦z|70$^&kq1^&^&0k7R/ 70T/ (#$Y70n`b1bq(1%eqU^&-w-%&_A-_8 ]1d%e [1b-]-(%e?/w7y7o7k(1%aqU^&-n%&p1^&^a 3`-4

z|7(y%&|0-0-f%e(^e' (7<1C`tL_A70('1-n%&#%e4.('%e C1p7<1b1b^&1b%e%&]1^e^W7#<1u%1b^-%e%ep7<1C`k_Ak%e#07%&(4b#m C1r71b2v1u%&r1_A021^&^07c1u$27<1C`?%&(#7%e4Wz|7c#"R/lqU^9%&%&0

C©

C17<1u7Y1L^e f7#"%e_^&L#1b%&1^.d1b%eqU^e-7<1b1b%&q ]7(^&'%eC1^#%&%&#^e4z|7C131^e^[_"o-0%e_"-f_8 Y70%e

Á Ã Ð Ã ° Ã ° %& R8

p c%&71-%&0cqr0`b1b0kq.7k#<1b [/w7%&v7]71d_"71k` m/w7_8 7'%a A1- Á ° Ë )L Ð 4w< Á )L7%ep%eo-%e_"c+.^&%&-0C13#<1 9/w7%&^e Á ° L-%&_A1ªu-%&%&1^M#7%&1^.#<1b3U7LqE1Lq21©b-%e(%e<1^W_<1^e^_070?0v7¡qM7%&0®P%e'(1_"0`-]#<1k_A---¡%&31L7%&'70-%&%&1^[#1?%&` 3yqU^¤4 9 Á Ð 7?#<1bk7<1bp'81b%e`?`b1b4pp7<1bp7k1bd18 -% %8o$-%e<1b? Pc7<1ucC1b]_"k0-]-%e_"?7k1k'(y 4o¹l f%e' Á Ã Ð Ã /lt'

Á ° %& %&07 ° %& ! ¤)8

/w7k70C1cqU #f_A»1?qU Á ° Ë )Y10- Ð 4cyt17pqU¸qUp77't1-%&#%e#1b%&1^M%&cC1b¬_AkqU0-¬_8 ¡1<1^e' nY70Ò ! ! "#$ (1#]#Tx%&4z|7%&o%et1#0ux%e]qU»-§bq~1-%&1(ycq21Y#7Ln1#^1bv1b'87L70-6ql7L-%&1(y W17R/w6%e6%&'$4q%&o710'^&qU70v10'8o#A%&81(#"%e8cf7k#7 [710'^&?1b7k#uxy%e¡#A%&8c%e @d1-70k1-0%&f7k#uxy%&¡#^1b?%e ÃkÁ Mv1 y4z|7m ÃÁ d70k1-0%1^(#AmqW70%e 2Á 1n_"o/w%a

Á Ã

$ @ Á Ã

° Ã b©m ¤$T

z|7tv10'8%&1^#"08q7t(y%&o70#7 ~Á %& <1n_"o/w%an1

Á Ã $ Á

$ @©r1 Á 1 C @0%e 3 ¤

z|7qUt7t%&o1#7?1n_"o/w%a

Á&" ° $

° " ° $ b©m ¤ª8

/w7"¬1- $ 170P-%&<1up1d'1#70%&(1#[4pz|7ªu-%&0%&<1^`%e]q70%&|%&

Á" " ° $ ° ° Ã b©m ¤b©m

/w7 Á ° Ë ) Ð c1_"yqUb4.pbw7<1bl_AC1b7p1'^e1bl7#ux%&#^1bp%e $ 70L1'^e_A/l70#ux-1C ]1b-¡7#7Ld1^W%&1^& P [Y7-%&%e-L#<1b%e'n_^&%eÏm^a 370'7¬7L#70(%&o1b^a ]C1b^&-¬/w7§#<1%&0'3_0^&%&Ïm^e

T

O

P

P’ P’

M%e'4.«04 .ux%e-3(1®b?1¬'1#07%&((1#YqU 17m P#A_"^e%&-8(1%&^&b4

70'7f7?#Tx%&3#^1b4wz|7m7%&pd1#3%&p1 ! 0(1#27<1#Aq.(1^e^'%&1#`-[4z|7%&2%&#^&%e71b|1d1b^&^<%e^&%el(1##A-d%&81(1^&^9%&^&b 010-Y2%&81^e^&%e#b423qE1bC A18 n%e^& <0d(1bw7R/ _%&'0 <%&wd1b##"-f%emd1%e^e4lz|7%&%&^&-0'1b%e^& 0/w7%ev7f1o7t'$-%ew%&70%&|#1b4

z|7 Á¶Ð `%&]#"-Y#Tx%&'7'7¡1d#^1b?1'mpd7?`yq.?_01v7fq7078 P#"_A^1qU 7b7`yfq778 P#"_A^1$4|z|71-%&0pn7#uxy%&n#0^1o%ew'%e`_8

à Á.%&7 ° 7

Ð Ã © Á

° 7 ° 7 Ð %&07 ° 7 Á

° 7

à Á .7 ° 7 Ð

%e7 ° 7

Á

° 7 Á Á

à Цà b©

¤

z|7tv10'8%&1^#1qW7 Á³Ð ?%e lÁ %e7 <_" Á Ã

Ð6Ã u©m ¤8

L70tv1b^[(y%&c%e

Á Ã ° Ã ° %e

Шà b©m Á&" ° $ °

Ð " ° $ ° b©m ¤

R

M%e'4.04 !$y`qU^e- P(%ec#<1b%& Á³Ð 78 P#A_A^e%&c#<1b 9#ux-n8L1%e^e /w%e71#A^&'%&¯ \ 44+.v74rq 72%&1'^&1b%etq<70~#<1b2/w%a7kÏP0%&^1u1^8%1'^&7<1C`P%&'31'^&tqoÕª)9 %e§_0^1v®9 ¯/w%e7%&^&-01C/w¦1-§C1v7§'#§bqwY%&1'^eo%e-[4%e'78M^&^&%e'7t%&^e|/w%e73s~¢ p^&4

/w7k70k^1c#dxo0_%e$~1b%&1Z" Ë%$AË P-%e<1bpqUp70#7%eC1^#"^&1P-%&<1u Ã Ë Ë 4.z|7%&w%e~7t1b(t1|7 Á Ð (y%&o'%a`n1_AR`b4

pbo7<1u|7'1#7%eod1#q7o<0%eo#7%&1^#1%&1%&$<%eo#<1b </w7%e^&70c'1#7%ecd1b#Yq¯7%&0<0%e Á Ð o0'81b%e`^e (0`-3#<1o%&20<0-L1_1^&^Aq1b-%&P4

p(1^&^a `P%&<1^e%p7k78 P#"_A^&%e Á Ð #<1L1bo1Y1-0-^&71#"-¡7%e'4t¹2$7/lk7<1C`#ux-¡qU»18`y78 P#"_A^&%&-nqry`^e0%ef%e¡M%e'?«d8Y1d#^&1b4z|7w1(%eM7<1u./2w7<1C`_"---L70 Á Ð w#<1b1.7|qE1b " °#$ ° 9Ð 2Á Ð %&1 <1b \ %&0®R/w®m%.#1/w%e7](y%& oÁ &" ° $ ° |Ð 4z|7%eok_A--0%&'q70 Á Ð 0`-6#<1%&831 \ %e®R/w®P%#1%&o1bC W_0t7L<1b^.1--0^&y7<1b#"-_"--%&0'n%en1+r0^&%e-C1b§#<1%&o^e 3`1b^&%&-]R`?1^e%&%e-¡1'b4z|70%a%e%e#A-%e'Y(1b^&1b%ep1-]bv1b%&1?'01u-_8 f78 k(1b%&p%&f7'#!0U©mp1#0#^&%e-3d70k78 $#A_"^&%e- " ° $ ° Ð Á Ð 4o<w7k#7%&1^ Á C1b <7%a%e%e|1t'1b-n_8 7t©L-%&0%&<1^v1u%&d1b%e|%e3!LE©m4

¹2C17%ecqU q7%&?7<11dqE1yL /w7%&v7¬-#"-t#"%e%&<|%&7%&cqUp+.^e%&-1n#<1 97?d1#0#%&'w1 ! 4l3''1#78 n10-3%e3^&' 70%&r(1r7<1ul7<1#Alq[d1^e^'%&1^a #A1C -[4.d#<1b%e^&1 m1b'^&10-1L#"%e81o4lz|70?0qUd1^"qE1|%&qUmq7+.^&%&-0C1%&o7R/w7<1bp11E~`^e(v~1tw#`-¡%eY7d1#0#%&'4p^&Lbo7<1u|qUw18 qW7c7?170od1#dq1L%&^&p%&|1k%&^&b4.z|7%&2%&|1kqU^#0#A Yq¯70o'1b#7%&d1#bqM1k'^&_A4

T

§1Y'81u%e`^a ¡0` Á Ð L#<1b M1b¬Ïm%&^&1b1^W%&1'^e7<1b?1b'^&71b1^e71]) 4p<?#<1%&^1b%&-^&'7370k1'^&p1Õª)9 ALÏm%e^1b1b^¯%&1'^eC1bf_A#0^1-310-¡1L#"%&8C4--0%e%e<1^"Ïm%e^1b1b^[%&1'^e|13_A?1---3L700%&-q7t^a%e'L'^1|70#01'n^&1-%&0'k(1L%&^&%e'kqW70?78 P#"_A^&%eo#<1bt/w%e7ny`$qU^e- P(y 4c1R/w%e'%e^e1-§C1v7¬%&1'^ek`¬/w%e7¬1b-%&%r1^e^.Ïm<1^.n7(%&-^&'7'%e`1_"10%aqU^#1b4.n7o#"%e%e`^e (0`- Á ° t#<1bo7t%&~1L#1%&0^1%e-o^&'7YqUw1Ïm%e^1b1^"%1b'^&pv771b|7t1b'^&w1Eª)9 Á <1-7%&~^eC1-01d%&^e%&'q.70#7/w%e7f`yqU^&-] P(y 7k/28 m%e--¬'^1b#A^e P7-]%&1b7-[4

z|7%&?q.70y$#<1-0%&'#<1%&?71bo7<1o70('o1b-]%&#%&#1b%&1^%&w%e

Á 0 Ð 0 Ã

Ð Ã ° Ã ° %e Á

0 Ð 0 Ã

Ð Ã ° à ° %& ¤«8

z|7%ewqU q7t%&cqUp1b30#1-%e'(70('1-3%&#%&csp%a`?%&|C1b^&^&-7<%e-(1$_"$¤5¦1^e®M[5 (y%e42(R`P%&0'o_`l7<1C`0v1bmc Ã Ë Ë M70?11^&^e-(R`P%&'L$-%&1b4r5j%e7 ÃÁ Á Á )LqU|T`P%e'L_` "7##"%&o%&Mx0|(70`b1%1_^e 0|%&|7?#0#Aw%e(o%&7k¹2%e'¹~1'qUwR`$%e'_` 7c%&p%&4W5j7-1^&%e'/w%a7Y^e%&'78~|%e~%e2q 8`0%&8w0c70 ! y --3_m Á

0 0y4.5j%e7Y7%ew`b1%1_0^&7[5 %&_"

Á 0 Ð ° ° %& ¤8

/w7 "" Á %e7 " Ë "]|%& "3qU Á Ð Ë ) ° 4¹2C10t7%e|^&P®m|^&%&®bt1LqE1b~%&w1\ %e®R/w®m%W(y%& 01b^&1|qU~7o`b1%&1_^&1- 70%&|%&w1§0qUd1^e`%&nqW7[5 (y%e4

5j%e77(y%&c/l?13-%a`t7t^1b%&07%e#_"y/2f7tC1b^&oqE1 0|1-7-70%eq 4oz|7kÏm<1u%&fqUc1(^&%&'7m1R 3%& Á )$ [1-3/w%e737k_`t1b7k%&'%en/l7<1C` Á Á )0

0 Á 0 Ã Ð Ã Õª)8

gg

0 Á"

à Рà ժ0T

<|1t$0-f%eR`$%e'P-%&<1u à 2%e20$- A7c!Y-P¢ -#"-3%&4 ^e%&'78p#^&k%e-]1bo1(^&%e'78^a ^1bp%& 0 ° 0w/w%&^e^_Ak%e`-¬1bo1(%& 0 ° 0 /w7

gg

90 Á

gggg

0

Õª8

R«

/w7%ev7'%e` 0 0 Á 0 04z|7c_`-/~1C`^&'7%el##A%&<1b^9 0 C m/w7%&^ep70%e-/21C`^&0'73%&|##"%e<1^A 0 0'%e`P%&0'

° Á Á

0 0 Á

0 0 Õªª8

R

¯; ¯V¯I<B¦GEH8@ 0

5§?1¡R/ <0-f7-% %8%1^ÏP1b%e37<1b'R`7t%&t`^&0%&nq7?C1b^&qE1y 0y4 oR/w%&'Y7%&p/w%&^&^^&^o1Y^eo1_A0os%e`4¡70%&c%&¡/lkv1b®L1%e^a py/|0%13#"%e8pbq`P%&/t 9Y1^e^[`^e$%e%&|/l%e-w/w%&^e^_"(1^e^#<1-3

4

z|7%eC1bn7<1b|70?#1u%&< µtµ 5 10-3%ew7mp%e%e'%a<C18~/w70f#<1-n

70td1bo-%a 4z|70k/~1C ¡Y<- 0%&p%e-t1Y#7Lq1-%e oR/t4?(R`P%&'L#<1%&^&t37qE1?q70%&#7/w%e^&^[71R`1`^e$%e q ÀYÁ C4|z|71^e1b%eq7o#<1%&^&c-0oL7t'1R`P%a YqW7t(1b%&1^%e%e-c7t#7?%e

Ð À0 ÁÁ

Á©ª 5 Õª©m

/w7%ev7¨%&?7Y1(Y1?7 -d]1¡#A%&8?d11b?7Y8q|70Y#70Y/w%a7671b((d1k171^rd1bbq|7(#7b4¡z|7Y'1C`$%av1b%&1^&%"yq~7Y8%e#07%&C1b^M70^&^ep/w%a7¡1-%&%¯'C1b7<1 c%& ! u4o?7<1b`¬1d^1b'#/l^&-8%&_00(71^e1b%ef%&k^a 3#0'1b-%&m1kqU "_0c/lk71^&^^1bt7<1uk%&¨t1^2w^&1b%a`P%e " ! vÒvÒ ! # uÒ #$l1-6kk_"Y%e^e--¦%&¬7'1R`P%av1b%&<1b^n4.56t7<1C`k1-% %"8%&1^Ïm<1u%&qUw7t1-0%&wqW7#07 0_0%en-~^a`t%e~/l-n(®mR/ 70T/ 5`b1%&|/w%a7 4

z|7L(1bo%&¡7%&o#0_^e»%&t1^e^M#<1tq7p0__^& T/t ¯n7d1uo%&%&-?7#07/w%e7 Ã µ v1C Pc%&%&-t70#07k%e%ep1-%1b^¯`^e$%e %&^&7<1n7`^&P%e q7qE1?qM7#7b4|z|7(1b%&1^[0%e-o7#70?7<1^1'|`^&P%a%e~71370qE1(q70#7n%et1C $0%e-4Lz|7%e%&#^&%a<p7L#_^&½7L#_0^&½q1b-%1^"_0%e|%e7t'1R`P%av1b%&<1b^"<^&-qM1L#A%emw(14

z|7t`^&P%e Y1b18 -%e1t131%e^e d_"oqU0-nqU 7t' Ïm<1b%e

À Á g g °

Õª8

q27L1^.' g g %e#A%e%a`b ¯7(sp%a`/w%&^&^My$#<1-¬qUy`4¹2$%aql7 g g %e'81b%a`b 7ts%e`/w%e^&^"#n$#<1-%e'1bw(o(1u$%&k0 %b 91-70n^&^&1#45§C1bf<-f7?v1b^W' 3_m 3#^e''%e'L%&37?`^e$%e À Á c10-f7?-0%e 65 %e370sp0%e`?R/t4rz|7%e'%e`

g g Á

Щ 5

ª Á

Ð 5 5 g Õª8

/w%e7n7t%e%eC1^-%e n1bw%& 0 p_A%&0'25 g Á ª Õ« 4lz|7mp%eq&5 %5 g 7s%e`/w%&^e^M^&^1b#b _0%eq5 5 g 7Ls%e`L/w%&^&^y$#<10-§qU`45§-0<7L1b%&q-%a YL%e%&C1b^-%a 1 Á 54 5 g 4rz|7mtC10w1L^&^&1#b 0/w7%e^&³t'%a`#A#A<1^Wy$#<10%&[4|%e%&1(18C 9/2?1(_%e#01'78(-d-0%a08p`b1^e ux0p1|/2t-LqU~7p__0^&o18C4

)

z|7t`b1^&obq7t%a%eC1^"-%e %ew_"7^1'o1-n(1^e^¤4Mf|!0%e

5 g Á ª « Á £«89 "6R) 'd±b Á R) Ë bª9 t±u ±b Õª8

/w7%ev7f%& #0v±u 3 4~5j7%&^et7%&w%ep1%&0^e 1L(1^&^-0%e A%ep1#0#"1w(_"kv7^1b'p71¡7-0%e ¡bql_`-§'1^1u$%e4to1C`P%&cÎ v71R«81- o%&70 aÓC«ª82'%a`t1^&0(%e%a d-0%e q~ ,) £8 "¦R) ' , \ #A 3 %&70t³_<1b-[4rz|7t%e%eC1^-%a %& £«9 "¦R)4 \ #A 3

Á @, @,

R))9 Õª«8

z|7mw7t-%a qM^e%&0~d1u~L_"tkv7n^&|71n7t%e%eC1^"-0%e 4

~w7t%e%&1^-%a /2t7<1C`7t%&#^ecÏm<1b%&

90 Á Õª8

/w%e737^&0%& -0 6%3o7k0(1^&%-nC1^e?qE1y%& 0 Á 0 0 6%3R4po37?77<10-[ <%eq¯70-0%e %& 7 ÀÁ Á 0 0 v4

5j%e77%e~/2C1ny/w%ac70' Ïm<1u%&3+.Ï"Õª

À Á Á Ð ° « 5 3ª E©8)8

/w7%ev73%aq/lt-%e`P%&-0c7'7n_8 '%e`

Á Ð ° 3 3 E©T

¹20k_A~7<1b Á 0 0 Á ° ~L70%&|_A(

Á ° Ð ° ° 3 Á ° ° E©m

ct7%e'/l1f#0tqU7%epÏm<1b%ef%e|7?1'qM7?sp%a`?'%e` p1- C4 %&|'%a`3_8 Á ^& 0 Á Ð ^&[ ° 0~

0 Á³Ð

° Á Ð

T ° ° E©8ª8

z|7?1'oqW70?s%e`0 %e|_0v1b%&-n_8 %em'1b%e'k70%&~qU Á Á )L'%a`$%e'

0 Á

° ° E©©m

$

0-10 10

1

0

2S

cale

Fac

tor

a(t)

Gyr from nowM%e'4 R)04 !$C1b^&¿qE1y¿ÑÒÓk%&ÈqU¨-% %"8 (P-^&¶qU # ¥_A 71R`P%e' Ë y Á Õ) Ë T.%&Y_^e [Õ)04 $ £)04 .%&Y(1'8v10 Õ)0 £)8r%&Y'[ ¯ )8r%&(_^1v®(1-¬Õ$ £)8%e-[4r^e^[7<1C` Á 8$4

q78-%e ]%ec'^&%e'%&_^e?#<1-¡70%a%eC1^W-0%e 77sp%a`L%e1^e(w#0 "1- )04|n7%ep^e%&%e 0 Á 4|q7?sp0%e`k7<1w7%e%&C1b^-%e Á 1b- 0 Á bª04pz|70kmc_"c_`-]`1b^&pqUw7#P-y 0 o1d7%e'7~7<17 Á (P-^Õ¢£2#-%&y%&[4

-n7%e'k/l?13#0o%e~7o%&c`1b%1u%&Yq c4l< +.Ïm¯Õª2/27<1C`

g g ÁºÀ Ð Á Ð « 5

ª Á E©m

qM/lt-%e`P%e-c7%e|Ïm<1b%&n_8 « 5 ªk/l'ª « 5 Ð Á

5 Á Ð E©88

¢£|1^&^1b/w7<1b|`b1^ecq 1b Á R) $ %&2--L'%a` Á ) aoR/t4rz|7t-0%e 1^&p^e%&®b ° 73/w7%e^&c701-%e 1^&p^e%&®b ° | Á Ð ) 8 5 1-

Á ) 0o4£))))L1u Á R) $ 4rz|7%&w%ep1k<^eo7<1u|7k_A1yP1-0%&<1%&^a &%"y%a`kv7<1b%&¸qUp%&'(7?%&%a%1b^`b1^&q 1`b1^et` ¡^&Y%a 4psp%a 1- (1c7o0^e 0$-f#A%em2qUc _00%e d%&|1bn01_^&c$0-f#A%&84z|7m7cqE1y71b %e^&?(%a 3%e7p(1p7<1b18y "%e¢£xc1d%&%&-b _9y A7?%&1nqUjL_At1b^a 4

z|7qE17<1u7-0 P<1%&q 0l1|7p117-$ $1(%erqbq1?#1%&^e|(R`P%&0'1b-%1^e^e (%&7'1R`P%av1b%&<1b^<^e-3bq.1(#A%em(1wC107<1b/2C13#o#^e¢ Ïm<1b%&qU_%ew1^&^1b%&0

Á Ð ¯%& E©m/w7 %&|7 c/w7%&v73%&Mxc##"%e<1^"L7%& %&w7 ! u 1- %&~7 ! u4z|7!"]10- $ P-%e<1bw1'%e`_m

" Á d Ð $ Á Ð %& E©8«8

/w%e73%ad1Tx|1u$%& (4~!$%et/l/2181-%&1^[%e/w%e7 $ Á )0 <^&1^a Y/2- Á 4z|7mw/2'1L#<11%&cÏm<1b%eqU 0

0 Á Ð %e Á ´ Ð E©88

2^&1^a 37LÏm<1b%&t1b##^e nn1Y^&-¬sp%a`L%& 1v71Y(1u$%&k0 bq| ´ 1u³Á 61-70f^&^&1#4.zW(w70v18 1- ´ /lt-3L

Á 0 Á ´

%e Ð

Á ´

Ð Ð %e Ð 3 Á Ð ´

Ð

Á Ð Á

Ð %& Á

°

¤)8

z|7m Á Ð Ty ´ Á ¤ Ð 910- Á 0 0 Ð %& y4ro71b

0 Á0 Á

Ð %& 0%e Ð

¤$T

<wy01#^&b /w%e7 Á Á $ /2'y Á $4lz|70 0 Á Ð Á ) )«$4z|701u%&bq7o%&o1bw7¹2%&'2v7¨ ³Á W2L7tmw%&o%&~70

0 0 Á

Ð Á

£))« ¤

qU Á $4

ª

<w1#A3sp%a`t/l?v7<1b'o7t#<1b1%&Ïm<1b%&0 Á kE%&7 ¥Ð Á ´ E7 ¥Ð T ¤ª8

5§' |qU w%&' Á

° 7

¤b©mz|7%e'%e`

0 Á0 Á

%&07 pE%e7 Ð U7 Ð T

Á ° 3 ° £ 3 ° $R)8 ° ²

° b©m $ ° ² Á

$ ° Rª9bª)8 ° u©m $ ° b©m ° Á

ª m °

) Ð ¤

<|y01#^e %aq Á ) e 737 Á $ %e7 Á « £© Á £««810- 0 Á ) £«©804

<o_A7]70#"610-¬^&-§sp%a`C1b W7`b1%&1_^& %&o##"%e<1^W7 ! /w7%&v7 %e<1^&^a 6-0- _8 A4620qU(1^%&(qU^&^&R/w7YÏm<1b%e0 Á 0 ]1b-]/21%e^e 37<1b 0 Á ´ 0 497^&-¬sp0%e`17%&c%e(wq 1- %&

Á/ ´ Ð ¤8

_0 Á

² Ð Á ´ Ð %e ° Ð Á

´ ¤

L70%ec%& Á Ð ¤«8

]1d0qUd1b^W#<1y%&-%&1'13 /w70%&v7]#^e 17?#<1u%1b^$-%&1b?1- 17%e(pP-0%&<1b P/2^&-^e%&2qW^e%&'78~1C $1^a/~1C P|7<1C`t^&#A~bq4l!$%e7o1b'oq %e|) ]qU 7t¹2%e'¹~10'Lk7t¹l%&'20v7[ 91-%&c7o1'cbq %&|)d ]qU~c%e#1-7t^&-3sp%a`b A/l?t7<1uw%e|v1b®^&%e'78|7tm%&t%&qU ¹2%&'¹~1b'¹2%&'20v73%&<1C`P%&'81bc7s%e`4

¯;E:<; (GUS OuNP@C@ WOTN

qM/lt%&^&-0o#0?7/l71R`(P-%eq 71^&1b%eÏm<1u%&

Á³Ð© ª 5 ° ª

¤8

b©

z|7%ep_<1b%&1^&^a d#^&17-%e n_8 7t1q7' n 9_0/2t/w%&^e^70%&p^ew/w%a7$p#0Pq4rz|7/lv7<11b%e%etC1p/w70#?%&|%&'%a<C1bmp1qU1-0%1b%&-%a ¡10-f`b10 ' 3-%e 4p '81bq.10-^e -%e-¡#7bkE18 ^1u%e`P%e%e#<1b%e^ev2711L#0'%a`3_8

Á5ª Õ)8

z|7%e7<1M7~%.q9-0_^e%&'7~%%e`|'1C`P%ev1u%&<1^qU4¹20M7~#p1b^&v7<1'70/21C 7<1b-%a `b1%e|/w%e7n-7%eq 4lz|70?#-Pw/2®1'81b%&|7ty$#<1b%efq70tsp%a`b 91-7%e~^&|qW0'b Y-w7o-%a 4.5§o7<1C` Á Á ?ª 4z|7%e2k2_A_01y-YqU 70pbv1^90'b 5

³'%a`P%&' A 5

k Á Ð 5

4.M%&1^&^a

/l?<-n7<1u!5 - $ - ° $ qUw1-0%1b%&[4?.0%&'L70%&w%&8L70?qUtÏm<1b%&f+.ÏÕ8'%a`

Á Ы ª

5 $ 3 Õ0T/w7%ev73_A(13' ÏP1b%e

À Á g g °« ª

5 $ Õ8

pbo7<1u7fbqU-_^e%&'7?%%e`-%a 7'77f/l%e'78qM7t#0/21px7dqE1y-- ¡%e8'1b¡ 3C 10-¦7Y^e%&']%e%&1^r-%e ¦qUk11b-%1b%&-0(%e<1b-nC1?%e%e^&^ 5 g Á ª E« y4r5j737-0%e %ew%a%eC1^Õ g g Á )0 1-70^&$%&7<1|7oqU -0 6 4

<c`b10 ' ¡-%e ]7L#0d%e Á Ð 5 41%a`^a ¡0L7%&0®Po7<1bt7

`b10 7<1b -%e 6_0%e¨#%e%e#^&(%ek1 7<1C`1¡-%a ¨%&0--¨_8 ¨Ïm<18<y<1u%&(1b%e'¦10-,10%&7%e^1b%&'¡`P%&<1b^#1%&^e#<1%&4,5j%a7 Á Ð 5

27

' w%&1k^e%&#^ecqW7t%&b <1-n%&~7m8 %&8`b1%18C4.21%&0^e d/ly$#Ayo7<1bp7' ¡cq.7?`b1½71d_"¯8 k%&8`b1%&18C A^&k%e/l^&--y<1k#qU-nqU1(b4qo/2t0#Ayw7o0'b 0wq¯70c`1bL_A 91-70 w%&w8 t%&8`b1%&18C _00w%&~7t(y%e4

¹2C1373#0¡%&L'81b%e`b 270n/l®¨-0nÈ73$#<1%&È%&L'1b%a` 1-¬7R`1^e^' ¬88kql7L`b10 'R/w?17(sp%a`(y$#<1-04§qE1yC Á Á Ð 5

dÕª ~/w70%&v7¡v7<1b'70'b 38m_8 A5 Á ª 5

5 Á ?-%&'7Ly$#<1%&4z|70%&t%&t1<1_^e ¯_"C10%eqr7L-%a %&o-0Ïm<180 <01b%e[ <7y f7^e-[¢ c1?1_A0/w7<1b7ks%e`k%ep-%&'4|z|70k# %e7oqUtÏm<1b%&(1®|7oqUc%e(2/w7<1b%a|/20^&-7<1C`_"[ 9'%a`P%&'

Á« 5ª Õª8

z|7^e0%e~bq7%&|ÏP1b%ef1b

-y$# 0 « 5ª ! Õ©m

pq 1kqU/ qU^e-%&'~^a d70#A%e%a`o0#A88%e_01-

Á « 5ª Õ8

5§?1b'81%&Y7<1b|7t%a%eC1^[-0%e %e

5 g Á ª « Õ8

<M7%&M`b1-(%e<1b-k%a<1u%&[ Á |%&.1cv1_0^&~0$-#A%&8C 1-k70%&.y$#Am%1^'T/|73#07<1t%"1v7<1b%& y Á oL'C1bw#0%&%&[4

¯;*)[; YNPVWNmOTI<D~HI<@N

c%eÏm%ak1 nd- 0w/w%a7]1(k_0%&<1b%&nq.7k-% %8®P%e-cbqrd1b4z|7#Am%1^'%e1^&^1--n^&%eC1^e 0

À Á g g °« ª 5 ° 5& 3 3 ° 5 1$ $ Õ8

/w7 5& w%&|70-0%e q-%&<1b b#(1b|1b<0 <yb4lc%a`P%&-%e'k_8 '%e` Á 1 Ð Ð Ð 38 ° ° ° u ° 3 ° C ° $ Õ«8

sp%&' Á ° 90 '%a`

T ° 0 Á 1i Ð Ð Ð 43m ° ° ° T ° 3 ° T ° $ 6

Õ8/w7%e^&o%&' Á '%e`

Á 1 Ð Ð Ð 43 ° ° ° 6 ¤)8

< Ñ$$ $ c(P-^&2/w%a7 ° Á Ë Á )0 070 0 w#P-y%& 0 Á

° ° uEª ° ª ° 3 ¤$T

/w7%ev7]%&^&1'p7<1¦kqU µ ) $4o!$#A#^e?qU^M7<1b7%&p%&pyqU^M/21R 3d0c77%e'7]_`-`b1^&q 0 o_$tqU^M7<1bt1 P(1b%&ko%&¡70-%&v1o%eo1(^&%e®^e (y$#^1b<1b%e[4

pb|7<1u7w-7%aq l1<1^&^a k-#"-L7#<11b(yW7w-%ev1bwq"7w_Px 70?_0`b1b%e%& 1-7t%e(oq%&%e[4rz|7?7?#<1b11t1%&-f_8

70?Ïm%&87<1bp^&%e'78|1R`^1b#A- 9_$p7<1bp%e^&^[^eC1C`p/l(qU#114~z|7

qUk^1btqU 0 '%a`]1_AT`1?7<1b7?%&tq._`1u%&¡%&w0$-[ [1-37<1bp7-%ev1bY7k`b1%&1o1dqU0%e¡qr7k%&%ef%e(t1b%eq 70^&%&'7mp#A-1%em4k561§1^&31b®]1Y` ]-0% %"8?Ïm%&oqUc1L/w%e7]0$-§(R`P%&0'-%ev1bb A70T/ -0$7?-7%eq w`b1 /w%e7n_`1u%&3%e( ¡370%&wC1?7?(%e%&%e(`b1%el1l1qUy%edq"7p_`b1b%&%e(~1u%&q 7p^&%e'78r#A-1b%&8C4(#%e%e#^&70%&%eo1(/21C f-0%&^e n(107k-^e1b%e¡#<11qr7sp0%e`nÕ$_[ MC«1u#79±b«)8$Ry4

¬-cC1b^&0^1b7L1bL1bo/w70%&v7_`-¦-7%eq cqUo(R`P%&'_Pxyt/w%&^&^v7<10' 0/lo-k1 Y+.Ïm¯Eª8l?7c0yPw7%&'7l- <1b-%&d7%&l-02/lo-k 0 ° 0 Á 0 ° ¨ 0 0 ° 1b- 0 ° 0v Á 0v ° ¨0 0 ° £y4|z|7%e'%a`

0 Ð ¨ 0 0 ° Á

0 Ð

¨0 0 ° ¤!$^a`P%&'kqU 0|'%a`

0 Á 0 Ð

¨ 0v 0 °

¨ 0 0 ¤ª8

5§1no70t-w^&0%& 0 Á 0|^&%e(%e<1b7( 0v 3 <'%a`P%&' 0 Á

0 Ð ¦0v 0

° ¨0 0 ¤b©m

z|7-7%aq w%& ° Á

0 0 Á

Ð 1 ¦0v ° ¨ 003 0 Á

° ¨0 Ð ¨0 0 ¤

z|7mw7t1utqv7<1'tqW70-7%eq qM1R`P%&'L_Px%&A ° 0 Á ° Ð ¨0

Á R ° Ð 1 Ð g g 3 ° ° ° T ° ° T ° ¤8<Ly01#^&b ~%e-d1¬f/w%e7 Á ª¬%&È16sp0%e`f/w%e7 Á 4,56n' 0 Á T ° Ð ° Á Ð ©4,z|7%e(%e0'81b%e`3_A1n7%eL(P-^|%e-^e1b%e' <-70%eq w-C1?/w%e7n%&4rs0qU<1b^a 70t`^e$%e v7<1b'?1$%1b-/w%e7n7%&w-7%eq v7<10'?%ew^e À 90 Á

0 ° Á¼Ð d±bR±u PwqU Á 8P <

%e|/w%e^&^"_"o` -%aÊ^a~(104

[; |DEI$STVWNP@C@JDWVWNP@C@+`¨%&7'01b^1/w%e7§1-%1u%&[ ¯d1bt1-§`b1 -%a%& W7'

Ïm<1u%&n%e|%&^&^ g g ÁÀ Ð

« 5 ª Á Ð « 5

ª Á ¤

z|7mw/2%&^&^"' Ð Á

5

¤«8

28^e ¼R)4 $ _0wqU R) $ 7t1-%&1b%ed/w%e^&^-0(%e<1b7t-%a 4

-0c^e fC1^e^&1b7-%a ]-%&'Y7L1-0%1b%&3-%&<1b-]#"Pv7¬1b R) $ /l?-nL0%&-0|7 ! " $ 0Ò b 84rz|7%e|%&w'%a`_8

Á Á

A $ Á

©ª 3 ¤8

qUo1Y_0^1v®m_A$-0 f1-0%1b%&n<^e-]q#74¹20c7L1L1b^&d0%eoqlªd P#" ¯C1bv7/w%e7n1$%1b-318%a$%e4.<~qU(%e27t' -%a %&7d1^Ïm%&^e%&_%& %&

YÁ

Ay$#W 9 ° © 3 Õ«)8

/w7 2%ew7P0k_"pbq#0%&n-'qWqU-n4~<|00%&0/w%a7n#%e§ $ <t/l^&-y$#Ay Á _00t%e0^e ¡7^e%&%e nql0%eocy$%eo/l Á 4<(1^&w#<1%&^& Á

1-/l?'y

Á © 3 " 3 &" ° Á

R $ Õ«0T

z|7mw7t8#8 -%a qM(1^&|qU(%e~%e|'%e`n_8

Á Á

©ª R 3 Õ«8

!$%e|/l7<1C`p1o1^ qoqU.0%&l1-(18%i0%&.(%e'78.y$#A~1(1--%a%&<1^m%e_0%eqU0%e|7<1up%ew©m$Rk%&~70?#70n8#8 n_0w701y<1b^P0k_"%&od1b^&^&_A17L#7c/l§70C1b-n_8 ¡7L1b%&70%&^1u%&fqr70 #<1b%&t1bc7(#A1b0bq7ksp%a`qU^&^¯_A^&R/³1 \ _007k0%&/21b^&1-0 -0#^&-/lc70C1b-[4c!$%&d7C1b%&w1qU-]%&8dp0pqr#%&?q70sp%a`_"C1q7'%a 07t8#8 q#700#0^& #^1b(11bw#A1u ° ~%&|8%&^a 1qU-Y1#7bY'1~1bl(#A1b 0 ° y4.z|7o#%&dqE1bqUl^e0~%& Á 1-n%e~%&w1^e(qU|#"%e04.z|7%e'%e`13Ïm<1b%e

©ª ° © R ° 3 Á ©

ª 0 ° 3 Õ«ª8

° 0 ° Á © 6%3 Õ«©m

Á @ 8 4¹2C10ql7%&cqE1b 7L1b--%e%&1^M8%e_0%&]ql0%&o708' -0%e %e?E©mPR8U© $R $ 6%3 Á ) £«04rz|7mp7tmp0'b -%e %e'%e`

«

_8 Á $ /w%a773%%e`1b%e%&C1b^/2%&'78 2Á ª £ª04¹2$78p8#8 -%a %&|'%a`_8

Á©ª 3 ° ª © ª « 3 Á ©

ª 3 Õ«8

/w77¬&%"%e`v1b%&%&1^/l%e'78qUc8#m %e Á ©8ª$ Á ª £0L1bo708%e(b4¡T/¶/ld/218¡1^&^1b7Y-7%eq L1b-¦-%a ¨1b?7Y1^e%&%&L/211<1_^a 0%&-0 7 .^1v®(%&c'%a`3_8

0 Á

Á 6 6

6 Á © "¦C) $ $ Õ«8

~7%&w%e(o7k__^e18o%& Á ¤0|qUp1d1-%1u%&$-(%e<1b-Y%e%&C1b^-%e sp0%e` 9

5 Áª « Á

ª

ª8 Á@ ²b© "¦C) 'Y±b Õ«8

5§1nC1^e^&1b7o(#A1bt%e'

5 Á $ Õ««8

/w7 %&7k q1^&^¯70 v¢ qUp_"c#0^&t@«(qr7k0»q.7 y¢ qUqU(%e4c^e d#<1%&^&2/w%e7np(1w^e~7<1 1o%&^&--%& 4.7?!P1-<1- \ $-0^ %ep3R)04 n o^e_¡Î zW ~z|7k+r1^e ns%e` [M%&'0ª04 1u7%e'7 4wzWd<-f7-70%eq w/2t

Á©ª 3 Á ° 3 Á ° 3 © ª

©8ª 3 Õ«8

z|7m

° Á ª 0

6%3 5

$ 6 $ Á ª&"¦R) 3 " R) ²

6 5 b© "¦R) 'd±b 6 $ Õ)8

pb|7<1u7w-#"-c7w^&1b%a`^e k0v1b%& qE1y.%e^e 6 4z|7ÏP18%e 5 2Á 54 ° --n<- : Ð t%e|'%e`n_m

5 ° Á

ª £0

6%3 $ 5

6 Á 5 C)

6 "&"¦R) ! 'd±b Õ0T

<~70?-%a n1bw7 .^10v®d%e(c7%&w%&p aR "¦R) l'd±bo%aq Á C) $4¹207t8`b1^&0oq,5 %&Mx 5 Á 5 g Á ««« "¦C)4 l'Y±bb4M%e<1^e^e

Ð Á « &"¦R) PR) 6 Ð Õ8

z|7mwL' w_"y/2])$4e1-fkÏP0%&|/w%e7 Á ) L1b- Á R) ²Ïm%e

) £8µ µ

£))))))))))))))))))))))))))))))))))))))))))))))))))))))))))© Õª8

0 5 10

Sca

le F

acto

r a(

t)

t [Gyr]

Density 1 ns after BB

447,225,917,218,507,401,284,017 gm/cc447,225,917,218,507,401,284,016 gm/cc

447,225,917,218,507,401,284,015 gm/cc

M%e'4È4 !$C1^edqE1yYÑÒÓ%e(qUk#A l%e%&1^21b- ^&-Zs%e`L/w%e7¨-%e 1u<10-f1bq ~7¹2%e'¹~1'L%&0-%&1b-[4

/w7%ev7¡%&w1^&^a yv7%e'(7_A-0pq%e%e-4|z|7%ep%ep®mR/w]1b7 vÒvÒ vÒvÒ#_^&­%&^&' 4¬^1b%&o-§_"C1(7L%a%eC1^-%e ¬s%e`(71 91b#1b%&1^"y%& P/w7%&^e^e-%&20-_A1o%aq[70osp%a`7<1- Á ec1b|1?%&?C) $ 30-o1bq p7k¹l%&'Y¹21' A%ew/l^&-f^&^&1#?%e6R)4 $ -4cz|7mc%ef-d71R`1sp0%e`1w^e-1ww/w%a7 w^&oÏm%ej` ` ^&t?1uwC1^e Y%&4

[;Õ:<; WN |DEI$STVWNP@C@JDWVWNP@C@ |GEF¯OuNz|7C1^e^&1b%e~%e8`^a`-n%&7 91b0^e-p'11|qU^&^eT/w z|7 02qU~7

^e-[ <^&^&1#%e'k1%&~qU0-#<11b(y%eC1^e^e %&'

Á Ð 0 Á ¥Ð %e Õ©m

70#0^&-1't%&w) 0 %& 1- 04

ª)

z|7 91uo(P-^/w%e7f701k1^&%e'Y%e'%a`_8 f7k^eC1-%e'dcqr7kÏm<1u%&1_AR` Á Õ 6%370 6%3R4.5j7 0 Á 7 Á £8$Tb04

z|7`b1^&q /w7 %e(1^&^2%&L-(%e- qU ¨Á ° y4Èz|7m Á ° 4~5j7 ³Á ) ))88$R0 /w7%ev7f%& ° Á R)))qUw7%e%eC1^-0%e C1b "7 Á Õ Ð Á ° Á ))8«qU7k^e-¡C1b4cp?71by`§1u70%&C1b^e ]%& 70(0#1%e61b qUt7^&-6C1(%e1^e1-0 ]--¨^1u%e`7%e%&C1b^-%a C14.56t13#0o71(8wq7%&|-0%e%e'

0 Á%& Ð %e Ð

Á Ð b8 3 ° £b8 3 Ð $Tb)8 °

1a Ð u©m $ ° 3 Á

ª Ð )8 ° Õ8

qM/lt#<1c7%e| Á

° Á ° © Ð Õ8

/l((7<1b^a )98 q27(%eC1L%& ¼%&tC1b-6_8 ¬%&C1b-§-0%e W/w70%&^&L©8)8»%&C1b-]_m n70^&R/l`1b^&q -0%&0' 5 g 4pz|7P071<1^¯qU1y%e<1^¯-%a f%eC1%&]7^e-§1L%&t) "§) £))8« Á ) £))0R$4kz|7LqU1y%e<1^-%e ]%eC1L^&1^a f'$^&%e® - 0wqUC1b^e %&4z|7%&p'R/|7]bq 54 5n^e%&®b 0-%e_"70k^&%eC1Ed1b^&^1#^&%a-0R'R/|7ql#"_<1u%&c%&¬1Y%e%&1^M-%a sp0%e`4q/2LyP1#A^1u7^e-¨C1Yy$L-%a ¦q)$4eT@8­qU ° Á R)))n Á )0 M/l'k13`b1^&0dqÆ Á Eª9)8T W 6%3 Á £«?qU~7t^e%&1^a d$1#A^&1b-n-0%e 01 C1^&^1b#b4

z|7#Ansp%a`$-^[%&

Á 7 Ð 0 Á %e7 Ð Õ8

z|7t1b'o%&~) ¿/w%a7%e7 Ð Á .4.z|7 ~qU~70%&~$-0^[%e27t^&1'w1b-%ew%e|-n(0(1^&%7t0`4lz|7o`1b^& Á ° 7 ~ Á ) aR8$4

pR/ 7'1^y`^e0%e]q %eL Ð T05 Á C4< ` ^&k]70%&_A( 5 Á C4rz|7qU A1bw1^a d%e(~7t-% %t_A/l37t%e%&C1b^-%a 1- 5d%en7%&w%&'o%&w'%a`n_8 5 Á Æ yEª b« ° 4r56t/2187%&|(_AtÏm<1^n'd±bb4c<p1]1'q 0 Á Lo P Á £ªd®mY±bC± \ #AqUp7%a%&1^¯-0%e 3C1bR 70%&|%& 5 Á a "6R)4 T ° 4z|7mw/l?-6 ° Á ª "¦C)4 $ 4

d-C1b^&0^1b~7%&|#A-%e'?7%&-70%eq C 8/l-d78#m `^&$%&n^&1C/t

Á E©9ª8 3 Á T ° 3 Õ«8

ª0

z|7k8#m 3-%a 30T/³%ep'%a`¡_8 Á E© ªE©ª9 3 4z|7qE1yE©8ª|1^e^&R/wqU700%& </w7%&v7]1b?1(-f(_"(1^&4wz|7qE1 L1^e^&R/w|qU|7?P0k_"pbq&%"y%a`^a ¡(1^&o#<1%e^&?#A%&1bo1Y'%e`¡(#A1b041##AC1bc_A R) qU ÔR))]o4+M$#$L-%e'f1%e%&/w71f^1b'(#<1q|70#<1%&^&?1P^1b%e`P%&%e m/27<1C`o70' -%a

YÁª© Á

ª $ $ 6%3 6%3 $ ° $ Õ8

<o ° Á ª "C)4 $ 10- kÁ R) ²$ P7%&2%& YÁ "R) $ 'm±b 3|~1Ïm%a`1b^&8|(1-%a q,5 Á ©© "6R) %$ 'd±b 34r5§om`70%&~1k%e(o0%&0'

5 Á 5 g Á ª « Á

ªª8 0

R))8

z|7%e#"0-d1%e(q.)04 ©8ª42271R`?-0-37%&w%fn0k /w7%&v73%&~qE1%e|0'7%&¡7Ly$#A8vy W1-§1-ux-7L%e%eC1^-0%e f(1bv7]70%&c%e(b4?z|7mt70L1<1^ 537^e-_"L)04 ©8ªY'd±b [7k<'0%&`1u%e`L%&f7L%&#^&%e-311y ]%&]%e%e%1^-%e%&0|--nL#P-1(s%e`t^&%&®bo4

pbo7<1u 5 - 5 g ° - 6 04

ª8

[; nGE@SRIV"SJLKNPHST@

f'1^[<0-3701#0#"110qM-0%&18_Pxyk <$31b-f1b'^&1|%R~/l?-nk1(%e1^&^1u-n%&'Yt <_0qUw7%e(#^etC1q Á )0 <7ks%e`%ep(#0 1-70?1?'1R`P%av1b%&<1b^"qU "(#"%&1^^1b%e`P%e dC13_"t-[4~3#A%1^^1u%e`P%a 70%ec%&

Á 90 Ð " ° $ ° Á

0 Цà mÆ ° Æ mÅ R)0T

z|7/l^&-^e%&pqR`$%e'd'1^1u$%ep1^&^¯7<1C`?Y%emyt1bpy`mo/w70%&v7f/lk%&-08%aq 17¹2%&'(¹~1'04pyC¢ v7P7?%&`81w7 Y#A%&8qUw$-%e<1b4~5j%a7$'1R`P%a n1^&^[7(R`P%&0'('81b^1u$%&w(R`31%&'7mp^&%ew(qUp18 n#<1%&^1|'1^1uP ´ /27<1C`

" 0 Á 0 Ä $ 0 Á 0 Ç 0 Á 0 É R)8

/w%e7 0 Á 0 0 C4tpR/l` ¯70k#A%1^^&1b%a`P%&%&t%e(t`b1%&1_^& 0C1]bo_"-§1bc7%&?%&`b1%1_0^& A_AC1b_mxt1b71b( 0p71R`-% %"8o##A%&%&0k70¹2%e'Y¹~10'YqUpT`P%e'Y_`4tz|7y`8c7<1bc-Y7<1C`k7k1(?##"%e(¡%&70?¹l%&'L¹~10'qU|T`P%e'_`^&%ec317m P#A_"^&1-<0-f_8 Á 0 ЦÃ

4

z|7mc10v1bmf78 P#A_A^&17<1bd_A 91u-3%&8(1(#0^1b42z|7%ep%e(-0%1b^e ('%a`y$#<1b%e¡`^&P%e%&p'C1b7<1

%&f-%&v18c'%epq.7ksp%a`b4oz|7%&c%e0qU7

#A%&8o(1-k1^e%&p71bc70Lp__0^&^1C/ `^&P%a%& ÀnÁ ­1_"^&1'p7<1]7#"-q2^&%&'7m4(z|70(C1^eqE1yt_A( 9 Á 0 C4Yz|7m?7p_0_^&0v1bm?%&t'%a`6_8 Á/ 0 Á 0 /w7%&v731'|/w%a7wC1b^&%e~1^&^1u%&[4

[;E:<; +V¯F WDUIOY@CG8N WGE@SRI<VWHNpR/^&L0%&-1 _`b1b%&¨/ln(1®bnbq1bÈ_mx(1bL#"%&1^~^1b%e`P%&%e

P-%&<1u " Á 1-0 Á 0 Ð 4pz|70%&_Pxyc%&^eC1^e f#<1c^&%&'7m "%e

R/ %&|7y`8t1u " Á )d1b- 0 Á 0 C4|qM7_Pxyc7<1p1(-0%&%& #A#A0-%&^1|70k^&%eyq%&'78C 7¡/l®mR/ 7<1bc%e/w%&^&^¯_0-¬11'^& Á _AC1bk7L!0P-%&<1u-%&_Ak1%&#^eo' 4z|70%&-%&v1-y<-]_m fÁ L%&®mR/w170 $ !wÒ &Ò y4Mz|7-70%eq lq7p_Pxy|1b " Á 1d_AwqU-y`1^-0% %"8/21R P A_00

Á &Ò # 4.z|70<w/21R 0w70^&c7<1bt ° Á ~ 4

z|7(%e%e( Á 0 Ð Ð ° Á

0 0 Ð Ð Á Ð 0 R)ª8

ªª

!$^a`P%&'k7%&|ÏP1b%e3'%e` nÁ

0 ° °

R)©m

z|7k-¡/21R n(<- 1b %ed^e$®1u70!0¥`^&P%e ÀYÁ 0 Ð 1b-

(#$o7?!0c##^e|70%eq

° Á ° À

Ш
Á

0

0 Ð R)8

/w7%ev73^&C1b^e d'%e`|701o^e4

[; ); WB¦GEVW>A@CG S GE@SRIVHNz|7 <$nqU 1f_mx_$0-%&'d1¡1b'^& LC13_"tqU-3%e'(7tqE17<1u7

mk_Acbqr#7#A(P-%ep0ov7<10'-]-0%&0'd7y$#<1%&fq.7ksp%a`b4t9c1_^&1v®m_"P-0 n7km_"qr#700c#"c$-?%&kEy$#¯ Ð T 4o<71b¡_Pxt1b-70%eq A7#07(%a-f1u º1%e`/w%a7nqUÏm Á ° y4p!$%et7mk_Apqr#7c#Ap(P-1R P7k1(b 1(_^1v®m_A$-$ 3(%a%&'(1bo1#A1u /w%&^e^[1#0#"1|_"t1L_^1bv®P_AP-0 qW(#A1b ° y4z|7mp13_Pxy/w%a7n^&%&0%a , Á © $ 7<1w1 <$ Á $ 4.z|70 $ RÒ &Ò %e|-<0-f_8

Á,

© R)8

Á ,

© Á

$ Á ° R)8

[;[; XYIWGUI<D GE@SRI<VWHNz|7t1y<1b^[-%&v10c71b|70^&-'%&8k7tp_0_^&o¯1C/C1_Ao(1-_8 Y(R`P%&0'

_`o%e'd1-<1#^e8lx_"yqU?1-f%a`-(x01bq p70%&o%e( [4-#070%&c-%e1b ^&yC¢ ck778 P#"_A^&%e%eL1-]%ek%&k7^&%&q18o##"%&%&?7¹2%e'd¹~1b'd%ec1(78 P#A_A^&1(%&3#A%1^W^1b%e`P%&%&o$-%e<1b4!$L^&y

0 Á w7 " Á

w%e7 R)«8

/w7 %eo7L78 P#"_A^&%e61'^e4Lz|7-%&v10(1bv18 6_A/l 1- ° %&d'%e` _8 Ð §Á &" Ð

0 /w%e7 &" Á

w7 10- 0 Á w%&07

ª©

A BC

D

E

M%e'4.T$4 !$#<1y¤%&-%&1'1j#^&-%eo#A%1^^&1b%a`$%e%&M$-%e<1b[70T/w%e'w7.18%&c%e( n7m P#A_"^&1 91b-7t1b-<1|#^e0-LC1c7t1-0%1^"-%&v1oqU +6%e Á ©_0%&'oÏm<1b P/w70%&^&~7|%eqUwqA7w%&^&2/w%a7L8,71br81%&+%& Á %e(~©4 _0%&'Ïm<1b|/w7%ev73%e|'1b~7<1bf 4.z|7m7%&|P-^"7<1w78 $#A_"^&%&'(y 4

Ð Á 9 E7 Ð %&7 4¡d7d-%&v1d%e 1b-670d1^r1-0%1^

-%ev1bL%& 4¹20t70%&LqUbq~1%e^&%&o'%e`§_8 ¬ " Á

w%&7 W4!P%&

%e7 070#<1b%1^[y%&wqM7 L-%e ns%e`1bo'81b%a`^e `-[4

[;W; XY>9K.NPORST@>"V ¼I<D9NmOYB6N8SROuGEH

5§1/w%ec7tm%&%ec%&^&'%&C1b^A`b1%1_^e|R/

Á Ð

9 ° %e7 mÆ ° Æ PÅ R)8

ª8

z|7%ec%&cbq ]/w%e]%&' Ã(Á %&7 1701-%&1^¯`1b%1b_^&b4t!$%&0 Ã(Á 7 1-7 Á ° Ã 7%&|'%e`

Á Ð

9 Ã

° Ã ° Ã mÆ ° Æ mÅ R)8

z|7%ec%&1Y_"$¤5¦1^e®%&/w%e7f'81u%e`k0`b1b04o-%&_Aoq.7?7ª³#<1/w7%&v7]1bt%&#%&10-37('4|z|70?7(1b+.^e%&-1f#<11-778 P#"#A%&1^ª¥0qE1oqW1k©8 _<1^e^¤4.s<1b^&^e 0%&2-qU27(%e%e(`1b%1b_^&%&1-q [4

'01b^[qU qU~7t%&obq1%e#%eo1-n7'w(^e' (%&

Á 0 Ð. 0 Ã

Ð Ã ° Ã mÆ ° Æ PÅ T

/w7 Á Ð Ë )YkkqU70'81b%e`^e 30`- U7m P#A_"^e%&-1^ 91uoo#A%a%e`^a 3`-E78 P#A#7%&1^ |C1b 0~/w%e^&^[_A#0-n^1b|%&'' 31'8 91-n<<1^e^e d71b-%&|bqM`b1b wq7sp%a`%&|'%e`_m

Á Ð Ð Ð T

/w7 p%&~708p1b%&LqW7o`b10 -0%e §U(^&'%eC1^A18~L7t%e%&C1b^-%a ¬ª « %&o7(8?1b%&q27-%e q2#^&k(1bc70%e%&C1b^-%e 1- %&7?8o1b%e(bqr1-%&1b%e-0%e ¦ 5 Á

|7k%a%&1^

-%a 4cqw Ð Ð Ð )(7 Á Ð A/w7%&^e%aq| Ð Ð Ð µ )(7 Á ° 45§t1®t70%&o1^¯w^&1b%a`$%a d^e|/w%a7$w#Pq4

q n7tk_0%&<1b%& 0 w%&wv7<10'- 0y4rz|7%ew#0w70-0%&%&2q-%e18 04rn7%&|^1 <l/w%e^&^"v1C /w%a7n1-%&%&0^& 10- 0 Á 4

c%ep#A%&_0^&tqU1^e-]sp%a`?/w%e7 Á ° d$#<1-¡qU`c%aqM70^&'%&C1b^18 ?%eo^1'0'7[4Lz|7L<1^1P%1u%&]q2^&-§sp%a`/w%a7^e^1#0/l®mw/w7n7o`b10 0'b -%e %e 4

ª

; YN$V¯NmOTI<D>9OuB WDUI>9OYI<V¯F WDUIOY@CG8NP@

5§71R`/l®-60o70(1b'^&1c%L-%ev1b`-7%eq tqUc7L#0 Á )sp0%e`4.56o71R`1^&k/2®-n7o'01b^[5 %&/w7%&v7/ltC1ck<-70o'1^1/2qUt1'^&1o%`?-7%eq 4Lz|7d1b'^&1c%L-%ev1bL%&o_m`P%e^a ]'%a`¬_8 Ð mÆ /w%e7 90 Ë PÅ Ë Ã3Á )$4fz|7%ekk_Ady`1b^&<1b-¨1u70Y%&%&¬%& 0 3Á 0 ~ Ã 4l¹20/27<1C`L<- Ã _8 3^e`P%e'1-% %m%1^Ïm<1b%&LqU^&^eR/7?#1^&%e'78|

0 Ã Ð Ã Á Ð0 Rª8

à Рà Ág g °

0 C©m

z|7%eoC1_Ak`$%e/l-§1oqU^&^eR/w^&%&'7mo1^e/21C $c1C`^&1b 7L-%&v1R`-6%&0p%&

904¹2$70%&-%&v10#1-c_8 f1qE1y ° w_"y/2]%e(01-3R/t [10-¡%e7(R`P%&'L-%e1t%eC1b-nR/t 97%&? ° 2qE1w%&|--[4~z|7%&8'1b^[7?¯c!qM+.ÏPC©8|%e|%a7|%& Ã Ã <|%e7 Ã -#"-%e'(/w7070 Á ° 9)L Ð 4

z|7%&8'1b^[7c!C1n_Ac/w%ef1g g °

0 Á

6

T

/w%e7 %&0'kqU+rÏm¯Õ)84?.0%e'L%e1^e^"'7w'%a`

nÁ °

%e

%&7

6

1 Ð g g 3 ° ° ° 6 R8

/w7 g g Á ° ° C4.z|7^&%&%e -%e1t%e~73'%a`3_8 Á

°

² Ð g g %&

%&07 6

Ð g g 1 Ð g g 3 ° ° ° 6 !

T

;E:<; =?ObG STGEHI<D N$VW@CG S VWGUQANmOu@N

< Á Á Á )0 07t%&8'1b^[q

g g °

0 Á

° 4376 Á

Ð ° 6 R«8

^e $7 C¢ wC1^¯01b- Á )$4.z|7P071'^&1|%o-%e1oqU~7%&w$-0^%e nÁ

° Ð ° 4376 R8

ª8

z|7qUt7t^&0(%e%a -%&v1oqU~7 Á t(P-^%&

Á ° Ð ° Á

° © ° T)8

; )[; "SRNmI "SRI0SCN VG QANPOu@N

071 ¬#A%1^C1bd%e7!mC1b-0 6!Pv1bYs%e`d/w7%ev7¦%&?13%e%&1^.-0%e `b10L-%&<1u-P-^Õ4r!$%&0 %&w1L0v1bm 0 Á y$#W ¨0 Ð 0 4.z|7

g g °

0 Á

g g $#W ¨ 0 Ð 0

0 Á

T$T

z|7!PC1-$ !P1b(P-^A7<1 Á )k%&0c%aq Á L P7 ~%&2(11_^e P_0~7c1b-%&lq0`b1b0'R/wp/w%a737$#<1%&3q70ksp0%e` [1b-¡7?-0$[¢ c7<1C`k1Y!mC1b-0 !PC1-0 4rz|7P0 Á )L1- wC1^e0C4.z|7%ew'%e`

Á

° T

1-70^e%&%e -%ev1bt%& Á

° Tª8

1(<<1b^#"%1b^1?%&-p7 Á Á Á )%a%eC1^¯-%a 31-%&1b%e-%&1b-]sp%a`b4!$%e Á _00t%eC1^eo0o%e]-%&0%&' 4!$%& 02-0 6 W ° 2-0 6 1-

90 Á Ð

° 3

Tb©m

z|7m °

0 Á

Ð °

T

1- nÁ/ 0 ~

°

0 Á

°

T8

M%e<1^&^a Á 1b^a 4

<|7t'1^1t/l7<1bp%e à 1-f%&7 à -% %|qU à 0^e %&70?_%&n4dR/2y` M70(%em'1^70dc!]q|+.Ïm¯C©mo-#A0-? 0o1-¬-% %oqU1Y^&%eC1bc1##0C$%&(1b%e

o%&¡7-¬-4z|7-§-o-`P%1u%&]qr7

1'^1%c-0%&1t1R/21C dqU 7c^e%&1~1b##C$%&(1b%& Á ~7m~-#"-w^a

70t%&c7%e qW70C1^ecqE1 04r5§tC1/w%a

0 ° 0 Á 0 ° 0 Ð T 0 ° T

ª«

/w7%ev73-y<7 $ ! " ! !

Á³Ð

T«8

z|7tqUoÏm<1b%& Á Ð U© ª85 ° ª qU©4e 9+rÏm¯Õ8 <'%e`w

Á³Ð Á

© ª

5 ° ª

Á ° Ð T8

z|7mp7 Á )L#0 ns%e`7<1b Á )0 7%e%&C1b^-%e ns%e`7<1b Á ) ²P 91-70!mC1b-0 n!P1bt$-^[7<1 Á Ð 4

o%e`n7ty$#<10%&nqU 0~/lo<-

0 0 Á

°Á Ð ° Á

C Ð R 0 ° £ 0 Rª)8

!$%e 0 Á Ð p° 2/l'0 Á

Ð ° ° ° Rª0T

z|7%&8'1b^[7c!qM+rÏm¯C©m~%e~73'%a`3_8 gg °

0 Á

° ° Á

m °

1 Ð Ð 3 ° Rª8

+.Ïm¯©m273'%a`

nÁ T Ã ° Ã 3 ° Á

° 1 Ð ª Ð 3 ° Rªª8

M%e<1^&^a Á ° Á

P ° 1i Ð 3 ° Rª©m

z|7%e%e|0%&mw/w%a7n~qU|#"%&1^C1 Á

° ~qU Á Ð

Á ° lqU Á )$

Á ° b© ° lqU Á ) ²$ 1-

Á lqU Á 4

w8Y/2® ¿-0%&18Yzr P#"¡16!0p3_8 ¿w%& aÓcR0 2#0 rzw¹~k zw¹~1u#79±b«)8b)0T''~71b µ )$ $/w7%ev7YqE1R`~1?`b10L' (-%&<1u-Ysp%a`b4

M%e<1^&^a 216yqU^pqUk^&1¬qU0-,_8 \ 1b%&'§qUd(1b-%&<1u-Z$-^&L/w%e7 Á Á )%e

Á

© Ð ° ° ° Ð ° ° Rª8

ª

pbo7<1u|qU Á P Á 0/l7<1C` Á

Rª8

y01y^a 4z|7%&c#1%&0^1pC1%&#^e%e<p_A1qU Á $ 7k1b-%&q`1uqr7sp0%e`?%e Á

4

;[; H>9OTOuNPHSTGU>AVQA>ADSTGU>AV

z|7|qUk^1 Á ,;E© .1##0^&%&M ! v1b^ <$$l1-L^e(%e%e%e4¯5j70m`%&0'%eY_<10-<$$ov7¬1 (1'0%e0-p "/l-¡d-Y/2Y7%&0'4cz|70<%&|L##A^a Y1qU7oqUÏP0y A(/lt#0o7<$ qU 7^&%&%e , 4z|7L0-§%ec##"^e 31qU»7L_<1-$/w%&-07¬bql7L_`b1b%&%&8Y7_<10-0/w%&-07fq7?%&%&[4lz|70%&%&w%a`P%1^[%aqM/l?0?7<$3#"pP1C`k1b-f^e(%e%e (#"Pv1C` %&?7qU1b%e<1^_1-0/w%e-07¡pmk_Apq.P1R`o-P[¢ cv7<10'/w%e7f-7%eq 4z|7m Á [ ° ,

© Rª8

z|7m7 <P3`Pp-07%aq c^1C/ qUw7 $3#"Pv1C`%&w701b(?1p7qUp_A^&(y%e<$"4< 7%e|/2tC1b%&^a Y'y

Á ° ,

© Á

, 6 © °

Rª«8

z|7L-% %0L_"y/2 [ ° , 1- , ^&1-c31Yy%&¬®mR/w61c7%&4+$#-¿1k(1'%a-0¡_"1b---¦¡71b##<18(1'%a-b M70%&%e

Â Ë Á Ð .^e' [ ° , , Rª8

qM/l®P%e'/w%e7n^e _1-n-<1bv1$ /2tC1bn/w%e

Á ° ^&' R)t#A ° Â Ë C©8)8

c_8`$%e^e ¡_`b1b%eto$-0^&c1--§n#0-0%&t70T/ 7L^e(%e%e n-#A0-?qUÏmy 31R/21C qU 7 _<10-[4

5j7§1b^&^M_`b1b%e/lLd1-0k%&f7#7b'1#7%ek_^e 7 %&0c0^&-_AÏm%a^&1'kqUc'81^&1u$%&o%&7 <$]-#0#0%&#%a0^e f1bt70©))Y­-'L-70³1- ^&%&0wq.%e%-nC1^e%e #^e|7¹~1^&|-'?%&n7m P-'[4¹20/w%e7n$-k^a%e_<1--<1b10 </2?C131^&^a 7 _<1b-3d_`'1^1u$%e|/w%e7 ) $ A1-

©8)

(#<1bc70 <$$w ´ _<1-n-<1b1n1_8 '81^&1u$%&4.z|7%e-0w70?(1'%a-01-nv1%em Y%&7 y%&[4

Y%&-0%eÊ^a ¦%e7#A%&_0%&^&%a ¬q`^&0%&[4¬ '81^&1uP ¦1u Á ) ²¡%&1##0C$%&(1b^e (o P| 'p71n7C1_8 3'1^1u$%e~/l?qUwC1b^&%&_01b%&[4rqM/ v110_"%&'qU- ¯7L_%e'78(1%e`Lv1bt/w%&^&^MC1bv7§70-6bq270%&t(1%&Ïm(^e%eqUb _A(-]'%&18o10-7]qE1-0L1R/21C 4?t1Y^aC '81b^1u$%&'yoqE1%&8o170 §'?^&-0 M1-67%&^&1-t]1n%e§37 <PP-7%aq k^&1R/ 7<1b?7<113^1b'v1%em 4d+`^&0%&%emP-1ny%&7<1b%&o#0#A%&1^ x^e%&®7 %&A4.z|7%&~71|#y`m-n7ooqW'81^&1u$%&k-0%& C <10-%&C1b~7o0%&^&%a q.7k-%ev1bmcz P#A1!0p?/2®94zr P#"1Y!0p1b7'78cY_Ak-d/w7%ak-0/21qUc%&_%e<1%ec^&R/w^e ¡1y%&0'n(1b%&1^W8%&^7y ]#<1t7(27<1-01®m7<1^&%e(%a1b-§$#^&P-4z|7L271-1®P71c^&%e(%aw-P¢ `^e`?/w%e73%& </w7%ev7¡0''c7<1b7kzr P#"1!0+(1R f_"'$P-]1-<1-C1-0^&4¹20o7k P#%&1^(1obq~1d/w7%a-0/21q~-Poy`^a`/w%e7%e(b 10-n/217%&'70|%&7t#<1 <L7t%&|%e^&^7t#"%e_%&^e%e q.1 $d1b%&t|%e7zr $#A1(!$pt/2®94

©

; WBK.NmO=?> WV"ST@

c®m%&-q^&'%&1^¯_`b1b%&]%ec7mk_Ac`<$¡^1C/t ¦ry4?5§C1b(#$7cy$#Ay-¦rl^1C/ qU`1b%&2^&'%&1^9(P-^el0%&0'k7c-0%&1 1b-"42z|7#78 P%eC1^¯`^&tqM7?7^e^¯_"y/2]-70%eq 1- ° %&'%e`f_8 70?qE11C1dq.7k#7k/w7%&v7]%ep© %&p7?7%&v®mtq7k7^e^/w7%ev7]%&

0 4

z|7mo%eqM/27<1C``-_mx Y7%&P0k_"c-%a f`b1%ep^&%&®b Á T ° 3R 707tmk_A|/l?0#AypL%&Y7t-7%aq 1'%e

Á T ° 3

0

C©T

/w7 %e~7tmk_Awqw/w%e7-7%eq ^&|71 #A|1-%1b[4

pR/l` ¯/l'1^e^e n-[¢ t7<1C`1Y(#0^&k0`y ]ql1^e^70_Pxyt^e71¬1'%a`§-7%aq C4%&tkv7¦(37<1C`d130`y ¦(#0^&¡1n'%e` <$§(1'%a-b4y,_"7 <$¡1- ,j_"7?^&%&0%a q70k_Px45§/w%&^e^%&-o1%e'^e^1pbq._Px 1b^&^[/w%e737?1?^e(%e%e 4z|7?C1?/w%e7¡11'?qM^&%&0%a%&%&o1%e^e f-6qU­1#A#"%e%&qly`1^1-<1-§1-^eLC14L5j%e7]71#0%e 7t^&0(%e%a -%&v1t%&

Á ,© C©m

1-708|` $31o'%e`3_8

Á T ° 3 ° $

A$

A$

0

C©8ª8

pR/ " Á Ð ) ?4376 ,;b©§10- Á ,;U© r2

Á T ,;b© W 376

6 °

"

0

C©©m

z|7<qE1yf7kc!%&w7¡+.^e%&-1 È/w7%ev7¡t/l^&-f'qU%eqU^e -%e%&_$-nc%e31$y$#<10-%&'(+.^e%&-1¡s%e`4|z|70? %e3_1v®yc8v1%e70y%&w-oL^&'b 4

z|7t1^[%em%e YqU 1b^&^%&w'%a`n_8

Á Á

R ,;b©¯ 376

6 °

A$

0

C©m

5j%e70w7?^e'%&1^y%&n 7%&w%& 4376 /w7%&v73-%e`'p1 )04~z|7%e-%a`'0%&w1b7v1b8qo^e_"¢ |#<11-C"4

©m

-2

-1

0

-2 0 2 4

log[

S

dN

/dS

]2.

5

log[S/S1]M%e'42Rª$4 z|7c#-%e-Yc82qU1-<1b-Y1-^e~%e(`b1%e(^&'%eC1^0(P-^e d1b^&%-d7t+.^&%&-0C184rz|7%e|%&~qU2_"^e%&<$$||/w%e7 , - 4 %&l7+r0^&%e-C1b <$1bw1-0%&1oq

4.z|7o(P-^&~1bL qU¶%e'78~^&q r!PC1-0

!P1bb p_^e]-<17- Á $ -j^e%&- Á p_^&1v®¿^&%e-c(#0 'º^&%e-c`b10L-%&1b-[ 0_^et^e%&-01-¿1^&%a PkqU|1-0%& 9_^&1v®Y-<1b7-[4

qM/ltt70$#<1%&|(-3-%e 0 Á Ð

° ° p° £ Á

° 1i Ð 3 °

A $ Á

° 1 Ð 3 ° £ C©88

/l?'y

Á R(,;b©W7376

6 ° 3 ° ° £ ° 1i Ð 43 ° C©m

z|7 w-#A0-1^&w0w%e7o<w/2Lw

Á T ,;b© W 376

6 ° ° $ C©8«8

5§ff71bd7¡%&Z -0C1Y7f¡8Y_A^eT/ 7]+.^&%&-0C1y$#Ayv1b%&[4z|7%& <1b%e'dq 1C`%e-7-%a`'%e(#^e%&-3_8 ¡o^e_"¢ #<1b1-C"4

©8ª

z|7-7%eq c/w70k7k8t-%&f%&c_18%&1^M%e1u7c(1^&^W%e?7ky%& %e ° $ <_8 Á ) 7t%&%&w1b^&1-0 Y1LqE1y|bq) ©4

5§kC11%e^e /2®n0c7ky01yoqU q.7^1b%e`P%&%&t%&¡qUc1dqU/³%&#^&C1b42<~7t#0 s%e`/lt'

Á

°

A $ Á

°

0

Á

°

Á R ,;b©¯ 376

6 ° $ C©88

<|^1b' /2t7<1C` - %&7%e|C1? - $ 4p - 4376 1b )04rz|7%e91b%&'?%&'7dkd1b®p7pv1b^A%e80%e L<0%eb $^e`P%e'kc^e_"¢ 2#<11-C" $_0027pv1^mk_Awq_`b1_0^&t0p%e|%&0%e4

5§C1 y$#7-07%aq %&¨kq7$ _8 ¦-y<%e' Á /w7 Á ,;E©

v ?%&7<$67Y/l^&-¨71R`%&¨1]+.^&%&-0C1 s%e`/w%e7

-%ev1b Á4z|7%e®q 1m1c1(+r0^&%e-C1bf-%ev1bk%ef-7%eq p%a4!$^a`P%&' Á ° ~'%e` Á Ð ° ° LLqU Á )k7 ¦r|^&1C/%e

Á C ,;b©W7376

6 ° $ Á R ,;b©¯ 376

6

°

T)8

<w1 Á (1b|-0(%e<1b-sp0%e`/l?'

Á

" Á

0 Á

° °

Á R ,;b©¯ 376

6 ° 3 ° T$T

<|^1b' /l7<1C` - %&70%&w(P-^¤ 7?8 91bn - ?4376 $ 4z|7%e0^e ¡^a`c^&_A¢£t#<11-C¬_0?1^e'%a`?1<%e1^mk_Aq~_`b1_^e4w<18 5j)/2?7<1C` - qUw^&1' "7%&w<%ao1^?8o1#0#^&%eL1b^&^A(P-^e2/w%e7 ¿)0 `7'7Y70o(P-^e2/w%e7 µ ?1bc#A$-0^&/w%e7%&0<0%e

©©

`^&4z|70k1^M0mt'%e`70P0k_"oqrt%&f7 yÒ !Ñ psp%a`b 1-70%&|%&|^ew7<17ov1^[sp%a`t^e Á )04<27%&w$-^ Á

Á T ,;b©W7376

6

° 3 °

T

<w1%e%eC1^"-0%e (1b-(%e<1b-sp0%e`/lt'

Á

° Ð ° A0 Á

Ð °

0 Á

°

Á T(,;b©W 376

6 ¤ ° Ð T ° 3 Tª8

qM/lt^&y Á ° 70f Ð T Á LÁ ° Á ° °

Tb©m

1-70t0m 6r|1o'%e`3_8

Á T ,;b©W7376

6

« ° ° ° ° 3

Á T ,;b©W 376

6

« ° ° ° ° 3

T

<w1k`b10L-%&<1b-$-0^/w%a7 Á Ð 7t^&'%&1^AqU0%&1

Á

° " Á

°

0 Á

° T8

z|7m Á ° < Á Ð ° ° ©

T

©m

M%e'4fC©04 z|7d$kq~qE1b%&8ÏP11k10-61b-%&n01¦_A(0#0^1%e-§_m ¬1b6`^e`P%e'#A#^&1b%e%&§137's%e`Y1b?7R/w¨1b?^&q ?1_AR`b4nz|70(Ïm<11k1L70T/w 1b^&%a^&o(1'81d^&%e?'8c_"C107 37<1C`1(7c^e%eqU%&o#<1-fd70k1'?q.70sp0%e`4rz|71c0T/^a Y1qUy/ºÏP11 <L/loo^a Y1qUy/_%&'782ÏP114¹20|/w70/l3^e$®¬qE1L1C/~1C /lf1n1^&¬^e$®P%e']%&87n#<1 ~10-Ènd18 ¨ÏP114ÈÈ70!PC1-0 Y!P1bcP-^A1b~%&'7m21_AR` $7%e2`^&$%&d/w%e7d%e(%&lw1^e^&R/l-[ Pk7c%&ly$#^&1<1b%&YqU~7ty$pqMqE1b%&8|Ïm<11p1-1b-%&L4

z|7mk_A|8w/w%&^&^"_"t'%a`3_8

Á R ,;b© W 376

6 ° °

Á R ,;b© W 376

6

©

° ° © ° ©

T«8

!$%e 7<1bC1b^&-]0%e37^eC1-%e'L( A7k8c%&p1¡%&00%e%e`70$-]<0-7L'(y fq7sp0%e`4+`§ 8t/l(0-^&07!PC1-$ !P1b$-0^My`§_AqU70(%eR/21C`_<1v®m'-/21o-%&R`-[4kz|717%&c/21t#A%&_^ek%&7<1bo7_`-§L8tq1-0%&Y?1-Ïm<1110%&8/w%e7§+.Ïm¯C©«8oqUt18 ]`1b^&Lq C4d01-6bq~_A%&0' 91uo7<170 - 6 +.^e%&-1¡#-%e%&[ 970k_`-8o1#AcqU-%e<$$ .10-6^a 91b§qUt` qE1%&8<$¬^e`^&4Yz|7Y#"?7<1¦+.^&%e-C1¬8C1n^a _"t_$v1%e-_8 v7<1'%&'L1#0%& r%e7~7-%e |^e%&%e q7tw/~1'C1bw%&7t#<1bC4zWw7?Ïm<1b1w8w/w%e731n%&1tqM-%e /lk-¡Y%eC1k1- ¦_8 f1(qE1yq ° 4z|7%e%&01%&wqE17<170 ° $ %&¡ -kY^&'b "1-](1bv7c7#_`-¬mk_A84rz|7m71^<-0%e q[ÏP112k0`1b L^&%e® . Á R ° 3u ° - ° _<1v®nY-7%eq cq ¶ ²P4opR/³-P7%&p^e^e$c7!P1-0 ¡!Pv1bk$-^ ¨z|7'(y fq.7L!PC1-$ !P1bkP-^W%&x0c7<1boq1 Á Ð k`b10L-%&<1u-3(P-^¤ 1- o7<1c1^&-¬0o%& ~4t¹2$c7!P1-0 !mv1bk(P-^1^e1c7<1b %e

©8

0Ò [L7( ° 3 %e+rÏm¯C©T~%e|-#0#"-[4rz|7%&w'%a`

Á T ,;b© W 376

6

ª

° ° © ° ©

T8

%&n7k!P1-0 8!mv1b$-^¤ 910-f7?%&(qU-0 Y1b-uxp7?0?-0%e 3`^&$%&/w%e7 4l!$%e7o1b##<18|o-%e (`^e`|^&%e®k ° /w70%&v7%&l^eC1^e 2v18 70!mC1b-0 n!P1bt$-^[%&|^&-0C4

[;Õ:<; I<B¦B§I¬XdI ¯Ob@yST@ 1R _0o1?7c_¶R)(-pq|R))uª))®b 1C P4wz|7v1^¯'

<%e?C)4 'm±b qUpqE1%e^e Y_%e'78c_7<1ucP0o1_A0pk1d(m7[4z|7mp7<$qU7_%&1_A0R) 'm±b ±b </w7%&v73%&|70?1(1w70?_A^&(y%e <$q1f g (1'%a-0?v14c¹20%e7k_0cP0/w%e70/~1b%e' "` ¡^&%a^&o%&p®mR/w1_A07%&04|#<1%&%&#<1u-n%&f1(C1v7¡qUw#0%eC1^¯8#<1c%en7dC8)0¢ p0%&0'70 .1%&%&tpy/2®qM(y|C114z|7?11b#07'1#07-78%&o`P%&%&_^ec®8 ` Y-<1®(0%&'782^&P®kqUl(y4 \ ^e%&#^ep1(1l#<11u-_8 3R)0¢ ~q¯®m%&^e(yl/l-§#R`P%&-0`P%&y/wbql7L(yc1b%&^&4o%e-^1C 56%&'78Î \ R2®8 ÈC8b© # r R8$ £.Rª8|1v70-]7^&pqUY-Y%e370kp_"C$oq 1C n_4!Pv1^&yq ^&'%e^11%e^& 8_021¡-bt/20^&-d_Ap1p7<1b9170-d(70d/l8~02Ïm%ev®m^e 4qM/ld11b--¡1-%e71t#^1 /l/l^e-371R`1L7%aC4sp0qU0<1b^e Y7/l^&bwq-?Ud1%e^e (-%e1-,#^&1b 91C/wvy A_0%&%&-4~¹l0w/2t/2?1_^et#T`7<1b|7t#0%eC1^#"R/l|/~1bp^e|7<17 1R d#"R/l4

tp¹¢ 1Y%&#%ed¦7Y®8 /w%a7¦]#0qUqU7Y'81b^1y%&#^&1Y7'81^&1%&t84<7b A7_0%&'7mp_pqU^e^&R/¥1 ¦ r- ? 8c^&1R/1##0#%1b|qUl0%eqU(^a k-%e%&_00-d4rz|7%el%e-%eC1br7<1b70 %e'%&1b|%e70rqU^&|7<1nt-%e®(C1b^&t7%e'78|qU 7?!$ <~qUqU71R/21C 7<1b7c%e'?^e~qW'81b^1u$%&4!$k7-%&v1c%&2%e7 µ R))?#"c1 R)) \ #A45j7ft|/21^1bv7-[ "(18 #A#0^&y$#"-f7?%e#0%&t#<1b3(_C1®-R/wnqU|7tqE1%&8w_/w%e7<0o-R/wffR)4 ! '8±b 7<1b7¹2.z!0+jy$#"%e(mC1f-4p01-[ A7qE1%emc_-%&%e_0%&¡%ec%&^e^M%&#%e [_$o7L8 91u]qUcqE1%&8c_04z|7mc70tp¹-0%&%e_0%en7<1c1bj-0' "_0o%ep#7%&1^&^a P(y%ek1-37k!$^1b!P Pn4

cq^&1-%&0'](P-^eqUk7%&%ek7<1b7Z-'¬%&k7-0'qp7_`b1_0^&sp0%e`45§p7<1C`p(7<1br7w0m/w%e^&^1b1^&^a k_C1®L1C/21C qU¼7+.^e%&-1¦7 r - ^1C/j/w7 ) ²$45j7-0C1^e%&'/w%a7t¹¢£l7c%e|11--0%e%e<1^qE1bq ° %e¡70m%&]_A1L71ukq_0oqU 7%&'7]-07%aq '%&w%&-0-¡_8 n7t%&t-%&^&1b%edqE1y ~1^e^1bw1qU ^&%e®o701#0#<18c1utq

©m

%&^e^1b%&(q.1u%&c^&Pv®m 91-31t7mw^&R/l_8 1LqE1b|q2 ° y4q/l1® Á ) qUw1_/w%e731 <0?qlR)4 'm±b $/2t<-31' Y^eC1tq

³Á © " " <u ° ¤ "§R) $ ' R)8

z|70 ° qE1c%e-kY7v7%&'bq7k_0t_8 37k-7%eq [Y7k(%a-_%&w7p7<137_`-]_4z|70%&w1^¯' n%&w%e-1_^a ^1'|7137#0%&1^<^&%e'78r%e-_8 d1t0#"R`b1042.P-%&'7%e^&1'Ïm<1bm%e Lq 1C P2%e.7#%e%e#<1^-%aÊ(^e (/w%e7n7t(^e'%eC1^A(P-^qUtp¹¢ 4

¹20py/ -<1bv1L_01%&0-n%e'(7¹l##Ab!Pp¾ 1b^&^e%eo7<1C`#0R`-f7<1uotp¹p¢£p11b^&'%&C1b^-%ev1b4z|7<1bp1b^&^e%ec7<11/w%&-<^&-nq`P%e/¥7<1b-¾p1C C110 71bC1^&PC1up7c#A%a%eYqW1Ltp¹Z© 1b01y 4lt-8^&^el^e/º7c1b^&^e%ew#A%em~17%e'7^e0%e¾p1C ^e#A1up7_0#"%e%& <1-¡bq f1qE1-0%&'¾p1C 1%e8k%&¡qUy`1^M701bq 7_0C4z|70?¾p1C ^&#A#0R`P%&- #"%e%&4o0-$_<1b-3^e#AcL1LqE1-%&0'd#0%&1^1b%e8o1bp71?#A%e%e[ A1-]%e¡1(qUy/C1b1k^&1'p-7%aq w7<1|_An-0%&-YqU27o#0%&C1b^"1%&8|_A1?1b_#0%e^&%e-o(1bn%e8`%&'L^&-q'81w1uw-07%aq |1o[4z|7t-7%aq wqW7tp¹ kc_A^&1'7<1b y4ctp¹8)8b)«(7R/2- Á ) «f \ ' aÓ& MC«0 A1u ª«8P «8«84¹¥)$Tª(/21o_`-¬#0%&1^&^a /w%e70%&d-tqr70L¹2.z!0+º%e'' 1-/21t§n%&Ln1#AC1b®¡_%e'78tq~bgih((1'0%e0- y`¬7'77-7%eq %& Á ¬U®^eq aÓ& ¯1u#79±b)ª8$Ty4?z|7 1C qU b)®b q7%e_~/21|ª"¡R) $ 'L Õ¹21- aÓ& AR0 P# 0 0zw¹~k Pzw¹~k $1b#79±)ª8b©my4Mq 1(qUy/¼877#0%eC1^1%&8o71qE1--1C/~1C ¯1b-¡7k%e<1^e^e 31dqE1%&8'81^1T$ 31b70qU(w#"%e%&q7tqE1-%e'(#0%eC1^[1%&m4~z|7'1^1u$%ew7<1C`?^1'o-7%aq 2qUy01#^e <77'1^1uP bq¹º8$T$©71 Á ª ©mn o^e®b1b% aÓ& WC«0 9p1b "ªª0 ª84wz|7%&p_c7<1b-]1 1C kq|@ e "¨R)4 '( 45j7%e^&o70-<1bv1$< 70^&'%&C1b^<1bq7¹¢ p#0-0%&-3_m 7%em_"p8p1-3%&b#m <77%&'7-70%eq ]qU_0o^eC1^e ¡7 #<1cq.7 6rp0`Ïm%ec1d` f/w%e--%e%&_$%&qM%e8%e%ettp¹ _%&'7804

©8«

[; pQ">AD ¯SRGE>AV > GW@NkI<H FAOT>WV W@5§?1f1^&^1bc7`^&$%&3qM-% %"?_<1bv®P'0-¡1-0%1b%&Y<^&-w/w%e70®mR/w%&0'

70?_%&'78pqM-%&v18'81^&1u$%& _A1?%eqM11-%&1b%eY<^e-3%ew7'010-3%e#%e^&%e®w7csp%a`b 0/2^e L0-Yk%e-21(1^&^<'%edbq¯#<14r(1'%&0p1?_%eC1^A'%&_A--_m 3(R`P%&'d(%e4p¬1d_<1_"c7#¡/w%e7]%&p¡/2#0#"%&'(/~1^e^&pw/w7<1bw^e$®m~^e%&®bt1%&0<0%eP0k_"|q%&(1'l-0%&'%fL%&0<0%e 01-7%e~^&P®mx^&%e®t17'1-%&#%&ts%e`4

!$^&y|%&-|7tÏm<1u%&nbqM1-%1u%e`1qU Á Ð Å R0T

/w7 %&7c#"%a<c%&8%e (%&Y'm±b ±bR±bv± c%&7#<1b7^e'b71^e'7c1C d%en %&~7t%&%e`P%e d%&'m±b 3±uC±b± b A1-3Å %&~7?1_#0%&PÊ%&8%& 45§-0<t70#0%eC1^[-0#07 Á" Å 1-n'|7tÏm<1b%&

Á

Å Ð Á Ð R8

/w7t7ttqU0%&È%e~7t1u%&bqM(%e%a`P%e d1_#0%&PÊ%&84

[;E:9; JDEK.NmOa@ cIOTI¯>q./lk1?7<1b %&-?d_0^1v®m_A$-0 v1/w%e7fmk_Ap-0%e "1-%&0 1-

(#A1b0 77|^&0(%e%a t#".%aqUÏP0y Lq[1c%&'^&~v1%e2, Á © ´ y4z|7L%&%a`$%a ¡%ec7 Á , 0E©W Á ´ y4z|7(1_#$%&]PÊ%e8ql71p%&x?T`7C1bfqU#<1b7[ "1-¡%ep'%a`¡_8 fÅ Á 4|5j7¡/2k^e`?71b-%1b%e`1qUwÏm<1b%&/2t'y

Á y$#W Ð E)8 ° 1 Ð y$#W Ð 03 ´ Rª8

z|7mw/w7 7t%&8%a 'P| ´ y 70qE1b_%e'78q1v14~!$%eo7®8 %e|kv7n-<1®bw7<1b7%& <7%&0'%&~/w'/w%a73c^&_A¢£w1#0%&4

¢£wC1b^&0^1btÅ qU 70_`-¡^&0(%e%a -%e ql "§R)@'?, \ #A 3

Å Á Á "¦C)@'Õª £)« "¦R) %$ 3

Õ&"¦R) ¼R) $ 3 R©m

z|7m¡C1v7 Á Y/l-¨]'3 Á R) $ 3 /w7%ev7¨%&YR) ^&%&'7m? 14¦!$%e70^&%eqUy%e(q7Ls%e`L%&okv7^ec7<1]70%& [/lL-¬%&-c7%qr70y$#<1b-%&0'ds%e`?7tÏm<1b%&qM1-0%1b%e`p1bqU4

©8

; )[; [HI0SCSCNPOuGEVWF

q ¡71b_#0%e¡$yÊ(%&mc%&^&-c1b%&'Y-0-_8 /w70%&v7]'1bt1m%e_0%e q </w7 %&|7k1C`1'R`^&%&-31'^&tq7?%e80%e 4~5j71C`1'-]R`p^e%&-31'^e 91b%&'(C1^e0pqUp1(-% %?_1v®m'0-[4z|70%&%&_"C11b%&'L^a dv71'w7o-%ey%eq#7 1-n1^&^"-%&y%&|1oÏm<1^%e1%&#%&%a<1u%&[4kT/l` /w7§^e$®m%e'1bt%e-%e`P%e-<1^W0 W1b%e'%&lx?1o&%"y%e`L%&-%&'7%&c`P%&%&_%e^&%a f1bt1_0#0%e[4z|7qUL/2(1L%em-§%&®mR/w%&'70#0%&1^[-#07^eC1b%&'_A/l37t`8YR/wd1b-3y`m1bw-7%eq fw#<1bp^&%&'7m042p(%e'L7<1b1^e^[d1uw%&w%&0%-[ 70?#$%&1^-#073%&w_01%&-_8 Y%&' Á

0 1-# C Á ° 3 CE)8y4r<21kd1b-0(%e<1b-Ys%e`c/w%e7

: 18 7|-0%e </lt7<1C`

Á CE)8

° 3

° ° R8

z|7PÊ%e8~%eqU8l7<1r7%e(#^e|%&8#1b%eLq[_A%e'7#0%eC1^<-0#07(?1?-0%&1Ïm<1b^(7__^e1-%&0

c%&¡1($y$#<1-0%&'s%e`4t<1( P#%&1^ RE)8 Á

#At_0%&L(yt1^&^eT/l-_8 ¬¹2%e'3¹21'np^& P87%e 7%&o%e! Õ)8 Mv Á R)443 [4

z|7mw7%e|#0%eC1^-#073^e _Aw^1'qU|^&1' 1-7t#0%&1^[-#07n%&

¼R) 43 376 ª R8

z|7%eo^e-¡_A%&'%e<18cqU ¸C) _0t0^e 3%eq.70'81c%ec%&0%-[ 10-]%&0k70%&c_AqU70y$%eq.Ïm<117'81%ep#0_<1b_^e 01^W8%&^ Á R)@3C4w~7%&#A%&8C 90?7%&%-qU1y%e%&w`]1qU/¥#Am <7#0%&C1b^[-#$7f%ewÏP0%et^&1't1b-f#A%&8wC1b3_At[4

[; [; =>A@CB§>"DU>9FAGÕHI<D ¯I0STGU>AV¿> lOuIV@ ¤NPO

ct/l?7<1C`-%e#A-fqMC1u%e' 91-n#^1b- ?_8 0 /l%&^e^-fd1^e^&R/jqU

70k8%&m<1^Wv7<1'%&3qUÏm%eoC1b-¬_8 n7y$#<1%&]bq7ksp%a`b4oz|7C1%&/21R 3Y-0Y7%ec%&Y#^&1 _8 ]1dÏm<1bm%e 37<1b-Pov7<1'-%e'd7ky$#<1b%e[4z|7km_"cqr#7b#"$-b Õ 1 3 y "`b1^e<1b-]1b Á T ° p%e0kv7Ïm<18%a 4rz|7%e'%e`

° 3 Á

0 ° 3 Ð Å R8

2%&-oc^&_A¢£#<11-Cf1'81%e[4|?/lk7<1C`1(^e(%e%e Y-0%e Á © R/¥1b-7<1b27t^a (7%&0'k7<1bwv71'w/w%a7-7%eq w%e~7o-%a '%e'k^e%&® ° 3 70 uÑ ^&%&%e L-0%e Y%e~18C4rz|7m Ë Á Ë Á )8 ° 73R4 1 w_"

)

71bT`P%e'`^&0(p0#1-]10-¡81yc17?sp0%e`k-P4 3?!$%eÅ %epdd1^e^[/2/w%&^e^%e'o%eC 0'%e`P%&0'7tÏP1b%e

Á 0 R«8

<~70tv1b^[|_A^&%e%&8%e Y/l?%e8'1boT`|qUÏmy n'%e`P%&0'

Á Á

0 Á ©

0

° R8

z|7mc70_A^&%e%e80%e 3%&--_8 3qE1ypqp ° 1b-¡%&1^&d^e%&%e-_m n70<%aL1'ql7sp%a`b4¹27%7<1C`(#<1b1_^ek(1'%a-%et%eo#"%e8^&c1'1_A0p/w7%&v7¡qE1b%&(%e(#A18C 9_0c#"#^&-4t< ¶" R) ' , \ #A 31- Á 0/2'y

Á &"6R) '1"f© "¦R) 3 3:"]ª)))©rÕª £)«&"6C) %$

° 3 Á« "¦R) 'm±b ±bR±b Á «o05±u ±u

T)8z|7%e?%e?1b§' ¬-%e q2©

Á ) £))8Yyt±b 3 /w7%&v7§%&)04£«98»ql7d \ ¹ '

-%a n1-3&"¦R)4 ! qW7t%e%&C1b^-%a qU Á 8$4

<p17py01#^&b "%e-7¾p1C n_<1v®m'-]#$-0-f_m f1d7b%em'81^1b%e-%e E \ /w%a7 Á Õ)8 ° 3R4­z|70¨%&%e`P%e jbq1¿7f#^1d1Z%& Á y$#W Ð ¥10-71_#0%&%e|'^e%&'%e_^&b4Mz|7%ew'%e`

° 3

Á RE)8

° y$#W Ð T °

° 3 ° ° T$T

Á RE)8

° 00#W Ð b ° ° T

sp$qU<1b^e [qUt18 ]^e%&®^e n`b1^&q CE)8p70%&o_<1v®m'-¬%&yP^e ¡(1^&^Õ [1-]7y$#Ay-d-%&%&q7p#" q"7p \ ¹Z#P--(_m LC1b%&0'?%77^e0%&|0[ 970%&w(P-^%&w%eC4

21?<<1b^"1b(#^e m%e-21(P-^9qUl-<1b®Ld1ul%&%&'?q71C`P (0%&7<1u-C1C n%&8(1#07¡1-31(^e%&'78|00%&04w2`1u%&3qM((m '%a` Á ) 4z|7%&%e`P%a d%e

Á 5 Æ0 Ð ) ² 9« Tª8

/w7 %&27o^&%aqU%&pq¯7o$%e2/w70%&v7/2c/w%e^&^"1(t%e~kv7^1b'l717t1'cq70?s%e`^e Y1(1^&^AqU1y%&/w%e^&^"7<1C`-1R -¡_8 0T/t4rz|7

Á5 «

° 73Æ0 T ° Ð ) 9

° 3 ° ° Á

5 «

° °

6 h Tb©m

$

< Á t7%ew'%e` - 376 qU Á )#3L7-'1b Á ) [4r C1b<1b_^&^&%e(%a|n7?yP1'81^&1%&t_<1v®m'-¡^e%&'78%&70_^e?_1-¡%e?R) q7%a%eC1^-%a |© 3 µ R) 5 g

5 5 g

) 6 µ R) T

z|7mw7t^&%aqU%&qW778 $#A7%&C1b^-1R P%e'(00%&0|7<1|L_At^1'~7<1R) 14

:¯; rNPHST@ OT>AB cDENPHSROT>AV [HI0SCSRNmOuGEVWF

<1^a n#A$v7c/w70]7ksp%a`k/21o%&%-[ "^&¡C1b%&0'%&p7k-(%e<18v7<10%&»qUc1qU%&'0'b _"y/267L1-%&1b%e¡<^&-¬1-7L(1b4^&'17^ey¡#A1uk%&c^e7<1b§1b_"$kR) ' A7%tq^ey]C1u%e'70#A½C1]_AC1^e^&1b-]%e'Y70 t(#<1byLR8$ !$R`"4#.7m P4 +.z< [© ª)8Ïm<1u%&

$ Á " "

" $ ° ° " T8

/w7 ¬%e|7tmk_AwqM#7w#"w(P- Á 0 Ð T2qUw1L_^1bv®P_AP-0 0y " Á y 1-70 o#<10 $ %&|-0<-f_8

$ Á

0 T

z|7m $ %&o7^ey§C1b%&'n#0%&1^-#07¬%&o7L^&(#A1b(%e%eql7^e§?d147<1b7^e011(-6qU^e^&R/ 1 \ 1uP/l^e^&%1b-%e%&_$%&[ 0_$7<1b|7t#73#" %ew#^&y^e d1_%a1 4

!$%e7&o#<10ÏP1b%e¡%&p-%&_%e'd^&y¡1b%&' A/w7%&v7]#0`o7mk_Awq#7 <o<-w71b|7 $ -0%a`b1b%a`oqW7t#70-%a ­`1b%&7

$ -

" $ &"

Á"

" $ ° ° " &"

Á ) T«8

z|71b%e<1 6^&$%&kqw70Ïm<1b%& $ Á )1d7#70¨-0%&%e_0%ek%e70(1^WÏm%e^&%&_0%&0/w%e7f7^&4t!$%ek#07o1`-[ 7#7¡mk_A-%a §-0$?b?71R`d31'L/w%e7¬7(#076mk_A-0%e ¬%e61_^1bv®P_AP-0 ¬1b7^eyf(#A1b4z|7mo1d'1^M¹l+.%&%&f7d1^W-%e%&_$%&3%e1^e^&R/l- Á E0#" ° Ð Ty4lz|7%&'%e` $ Á )qU1^e^ 4|!P%&7¹l+.%&%&f#"%&c1Yv1u%&<1 n#A%&8qr7 o#<1cÏm<1b%& [%e%&7y$#A-qU¸qUp-%&%&#$-0-31b#APv7|/w7

° $ Á

° $ T8

<k70 '%e` _m Z¹2¹~c! 1- 73 \ ¹ 1%&#"1®¦7%&'78 l7%&-7%eq /w77%ec%&0Ïm<1^e%e 3%&c-§%&/l^e^M/w%e7%&¡71b-%1b%&3-%&<1u-]10 [/w%a71Y`b1^&0 Á C) b) )b©04

z|7L%&t1Y%&#^&k^&$%&f70 t(#<1byoÏm<1u%&/w%a7P $ /w70%&v7'%a`|7k!P8 81y`m ^e-R`$%ev7¨R0 0#[4lÎ !$#[42!$%¤4a <© 9ª)0T2 $ #Ay1b^W-0%&%&4.z|7%&w%&

ª

-100

0

100

0 5 10 15 20

Res

idua

l [kJ

y/sr

]

ν [/cm]

yµ

M%e'4oT$4 Mc!n%e-<1^e1b-f70(1u$%&k 1^&^eT/l- $ 1- -%&%e $ Á " C)4 1- Á "6R)4 4

d1b^&^e Y-<0-]qUp71k/w70& µtµ µtµ 4c!$%&07 "]`b1%&1_^e?%e-y<-

1: 71b0(#0%&0(1®b &"3` (1^&^Õ 10-n7P07t^e d71b8%&_$%e'%a<C18^e f $ %et7 "¨ 7 Z10- ?1b%&#A18t%&]7%e^&%e(%aC4?¹20o/w7§7L%&%a%1b^#70]<^&-¬%&t1_^&1v®m_"P-0 ¡/w%a7¬1Y#A1u (/w7%&v7¬%&^a Y^&%&'7m^e (_"^&R/º7t^ey#"1bc/l'1-%e%eqW7o17<1#A4%&0'

Á m /l-n7<1b|7t%&%a%1b^"#70<^&-n%&|'%a`3_8 Á 0Ey$#¯ "" Ð T4.z|7qU

° ° " Á

y$#W "" Ð °

E0#W "" Ð T Ð

$#W ""Ey$#W "" Ð T Á

Ey$#W "" Ð ° Ð y$#W ""E$#W "" Ð T Á

Ð 00# ""Uy$#W "" Ð R

Á Ð " R«)8

z|7m|7t-%e%&Y71w1!$8 81y`8 ^e-R`P%&v7n7<1#At_0w%e~--3%ed1b'%e-c_8 1qE1bb©

Ð @ 4rc<0%&'70f-%&%&0' $ 1 $ Á [ Ð

0 R«0T

/l<0-n7<1b|70t<1^#Ay %&|'%a`3_8 1kqUÏmy 8-#"-8o#"1bo'%a`3_8

Á ° $ " ° T Ð Ð © ° R«8

/w7!" Á R4.z|7?Mwo!Y#Ay %&nM%e'Tk7R/wp7<1b $ µ ²&"6C)4 4z|7t0'b -0%e (1qU-qU¶7o70|^ey~70oP^&~#7|%eY7 $

-%e%e%&|1%e^e d#0-[4rz|7t0'b -%e %e|'%e`n_8 - "3 &"¡ $ Á

" " " $ " &" Rǻ8

/w7%ev7n/w7f%em'1b-_m #1~/w%&'%a`

$ Á Ð

" $ " &"Á ©

" 3 &" Á ©? R«©m

z|7mo7^&%&%e $ '%a`t1Y#"0-%&'^e%&%ew]' ¡1qU µ " R) 48 3' 3/w7%&v7]%ep1qU-]%e8(7k^&yo1b-7%aq ¥L/w7k7L2(#0P^e%&'Y%&%&t^&t7<1¬7(p0__^&%&L/w%e^&^_A1qU-¦%emn7L#7§^&-§1-#$-0L1 $ -%&%&[4!$%&07L1R) c%&p(k#7007<1b§1bm f70c#<1b%e^ey$#0oqUw70k$%e "70k#A%e<?7C1bcq70k#7¡'81b%&pR`/w7^e(%e'^a -%&<18 1-n7^eyp1#%e-^e $^E%&31(2(#$3P^&%e'k%e(C2_<1v®%&8Ïm%e^&%e_%e /w%a77#7b4?z|70' f'81%&0-¡_8 f7#7b%& Á © $ $ /w7%&v7ko_AkÏm<1^Y700'b 3^ew_8 70?^&yp1-n%& p@ ² ° y4w!$%e $ Á

0~/l

<-702(#0P^&%e'k%e(

0 3Á °

© Á

© "¦R)4 ° $

R«8

qU1j%e ^ej1b%e¨qd© $T$4¼z|7%&_A(nÏm<1^c¨7¬p__0^&]%e(b Õª )««&"6R) ! R W ° lqU Á 91u? ° Á $ 4

~w-70%eq Á C) 07t/w%e^&^"_"o'7^&yC1u%e'qUc7o#07%&8f17(1^.-%e%&_$%&¡/w%e7§1 -%e%e]%&01-6bq|1 $ -%&%e[4(pR/2y` M7d1b^qU qU|/w%e%&'1 -0%&%&-0$pbp#0`7?#073mk_A-%a 42z|7m/lY7^&-¦k_%e(7 -%&%&§/w%e7¦13#"1b(v7<1'd¡'%e`d1¦%k7<1b

#`#073mk_A4rz|7t#73m_"-0%e v7<1b't/w%e7 %&|'%e`3_8

- " &"y$#W" ° Ð

Á

" &"

Á

3Á w AÕª8 Ð A¤ ° £ R«8

%e(%e^1C1^e^&1b%edqU~7t' -0%e 7R/w7<1b - AU©m Ð AÕª ° ² R«8

-0~(1%em1%& Á

0 7c(#A1bcqW7o#07^&-v71'_8 1b31b(0m < Á A¤ Eª AÕª8y4Wz|7qU <7t' -0%e Yv7<1'?1bw18 %e

Á © A¤ª AÕª8 Ð AEª8AU©m Á ) $C© R««8

z|7mo7Mwo!f^e%&%e µ " R) %&#^e%& µ "ÈR) 4z|7¬%e(#0R`-qUq7 -%&%e[ [/w%e761 ¶1-0--¬®# 18C M1¬_"L'%a`§11qUÏm -#"-8p_%e'78w(#A1b

Á ° "Õª"Eª8 Ð " ° R«8

7%ewqU%aw%&|^&C1b~7<1bp1 -%&%&7<11-0<%ewqM^&R/' #7b10-f1L#^&0q.70%&'73' n#7b/w%e7f#Aycd1(_^&1v®m_"P-0 4wf7%&%e%ep^e%&®t70 $ -%e%e[ <_$70R`?qUÏm0 %&o^eR/24Lz|76%&#R`-YqU­q7 -%e%e]%&o#0^&-%eM%e'R$4

M%e<1^&^a ¯1b7%e'7¬0'76-7%eq 7#$?q~-0_^e(#7062#061b%&'_A(qE10'73(#$-0t7yP1(#07p0-0-f(8`o1-%&-n#Ay%&8f1n_^1v®m_A$-$ 4Y5j7`L13#07§/w%e7§qUÏm0 ¬1bk%Z1§^&[ W7%&?1§%&#^& - 1qU-§7(^&[4z|70%&#"0-?¡161^&1b%& -= (

|qUp1(%e(t%&8`b1^ 0 - "4pz|7k0'b f1-%1u-3%&3/³#7bp%&7m

- 3 0( |/w70%&v7]%&1-¼Å 4c!P%&?701ubq.1b%e'p#"#7b¡%e

- ° 73R $7cR`1^e^"1bpq¯/º#70d1b%eY%e- ° /w7%&^e7o__^e%e(%& -­ ° 4Lz|7P07(#07¬1b%e§1b#A__^eL%&%& -­ ° 31-1bC1^&%&w0'7f%e(c1_^1v®m_A$-$ 3#"»%&#P--]Y(1b7R/³kv7¡' 3%&1qU-f(7#70n<^e-[4wz|7(%e%e`P%e qU-0_^&#7]2(#0fC1b%&0'd7<11##0C$%&(1b^e k7p1p#"1^A7<1#Ac1bqUy¤qU%&%e[ 8%ep_"b7Y1b-p?%e(#0^&%e`1^e1b%e4.z|7mw70?1b--%e%&bqM#700w7t1b-%1b%&Y^&-13_At-%&_A-n_m

$ Á

Ð " 3

Ð Ð R)8

0

1

10 8 6 4 2 0

U/[(

1+z)

4U

0]

log[1+z]

dU/U

M%e'4»C04 z|7061b-%1b%& ' º-0%e Ô-0%e`P%&--_8 T ° $ 4z|7§^1'(x#1u^&' « £ª%&2/w7n7 #<1%e~#^1b(1k1%e7%&^&1b-[4Mp8 YqU7|%e#0 $%&0'L1bq gih Á R) 3w%&|^e%&%e-dL_A µ "¦R)4 %&01-nq7)04 7R/wf%e7M%&'b4/w7 ³%&w70?1b%e(qM#7f1b%e3`P%1L-0_^&#7]2(#0nC1u%e'dwqUy¤qU%&%e(7%&C1bq $ 4~<|-_^&#7bf2#031b%e' C1^e^&%&®b( ° 4¹2C17t#71o1b-3#0%&(1%&^e 1uw^&R/qUÏm%e ""|1##81v71_^&1v®m_"P-0 qU " )$ /w7%&^e(70YqUÏm ¦7%aq k-0Y¬2#0¨C1u%e'1d%&^e1^a 1qU%&'#072^&1'l`b1^e|bq "¯4 %&2` Y(1^&^"1b~-7%eq ~/w7t-%&%&210`P%e` 8p7~#07kC1b%&kPM#%ed1%&^a o1b" 4<18 Á Ey$#W " ° "" Ð T y

° ° " Á Ð . ° T " R0T

L/w7 "" Á y$#W Ð " ""~10- " Ë " Ë 1b- 1b1^&^ 0%&#^e P%&0' ° " " " " $ ° °

" Ð <y$# Ð " """ " $ R8

z|7%e1^&|7 $ -tL#7bn1--0%e%e[ P/w7%&v7n%& $ Á

Ð " 3

Ð Ð <y$#W Ð " ""

" $ Rª8

'%a`$%e'1?Ïm<1%aÏm%&^e%&_%&³^&0%&[ m%aq " Á 4M5j%e77%&rqU qU nw<-0~1?0l#71--0%e%e1uoq

$ Á

" $ "

Á" Ð

" 3 Ð Ð

&"Á " Á R©m

!$%et7t-y<%abq#7bp1P%1u-/w%e7 %& ª0 <0<0-170(1^e%C1u%&Y1bt#"%a $ q

p^e $ Á

ª

- ° R8

!$%eL ° $ - ° $70cR`1^&^A1upqU2^e%&%&<1u%&0'?1 -%&%edC1^e~^e%&® ° 6 #Ap_0_^&%&4| ##"p%e-1b%e¨E¹2%&'811 aÓWR0 A# 0 ª8b0 lq¯70%&~%em1%&q¯7o#7C1b%&#$w/w%a770t(#<1by|Ïm<1u%&7R/w71b|7t-7%eq wqU /w7%ev7§ ?qM1%&%a%&1^"-0%&%&1n`$%a`%&

gih Á© ²u© "¦C) 1 3 $

R8

/w7%ev73%e gih Á £ "6R) qU ~Á ) )b©4

«

9 10 11 12

-5

0

5

10

log(

Rat

e [/s

ec])

log(T [K])

T5

H

M%e'4 T$4 p1ukqU7$#<1%& qw70sp%a`b 2 %&¨(1'm1 l1- m^eC1C1y%&1u W%&¬_^e/w%a70t7LqU(-C1C §1-§-¬/w%e7¬7qU$¦-1C r1b-¬qU %&_0^1v®94r ^e%&o%e|7R/wf%e'[4

:A:<; GEF kI<V¯F WH8DENm>A@ ¯VAS WNP@CGE@z|7kqUd1u%&3qr7k^&%e'78^&(mLÕ [k "pL10-¯%w%ecq.7?70<-

#-%e%epq70k7c¹2%&'d¹~1'YP-^W%&3(^e' 4pz|7%e$-0^¯/~1%e'%&<1b^&^e (##"-1o1b¬$#^11b%efqU7qUd1u%&fql1^e^W7^e8o_8 t1R/t [p(11-]p^&#704¹2070k1_q.18 3v1_0^&tm^e%¯/w%e7f1b(%eod1pm_"p Á (1®p%a%&#"%e_^&(#P-¡#1%W%e37?_0%&yq%e(t1b-¡^1b%e`^e Y^&R/ _<1b ¡-0%e 31C`b1%&^&1_^eo-%e'L7¹2%e'3¹21'4Lz|7m^e?p %e0P_A0-§_8 ¬)04£8 \ y^1u%e`knp $ ° W/w70%&^&L% %em_A-n_8 ]4£8 \ y`^&1b%a`p $ ° 4r¹2 ' %e|m_"0-3_8 b©®b³^1b%e`p $ ° p $ 4%*'o_A1-0C1C Pt%&)04£«-0 W1-¬¹ '-1C $t%e)04 «-t_8 ]^e]1#0b ¯/w70%&v7-Pc071##A1bp7?7%&'73#A1u-0%e'd70?<cqUy/ (%eP$4c¹2$70k$?C1b_A1-d7C1C`P%&~^e8`$%&1k¹ ' %e2%e&%"y%e`-07^eR/j-%e%&21-7%e'72^&__<1%e4wc1^aC 97qU(1b%eq.1_A¡1b-¡77C1C`m 3^&(8#0P-70'770k%e#^&Å 1%&]%e¡78tq-¬'%184?z|70-0%e%e/w707%&cPo71R`-%a%&qwC) ! 'd±b1-f#"1bcq|C)@' [10-f%e(1^&qwR) $ 4c5j7¡7sp0%e`d(1®(70#"1b%&1_A0R) # _07-%a §bq~_<1 0%&t0^e &"¦R) v 3 'Y±u Á &"¦R) 'd±bt1b-n7t%&C1^ec%&w0^e ª%&m0 <7#_<1_%e^&%a Yq1L7?_A$-$ ^e^&%e%&$%&0'(%e0'^e%&'%e_^&p`f70'7n7t(#A1bt%&

0 1 2 3 4

-10

-5

0

log(t [sec])

log(

mas

s fr

actio

n)H

n

D

3He3H

4He

6Li

7Li

7Be

M%e'4kR«04 \ 1qU1%&fq.`b1%e%e#AkÑÒÓ"%&-%&'(7qU/³(%em0o1bq 70¹2%e'¹~1b'4z|7%e2Y%&rqU1?_1 Y-%a dq 7 ) £)ª/w70%&v7Y%e70%&'77<1d7_"20C4

7%e'7[4w¹2C1kq7^eR/¥d1uw-%e "/lk-f(081bkfC1y%ep7<1bp%&8`^e`(1%&^a ]1_0-<18?#<1%&^& ¯/w7%&v761L7#7b M0%&?1b-§7(^&$#"%e#^&1(1UqU R) vy4

z|77(1^¯Ïm%&^e%&_%&_"y/2]0c1b-¡#01b0 ?%&d1%e8v1%e-_8 /lC1®%em1%&4.z|7t%&nqU~7tC1y%& ° ° ¡%e|'%e`n_8

Á 3 À C °

R8

/w7 Á Ð u Á ª \ y "7qE1y Á ª© W_^&R8$Tw1- Y%ep7

03C1bn^e%eqU%e(qM«8« t4< Á \ 7%e|'%e` Á &"6R) $ 3l 91b-70?y%&f1^&p'70^e ^e%&® qUw7%e'7n' 4~z|70%e(-0%e %&w%en7d1^Ïm%e^&%e_%e3 P7t%&81y%&n1b À %&|'%a`f1#0#C$%&(1b^e (_8

À © 3

$#W ° "¦C) $ 3

°

\

Á © 3 "§R) $ 3 Õ AÕ ° !

$ U©m AE©8 ? ° 3$ Eª8 AEª8 \ t

Á ) c w1b Á R)4 R«8

)

Num

ber

Abu

ndan

ce R

elat

ive

to H

ydro

gen

ΩBh20.001 0.01 0.1 1

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

DHe-3Li-7

He-4

M%e'4cR04 M%&1^¯1_0-<1cqM7^&%e'78p^&(mc1p1qU0%&3qM7_<1b ¡-0%e 4wz|77%8v1^A_<1-0~7R/º7_`-`b1^& 01-Y70`%eC1^"_<1-7R/w~7_"~l`b1^&pq70_1 3-0%e 4

0

qU7 Á 1###%1bZqU¬0%&4 z|70,$%e -%a ³%& Á"jR)@3T<$C)4 t 3 43C4,z|731%& ° ° Lm%1^e^e ¨-0_^eL71uq È%&8v7<10'4¿z|7ny$#<10%&È1bq7ns%e`f%e ¬7/21®%&81b%e|/w%&^e^[qU ?0/w7 À µ §4~56®mR/¥7<1b70?-%a /w%&^&^_A8%&1^&^a Ïm<1b^7L%e%&C1b^M-%a W Á « 54ª04Lz|7L-%a ]/w%&^&^_"L-y%&-¬_8 ]770(1^[Ïm%&^e%&_%& -0%e Yq ¢ "¢ 1- ¯¢ 4rz|7%&w'%a`

Á « ª $ ° ª " ¤« $ ° &" ¤b«8 $

Á ) C)

R8

z|7mM7l/lC1®t%em1%&¯qU 20W/w7 ¼R)4 ?L 1-7%e^eC1C`M7 0 ° ) aC©4z|70p7]0-'d7v1-1-¡-0C1C 3q.qU0/w%e7¡1(C1¡^e%eqUy%&cq«8« ² 0-k \ 1b7/w aÓ& 1b#79±)©)«8ª8%e^70t#"1boqE1^e^&l0'7n1^e^&R/º-0%&qUn4

z|7_%e-%e'f' ¦qw-00%eÔ%&L$4 \ yk M1-¦70d(#A1b1b?7YqU 0q70L/lC1b®]%&81y%&o%&o0^e ¦ \ yk nL%&'78o$#"7<1b-0%e½/l^&-qU ÏP0%e1-%e^e 4¹l0?7dC1y%e ° ° 71?/lf1(#<1%&^&t¬7(^&yq 7<10-6%e-1-§^e ¡1(#<1b%e^e¬7%&'7m4!$%eL70(#70n_<1 61b%&%&1_A0cª "ZC) -00%e»/w%e^&^W_"qE1C`-¬0m%&^y$#W Ð Á R) /w70%&v7]P0/w7 Á R) 14[z|7%eo7<1##Ao/w7 0 Á R) p-4p1Y^e1b_"$LC© 8 bq70c-C1C 3%&8(#p_"yqU7y nqU¸-$ ^&1C`$%e'Y1(03qU1y%&fq) aC© "È Ð ) eC©8 Á ) eR$4t+.8%1b^&^e f1^e^Wbq7-$o'yo%&0#"1b-]%&8Yp $ 70k<<1^70^&%e»1_-1L_8 ¡/l%e'78t%& Ç ) b©4z|7%&omk_At-#"-t^a 3/lC1b®P^a ]70#7¡_<1 1b%e [10-¬%ec-y(%e-]#0%&(1%&^e _8 37'7§qr7k/21®%&81b%e [7L0$#0d1t-% %" W1-7m_"bq2#<1b%e^e P#"/w%a7(1c^ep7<16 \ ¼7<1bc8%&_$?d70ky$#<10%&]1bq.7sp0%e`k-%&'d7/lC1®nqU k0C4pz|7^e1'8c_A/l¬7#0-0%&-¬b©98¸1b-¡7?_`-`b1^&%&1d` ¡%e(#Av18p0(1b%efq.7k7bt¹2%&'Y¹~1'YP-^Õ4c )8¸v7<1b'k%ef7k/lC1b®%&81b%e1bt7y$#<10%&61uLq27(sp%a`(-%e'7L<kªn(%em0?1uq 70(¹l%&'¹~10'n/l^e-¬-0R ]70%&1'84LM%&'0R«70T/wt70L%&k`^&$%&¬bql71_0-<1qW`1b%&|%&#A|-0%e'7o<wqU/¥%&m0w1bq ~7¹2%&'¹~10'4

z|7-$%& 1_-1C1bd_A0-t-y(%e|7w_<1b d-%a Lq"7psp%a`b45§?1¡%e(#0^&%eq 701%&ny/2®n7<1bpd1b®p7^e%& ° p ° 4|z|7k_%e-%e'0'b 3%epb© \ `A "7`kC1y%&n/w%e^&^[bpP%&0-0%& -P[¢ pqU 8%e^ µ R))®4<r7%elC1y%&[ P/l'27pqU^&^&R/w%e'tÏm<1b%&qUl7-0(qU1y%&Ä Ä

0 Á³Ð Å2 Ä Á³Ð Å2 0 0 6 0 0 0 4376 Ä Õ))8/w7kÅ2 ~%&|70¡k_%e<1b%ePÊ8dqU-00p/w7%ev73/w%e^&^_A?d1^e^qUw7%e'7 #AC1®31bo%em(-%1b 10-¡7]_"k$#"08%&1^&^a 3##-61bo^eT/³_8 f72^ek__<1%e4.z|70%&|Ïm<1u%&37<1bw7t^e0%e

Ä Á 0

gÅ2 0 0 6 0 0 4376 0 ° Ä 0 Õ)0T

8

z|7t%e(`w(#A1bt%&|'%a`n_8 £« $

Á

ªª 0

0 Á@ ²« "6C) Õ)8

%e?7k-00%e»qUc1bq p710%&7%e^1b%&qr770(1^ ¬#^&1(104cp^&1^&^qr70-00%e»/w%e^&^_"/2#0#%&87^&%e»n7k<<1b^-$%&½1_0-<1%eo^a ^e%&'78^e (-#A-08 Ä 0 427<1'%&'`b1%&1_^e~ Á 0 02'%e`

Ä Á 0

©@0 Å~c Á

:3 0

a "6R) Å~ Õ)ª8

1-]%e7mo%e8`^e ¡#0#A%&1^d7_<1 ¡#7]1b%&(%&0 0 0 - 3 4oz|70%&1u%&%ew<1b^&^e dÏm-f%e(wq Á m <w%&wq Á R) "4l!$%eo7?#07-%a %&.®mR/wLt_" Á ©w 43.qU Á 4 ² /l|<- 0 Á ) © "(R)4 ! ±bb4z|7%e%eC1^"-0%e dqU Á C))®Pd±bR± \ #"t#A-0 ]Á @ eT&"¦R) ±bb <

Á) £© "¦R)4 ! aT "¦R) Á ) ))ª8 Õ)©m

< %&8`-%&8dp 3R "_$700»q. ° 3c8%eP0(qU^e^&R/1%&8`?_1 f-%a ^1C/t4

(1^&^[1(8wq.% ! %ep1b^&L#$-0-f%&7¹l%&'¹~1'0 91-7t#-%e-¡1_0-<101'/w%e7f7_`-¬1_0-<1%&fv1/w%e7f` f^&R/ (yv1^e^&%e%e (/w7%&v7]7^e-¡7<1C`^eY#0%&-%1^[1_-1 ¯1p^&0'Y17kv1c7<1C`1-%&1b%a`8`^&#A428`%a`8`^&#"~C1 L70^&%a7%e¼-0T/wY7b2'%eq[701 01-(^&%e7%&0 %&-T -n1bl7%&'7(#A1b04

2#<1%&6qw_0`-¿1_0-<10k/w%a7¦#0-0%&- 1_0-<10'%e`1¨1b^&^&R/l-1b'Lql_<1 ¦1b_-<1b?q| µ µ §Õ2#% aÓ& rR8 /w7%&v7¬#A-t Á ) )0©mº©©984!$v71b( ÎzWYR$ W1b#79±8b))p'%e` Á Á ) )81) ))b©4¹2^& Wp^e^&yC "z1b6Î z(R0 r. «8$ ©R8p'%a` Á a ¦) ? 2Á ) £)0R2¦) £)8b©k70c_<1 -%a d%el/l^e^"1%e-4rM%&'0R70T/w7?1_0-<1pq`b1%&0%e#A11LqU0%&nqM7_<1 f-0%e 42< Á 870%&'%e` §Á ) £)©mk/w7%ev7f%&wk0v7¡^&w7<1n7C1- 1-n` nkv7¡^e7<16 ?7os%e`c%el#%&(1%e^e d1-0pq¯(1br/w7%ev7-%&-(21®p#<1~%&7C1b%el^&C1b-%&'L^e%&'78|^&84rz|7mpwq7sp%a`k_" ! ~-<1b®Y(1b4

ª

-4

-3

-2

-1

0

7009001100130015001700

log[

x, x

eq,τ

/t]

1+zM%e'4b)04 !01b7<1oÏm%&^e_%e 1b-d1b1^`b1^&rq7w%&%C1b%&?qU1y%& "dqUr1~~ \ P-^/w%e7 Á )0 Á ) ª10- Á ) ²b)04tz|71b%&YbqlÏm%&^e%&_1b%en%&18tY701'obqM70?s%e`t%&w1^eL70T/w4

:4)[; rI<@S HI$SCSRNmOuGÕV¯F

C1bPv®A¢ RÒ #TÒ vÒl/2o<0-" ""0 Á³Ð ""

° Õ)8

/w7 »Á ª ",R) 6 3 ±bk%e?70k_%e<1b%&§PÊ%e8L%&8fy$%a-¨^e`^&4wk_%&1b%e%&8n7('0-¦1bd#P-Y1¦%e%%&0'3#70§/w7%&v7¦%e(-0%1b^e %&%c1b70t1b 1-¬1?7moc&%"%e`4z|7%&c0'^eo#7%&%1b%e|qU¸70'-n1bt_0|7n%¡/l^e^_"yqUo7t^1|1b%e'qE1b4p^&

90 Á Ð ª ) "¦R) ! < 6 6 Õ)8

2k_0%&%e'k7'%e`

A " Á Ð R ° < 6 7 6 Õ)8

" ?- < 6 y4.z|7t%&8'1^qU~#0%eC1^[-0#07n%e "0~10-3%& . ?- 7 1- 02- < 6 7#0%&1^<-#$7¡ÑÒÓm-07%aq 2%el%e-#A0-8~bq[^&'%&C1b^#<11(y4

©

exp(

-τ)

1+z80090010001100120013001400

0.0

0.5

1.0

Ωbh2=0.02

Ho=70, Ω

m=0.3, Λ=0.7

Ho=47, Ω

m=1

M%e'4r$4 z|7t#7bn`P%e`b1^qU1%&y$#W Ð <oÑÒÓ<-70%eq wqU~/l(^&'%&1^"P-^e4

1Pv®'%a` ) £ª8

R))) $ Õ)«8

<k70%&L1##0C$%&(1b%e Á ) ²f/w7 Á C)©m$4¨s%e']7Ïm<1u%&%& _^e¢ ! " vÒ #TÒ RÒ |.7<1C`(#$-(7p`27R/w%&(M%e')04Mz|7o!01b7<1Ïm%e^&%e_%e `b1^&q "

qE1^e^&l1b|-7%eq w1qU/7P0--%e|7%&'77<17o1y<1^ "¯4.z|7

1u%&bqM70%&c0v1bmqUwv1_0^&%&7%&0'%&%C1b%&Ïm%&^e_%e 7?1'oq7sp0%e` 0 W`b1%&cqU»qUy/ 87t^e%&'78^e 3^&o7<1Z /w7%ev7§0#0^1%eo/w7m ]7L%&0%C1u%&¡%&^e3_$b?Ïm%a%&Ïm%e^&%e_%e34z|70d0`P%e`b1^qU1%& (%&t7R/w¦%e¬M%&'0($ /w7%ev73%e--37R/w` ^&%e^ep`b1%&1b%e%&Y7 ¯ w`qU|-% %"8(^e'%eC1^A(P-^&4 Á ) ²dP1b ° Á R))04tz|7/w%e-07]qr7qE1Lq^&1oC1b%&0'#0-qU 70 Á ) ²10-3)$4²k#A%&8%e Á ª04

z|7o/w%&-$7%&T`P%e'1-0%1^A-%&v10t%& ° 0 /w7%ev7C1b^&|^e%&®bL < 6 4z|7?1'0^1~Ïm%e`b1^e8wqW7%e~/w%&-073%e

Á ° 0 °

Õ)8

/w7%ev761^&?%e¬1^&o71/~1C ]/w%e7§#11?1b7d1b'^&1o1^&qUo70<c##0^&p#"1®94tpR/l` 70k0-]#A-¬%ef70k#7$_<1 ]'81p_"yqUk_%e<1b%&%&%&8`^e`-[4z|7?`b1^e?%e Á © ² qUw7 |~ \ P-^Õ4o0y$#Ay7<1b |/w%&^e^_"

8

--§qU ¶ Á )Y_8 ]7%e8qU(_A/l§70LqU8?1-_<1v®]%&-oql7qE1q^1wC1u%e'4

: ; 3>9OuG 8>AV OT>9KMDUNPB

z|7#! (%&w7?'1b-%&v1/l1¡ Y7?-%&v10?1bp/w70%&v7 Á 4|q./l/w%ac7[5 %&c7t1-0%1^"#<1b%1^#<1%e|%&#^e $/lt'

Á 0 Ð 0

5 °

%&07 5 5

%& 5 ° %& Õ$R)8

1-70#0#A|1-%1b^[-%&v10o1_Px1b Á %ex

Á 5 Á

0 0 Á

°

0 Õ$T

z|7%e-%ev1b%&®mR/w1p7?70%3-%&v14p<1 Á kd1u-%&<1b-s%e` %&

4

q/l`b1^e<1bp707%(qUl1(_`w1bl-7%aq P7Y%&(R`P%&'?%ecU^&'701^&-n7t08p%&Ry P/27<1C`

Á

°

0 Á

° Õ$T

q~/ld^e$®¡1b?/l¡_^e_q~'11u É R))/w767Ys%e`d_A11#<18C #<11b- _m È1,1'^e ¿7f®m |7¿73R`P%&'§-%&v1f_A/lj7 %e%e @ 1 Õ)8 Ð 03Õ ~1-Z%eqw7%&%e'1bL7<1¿ 7/l§_0^&_bq'81b7<1C`n-%eUx%emk-(1%&q%e <b4 z|7%&C10L7<1b7n%e`8d%e #<1%&71bk%e%&6§7Y#1^e%&'78?0kqw_A7¨q|7/2_^e_4fz|7%ek$/w7`%e¯ @ ° Ð TM &,ª 4M¹20r70w/w70^&|®m L711t0%eqU \ ¹2¿#A1u/w%e7%&¨#<1%& R) 4z|7%e?1b##"1onÏm%e(1` §#"%&1^.%&%a%&1^-%a%e¡qUo7sp0%e`4

z|7%eoC1_A6^&C1b^e n%e§1 ! 9#1y%&k-%&1'134tz|7%eo%&t1Y-%&1'1 7<1b#^e 5ÑÒÓA70qU(1^%& " "--1 Á 0

90 Á °

904p¡q7%&

%e(p`1b%1b_^&b $70%eo_"

Á 0 Ð 5 °

%e7 5 5

%& 5 ° %e ! Õ$Rª8

1-7o#<1b7wqW^&%&'7m21C P1o_8`P%&^a (7 t©m ^e%&5 Á 5 Ð y4.-~(1®b1$qU(1^#<1y%e(-%&1'1 qU 1-%&1 f#<1%&-%1'1¸/2L<-%e`P%e-k7#1b%&1^P-0%&<1bo_8 0y42z|70%&d1®bw7t/l^e-^&%e|qMR`P%&''81^&1u$%&|f1%&'78#1-3-R/w[4|56t70¡yv7f7?%&t1u$%&C1b7k¹2%e'd¹21'((®b#¡7^e#"qMP0^&^¯1C P1b:o©m 4

8

M%e'4c$4 < #fd_" |18 Á L!mz¥%efv1-1-¡qU A_9/w%a73-%&v1c-0%e`P%&--_8 0 Rl%&c1u$%&v7-%&80qU(1^"%& 0-<21k/w%&-~`$%e/7R/w%e'7ts%e`%&|v73_0%&''~7<1b7t_`b1_0^&sp%a`b4

«

: W; VI0STGU>"V¯IO HNPV¯IOuGE>

: ¯;E:9; .>AV"SRIVWNm>@ B¦B6N8SRO kOTNPI GÕV¯F\ P-37%&pq#<1%&^&o#78 P%ec%em`®?#A8v10p P(y _0C1b®P%e'(($#^1%e

70fk^a%e#^&Y(1%aqUv1b%&bqt1§#d1b_^e 0%e<-¿%&81b%e[4 <L1b(#^e 27^eyR/lC1®7 n1bp-%e<1 '%e7R/w/2` f-0% %"8p_A71R`P%e l70?^e'b1'^eyd1'%&pqU(-%1b-_8 Y(1^&|#700 <10-Y7c` Y71'/21®Ym^&C1bqUY1%&-6_m §7dd1%a`d5 1- ¿_A4z|7Y/21C 67<1bk#"m1 P(y _C1®m%&0'#P-c70%o%&p7<1C`L1d P(%&?(P-^/w7^&R/lc' fv1u1?bc P(y%&4|p¡1fy01#^&q7%&%&p1`b1¸' n-%a 3/w70%&v7¡%e1LqU%&qW/2L<^&- 1- '%a`3_8

d Ë Á W Ð ° Õ$C©m

z|7%ep#A8%1b^7<1p1(%e'b7<1#A-n%&%ek¶7<1bp%&w%&%e8q1k_ "d%aw%&q C1b^&^&-§7 \ $%&C1b$7<1uk#Am%1^Õ4k%&_8`P%&0?71b7d#A8%1b^%e $%&-bv1b%&|%en7t/2(-%&%&1^ ¡#<1b "1-n7<1u 10- 1t1b-f%&-08%eC1^e^e Y%e770 4¹20ok7k P½^eo%&8Ykbq.7v1bc/w%e7¡^&R/lt' [7¡7/w%&^e^[_A/l(` n-% %mp$-wq%e^&^1u%&[456C1bf1t7<1b70? $ ^&p%e870?v1bt/w%a7 Á 610- Á )04z|7%&wC10w7<1bw70%&1L$ nÑ$ $ &" Ñ |%e ¤) ) 2Á 4~¯y Á Ð ¦10-fy$#<1b-f70?#A8%1b^' qUw(1^e^[`1b^&q 1-

<'%e`P%&0'

d Ë © ° Õ$T

z|7?¯1'1b'%1bY-0%e %e~7

Á Ð © °

Õ$R8

z|7%eo¯1'1b'%1bf-%&_At1Y(1^&c_A 1-1Y(1%e`k_A /w%e7]d1o M4

z|7kÏP1b%ec1bt/w%e¡%e' Á k10-Á Ad70%eqUp13' 3-0%e 31

/$ 1-¡70%acbq 1 y "Y70k%abq §1k1^e 4c!$%&0 ¨1b- ¬_A7f7<1C`70?0%eq A7PÊ%e8 ¡%ep1L-%e(%e^&wmk_A%&7t70 4|z|7%epv7<1b%&qUc#"m1o P(y ¡_C1®m%&0'%&c®mR/w¬1c70p%e''cv7<1b%&3 1b-¡7#1%&^e#-%e-f1btC1^e^&-p%&''|_"4

: ¯; )[; 2> .>ADE>9FAGEHI<D N NPHST@

c_8`$%e^e d7%&2(P-^"%&~0|^&1_A1bc0'7#0P-c7o^eyR/lC1®(qUo_"C171b7<1©(-% %mp_A04|¹2$7%&w%&#^&o$-0^[/w%e7n/ldC1^&1|<^e--$p-01b1qU-<181^##" q#A8v10p P(y Y_1®m%&' " $ ÒÓ|2%e-1

<^&-$<'1b%e/w%e7#<1b%&1^&^a (`b1 P%&' 10- <'%e`_8 Á Ã

" " ° $ Á Ã $ " ° $ Õ$T

z|7%et^&-¬0<'1b%e¬7<1o7 6<^e-§(1®m%&0'31qU^e^1b%e%& ¦#<1bY1bt7#<1b%1^P-%&<1u|(1®bt^&P#1-7 1u$%&4z|70' #Aw%a %&|'%e`_m

Á ©

à °

à ° $ Ð Ã ! à à Õ$R«8

zW%&0%&%|7o^1~ /2c/218 Ã Á 0_0~(1®b7 Ã ^&~71%&0<0%e /lk- E)8 Á )0 "1-f7Y Ã ¸^&%&%e~7?1b1up/w7%ev7f70?<^&-¡(1'%a-011##081v770%&0%&k 1b M4z|7P07%et1(%e%&k0 #A%&_0^&0'b #"o%et^e'b7qU7%e0<'1b%e[ A/w7%&v7]-y<t7 0Ò q.70 RÒ ?Ò ! ?Y_A7%&p(%e%&k0 Á y4r< ¼C))ok m/w7%ev7Y/20^&-_Ao1###%1bqU7_1®m%&'k7c^eyR/lC1® P(y $7%&'%&d%&~1b_"$|"fR)4 ! oo±b¶21YÏP0%e`b1^&8~^&%eC1bl(1l-0%e qw 'm±bn4c<7 C)4 ty --]Y_C1®31d'1-]0%e<-f7 70kd1b#A%aw^&'7%eoR) 'Y±un4

07o®m%&-qr#"^e'%eC1^¯-yqUt%eo#"%e_^&/w%e771^1p<^e-t1-¬1d`b100'b -%e Á wÐ 4(pR/¼7L<^e-tC1¬_"(11'-¬%&¬1n1-%&1^M#<1u1-1o#"%&8C ^eC1-0%&'ct1t#A%em^&%e®2#"^&'%eC1^m-yqUy/w%a71od1b ¼C)4 tyqU1 $#0%&C1b^2tspz| 4Yql7#A8v1b0 P(y _1®m%&'n-7(^&-0?^eC1-71-<1-§P-^Õ 7]7%eo#"%e8^&%e®k-0qUy7<1t1d1b'%&kv71'b W1-%&c7P0?1b^a1bd1%a`o(1'y%&(0#"^&4

: ¯; [; >AV¯> .>"DUN OT>AKDUN$B

q7L#A8v1b0? $ ¡_C1®m%e'$t/w70 ¸R)4 tyk 770L%&%&c1_"0 0 Á R)443 b 1b-¡7L%&''<^e-c/w%&^e^#0_<1b_^e 3^a f_Ak%aqU ]#<1uv7bq%

0 Á ª "ZR)4 n4z|7P01-%a q~1b_"$LR) ! '(0#"^&#"L^e-C1%&^e f_"

'1b-[4z|7$#<1%&qr70Lsp%a`%&k7%e%e(/20^&--k7-%a ¡_8 1qE1ywq|C)@' A1-3^e 1d1^e^[qU1y%eq70?#A^e~/l^&-37<1C`1R`%&-0-¡1b%&70%&^1u%&0'/w%e71¡#0#"%e^e nv7<1b'-¬#"^e _07k$#"-§8t-%a ¡q#A^&p%e%&^e^1_A0p#"p_%&4wo%e`7%&7%&'73(1 <7%e^eC1-0 Á R)4 ·2z|7%&%&|70 " " ! ³%&~7tv1b-<1-37b¹2%&'¹~10'P-^Õ4

: ¯; ¯; VMI0SRGE>AVÈSR>¬S ¯NfOTNP@CH WNz|77¹2%e'¹~1'L$-^[7<1|7#0_^e

)

0

10

20

30

40

50

60

70

-40 -30 -20 -10 0 10 20

log(

1+z)

log(t[sec])

M%e'4(ª04 z|70(-7%eq ÑÒÓ¯%&kqUc70(v1-1-§7?¹2%&'n¹~1b'3P-^U-<170-9t1-qU1$-^/w%e7%& 91u%&[4

4|7t#A%&1^%&0%e%&1^A-0%e%e|--fL0#0^1%e7 91bc1-n^e-wq78s%e`

$4|7t#A%&1^[%e%e%1^A0-%e%&|0-0-3Ly$#^1b%&7t1w%&#8 YqW7? \ ¹2 A1-ª0410qU%awq#"^e4

<<1b^a 61¡^&%e'78k$-%a<C1u%&6q|7#"b8%1^ Y C1b¨R`Y7#_0^&4z|7L$-%a<C1u%&¡%&d1®bk7L81^.7m(#%e7#Am%1^MyP^e 91b4kz|7mqU) µ µ /2L##AL7<1u $ o_00o7L^&#A µµ 34 1 z|70^&#A%&'81u%e`kq4 3YT/³/w77Lsp0%e`P^&d70#"%e8/w77#A8v1 P(y f_C1®m%e'Y/w%&^e^P 7 ^&-0c/w%&^&^W#_<1_^a n7<1C`L?`b1^ek_A/l6)10-4o¹lC1b %&1^&C1-0 n$ 0 "70k(#A^&/w%e^&^¯7<1C`1b^&1-0 n_A]'1b-[4oR/t _AC1b7^e#"wq7#"b8%1^<%ed1^e^¤ %ar/w%&^&^$v1®bc1t^&'t%e(~qUr7 <^&-r1v770?'^e_<1^(%e%&k0 1b Á M4|c%e'7%e|%& 7?sp%a`?7<1p1^&1'o`b1 0'b -%a $ 4¹21q[70%&.`b10 ' (-%e P7cs%e`0-'$~y$#Am%1^y$#<1b%e[ </w%e7 0?- y$#W 04~T/ %ew%&w0^e 1b n7<1C`t7mk_Aq ¤qU^&-%e'

$

-10

0

10

20

30

-40 -30 -20 -10 0 10 20

log[

(1+

z)t]

log(t[sec])M%e'4jb©4 z|7f8%&_0%& ¬7n0qU(1^~%&n#APv1C`f%&Z%e(b c ° 70 ~qUL701-<1b-n7¹2%e'(¹21'L(P-^rE-<1b7-91b-qUw1P-^/w%a7%& 91b%e[4

-%&'Y7k0#A8%1b^y$#<10%&¬_Ak^&1'p7<11_A0b)YY70C1b^&qE1y'R/wo_8 ]1qE1y|qlR)@3|b4rM%&'ª7R/w? ° Á ÑÒÓ%&/w%a7n1-/w%e70w%e 91b%&[4

z|7%e$#<1%&/w%&^e^^e`o7o7t#_^&(|qW70?¹l%&'¹~1'

4¹2C10k70k1^&qE1b'T/w_m §R) 3 -0%e'Y%& 91b%e[ A_0p/2(1^&% 0 Á R/t P7w`b1^&q 1ul71.^&1v®%e(w_A(R)443%e(d1b^&^&4M¹207p-%e 25-Pl2v7<1'-%e'?7p`b1 -%&<1u-(%& <1b%e<1 #A$v74rsp%e'7ÏP1b%e

t 0 Ð Á Ð 5 0 5A0 0 Õ$R8

/lL7<1bo70%e%e%1^¯-%a%&c ³1^1T0-§_8 1dqE1boqC) t7<1u2x1_A01bm Yv1b%e'`b1^&c/w%e^&^A/2®94

$4wz|77%§#0_^e½1(_A1(700qUd1b^M%e(_AqULk_%e<1b%&]/21k0v7¦^&?7<167d0qUd1b^r%&1bq _%&<1u%&[ W1-67d0qUd1^.%&

C1|7R/qE1b2^&%e'78~1Y1R`^[1kC1b^&/w%a71^e^"^e'7~C1^e-#Yk7%&~8%b4¹20|700qUd1b^%e(c%e|'%e`n_8

Á °

0 Á

0 ° l^&?0 Õ)8

c7|8%e_0%&k#A.^e'81%e7(%e%e(l%&8`b1^0%e'%a`L_8 #0 "( ° $7R/wL%&LM%e'b©04z|70%&#"1®mo1bq pk_%e<1b%en%&37v10-<1-f(P-^_00c_AqUk_%&1b%e%e370%& 91b%e<1 $-^¤4|zWY1C 3%e%&n/2- 1('%e¡ª "¨R)4 »1bc_A(7('_AqU%e 91b%&n1 1b-f70¡'R/wY_Akª "¨R) 3 »1u70k-fq%e 91b%&[4tz|7%eo'%&¡7'R/wt17cqE1yobq2ª "ZR) ! %e¡70(1^M70t¹2%e'¹~1b'#7<1cqU^&^eR/w%&'%& <1b%e[ P^&C1b-%&'L1k7('~#<1uv7]R)@3 l1 0/w70%&v7%e|^1'27<17t_0`b1_^&s%e`4

ª04wz|7t#A^e-%a %&~-0-3_8 1qE1|qR) w_A1t70o%& 91u%&Y$ !7k#A8v1bm0o P( n_C1®m%&0'4t!$%eC1-¡bqrk#A^e#A_%ek 7%ew1bww0#"^ec#Aw_`b1_0^&tsp0%e`4

5j7%e^&%& 91b%e¡/w%&^e^'y?%&-q2(0#"^& %eo/w%e^&^.1^e'y?%&-q2_<1 _8 -%a`$%e'70(y_<1 6-0%e -R/w6_8 ¬1qE1oqR) C4dsz|1b^&^&R/ 70(#A%&_%e^&%a fql#-C1C ¦1b- 1^&fq !$ vÒ&Òy /w70Y1f_%&<1u%&§q|13`P%&^&1b%eqw_<1 ¨mk_A`b1b%e¡1b-¡1L`$%e^1u%&q%e(o`1^M%e8`1b%1b1-37y$#<10%&¡qM7ks%e`^&1-|L701b%e3bqMt_<1b 7<1318%e_<1 4|c_8`$%e^e Y7%&|#$k$ !|%& 91u%&[42z|7?^1bc1^e^&R/21_^&c%&oqUw_<1 '%&c%ew7^&R/21® + \ ° /21®1%e%e[ /w70%&v7¬$?1b_"$(L#%e-§1bq c7¹2%e'3¹21'4z|7L1^e%&o%e(7<1b%& 91b%en^e-fPp%e7 .^&1v®%e(b "1b-37%&w/2^&-¡Ïm%e?1d#<11u^&$%&n(70#A^&t#_^en4c¹2y -]7%&p^&%&%e ` f^&%a^eoC1]_Ak1%&-nqU1%&¡1_"0c%e 91b%&[4!$((#<1#A1_A0%& <1b%e<1 (P-^&1t^&%e®t7%e%&1^R`^&7<131^¯7%& 1-]7 -%&_A#A%&_^e%&81y%&c7<1uo/20^&-_"L%em%&'%eC1-¬q%&81b%e71bc7<1C`YP4c1(^e %e 91b%&n%&p<1b^&^e -0%e_"-1p7 ! (Ò ! %&01-fbqr17 n178 $#A7%&4T/l` [%ecÏm%e?^e%&®b^e d7?%& 91u%&n-0%&-fP `70'7/2c-0[¢ ~®mR/j/w7r/w7<1bl7c#A8%&1^</~14.q¯%& <1b%e(P-[ 07d7%&1(qE1%e^e Y-<0%e?#-%&y%e¡(1-?1_"07k#%&-%&1^[-%a <1b%e7<1bc17-tqUc'1^1uP nqU(1b%&f1-¬1^&#P-k7Ld1^e^M1b%&#8 ¡qr70 \ ¹~ ¬_8 |o¹~+|4z|7%ec1^eY1qE1%&^e -y<%ek#-%e%e¡1b_"$70`b1^&?q w%eLPqU^e-%&0'-%&'%e 91b%&Y1lx1|^&%e®^e d1)k¤qU^&-0%&' m70o#_1_%&^e%e q1k'%a`1'oq 7<1|(_At##A%&<1^ ­/w7 %ew7tmk_Aq ¤qU^&-0%&'4.z|7mp7t#_1_%&^e%e (q) £ µ µ ) £%&~70?1(1|7t#_1_%&^e%e (q.) µ µ ) k/w7%&v73%&~70?1(1|7#_<1_%e^&%a qr) £ µ µ ) £(4z|7k%&1f%e0<%a?1k^&1b%enq.#_<1_%e^&%a 1b Á 4.Y`b1^eoq j7<1b|%e~-y<%e^a Y~Ïm<1^[o%&|`P%e-1'81%e2%& 91u%&[4.¹2027%e%& g g 0(1 <1bw`1b-0(%e<1b-$-^/w%e7 ° Á %e|0%&m/w%e7%& 91u%&[4

ª

: [; |D WHS WI$STGE>AVW@ OT>"B VMI0SRGE>AV

91u%&d#$-0lv717m'c0#1%ed7<1blÏP18 <y<1b%&0l7p(%e#%&1^&C1b6'T/¼n_"(^1'c7<1§7_`b1_^eds%e`4z|7Y#A_<1b%&t16_A70-q2qUd1b%&f1-¬1^eY/w%&^e^MC1uk70(1b%&#%&c¬_8 ¬|o¹~+ºqU#07%&C1b^7<1%eo%&-0%& $42<|#A_<1b%&|7<1b1?^&1'271

70oE

¡

/lcC1%e'p#0t'1-0%&8 P%&0c#o'1-0%&8~#P-c-Y/21R`|71b|1b1_^edp70#A_1b%ef%e¡1d__^e?%&4~f7k1b_kbq.#'1-%e8 A7-%a f#A_<1b%ef/w%e^&^`^e`%&n7k1?/21R n71bo1d70('os%e`k-P 1-/l?1t7tÏP1b%e

5 Ð Á Õ$T

1^e'L/w%e7371(#$%&7<1b ¶qUC1^e %e( "1- 5 µtµ 51p%&-0%&C1u-n_8 37(1^e^&|qW7 ¢£w3_8 n|o¹~+| 9L-%e`

Ð 5 Ð 5 g 5 Á Õ

1-n7 Á

穻 5 T ,l 3

, Á 5 5 g , Õª8

/w7 ,¿%&~7o(R`P%&'%bqW7t#"_<1u%&[4z|7%e%e~%&0-#A-08bqW7t1^&cqE1y|%ew-0$[¢ v7<1't-0L7ty$#<10%&3qW70?s%e`4

c%&'%& 91b%e]7(sp0%e`(%e?1b##C$%&(1b^e ¡%&¬1n1-0 ¬1bL/w%e7§18 §4z|7m7(1'%a-0bq ]qU#A_1b%ew/w%e73#78 P%&1^MC1^e

/w%&^&^_A?71qU

1^e^"%e(~-%&'k7o%& 91b%e<1 #A$v7[4¹2$w%&0c70%&|18w#78 $%&1^1^&o%e ,,1-701^&?qE1 v71'o_m f(7<1ª)Y-oqd1b'%e-?-%e'Y%e 91b%&[ A7%ecC171bp7d1'%e-tq ¡/w%&^e^[_"t701b(R`pª)-1-pq.(R`P%&0'(C1^e ,|4|z|7m/l'y|1?'#0-0%&%&7<1u /w%e^&^<_Ap71(1b^&^<_`1b_^&pC1b^&qU

2-R/wd

70C1^eo/w7%&v7n%&|L^e'w1^e/21C $w^&1'271n7t0-3#"-37%4.z|7%&wC1~7<1b 55 -5, Õb©m

7sp%a`L_A(P(^e f7'0t^&1'C1b^&ty`70'7¬%eo%ecÏm%e%&07'0|nd1b^&^[C1^e4

z|7%ec_"7<1C`P%&obq 6_A%e'Y%e-#A0-8qr1^&%&c1^&^e- " ! ¯Ò vÒÓc/21o%&'%e<1^&^a #-%e-_m ¡1%e R8)$ rpk ¯bubª)8|1- ^Õ¢£-0T`P%ev7ZR8$ \ pc!" <R)0 0C#91- W_0^&Î fR8)$ 8#0 C8$ m«0T_<1-1` L%e(#^e~1'8z|7%&wC1b^&t^&'7n#T`P%e--3_m 7tC1^e s%e` "1-7mw70?#A_<1b%e|7^e-_ALÒ ! ~1L#AT/lp^1C/t4|z|7qU - , 4|z|70'1R`P%av1b%&<1b^[#"b8%1^¯-%a`$%e--n_8

%&p1(#"08cqM7(y%& A10-¡%eqM%ep'p(#11_0^&td0%e 7f/w%e^&-n7%e'7<1##A[4q< µ )n7 ¨'k^1'qUd1b^&^2,| .1-6d18 ¬_^&1v®7^&/l^e-6qU34n¹20?/2_`(7<1bt70%&o-%e-§b?71##A[4z|7qU )04(¹20%eq? )7 ¦'?^&1'

b©

]^&1'C1b^& ¯1-¡7Lsp%a`/l^e-]_"k'^e f%&70('4?¹l0o/2_`7<1b70%&o%&o701b ¯ )042k_%e%&'d_"7^eoÏP0%&o7<1b Á )0 /w70%&v7¬%&t1Ò <Ñ! #A_<1b%en#"R/l#An4z|7%&w#<1%e^&1~#AT/l^1C/#"R/l#A %eC1b^&^&-Y7p1%&$ ^¤¢ -R`$%ev7Y#Ay34r|/21wy$#A-n7<1b|7t#%e(-%&1^9#"0_<1b%&070^&-¡qU^&^&R/³1p1%&$ ^¤¢ -R`$%ev7¡#Ay­_AC1b1^e^7t1b/lt/l/w'0 [_070k%& <1b%e<1 <1%&#T`P%e-t1d'$P-¡v7<10%&¸qUp#P-%&'1p1%&$ ^¤¢ -R`P%&v7#Ay34

!01v70oÎ 56^aqUYR8P "p#0 MC©8$ [bª8w7R/ 7<1bc1d'1R`P%av1b%&<1b^#"8%&1^¯#"_<1u%&#$-0p1n1%e#8 bq7? \ ¹~/w%e7d1'%e-

Áª

Õ

/w7 È%&ky`b1^&<1u-Z1b7%emy%e¨qw7^e%&q%e'78k10- 70qE1q^11b%&'nU~_%&<1u%&1b ¼R))84z|7(R±ª8rqE1b|1%e|_"C1t^&Pv®m|qE1_8 qE1? °

|%&31'1C`P%ev1u%&<1^[#A8%1b^¤ 91-n/2?C130%&-0w7y$#<10%&¡qM7

sp0%e`(_"1(^e$v®94!$%&0?7C1^e?qE1y%&w`b1 P%e'Y1 - 0 6%3o1bck_%e<1b%e[ <_$qE1py$#<10%&]^&C1b-p1d-1-]#A1uk_8 < Á Ð ¤@ª8

/w7%&v7¡/w7

1--0-¡Y7k(1^¯'1C`P%e1b%e<1^¯-70%eq Á P%e^&-07T±ª|qE1y1_AT`4

z|7?1%e#8 Y%e|1^&^a Yy$#<1b--3%&#07%&C1b^7<1%e

[ Á

Ç c Õ8

¹2C1p7cs%e`%el1b##C$%&(1b^e k%&b#%&~7p#0_<1b_%&^e%e k-0%e%erqUl1^&^07-0% %"8]¢ k1b?13'%e` (1b%&-m%&1^¤4(<7( ¯7y$#Ay-¦`b1^eLq o%e?_m`P%e^a 1-¡7P07y$#"-]`b1^&q.7 p¢ c%& 4o¹l0c70?`b1%&1q.7 p¢£%&p1C11_0^&cqUy%eq b <-y<-¡1

Á Õ

z|77<1b%&%&0-y k1$%1b-f/w%a71]1b'^&1pC1^e d%e'%a`f_m R«) $ "_0c7bv1^mk_Apq#7%&1^W7<1%ewm%e_0%e'LL71%&#8 #AT/l1b1'^&1w1^&Y%&'%e`_8 k%&o ° 4?z|7m7<1C`LÏm<1b^.#"R/lt¬1^&^W1^&t-o7<1C`?1##0C$%&(1b^e - 4~o%e`7<1u7tÏm<1?bqM70?1b'^&1|((m #A1b|%&1y<1^e^e ° Ty %aw%&|bp#0%&%&'7<1bw71y<1b^¯1'^&1~#AR/2p#" qW7? \ ¹2#-%e-3_8 ÈÏm<1^#AT/lw31^e^1^&%&

Á©

° R Õ«8

/w7 %e7y$#"-¡`b1%&1?qM7 Á L#"8pq70®8 "/w7%ev7kc_A-%a`P%&--f_8 _A17 p¢ o1-y<-¡d_A-0%&%&^e4z|7©[(1%&?_A1(70(C1¬q Ç %e( E©¯y ¯n7 ¢ k?_A(©Z%e(t^1'o(#A1bb4M%&<1b^&^e 70Ïm<1-#A^&7<1(#A8w/w7%&^e ~%&|70?`b1%&1bqr1(%&'^e

(#Am "'%e`P%&'7¡b(%&37-0%&1b4wz|7|o¹~+º \ ¥y$#A%e(8c-y(%e- Á C« k 91b-7<1bw7 ¢ wqU Á Á b)/l?%&8w/w%e7f+.Ïm<1b%&3«$4

z|7?1'0^1~^&1b%eYqUy%&nbq71%&#8 Y%e|'%e`n_m

d Á [ Á

©

Õ ° T yE Õ8

/w7 2%&1L'-#A^e P%1b^¤4q7o(#A1b0t%&wC1-3%e31L_AC1/w%a731L%e_AC1/w%e-07 A7f7?/w%e^&^¯_"-y%&¡%&n7?&%"cq.7%e'7 t4p<y01#^&b A%aq70_AC1»%&o1#0#C$%&(1b-]_8 ]1t1%1]/w%a75º \ '%e`]_8 «.^ew$ [70]7#"0 Ç /w%&^e^[_"--]_8 n1qE1ywqMy$#W Ð ) ° T 9'%e`P%&0'(1b3%%a`?^&1b%eqUy%e

Á k Á©

¤ ° T Py$#W Ð ° T U Õª)8

z|7%e~^&R/~#12^e%e'k#~7o^&'1%a7%&|-%a`'o71b~/l^&-b7/w%&cy$%e1 )qU - ° T4 \ y$#A%e(8U70p7<1|o¹~+j10-35 \ 1l-dbc#$-01d1#¬ql7L/w7^e(®m 4C1-§7y (1#"1b-% %0?_"y/2¦#A%em#<11b-¦_8 6(v7#0#%&'f1'^e(§70d®8 43 %e'^ey_01y-0fy$#A%&8?/w%a7v7#0#"p70R/ (C1 < Á 1 Ð k ° 3 C4|z|7`b1%10tq7%&(10-`b1^&0o%&

Á ° ° Ð k °

Á (Õ) Ð d Õª0T

^&-%e'L_"b77t%pqMv70##%e'1-7t_AC1%o'%a`

Á E)8 Ð Á ©

Õ ° Tmy$#W Ð ° T ¤ Ð U,Õª8

\ k(#^e%&1b-fv7#0#%&'#1b0cv7¬1-_^ek0_01%&f/w%a7f/l%e'78)04²P L10-)$4²f1b-¨C1%&^a §_AY- %&01-¨qw%&'^ed_01%& r1-¨'%a`Y$-0%e<1b%eq|7 -#"-04

: [;E:<; XYNPDUI0STGU>"V > >9SCN$VASTGEIDI<V NPV@CG S cNmOTS WOTKWI0STGU>"VW@

z|7-0%e Y#"0_<1b%&0w1t<1^&^a Y-%&_A-n%&wq

Æ$Ã Á 55 Á

Õ W7376 6

Æ

Õªª8

/w7 %&w70`^&qr1(_ACn/w%e73#"%e$-%eo_"-<1 n-0%e%e4!$+rÏm<1u%&¨¤P4 ª8

%& W_0^&4Ys%&0'f1d1b^&%%&'d_"C(1®t%etC1b%&on®#§1v®]q70(-%e(%eoq`b1%&1_^e4L7<1b?Æ0Ã o%eo-%&0%&^&o_0?Æ 71t%etq~^e'7 376 4Lz|7L/23#"%&8^1b%&YqU0%&qW7t-%a %&w'%a`n_8

à Á ¤Æ0à Æ$à ° à lÁ ¤ W73

Æ Æ Á

¤ W73

Æ Õª©m

¹20%e7?#<1%&'(q7"¢ %e37»%ep'%e` ?Á @, 9/w7&, %&w7?^&'7qr70_"Cf%& "¯ [/l7<1C` Á ¤ ¯ 3

4t56k-0<7#"R/lo#"­qr7

-%a #"0_<1b%&0w1( Á Æ Õª8

/w7%ev737<1bw7t%a|qM^&0'7 3 <1-n'

à Ád 3 Á

d

Ád

Á ©

(0 %e à à ժ8

5j7¬-0C1^e%&'d/w%a7]#A_<1b%ec%e]1]0#1-%e'nsp%a`%ac%&(om`%e8t/l®%&3R`P%&'(P-%e<1b4<W%&¢£cÏm<1b%ef%e8`^a`p-%e`b1b%e`p7<1bpk_"v1®b%&n#78 P%eC1^WP-0%&<1bw'%a`3_8 "]/w7 0w%e|7?C1b^&tqE1 <(1^&%- 0 Á 4q Á /2tt7<1b

Á

W "" Á Ð Á © 5mÆ Õª8

%&0' Ã Á

¤ W 376 6

Õª«8

/l?o7<1u Á Ð © 5 Æ Õª8

!$%e 5 ÆY%&t%&-0#A-8kql%&kqUt^&%eC1bo#"0_<1b%&0^&1'c71§7(-§#A-7%f/w7%e^& A/2kL1'1%&n7<1b ¬%e%&0-#A-08oqrC1^ek-%&'7k$#<1%&]q70?s%e`4r5§131^&-%e`o7t^&1b%eYqUy%eq7t#"b8%1^ <1b%e

$ Ã Á © 3 5 $ d %e¯ Ã Ã Õb©8)8

_0t%& 5 Æ(%&o%&0-#A-08ql%&k 0 [/2L1¬/w%ek7%et1 5 Æ Á 5 g 0 Æ$0 v4sp%&' < Á 0Õª |'%e`w7 < ¥^&1b%eqU%&3%&bq7-%a 3#AR/2

#Ay¸1b 0 ( Á

P à $ Á $ ( %e à à Õb©T

1-70^&1b%e70%&#Y_A/l à 1- %&|'%a`n_8

ÃÁ r%& Õb©m

/w%e77t(R`P%&'L1-%&0|q7tqE1tqM^1|1b%&''%e`_8

Á

Ð ° Õb©8ª8

!$%ek7'-#A^a $0(%&1^&1k7'<1^%&1 Ð Ë *3Õ [/21]<-]7 ¢ cqU( ~%&'

yE d 1 3 Á ° ©

Á

Õb©©m

z|7m Á $ ( %&[¤ l%&¯

l%&¯ U 1 3 Õb©m

qM/ltt70$#<1%&nqM1L#0^1c/21C`?%&8L#07%&C1b^7<1%e

Á ©

Ã

Ç Ë Ç c Ë

Á

¤ ° R Ã E Õb©88

/w7 ""~%ew1L#7%&1^¯¹2^WqU0%&[ Ë 2%&~7t-%&y%&nbq à W Ë ~%&~7t-%&y%&q M10- %&t70d10'^&L_A/l ¬1- à ¯/2(C1¬<-¨1n(L8`%e8kqU½qUt7^1b%&07%e#3_A/l (010- v4pz|7k-%a f^1u%&3_A/l/l#A%&8à 10- à /w7%ev7f1t_"7%e<1b-7t^1bw1b%&'L0qE1Y à Á" $2%e|'%e`n_8

Á ¤Æ$à Æ$à rÁ¤ W 3

Æ Æ

ÁÕ W 3

Æ Á

Õ W 3

Æ ©

P

Ç Ë Ç Ë

" © Ð $

Ç Ë Ç Ë Õb©m

pR/¥7¸T` /w%&^e^_"?8`-]%&8Y1¡%e8'1^R` 7<1bp/w%&^&^%e^e-?1f%e8'1^R`k Ë l/w70%&v7/w%&^&^"qU Á 1- Á <%e

Ç Ë Ç Ë Á Æ Æ Õb©8«8

«

'%a`$%e'

Á ( ©

P©

Ç Ë Ç Ë Õb©88

pR/7t0 qM#7%&1^7<1(%&~%&

©

Ç Ë Ç c Ë Á ¤ ° R yE Õ)8

/w7 %&~71'^eo_"y/2 Ã 10- Ã Á © ¤ ° T E

d $ Õ$T

\ ^a%e#^e P%&0'k_8 © 5 ª Á © $ $ Õ

L'yw7t^1b%&YqU0%&qW7o#"1bo'%a`

d Á $ ¤ ° R yE

( P Õª8

qU /w7%ev7n/l?1nC1%&^e d1-%]710'^1b~#"R/lw#Ay

Á © $ d P Õb©m

<~70%e 91b%&1 (#-%&y%e d Á /lt'wqU~7tÏP1-0#"^e Á © $

P Á © $

"" &"" Á

ª $ Õ

2k_0%&%e'k7%e~/w%e73+.Ïm<1b%&f«k'%e`

Áª

$ © Õ8

!$%e(M7<1b-0%&%&Mq^e'b7 3 m%a.%&.C1<1_^e|td1^e%2%e1b-1^&®?1_A0r70-%e(%e^&.k_%e<1b%e Á

3 d y4.<7|%ar%&r'P$-k?0p1-%e(%e^e

/21R`mk_A Á y /w7%ev7¡1^e#0-%ev1bpf1-7%eq p1^&b4|!$%eo/lk1y<1b^&^e

?-7%eq wL-%&0o-%&v1|70%&w%&w1k` C1<1_^et(1^e%C1u%&[4¯qM/lt/w%e

3 d Á

Õ

70/27<1b|70 \ ¹~¥1%e#8 '%a`p1k`b1^eoq

Á $ Á

T Á Eª ªª<,) ²b8"6R) Õ«8

71bw%&|-%e(%e^ew1b-3%e-#"-8pq|v1%em n1b_"$ 4

: [; cNmORS ¯OuKWI0STGU>AV@

z|7]7('10- %&b#%&3(P-^e/l]7<1C`-%e-º¦qE1d1]1¦'$P-#m1b%edbq70s%e`L70p^&1'r^e'7(C1^e $_$2(1^e^&M^&0'71^&l^&1'%&07'0%e%&|_8`$%e^e ny$%&C4wz|7qU/lk-fd-0 37R/ -0%e 3%&07'0%e%&'T/ -7%& <0bq.'1C`P%e "#A%1^e^e %e¡13y$#<1-0%&'dsp%a`b4¹2$p<p/2/w%e^&^/w%at7Ïm<1u%&qUp78 P-P-0 P<1%&pk_%e-n/w%e7f'1R`P%a %&31(1b%e<1 _<1v®m'- z|7?1

5 0 °

5 À Á ) Õ8qU|`b1b%&qMd1 <1b-

À 0 ° &À

ÀkÁ Ð

Ð

5 Õ)8

qU|`b1b%&qM(8 U Á y 91b-W%&¢£wÏm<1u%& Á © 5 Õ0T

5§?R/ ^e%&1%c70?Ïm<1b%&0p%&'(Æ Á 54 5< "1-3(k_"%e'7<1b70?0#"0_A-ÀÁ )0 01b-(7<1b270#"_A-Y#0¥%&l1?18C4rz|7»&À

À %&--

%&7o`^e$%e Y1-nC1n_"t-##A-qUw1^&%eC1~1<1^a $%&4

z|7^&%eC1l`%e3bq+.Ïm¯¤8~%&9Æ 0 Á Ð

À Õ8

1-n%eq¯/l1®107|%&c-%a`1u%e`c/2'y

Æ 0 Á³Ð

À 0 Á

°

5 Õª8

/w7 /l_0%a0Y7^e%&1%-6(8ÔÏm<1b%&¨ 7c!"4sp%e' %&[¢ Ïm<1u%&31b- Á

5< </w7

~%e~7t-n#A-[ 9'%e`w Æ 0 Á

© 5mÆ ° Æ Õ©m

z|7%e71|7t-%e#A%&^1u%&7%e#UqU~/~1C`qW70tqU Æ-$#M " Ð

0

Á Ð © 5 Õ8

z|7mt7c/21C`^e'b7¬#"0_<1b%&01R`^.1bc0-]/~1C` W_0c/21C`/w%a7f/21C``y µ © 54 t1(01_^&('R/w%e'f#A_<1b%e4nz|70%&%e7 1?%&v1_%e^&%a W1-70k^&'7 , Á

© 5%&p7 C1bo^&'74oz|7k(1u$%&k¸'R/|7]1ukqr7 C1b

%&0v1b_%&^e%e %&|0 ¤qU^&-0%&'k%en1%&o'%e`_8 0 Á © 5<4«)

313$#<1-%e'(sp%a`b A/w%a7n1_1v®m'0-f-%a '%e`n_8 7t%e%&C1b^-%a <7y$#<1b%e3bq7sp%a`-%&'L 1|%e(c%e

0 Á © 5 Á ª ª

« 5 Á ª Õ8

7<1u_AqU1L#A_1b%ef1 ¤qU^&-?7s%e`71'bf1b_"$p3%&w^&-k/w7%ev7]%&1c7¤qU^&-0%&'L%e(_8 ]1(qE1ypq.70b4tz|7qU7$#<1%&]q70s%e`?711^&1'o%p7'R/|73qM(1^&^1#^&%a-o-0%e #A_1b%ew1-/l?k0wy$#^e%&%e^a Y1b^&^&R/jqU|%aC4

: ;E:<; IV WGÕV¯F kI<H [F9OT>Vz|7/21C f1^&^eR/ qUp7k0#1%e]%&Y^e%&1%1-1d70(^&'^a y$#<10-%&'

^&0%&[4¯ywty/ `b1%&1_^&"]1b- --3_m

à Á 0 "À Á 0 " ° 0 Õ8

7/P-%e<1b 0` /w%&^e^[7<1C`tL_At-%e`P%&-0-_8 91-

À 0 Á

0 " ° 0 ° 0 0 Õ«8

z|7k<o ¡7c!f/w%&^e^Wk_%e/w%a7f7'1C`P%e1b%e<1^¯%tq.7#A_"-_<1v®m'-3d'%e`w7?Ïm<1b%&nqU 71bp/l71R`1^eC1b-0 -%e0-[4!$(/l?/w%e^&^-#%ep10-370?'1C`$%av1b%&1^%cbqM70?0#"0_A-¡_<1bv®P'0-[ [10-x0 0w 01-%e`-C1b^&%e4Mz|7o-n Y7oc!d%emP-w1%%a`c`^&P%a d-0C1C (/w7%&v7%eC1b-¬_8 n7qE1p7<1uo1d18 À "/w7%ev71<1^e^e #A-p YqUb ^eC1-1 71bc-C1C Po^&%e® 4z|70k70v71'/lk7<1C`Y(1®b%&w71bc%&?70k#A_"-`^&P%a À %e^e' 0 78`%e` &À

À C1]0^&'_"k-0##A-¡/w70

^&%eC1b%%&'k7Ïm<1b%e[4wz|7%ep¸'%a`7?&%"yc-?(7?qE1b7<1b 1b "%&#^1-_8 ]7L`b1^&0q 1u " Ð 04d¹20t/w7§7%e<%&-¬T`%&8 "¯ W%et%& À W 7<1b%e182qUrqUpqU%&[4Wz|7cv71'p%& "W " Á 0 0#0P-~1v71'p%&À bq " /w7%ev77n1-0- k7o8`%a`tn4.z|7%&~8%&_0%&%e~^a (w-|%&Y70#A_1b%e1-nkw_"t®#0C4rz|7ty^ew%ew1(8`b1b%&Ïm<1u%&n'%e`_8

0 °

°

YÁ³Ð

5 Ð Õ8

/w7%ev73%e~73k_%e-/w%e77td1b|`b1b%enÏm<1b%&AÆ 0 °

1e ° Æb 3 Á ) Õ)8

«0

1-70 W%&nÏm<1u%& Á © 5mÆ Õ$T

M%e|1®o7o%&c-%a`1u%e`oqW7t^&%eC1b%-+.Ïm¯¤)8 Æ 0 Á Ð

0 Õ

1-70no70^e%&1%-Y`%efqM+.Ïm¯¤8 Æ 0 Á Ð

Ð dÐ

5 Ð ! Õª8

spL+.ÏP¤)#^&1

/w%e7 Ð AÆ 0 W'%e`P%&0'(70^&%&0C1%-f#A_<1b%e]`^&$%&Ïm<1u%& Æ 0

° AÆ 0 Á

Æ ° © 5mÆ Õb©m

<%&#^e12/lcC1d1<1^a m%&1^&^a k^e`p70%&Ïm<1b%&[4.q7p%q7p#"0_<1b%&0%&wk0v73'C1bw7<1b

7n7

Æ n7c!C13_"t-##A-[4lz|7%&w-%e%&

/w%&^e^_"?(ypqUp#A_<1b%e%&f1((1b-%&<1u-ns%e`k%e7-]#A-%&|d1b^&^¤4M<|11-0%1b%&$-%&<1u-(sp0%e`%a|/w%&^e^"0^e Y70^&-YqU|#A_<1b%&|_0%&''27170cp0__^&p1^&

»_AC1b7-d#A-Y/w%e^&^<_A

ª$41?(1b-(%e<1b-L%a%eC1^

-%a nsp%a`o70?+.Ïm<1b%&n_A( Æ 0

° ©ª 09Æ 0 Á © 5

g Æ Á

ª 0 Æ Õ

/w7%ev7¡7<1p#"R/l^&1C/¥^e0%epÆ - 0d/w%e7¡Å Á ª(1-¡Å Á¶Ð 4wz|7?^e0%en'R/w/w%e73%&t/w70%&^&o7-¡-C1C P/w%e73%e(b4|z|7'R/w%&'$-7<1p1]1b(#^e%e-tÆk7<1u%&w##A%&<1b^"L70C1^eoqE1 <d13)04£)08 #A_<1b%&n1b ° Á C)))k/w%&^e^['R/_AC)98 1b Á )04<|1L^&R/-0%e sp%a`t'y

Æ 0

° 09Æ 0 Á ) Õ8

/w7%ev7¬71o#"R/lo^&1R/³^&0%&0p/w%e7Å Á )1b- Ð 4k!$Y7'T/w%e'Y$-0k-Poc'R//w7f7t-%a n%&|/2^&^_A^eT/7%e%eC1^-%e 4~qM7?%ep1L^&'%&C1b^1870/w7f%e~-%&<1b~7t-%e Y/l7<1C`

Æ 0

° 9Æ 0 Á ) Õ

/w7%ev7]7<1^&$%&Æ Á v18t10-¡y$#W Ð 04z|7mc7'R/w%&'YP-?#0c'R/w%e'/w77Lsp0%e`_"c`b1-%&1b-[4cz|78t'R/|7]1bkqr7'R/w%&'$-EÆ0 0 Á ] 02%&|bq 31##0C$%&(1b-31b

p^e ^&

Õ«8z|7%eqE1yk_%&0-/w%e7n7(10`b1b%efÏP1b%e¡1^e^&R/w|#0?#A^&%&1`^&P%a%&~qU -0%e Y811b-n`P%eo`1$4

«8

: [; )[; !k>Z=?>AB .>AV¯N$VAS ¥> ¯NPD5§(1§0(7Ïm<1b%&¬-`^e#"-¦1_AR`LnC1^e^&1bk7^e^1#Lq2-1®](1b

m1b%&0l%ed1t%aqU _1v®m'0-Yq1-%&1b%e[4W(7%&rC1bp7^e`b18r%e(|%el-0%&0'(1b1-0%1b%&Ïm<1b^&%e 31b R) $ 4cpc1d^ec7?%&?-0#A-LqM7kC1^e?qE1yC1b_"?-%e_"-¡_8 ¡1%e(#^e?#AR/2^&1R/ -0%e'(7%&#A$v74pz|7?`1b%1b_^&o/l/w%&^e^k%e$ Á 5& 5 4!$%&0 5& - 431- 5 - $ 0/ltc7<1b $ - 45§o-m`7c%e(-%e`b1b%e`wqMÆ?L-%e`b1b%e`|/w%e7n#" $ %&'

9Æ 0 Á

AÆ $

$ 0 Á

AÆ $ Õ8

1-70 Æ 0 Á

0 9Æ

$ Á

9Æ $

° Æ $

Õ«)8

5§17<1uc7?1^-0%e ¡%ec1^a/~1C P7k%e%&C1b^-%a 1b-]?7k'1C`P%ev1u%&<1^qUtÏm<1b%&

Á³Ð© ª 5 ° ª

5 Á Ð

© ª

ª« °

° $ Õ«0T

z|7© 5mÆL½¡7Lc!f70^&-0^e n%&^&-07(1bp-0%e ¡%&071-0%1b%&<^&--P¢ p#<1%&%&#<1uc%e7t^e^1#04Mz|7?(1b2-%e %e

5& Á ª« $

° $ Õ«8

5j%e7n1^&^"qM7_%e0%e|/l?7<1C`

Æ $ ° ° AÆ $ Á © 5&lÆ

Æ $ ° $ Ð ° $ $ ° $ AÆ $ Á ªÆ

$ ° $ Æ $ °

° ª $ $ ° $

AÆ $ Á

ªÆ $ ° $ Õ«ª8

/w7%ev737<1bp1'R/w%&'L$-o'%e`3_8

Æ-¼ ° ª $ Õ«©m

z|7mo/w7%&^e?7sp0%e`%e1-%1u%&f-%&1b-f7$#<1%&]%ecYqE1c71bo(1bc7<1b^&%a^&kv7<1bLn^e^1#04¹l f7L%e(k(1b10-§1-%1u%&1LÏm<1b^%e-%e %e%e%1^#A_1b%eo%&¡7Ld1uc-%a ]7<1C`'R/w_8 1YqE1oq~$4 $4kpq

Á R) $ [7(1b|#A_1b%e|'T/_8 17|qE1y|bq2R) $ 4

ǻ

: [;[; HIDENP@LDEI0OuF9NmO(SWI<V

r ^1b'oC1^eo#"0_<1b%&01_"oC1u-31w#<11bt7'sp%a`4z|7Ïm<1u%&/lt-%e`-qU~70o`^&0%&q2 Ð Tl13_Ao--y(%ec70%&2_"7<1C`$%e45§®mR/ 7<1b

Ð 1-

5

- ° qU|d1u|-%&<1u- ° qU|1-0%1b%&Y-0(%e<1b-[4 Õ«8

<w7k(1b-%&1b-317%&p'%e`p'R/|7]#0#A%&1^[d7C1^e?qE1y.x^&%e®70#`P%&0o1<1^a P%&%&n7%e%&4<1-0%1b%&n-%&<1u-3C1/lk'y &uÒ !w'R/|7 Æ - -04z|7%&t%eo_"C1qUc1^&^&1'c71

§ #7101_^ekC1b

0tbq~1-%a ]71(8C 1-]7%&o'1C`$%av1b%&1^W^&-8%e_0o70'R/|7¬q70d#A_1b%e[4d5j7%e^&70d^1b'L1b-%1b%&#Y^&1-t3137%e'76-¦#"-[ 7#L'1-%e8o1bk%&^e^^eR/ _"C1Lqr7k^&1'^&%eC1b%kbq.7#A_<1b%e4z|70$-%a<C1u%&|(7Ïm<1b%eqUcÆL1k1(qE1yq.©8±ª(%e370(1p`1u%&¡Ïm<1b%&1^e^&R/jqU~70%pq#0

9Æ 0 °

©ª

1e ° Æb 3 Á ) Õ«8

1-31kqE1|qW/2%&01t%e7t'1C`P%e1b%e<1^AqUo1^&^eR/ºqU|#0%&

0 °

°

YÁ Ð

5 Ð Õ«8

z|7_%&-^&%&0C1%-Ïm<1b%&%e~7

Æ 0 Á³Ð

©ª

Ð dÐ

5 Ð ! Õ««8

spw+.ÏP¤«o#^1b /w%e7 Ð Eª9b©m AÆ 0 m'%e`P%e'70~^&%eC1%-k#A_<1b%e`^&$%&Ïm<1u%& Æ 0

° 9Æ 0 Á ©

ª

Æ ° « 5mÆ Õ«8

qUo70(1-%1u%&]-%&<1b-C1b4Y9C1^e %0 W/w%e7 5 Á 5 g Á ª9Eª8 0 o1-

Á Õ 0l70%&|_A( Æ 0

° 09Æ 0 Á

0 Æ Õ)8

/w7%ev7]7<1c#AR/2c^1C/ ^&0%&Æ - 0 qUcÅ Á Ð E1Y-1C $%e'$-C1b-Å Á 1d$-0'T/w%e'L^&%e®c70C1^ecqE1|Ïm<1b-4

«©

: [;W; = ¥> WNPD5§R/j7<1C`7p#%&21 d#0'77 ! !p¤~ \ .$-^¤4

f7%&#^&w`%e]q7%&$-^7?^e #"08pq70ksp0%e`17k \ ¹~Õ1b-n7d1b^d1^e0%&m~1-%1u%&1-f#0^epd1u?E7 Rl/w7%&v73-$rC1b P1__L.(%a^eyd1'%&~1-%1u%&E7 !y4z|7w%&%a%&1^m#"0_<1b%&01 y /w7%&v7¦C1b7<1bt70d1b-%1b%&1b-6(1bt-%a §#A_<1b%&1(%e#7<1b 1-]7<1b!@ Á R4z|7L%&0%e%&1^¯#"R/l#Ay0 %&o11b%eP ^Õ¢£-0T`P%ev7#Ay (0 Á "4

q21#A_<1b%&7<1t1C1^ek7<1bt%eo^1'p7<1 1bo70k%&7<1bo70(s%e`

'PwqU1-%&1b%e$-%&<1b-dd(1b-%&1b-¬U70%&w%& ¼ © "¨R) $ & 973%e

/w%&^e^W1^e/21C $_"?0%&-?7k-]#"-]7%[4pz|7%&c71##Ac_A1?7s%e`%&d1b-0(%e<1b-7-#A-§-0#p 4?¹2C17%ec#"_<1u%&¡%&o1b^e/21R P^1b'~7<1

%e|/w%e^&^'T/¥1Æ#- 5 |1bp1^&^"%& /w7%&v7f%&:- _"yqU 1--

1bq 4+.`§%eql%eo-Pt7L^&%&'7mc#A-§7%§1uq

1-]7L#70¬-%a

#A_1b%e'$w1C/~1C <7td1b|-%e #A_<1b%&%&^e^'T/w^&%e®tÆ- E CR04 y4

¹20%aqM1#A_<1b%e7<111^&c7<1bw%e|Ïm<1^[­_AqU

$7f1bq ~7t#7

-%a ]#"_<1u%&¡7<1t1(-1C/~1C 7Ld1b-%a ]#"_<1u%&]-$ot'R/8%e^

4z|7P0%aql1Y#"0_<1b%&f7<1t1Y1^&k7<1bo%ecÏm<1b^M

1b

7%e

^&1qE1yq q.'R/|7[4!$%&0t7?#"R/lc#" '$p^e%&®bÆ 9/2k'7

<<1b^ d 2%&d Á µ

$

Õ0T

!$LR/ /lt-3Ly`1b^&<1b 211qU0%&qW7tC1^e "4.z|7%e%e|-t%&' 0 Á

° Á

0 Á

° ª

ª8 5 Õ8

%et/l1t^e Y%&8-f%&%e(|_"yqU /l?0t71-0%1b%&-(%e<1b-qUk0^104

z|7%e'%e` ° - ª

ª 5 Õª8

?7#"R/l~#"¶7<121?©?%el_C1®L%&7p#"R/ll^1C/ %&0-yd1b7 /w7 Á 4

z|7t/~1C`mk_Ap1bw7%e|_1®9 /w7%&v7n%&~7t#"1®Yq d y 0%&|'%a`_8 - 5&

5 ª 5 ª - Õ©m

%eo7t1-%&1b%eY-%a 5 w%&~/l^&^®mR/wnqU 7? \ ¹~t4

5j7¡0y%&0'd7 \ ¹~¥ d y <7%&#^&?!01v705§^aqUqUk^&1t^e /l®qU Á 9_AC1bk%ef7pC17?'1C`P%e1b%e<1^#A8%1b^ ¬%&1(qU0%&3q%e(b <^&1-%&0'

«8

-1 0 1 2 3

-11

-10

-9

log k’

log

P’(k

’)

M%e'4.P4 ~ \ #AR/2~#AyqU Á ) £«0 0)04²k1b-)04£ª?qU¶#d_An4 Á v

1- Á 3 4

/w7<1b%e1^&^e-]70(%em'1b-¦!$1v7¤56^eqUL&%"yC4dq ¦v7<1'/w%a7%e(b ¯7L' '81%e-_8 Y1k#7qE1^&^e%&'%&8L1k#A8%&1^"/l^e^[%&~-0% %"8~7<1b7o0'b %e2^&|^e%&k_0%&'0qW70#A8%&1^/l^&^Õ 0/w7%ev73C1up1 4rzW(1C`%&-n0%&-0%e'7%ew&%" /2t/w%&^e^[^a %e- Á 4(!$%&7( \ ¹~ ^&1'C1^eL1%e#8 ]%e'%e`§_8 - $ /w70( Á dqU|(1^&^ " 070#AR/2p#" qU|d1b^&^C1^e?E^&1' 2%&|'%a`3_8

d - $ $ 43 - $ 3 Õ8

!$%e7dqU1%&1^r-%e ¬`b1%&1(¨(1^e^C1^e?%&-0%&-¦_8 3 d y M/lY71bo7L-%a ]m1%&c%e-#A0-8?qC1b^&3UqU(1^&^0'7§C1^e_0t71b%eq2-%e 81b7d \ ¹~¶1%e#8 `b1%&t^e%&® 4(z|7%&o00tn_Ad1R`%e(#0^&%eC1b%&[4lz|7k1b1^¯_1®%& d ~%&ÏP0%e'1-<1^W10-f--[ 1b-37k1y<1b^^e#A?q d ~fC1^ep^e`b18^&0%e'dqM'81^&1u$%&w%ep^& (?- w 4~p1^ao7L1u%&dql7( \ ¹~ 7L1#^e%e0-kq^e%&'%&« \ #AL#70?%e1##0C$%&(1b^e ' - [4

z|7qU­qUo7d#AR/2~ \ #AR/2#" qU^&^eT/w%e' _^eYR«$ p#0 Mª0

«

-4 -3.5 -3 -2.5 -2-4

-2

0

2

log zM%e'404 ~ \ R#A%&8o^1u%&¡qU%&]qU Á ) £«0 W)04 1-§)04 ªqU»#¬n_A1b^&' Á¼Ð ª04 Á Ã

91-n71%e'78^&%&0o%&w7_`- Á

b))®m( ! ! 42z|7

0`c1o-<17-nqU|'1b%a` 4

«8

.Wl1wy-f%&n+.Ïm<1b%&3$4 kq ! " #TÒ RÒ p%&

( Á ° Å ° Õ8

/w%e7Å Á «90 < \ #"|1b- Á © ²@ < \ #" 47<1b72%&8%&kbq72^1'21b-(1^e^[1^&?1 P#0b%&t_1v7q7%ed ~$1b Á Á ) ©8 \ #A y4(|bqM70-0%&%&^e~Ïm<18%a%&|%&n+.Ïm<1b%ef«0 07%&|%e

Á T

° Å 1 <93 ° 1 <903 Õ8

/w%e7]Å Á Å < bª))) Á ) £))8b8d1- Á < ª))) Á ² " R) !4oz|70#<11b(yk_%&1b%e < 7<1b8^&77<1b#"q %&q Z1^&^e- 1-¨7_"k_`1u%&oq^1'kC1^eL''o71b ) £ªqr/2LC1b^&0^1b7^&1b%eqUy%e%e' <%e|<1u1^&^a d(w0w%&-7%eq %a

Á © %&¯

Á © T $

3 ° Å °

%&¯

Á © T $ d Õ«8

/w%e7 Á 1-d "" Á

3

° Å ° %e¯ "" " Õ8

c_`b1b%&w''7<1b à Á tqU ÃÁ \ #"t|7<1b Á tqU Á ) ))$R8$ 1-§7<1b à - à ! ! 456((71b ("" - " ! ! qU!" ») )))8 Á ) £ª "¦) £))0R$ %&0-%&1b%e'(7<1bc7^e#"qr7^1u%&fqUy%&]%&o1_A0c%&'7mpqU Á ) £ª0 10-7<1b(Õ) £)))8 " C) 4z|7%e'%a` Á ) ©Y1b Á ) ))$R8%eq Á ) £ª04o!PY%eq p/lÏm<1b^¯ª)®Pd±bR± \ #"b <7f_A770?1b(#^e%e-cq7t^&%&'10-n7t^&PC1b%&YbqM70#AC1®q |/l^e-f1b'/w%a7n_`b1b%&4~z|7%ep%ew7 " ! $ 2(P-^Õ42¹l0%&o1##AC1d_")d8®Pd±bR± \ #"b [7¡7L1b(#^e%e-tq(1^&^¯C1^ek#"_<1u%&1##AC1bw_"oP7%&'7 91-7#"1®q w1b##"1|(P1u$(1^e^1C1^e4l¹27#_^&(o^e-§_AL^a`-§_8 ^&R/2%e' /w7%ev76Ïm%&^&R/l%e' %eq6%&c0$-[4!$1]#A¡sp%a`k/w%a7 Á ) ªd1-1 91uc`b10L-%&<1b-n(P-^W/w%a7 Á ) £ªY10- Á ) ²Y7<1C`_A7_A##A-61c`b1%18oql71-<1b-6~ \ P-^Õ4kM%e<1^&^a 1%a$-n-<1®d1bP-^/w%e7f1b_"$c8qM7-<1®(1bw_A%&0'((1%e`?0%&p7<1b_Af##A-[4|z|7?$%ewqU?1¸0pq-0%e n#"_<1u%&1b-37P0^&R/lw7(1^e^1^&t-%a m1pqUw1L'%e` L4

««

-2 -1 0-4

-3

-2

-1

0

1

2

log[a/aeq]

log[

∆ γ], lo

g[∆ c]

M%e'4$4 z|7#73Î ^&-n-<1®dd1b|-%e #A_<1b%& kÎ qU|`?-0% %"81^& YÁ Ë R) Ë ) Ë ©8)Ît«)?qU_A L#n1b|7t^&q 4

: ; > |D G + OT>GÕB6I$STGE>AV

z|7%& %&_<1-È 7Y/l <0%&- 1##0C$%&(1b%e¦-%&_A-Z_8 !$^ x1®,Rb© 1u#79±b©8)))82%&/w7%ev7370?_<1b c10-3#700c1t1b-]11%&'78^a Y#^e-%&-/w%e7f# "/w70%&^&o7^&-n-<1®n(1bw%ew1b-]1p1(#^& <0%&-[4|z|7/2 <%e-%&81b|0^e ('1C`P%e1b%e<1^e^e 4 (_"c7o0qU(1^9%e(b Á 0 /w7 02%&l7oC1^eqE1yp(1^e%-3Y%a ¡1bp78o%& 0 4t c_"7k8o0qU(1^¯%e(b45§®m%&0'%e7py/|0%1'810't'%e`~70#"1b<01b%e%&-%&y%& §1b

[ Á

1 W ° Æ

© ° À ° 3 Eª))8

p §%ep7'1C`P%e1b%e<1^¯#A8%1b^¤ "Æ (%&7#70]-0%e ¡#A_<1b%&]1b- À w%ep70^ey6`^&P%e 4¡7<1b?7(#A1u <y<1u%&6%&(b©3q|7d#7¦-%a <y<1u%&[4 §%ec7Lz|7(§C1b%&0'n#0%eC1^-0#07¦1^e'Y70^e%&q%e'78C ['%a`¬_8 Á A4~n7^&%e(%a~qr1bf%&$<%e^a d70%&3!0! ?-(1dc%e1ÆCqU0%en1b 7t0qU(1^%e(c1bwk_0%&<1b%&4.+.ÏP1b%enª))k73-0w

[ Á M ° Æ 0 © ° À y °

W 0 Eª)0T

«

z|7^a%&0'L1'^&1~#AR/2p#" %&|'%e`3_8

Á ©

$ k

Á ° Æ © Ð ° À Ð

°

Ð 0 0 Ë Eª)8

/w7 %el70c#70%eC1^¹2^qUy%&|1- %e2-%e`b1b%e`4.z|7c#A_"-ÏP18%e%&~1`b1^e<1b-n%& m#<11b v4 $0|-07t#%&-%&1^#AR/2p#"¸qW7#Am%1^W ¯<1^e^e 3y$#- 11#"R/lt^1C/ $1- $ 4z|7qU0%& %e#A1bc7-<1#%e'&%"y-o70t7%&v®mpq7W!!"4

z|7#7`^&0%&ÏP1b%ew%& m#<11o'%a`3_8 Æ Á³Ð

©ª À ° © Ë À Á

0Æ © ° W À ШÀ u ° Eª)ª8

z|7_<1 31-3~ \ #"0_<1b%&0~qU^&^eT/

Æ Á³Ð À ° ª Ë À Á³Ð À

° © 5 ª 5 À ШÀ °

Æ Á Ð À ° ª Ë À Á³Ð À ° Ë Eª)©m

z|7' 1-n(81%e8wÏm<1b%&w'%a`o70Ïm<1b%e|qU ¡10-

Á Щ 5 ° ª

Á Ð

° © Ë Eª)8

/w7 5 Á 5 ° 5 Æ ° 5 Æ ° 5Æ 21- Á $ 3 5 ° 5 À ° 5 À ° 5 À v4lp 5 1b- 521700%&1b-~ \ C13-0%e%& #"%a`^e 4c!$^ x1®#^1b-f0%eY-%a ¡10-`^&P%a #"0_<1b%&0w/w%a77?#A-%e'(#07f#A_1b%e42z|7%&_"%&8`b1^e%&-3(1^&^[C1^ep-t(7tqU1%&'Lq.00%&0 9_0p-Ppp1 %"p%e'%a<C18^e Y7<<1b^^e4l!$^ x1®d1^&0'^e-710%&b#%&c7C1bp1b-3#A%&_0^&o0`b1b0o4

z|7(1_AT`(Ïm<1b%e1##^e8-6_8 ]70(<%&-0d10]Ïm<1b%&[ /w7%ev7¦1bt1^a %e(?U/w7]1(#A%&_^et(^e'%eC1^[v18cp`b1bt¸C13_"'^&-9%ep'%e`_8

Á «

ª 5 ° 5 ° 5 ° 5 Eª)8z|7^e0%eY7%&|ÏP1b%e%&

$ Á

ÕÅ "" ° Å " Ë " Á 6

Ë Eª)8

)

κ

φ,v,

δ

0 20 40 60 80 100

-1

0

1

M%e'4¥«$4 .^&dqo7f#"8%&1^w#"_<1u%& W ~7]1##1md#A1u¡#"_<1u%&Æ Á ° Æ b© 1-f7?`^e$%e n#"_<1u%& À 1b7W!!31c1(qU0%&¡bq7?/~1C`mk_Aq|#A_<1b%& 4nz|7d<kc##^e#"1®§#"0-37(^1'(0'81b%e`d#AC1®%&6Æ31uYÁ £©0 /w7%&v7n'%e` ° Á ))Ln7t®8 4

/w7 Á 5 ° 5 5 ° 5¶© "ZR)4 : E1(%e'Y70 <1R`tq(1^&0%&y ¸C))dqU7Lv1b-<1-¬k_%e<1b%e[ Å

7 Á ° %&70?`b1^&0q.(1b-%a 3$-<1C n%&3%abq.%e%eC1^¯-%a 31- ¡%&7`b1^&q__^e18$-1R Y%&%a|qlR))®mY±uv± \ #A4

%&0'7%e'78o0#^&%e'^&%e(%a [/w70%&v7¬%&t1'P$-¬1##0C$%&(1b%e¡1^&^1b'l71Y7!P%&^&®L-<1b(#%e'C1^e #^e27o#7bw1b-_<1 |%e8L1%&'^e <%e-d/w%e7Æ Á 3

$Æ L1b- À ÁÀ m4~z|7?1_AT`?Ïm<1b%ey/w%ef%&q-%e(%e^e~%& "]1-

-%e(%e^&~/21C``y YÁ _"Æ Á Ð À ° ª À Á Ð À ° Æ Á Ð

©ª À ° ©

À Á © ª ° $ Ð $ À ° Æ ª ° M©ª ° $

Á Ъ 4 ÕÆ ° ª À

0

log[κ]-1 0 1 2-2

-1

0lo

g[φ]

M%e'4 04 W8%1b^#A_1b%e ¼1b¡k_%e<1b%& ÑÒÓp/~1C`mk_A (#<1b- _^e¢"1b##C$%&(1b%&d7?~ \ 10qU~qU0%&n%&-[4

Á Ð ° ª À

Æ ÁÆ 1i ° 3

$ $ Ð $ 03 ° $ Æ ° $

À Á À 0 $ 3 ° $ Ð $ ° $ À ° $ Eª)«8

/w7t7t-%e`b1b%e`w1t1®3/w%a7#A "¯ $ 5

5 Á 1 ° ª "« © $ 6%3 3

$ Á £« $AË

$ Á $ Á Ð

P «8 $

1-¿__^eL#<11(y~/w%e7#Ayp "¯ Á ^&"1 3 &" Á Å2ÕÅ " ° T 0ÕÅ " ° Å""4pb7<1b $ %ep70k1b%&(qrd1u-%a 3Y1b-%1b%&n-%a $ |%&p7k1b%e(qr^&-

-<1®f(1bp-%e 31b-%1b%&3-0%e _0 $ |%&7k1u%&dq_<1 -0%e 3#70-%a /w7%&v7n8%&87t0-3#"-[4

z|7(%&%a%1b^0-%e%&1b " µtµ ] /w767d0%e`Y%&1b-%1b%&-(%e<1b-9o1- µtµ ]U/w7067d$-0(%e?^&1'o7<1¬7dp_0_^&(#7Y1-%evt1 Á d37<1b

8

$ %e]+.ÏPÕª)8%&7?^a 3#0^1?/w771y<1^W#A_1b%e]1#^&%a-0%e#"%e-[ 1-¡Æ Ð W4z|7k^&1bp1%ep_"C107#A%a%a` ¬C1bc^e$v®md0fqE1 [10-370y$#<1b%eq7ts%e`o%&Y7c1-%1u%&$-(%e<1b-L%&%a%1b^A-%a%eY'P~^e%&®b##"2%e(L70 L#AR/2 97o#"1bt#A_1b%e3%e Ð k^&C1b-%&'dÆ Ð W4~R/2y` 1L(1^&^1b--%e%&1^[-%a 3#A_<1b%&%&w--f('%e`o7t?-0%e n-%e--f-%e`1#A%a%e`o#"b8%1^[#A_<1b%&[4.z|70%&|'%a`

Á Æ Á Ð °

ª $R

Æ Áª© Æ

À ÁºÀ Á Ð Æ © °

° $ $ 3 ° $ Eª)8

¡-w(®#¡1v®q7C1^Õ "1b##A-f(70'810'?%e--[ A-%a f#A_<1b%e/l1^e-

Á

0 Á

$ $ &" Eª0R)8

z|7370C1^-%e #A_<1b%ew1t'%e`_8

Á Æ ° ª Á Æ ° ©

Eª0T

z|7Ïm<1b%&o0-¬_A`^e`-§0m%&^ " Á 1eEÅ ° T 6 |Ð *3 Å ¸4kz|7%&`^&$%&q7tÏP18%e%&~%&|#^e-%eM%&'0tqU YÁ Ë R) Ë ) Ë ©8)Ît«)%&1(P-^"/w%e7 Á ) ª0 Á ) £81- Á ) )8P4.z|7o`1b ' -%a o%&|%e^&y`b18w_"C17`b10 0'b -%e %e|'^e%&'%e_^&#%&~k_%e<1b%e[4

z|7d(7<1b8%&_00f7 \ ¹ 10%&b#m §1(7Y1#0#<18k(#A1b#A_1b%e ° Æ d1-70k`^e$%e À 1bo7LW!!"4z|7(1#^e-¬1^e'Y/w%e7 ¦11qUy%eq 1b " %&nM%e'«04

z|7?#"8%&1^#A_1b%e3`P%a`$%e'((k_%e<1b%e%&1('$P-3#0CP nqUw7d1b1qUqU0%e[4M%e'kd7R/wt7%&p#"b8%1^#<1-f _^&¢ ° Å ° 1##0C$%&(1b%edL70t10qU~qU0%&[4

z|7t(#A1bt1%e#8 0#0-f/w%e77t-%&0%&^&~`b1%&1_^e~%e|'%e`n_m

Á ©

° Æ

© ° " "

° À " l^e Ë Eª0T

ª

/w7" W%e70r1'^&1[-%e1~7W!!c%&o0%eq "1b-o7.#A8%1b^#AT/l¯#" %e1-o_A 0 Á 43 4z|70~ Á 1 Ð «9 $ " ° R " $ 3R" 03 $R) $ " 1%&oqU 7L!P5 &%"?-7L#"b8%1^M`b1 P%&'/w%e7]%&-%&'71b%a%&#A%e$-3qU¸71-%&1b%ef-(%e<1b-f(7(1bp-%&<1b-¡0%e`45j%e7 Á ) ª1- Á ) $ $ " Á b©1-#" Á ) ©L1b- Á³Ð ) £)8$4

pbo7<1u7t#70%eC1^W¹2^qUy%& ""|1?1b P(#$%&C1b^&^e -%e¯" Ð "f%eq7'L%&~`b1 P%&'PL1#0%&-0 (7370%e8'1-qU2%ex1- 1a °

$° " ° À 3¯%eq

1C`1'T`p1_<1-nq Á ©4l!$%&0 ° $1- À k1o`b1 $%e'L^&%e®o%e1-n%&tq

(1'^&cqU|^&1' <0t/l^e-3'p1%e#8 _$p0%&^&^&1b%e21bw^1'o/w%a7$|7 f34

©

: [; OTNP@C@ H WNPH "SRNmO ¥N8S ¯> lo

g[δ]

log[t/tc]-4 -2 0 -3

-2

-1

0

1

2

3

4

5

6

M%e'4.ª)04 c0%e Y81qM1#70%eC1^R`-0'%&n%en1L%a%&1^-0%e nsp0%e`4

p$^e%&1~'T/|73bqM#A_<1b%e|%e|7<1-qU^e^&R/1<1^a m%&1^&^a 4¹20w70t%ew1L%&#^&$-^7<1bo-Pt1Y(1®u1_0^e n'P$-(x_4?z|7%ec%&p7 .!$v7v78?(y7P-[4z|7_<1%&%&-0C1%&~7<1bp1#7%&1^ P(y%&oR`-?'%&/w%&^e^[1v731(1u$%&k0 1-%&0 91-70^&^1b#1b^&1#A%&8C4o5j7]7'%e]%&o1uod1T0%ek¸1b-%& [%ec®m%&y%ek' f%&(1-7mwP(d1b^&^"qUp1 $ %e`$%e%&1^[Ïm%e^&%e_%e34W5j73%ew^&^&1#|LC1b^e 1b-%& <7?#"8%&1^¯' n%epk0v7¡_%&''w%&3d1b'%e-o71f%a/21o1u(1u$%&k0 1-0%& 1-¡7m70®P%e%&?' 3%&c8%&1^&^a 3Ïm<1^Y7d1'%e-q.7#A8%&1^' 4z|7%e%eoR/¶1YqE1tq/2P^1'kqUc`P%&%1^Ïm%&^e%&_%&¸q27L P _"-tn11b-%&7<1uo%&/w%&k7k1-%&0c1bo(1u$%& y$#<10%&[ [7®P%e%&?' f%&7<1^aq7(1'%a-q7t#"b8%1^[' n1w-%&-n_8 Y7o`P%&%1^A734

z|7-0%e Y#"0_<1b%&0|C1n_"t-%&_A-n_8 n1kqU%&

Æ$" Ë 0 Á 5A " Ë 05A 0 Ð Eª0Rª8

8

M%e'4 ª04 #<1y¤%&¨-%&1'1b 70T/w%e'1º#7%&1^R`-0,'%e ^e^1#%&'j1b-`P%&%1^e%%e'4

^&'d1p7k-%a%& 1- 0 µ ,?0 ° p1k(yC "Æ'R/wo1bp7?11b

17kC1^e?qE1ywqU7sp%a`b [Æ&- 0 6%3R4z|7%eC1b]_"?]%&]%&'ª)04R/2y` R`-L'%&p/w%e^&^`81^&^a f#¡$#<1-%e'1-f^&^&1# "1c]%e]M%&'?ª0470-0%e %&01 A'1C`P%e1b%e<1^9qU'yp^&1' 0^&C1b-%&'kd1L0^&%&0C1~7<108q70?-%a n814w+`8<1^&^a 7R`-'%e^e^1# YY1L#"%&8wqU1(#AqU^e P(y%&10-¬70('oR`-%a 3_0%&]'1^M1Y`$%e%&1^&%-3^e4~o7#A%&8cbqrd1u$%ek y$#<1b%e[ "7kR`-%a ]7<1 Y®m%&y%e0'b 4o]-1u%&q 70k`$%e%&1^7n [/w%e7 Ð r+ Á @t+| [70L`P%e%1b^&%-3^&0t7<1c7<1C`(11-%&0c7<1bc%&7<1b^eqq71-%e1bw(1u$%&k y$#<10%&[42z|7-%e%&Y7<1b:,; ° <

702(1

71bt#L'1-%&8t1%&#A18c%&¡7`^&$%&]qr7R`-('%& [70Ïm<1u%&|qUw17'0s%e`1b##^e '%a`$%e'

ÃÁ Ã Ð 0 0 Á

0 Ð %e 0 Eª0C©m

<|(1^e^ d7%&|-Á Ã

© T 0 6%3 0 6%3 Eª0T

1-n7%e1b##^&%ey01y^e (70?%e_A-<1b nq70#"0_A-¡'%e[4|~7?^e^1#%e(b P7o1u%&q¯7`P%e%1b^&%-(1-%e Ã

ÁÃ k7o1-%&0~q¯7o0#"_A-'%&

%&w1k0$-3`b1^&0 <10-3%a|0_"t'%a`|7t#"¤`$%e%&1^&%C1b%&-0%e 81

5

5A0 Á 0 Ã

3 Á R« Á R Eª0R8

c(13'%e7<1^e^1#0- W%at-%a §(1%&0t$0-[ M_00?7-%e ql7(sp0%e`m%&m-0^e%&o7t-0%e Y81p%&01w^&%&®bc7t_"tqW70C1^eoqE14

.tÎ !$v7v7m(C88|#"%&8-¡0p7<1bp7^&%&0C1^e $1#A^&1b-¡-0%e 3m1U7o-^&%&0c%&M%e'cª)8271w10$-`b1^&c1b 0 v4.z|7o-%a 811b18 d%&c#%el70^&^1b#tC1b¡_"qU-f_m nb%&0'7<1b7-0%e n%&n7?T`-'%&n'Pp^&%&®b à 43/w7%e^&c70-0%e %e7t#A_"-f'%&'$w^&%&®b 0 4rz|7m

Æ$0 Á © Ð %& 0 Ð 0 3 Ð ª

) ° ªb) R 00

6%3 ° Eª0T

~o70^e^1#%e(7%ec'%a`c7%e%&C1b^M-%a ¡m1?Æ Á ) aTT W 6%3 Á £«©8$4z|7^el1bwy01yqU.#7%eC1^e^e k P(%&b 87'0R`-0c'%&0.k_A--0-%&31L%a%eC1^-%a 3sp%a`b4<rcζ!$v7v78'1^e%-7%e(1R 7<1b/w7y`7^&%eC1b^e LP1b#"^&1b--0%e d811R`1'-nR`w1L#7%&1^'%ey$-0Æ v $707<1u'%&/w%e^&^"7<1C`^e^1#-[4

pbk71bo7'1C`P%ev1u%&<1^W#"8%&1^M#A_<1b%&]%eov18?1t1dqU0%eqr%e(_A73_"yqUt^&^1b#t%&70^&%eC1b|'%&/w%e7 0 µtµ 0 |1-f1bq w^e^1#t%&7'%&/w%e70 0 v _0o70k/218-% %"c_8 1dqE1boqR)9ª0 70$^e%&1^&^&1#1-`P%&%1^e%C1u%&((1®o7t#"8%&1^/l^e^q7tR`-0'%e-#"4

c%&R/ ^&yq /w%a7¬7%e(#^eo#_^e q2%&-m%eq P%&0'n'%et/w%e761n#7%eC1^e^e 1C`1'-¦^&%eC1b^e 3yP1#A^1u-¬R`-%a §7<1b%&t^1b't7<1§Æ v4Yz|70%&tC1§_"-0(_8 m`^e`P%e'70-%a d<^&-(/w%a71?#7%eC1^A#$7<1bl$b7%e'qU0%&d7<1b2%&v18~qUà µ 1- LqU à 4%&®bo(wm`^&$%&n#0_^e 07%&|t_"wkv7n%e(#0^&%&¬7d<%et-(1%e[4z|7Y<0%&o1bqU q~70d#07%&C1b^#$71bC ?%at/w%&-0T/qUy%e[ %e|'%e`n_m

Á U© 3 ª y$#W

" 3 "Á

ª 1 %e¯ Ð T 03 3 ¼ Ð

R) ° Eª0R«8

z|7?<%e210qU qW7t-%a <y<1b%&%e|-<0-f_8

Æ$Ã Á 55 Á

Õ W7376 6

Æ

Eª0R8

/w7 %&p1d_AR3-¡qU-%e%%e'Y1b-¡d1b^&%%&'k7k<0%&10qU(4c!$%e7

-%a 3bq%&n7?¸%ep##A%&<1b^[ 7^1u%&7%e#3_A/l¡7`b1%&1q

8

-2 -1 0 1 2 3

-3

-2

-1

0

1

2

log(hR[Mpc])

log(

R)

σ

M%e'4ª8P4 z|7^1b%e`-0%e <y<1u%&/w%a7%eL#72q1-%e qU Á ~ \ $-0^&/w%e7 Á YE^&%e-9y $)dE-<17-<21-¡C))YU--91b278~%&kU_^1v®$1-1b Á E'1C 0y4oz|7k70%8v1b^-<1b7-¬^e%&70T/wo7k%e%&C1b^WR`-0%e ¡qUp^e^1#0 "Æ v "/w7%&^e?70`%&C1b^-<170-f^e%&7R/wp«9 \ #A4

Æ$Ã 21-7c`b1%10oqÆ %e||v71'-¡1 %e~v7<10'-[4z|7o`b1%&1cqMÆ %&l7 " !Ò " !$ ( Á Æ Eª8)8

!$%eoÆ 7<12%e~qW0'7 376 $7c#AR/2|#Ay07<12%e~q`^&4M|%&~8`%&m|(1®c7c#AT/lw#"-0%&%&^e~_8 Y-%a`$%e-%&0'_8 Y70tp__0^&`^& 01-C1b70/~1C``f%&f0%eqr1-%1b#Ao__^e1-%&04cz|7%e'%a` Á

73 d

/w%e7 Á 4<~%e%&C1b^-%a n~ \ (P-^e P7t#AT/lw#" %&2'%e`_8 _^&C«8

Á T

° Å 1 <93 ° 1 <903 Eª8$T

/w7 %ep70 \ ¹ \ !fÏm<1b-#A^eR«1 @ ¹2y aÓR8y Å Á ) £))81- Á #"R) !4r9~#A~`b10L-%&<1u-((P-^&27od1^e%1b%e(%eY~q70k \ ¹v7<1'c-t7%&8'1b-]!01v705§^aqU?%C A_0p771#"?qM7#"%&^e^M-#"-t^a ¡]70#<11b(y <[ [/w7 ¬%e7__^ev18%&]0%eoqR))®mY±uC± \ #A4 \ %a$-6o1® \ 1bd \ \ t$-0^&c7d7<1#A(bq270(7%e'7$ 0% %ev7<10'-[ "1-nqUpo1® \ 1bw70?7%e'7$ 0%¬%ev7f7<1#A4|z|7?`b1%10o/w%e7%&

«

0 1 2 3 4 5

Gro

wth

RedshiftM%e'4ªª04 z|7¡'R/w%&'¦P-§ÑÒÓ -7%eq YqU Á E^&%e-9y Á ) Ë Á ) ²E-17-9y A10- Á ) ² Ë Á )nE-0-94

1#70%eC1^[#$7<1bwP7%e'k<^a|bqM1-%&0 #A%e<-3%e \ #A <%e|'%e`n_m

Á © ª 1 %e¯"" Ð "pR""03

" 3 Eª8

/w%e7 " Á ª)))04kM%e'ª8d70T/w jÑÒÓ qUc`1b^-0% %"8t%a%eC1^-%e ¬~ \$-^&4¶~ \ $-0^¯/w%e7 ª)d%e%e8o/w%e7]1^&^W08 \ ¹ 1-]^&1'C1^eyL-<1bv1$ [_0t%eco%&8t/w%e7]-%&1b%ebq ¥qU½-0 P<1%& [ qU #AR`b14l^& /w7%e^&c70^&%e-_^1v®d`'%e`p1##R$%ed1b^a d70y ' R/t 70'1C ]`L/w70%&v7¬7R/w 1b Á %&t1^a/~1C Pc/2^&^._A^eT/ Æ v W` ]^&%a^&/l^&-(qU 1bl` d70%&'7Y-7%eq 4r¹2$|18 ((P-^</w%a7d71(`b1^&pq <'%e`27171#"oqU ZÑÒÓ 0(1`b1-(%e<1b-(P-^/w%e7 Á 81- Á ) ©%ew1'$P-YC4

c/21C Yk71R`o(c00t1b27%&'70~-7%eq 2/w7%&^e(1%&81%&%e't7c1c^&y`^"q08cy%e(-70?^&1bo%e(t'R/|7fbq#A_1b%e4|z|70'T/w%e'(P-t%&

'%a`n_8 ¬ W_^&?Rª8] 0 Á

Ä

Ä 4376 Eª8ª8

/w7 ]Á ° t10- Ä Á ° ° Ð Ð y4(p %eo7-0%e #<11qU-%&1 §d1u .<1^e^e xC1b^&^&- c l1- Y%e7`b1 -0%e -%a`$%e--f_m n70%e%&C1b^W-0%e q ¡-0- ¯49 Á Á )(7%&qU%&3%&.x] 0:- 0y _00cqUo1d`b1-(%e<1b-¡$-^/w%a7 Á ) $ Á ) (70'R/|71u^&R/wp-R/wfqU µ 4|z|7%&^eR/2'T/|7[ Ak_0%&-3/w%e7¡1Ld1^e%1b%eY ' R/t ^&1-Y^&1'w-%e 381t1b Á 04c<p1¡#Af(P-^/w%a7 Á ) (10- Á )70o&%"w%e2y`n^1b' 0%&c'T/|7^&R/w~qU µ ª0 <1~7R/w3%eM%e'ªª04.z|7o^&R/w-R/w%&7?'R/|7n1btq#A_<1b%e|%e3^eT/$-0^&|(1C _At7tC10bq7?-0^e%&o%en7\ 1-13`?_A/l Á L1b-7t#8C4

z|7 .!$v70v78(7$-6%&(1^e^e 1#0#^&%e-§f70d(#$v1b%&§q|7(d1bqUy%e]q^e^1#0-1b-]`$%e%&1^&%-3_Px4kz|7(1 -y<?1(R`P%&0'Y$b7%e'1b-%&~`P%&1 Á U© ª805 3 4.z|7tqU1y%eqW7d1u271b%&|%&^&^&1#-_Pxyqd1 w'1b|%&

d7 Á Õ W

6 y$#W Ð ) " " Eª8b©m

z|7mw7t(R`P%&'L-% %m%1^"d1b|qUy%&nbqM_mxp%e|'%e`n_8

. Á5

Eª8

R))

: [; OTI8Q¯G SRI0STGU>AVWI<D rN$VW@CGEVWF

o1C`P%ev1u%&<1^[^e%&'%&|70?_A-0%&'(q.^&%e'78w_8 3(1%e`?_AP-%&p1b^&'L70?^e%&oq%&'7m4f7py/|0%1j_^&^e($-0^qU^e%&'78 97-0 <%e]qr1(1C n#<1%&'Y1dd1b /w%e7%&#<1yw#<11(y Í %&w'%a`n_8 Á 0 ÀÁ

1 Í 0 °ÈÍ 376 3 0 Á 1 Í

3Õ4

< Á 1- Í Á" P7%el%e~) £«8 4.¹20l7qU^&^9^&0%&7c#0_^e q¯^e%&'78#<1%e'1#"%&8wd1bw%&no1^¯w^&1b%a`P%e ('%e`1n1/27<1b%&~/w%e1w^1'

Á© ÍÁ

Í Eª88

\ 18qW7%e~_"-%e'L-%e'k70C0R?v1^^&1~^&%e#o(1-o+.%e%&n1/l^e-0/w%&-0^&_%a 4r3'%&o#0%e~70%&w_"-%e'L%&|C1b-f_8 n1L%&c-^1C bxp1|7t_A-%e'q^&%e'78w_8 n1'^&1^&w%&wC1b-¡_8 7t%e(o-^1C -tL70?%e-ynbqyqU1y%e3bqM70?'^&14t'%e`1k%e(c-0^1C YqUw1L1C 1%&'1-n0-%&'1bw1-%e à q

0 Á©

3 ^& Ã ° Ã Ð Í

Í ° ÃÐ ÍÃ °ZÍ Eª8

71b1b?7(_`-¨_"-%e'4Yz|7%eo%&L-^&1C ]/~1-%ey^a ]_`- 1t70 \ 1bc%e®m%&'(^1-0/28o_"7%&0-f7!$]_8 ¡1%&t^&-¡_8 f/w%&!$71#%& "1-¡%e®mR/w17!$7<1b#%&-0^1C 4

z|7o- <y%e-y`1^[(1|%e2'%a`_8 (7c q¯7c-0 <%e~#0P--_m C1bv7d1 $1-d7p%&w-^&1R %e7c0 bq[7%&-%a`P%&-<1b^%&w-^&1C $4rsp<1^&^a 7p_"-%e'q^&%e'78|%&'1R`P%av1b%&<1b^^&%e'L%&~` nd1^e^¤ $1-7t-%e#^&1(8pbq7t^&%&'7m~1C qU %e%&'%e<1^#1b73-%e'%ew#<1b'?70'7n7^e%&'L(1%&w'^&%e'%&_^e4r37%&w1/27<1C`1 #$ 0Òy "1b-f70(1p-%e 5q7^e%&'(d1u%1^1f_A^&^&1#-f%e8Y1qE1-%a o" Ë $ p1#0^1?#"#A-0%&0^1c^e%&?q%e'78c7'7]7k^&4z|7¬7^&%e'L- %&n-oL7o1^[(1w-%e%&_00%eY%&

Í Á Щ

o Í

Í Ð Í Í Ð Í Í Eª8«8

p %&p1/ld-%e(%e<1^¯10'^&t` "1- Í %e1L/2Y-0%&%&<1b^[`yp%&n7^&%e'#^&14

z|7k%&-^1C ¡%ec##"%e<1^¯Y7/l3-%e(%e<1^¯#A8%1b^ -0%a`-¬qU 70qE1(1-0%e _8

" °

$ Á © 1 Eª88

pbk71b %&oÏm<1^7%&8'1b^.1^&'d70^e%&q%&'7mtbql7-0%&<1 ¡'1C`$%av1b%&1^#Am%1^Õ 10-n7<1b|70t%&c-^1C %& Á Ð 34

³7<1bw/l^e-fd1b^&^e Y1##AC11bp#A%a%& ¡n7®8 n/w%&^e^1<1^e^e 1#0#"111%ed1'1b2#"%e%& $ P/w7%&v7C1027<1u270o^&%&0pq¯%&'78|C1v70~70c0o#0^1p%"~_m

R)0

1(#07m P%&C1b^M-%ev1b 9 Ð Ay 9/w7 Y%e7k1b'^&1p%?-%e1qU 7_0`7tb4z|70-0 <%enq7o^&%e'78|1C _8 1b31b'^& #$-0p1%"yp%eY7t#^&1q /w7 Y%e7k1b'^&1w%-%e1?q71¡qU¸7^&0 1-Y7%&l- %&|1^ 9 Ð "4rM%&<1b^&^e 87c%e(#1l#<11(y2%&(7o^el#^10%&|'%e`3_8 /w70 %&~71'^&1~%t-%e1tqW70^e4.z|7qU

Á Ð Eªª)8

z|7?1'0^1~%-0%&1cqU7t^&~L7tt%&|'%a`n_8

Á 1 ° $3 1 1 ° 3 v Ð 41i ° 3 3 Ë Eªª0T

/w7 Õ Á %e¯¤pqU Á L w¤ Á %&7¤qU Á Ð 1b- Á v ² Ð g g ²4<¡70¿+.%&0%&$-È!$%e](P-^k/w%a7 Á k7Z-%&v1§1 Á

¤v ° Ð ° < y Á Õ

v ° $ Ð ° $ y l1-

Á ¤v ° < Ð ° P ° 04

z|7t0qE1o_%e'78||%em%e (qM1%&(1'p%&~b|v7<1'-n_m d'1C`P%e1b%e<1^A^&%e' d1^&^bq7v7<10'%en7 <PfbqM70%&(1'w%&w-(7v7<1'?%&7?^e%&-n1'^&qM7%&(1'#<1-700^&-f4z|7%&|'%a`w7td1b'%eC1b%&Y(1b%a

Á Á

Ð Í

Eªª8

z|7<$(1'0%e<1b%eY%&|'%e`3_8 Y7t-(%e<18wqW7t(1'%a<C1b%&dd1b%i Á -R Eªªª8

!$%e Á

0/l?131^&L/w%ec7t(1'%a<C1b%&dd1b%i1

Á Á

Ð

" " $

" $ $ Eªª©m

: [;E:<; ¯B¦B6N8SROuGEH3=I@NP@

qr7^&0%&0'Yd1b%ec%e^1^e $%&b A7]70kqE1(1-%a ¥1-¡7- <y%&§1bk0^e nqU%&0cq1-0%& Ã(Á " ° $ ¯10-¡7- <y%e]%&o1b^e/21R Po%ef71b-%1^-0%&%&[42z|7%&pÏm%ep71b qUp1^&^[7%&(1'10-f7^e-¡#A%e%e ¬1^e^_"1?^&%&070'7d70%&'%e(q7c^e4q/2ov1uw7c$-%e<1b P k(1®bp70%&2^e%&70!"1u$%&~7n/2tC1b3-#31^&^A7o`p Pk_"^&4

z|7LC1b^&0^1b%&3qr7- <y%eC1_A%&#^e%e<-3qUc P(%&^&0o_A1L7- <y%&¡-Y1%eqU %e^1%e'qrd1bw`1b%&7qUp^e%&'781C Pp7<1bc#17'7

R)8

θ

φA

B

C

θ

φA

B

C

M%e'4ª©04 q .!$#A%a%& Y`P4.%&(1'|#A%a%& tqUr1t#A%&8d1br^&4.<18 L#A%a%&7o1/2%ed1b'4w%&'78%&'0^1%&7(1^9#70^&04.z|7c%el0c%&(1'q-%&v18E 1-f|~_0w/l(%ed1'~qM1LC1_8 0dÕ¹~y4

70%&8%ewq7%&' A10-fqU1C Pp71b#17'737^e#^&10%&-t7?%e'7- <y%&3%e~7t1b(t1|7<1b-o1#A%&8w(14z|70yqUo7t- <%&n%&|'%a`3_8

Í Á© y µ Í

Í

Eªª8

/w7 y µ Í w%e7?(1p8v1%e-n/w%e70%&31y $^e%&-0q1-%&0 Í 4|z|7%ep(1%&w#uxy-%&8L7t%e^eoq1-%e Í %e7t^&%e'#^1b4

Ó Ó Ó uÒvÒ 0Ò

z|7#"%&8|(1w^&w'%e` Á Ð

©

Eªª8

/w7%ev737<1bw7t^e0%e

Á& ° ©

Eªª8

/w7o7 0Ò ! c1-%e~%e|'%e`_8 Á U© 0 y4.q¯7to%e

-%ey^a Y8-3_"7%&-70^e 73t'p1(#0^&o%e'q1-%eqUw13%ed1b'4

z|7d1b'%eC1b%&Y(1b%a(qUw1 P(y%&o^&|%&|'%e`3_8

Á )) Eªª«8

R)ª

θ

φ

A

B

C θ

τ

τL

τG

M%e'4Mª$4 yq .!Pw#"%e%&k`P4.%ed1b'2#A%a%ekqUr1o%e'^&1%&70(1^$#7b4l<1?o1bl#A%a%&º7p%&^e Lp%ed1b'4o1bl#"%e%&¹¿'%e`l7%&(1'41b#A%a%e3º%&1bw7tC1%e A1-n7<1%&0%eod1'0<C1u%&[4r³^e|/w%a7nd1u$%ek0qE1?-%a n^&|7<1n7%e%&C1b^[qE1-%a 1 -<1b7-¡` 3My`#$-0k^a%e#^&%&(1'4w%&'78rz|7'(y%&o-^1C M <7t^&%e'-^&1R A A1-7obv1^-^1C YqUw#A%a%&¨¹4Mz|70(%e%&(131b- d1u$%ed1nq|7Yv1b^2-^1C ¦1bY%ev®-È1b-¨#A- ¡70%&(1'#"%e%&4

L70$(1'%a<C1b%&(qE1|%&|'%a`3_8

Á

Á? ° © ? ° ©

© Eªª8

qM/lt- YÁ " Ã 0737%&|%e

Á ? ° ©9 © ° © Eª©8)8

pb7<1u/ln%&(1't1b^e/21R Pty$%etqU1#"%e8td1t^&0 W1-7<1u7L1b%&ql7 <P(1'%a<C1b%&0|%&'%e`f_8 701u%&q7?Ïm<1cqM7#<11u%&qU 70^&4|5j770^ew%ewqE1b~qU7t^&%eoq%&'7m <t%&(1'%&w8%1^e^e Y0d1b'%e-n1-nC1b^e 1bw7^e-¬#"%e%& A/w7%e^&70-§%ed1'?%e¡` ]^ekY7^e]7#0#"%ek%e- 1-n7%e'7^e (-d1'%e<-[45j7370tC1b^e 1^&%e'-Y/w%a770^e 7 @ 3 %e7(1'%a<C1b%&d'w` ^1't1-_A7n%&(1'|1o_0%&'7m4

¦%&^e%&'ny$#A%e(8^e%&®b §w ¯0^e 7(Ôq~7(1'%a<C1b%&02q7o/l(%ed1'~%e|(1-[ /w%a731k1^[(1'%a<C1b%&d'%e`n_m

g g Á ° ° ©9 ° © Á

° © °

Eª©T

R)©

/w7%ev7d%&1oqE1rq4 ª©t/w7 Á 10-d-%a`'l1 )04.<1t^&0lR`$%e'o/w%e7(181'^1t#"-¨%&¬qU8qw1f_<1bv®P'0-¨v1b 0 Á ° 1 0 Ð 0 8 0 3 4n¨18 '%a`f`8C [0^e P 0 d1- 0w1]_A?qU0-[4<p1(^ep%&n7 \ %&^&®8 561C 371^&/w%e7 Á R)®m#"b 91t%&Y7 \ j/w%a7 Á YÐ Á ©8)®m#"o Á «®P#A 91b- Á ) 97n7?+.%&%&f%&'L1-%&0%e à Á « "¦C)4(3~ Á ?1b[ A1-f%aw_$0-1]1b'^&qr)$4²L(%e^&^e%10-4| ^&0%&n7 \ %&^e®8 n561C n7<1^&/w%e7¡1(1`k`^e$%e qwR))d®mY±b/w%e^&^¯1R`k70+.%&%e¡-%&1(yo à %e0 Á ))d-1R Pc1Y(%e^&%e'`8o1o1(v1%&70k \ (_%e'783qUy`1^W(874wz|7/w%&-07fq7?+r%e%e%e'Y-#"-t¡7k^&%e'Y(1 _8 ¡-$ $%e'Y70-%&%e_0%&3q`8t-1u%&70 P#%&1^(1~C1_AcqU0-Yk_A ) 4. kv7<(~(1~%&(1bp^e-Y_Ac_01%&-%eqr7+r%e%e§%&'1-%&0c/2(1-¬-%&y^e f%&1-§bq2%e0qU-]qU»7L-1u%&-%e%&_$%&[4.z|7%&C1b3_A?-0t_8 371R`P%e'1L^&#"%&31L7^e%&P8%&_%a%ew%&w^&tL1¬1C/~1C ¡qU¸7L+r17[4t5j%e7¡/2%&^&%e'Y^e%&'78p`tqU»#<11b-§^e$1b%e1]<- à 1-]7k1`L`^e$%e 4kc1¬1^&Y7v7<1'%&¡70L+1b7¢£`^&P%a f-0%&0'd7(%e^&0%&0'(y`8td%&(1b à _A1k7y`8^&1pqUc1('$P-qU1b%eqM1 C14lz|7m%&^&%e'k%ep1k/21C qM-0%&' \ 1%e`k2(#<1bp1^ec_Pxy \ ~c 9/w7%&v731##AC1~Ld1®bt#f1b_"$p)98 bqM70-0%e qW70 \ %&^&®8 (5¦1C 7<1b^&4

Ó ÓPÓ $ !vÒ # ! "# ! 0Ò

%&#^&(P-^WqUpyP--§ $%&?^&0c%&7(Ò $ !&Ò # ! ¯Ò "# ! Õ!$!y /w%e7`^e$%e -0%&#A%e 1b--%e

5A Ã Á

à Eª©m

5j7%e^&7(!$!¡7<1t%&0%ekd1b %at1C`1'-0%e ]ÏP1^&c7L%a%eC1^W-0%e ]1bt1-0%&ÃdÁ 64z|7LqE1L(1o-0%e ]qr7!$!]%& o Í Á ¤ Í y 1b-]7mo7L(1m1%&0-f/w%a7%e]1d P^e%&-qr1-%e Í %& y µ Í Á Í 4cz|7qU7k- <y%&]%&70!P!^ew%&

Í Á© µ Í

Í

Á © Eª©8ª8

/w7%ev7]%&o1dv18C %e-#"-8tq.7k%e(#<1bp#<11b(y4oq 4 m©r

70t%e~^a d0%ed1b' m/w%e7 Á ° m©r 4.q µ 4 m©

7072%&W107M%ed1'.?72#0#"%e%&-lq072^e¯/w%e7 Á Ð 4 m© 4

qc73f%e(#AqUy^e Z1b^&%&'-[ r/w%e7 Á )0 27Z7f%e1,+.%&0%&Z%e'¬/w%a7 Á P©

42<w1L^ewq'1^1u$%e~/w%e7 Á R) 3 ®md±b A1b Á 0 1-

1L1b Á ª/w%e7 Á /l7<1C` Á ) aT0y Á )

v 91-n7

+.%&%&%e'L1-%e|%&o© £© 4

<7%&c(1c-%&%&_0%& @ Á Y7(1'0%e<1b%ef%e Á @ 4tz|7P0t71u%&bqM70(1'0%e<1b%e~q7o/ld%ed1'|%&|'%e`3_8 7?1b%eqM7%e|#<11u%&|qU70^e4

R)8

Ó ÓmÓ $ ! vÒ # ! "# !

z|7c-0%e Y^&1C/5A Ã Á 5 Ã ° %e2q C1b^&^&-Y1d%&b7(1^"#7 0`70'7%ep%&pc1d^e0%efbq.7^1R`3Ïm<1b%ef/w%a7]1f%&b7(1^¯-%&%e_0%&qUy%&[4cz|7%e$-^['%a`

o Í Á 5 Í °

y µ Í Á 5 Í ° Ð Í Á

« 5

Í ° Ð.Í Eª©©m

5§1<-7L%&(1'?#"%e%&EvpqUt1^ec/w%a77%eod1bo-%e%&_$%&]'1#07%&1^&^a _8 #^e%&'k7p!bq7tÏm<1b%&

Á Ð Eª©mÑÒÓ $ $1l7R/w%&dM%&'0pª8$4.c% %82c#A%e%e n#"0-Y-0% %"8|#^1b8q.70%8v1b^W^e%& "1-3C1¡^eC1-n¡?pªd%&8%&n/w%e7f7?^e%&-n`b [#A-%e'3pªd%ed1'4|3'01b^$%&'0^1w^&c1^a/~1C Pc7<1C`k1¡P--3P0k_"q%&(1' 970t/l%&(1'|$7%&_%a-n_8 Y7?!$!31b-#"%e8wd1|^&11(1^&%e4

5j7¬70#A%e%e¡%eo1b?¥%&¡70k<' [707%81^M^e%&?%&1'mo70`b4wz|7%&^&1-| @ Á 10-f7?%&0<0%et(1'%a<C1u%&YqUwc7/w7^&%e^&t/w%e7f1-%e 4pz|7%&p%&^e?%eC1b^&^&-¡1 8Ò y 10-¡C10%ecPp/w70y`o7k%&1(v71'k%e37mk_Apq.%ed1'4w¹l0ck0^e%e#^&o%ed1b'wC1b¡^a $p%eq7^&#A?bq781b^#<1qW70`?%e|'1b%a` 91b-n7%&|71##A^a Y%eq

Í Á

© oÕ)8 Eª©88

z|7mw7t%&1%e%eC1^"qE1t(1w-%a YqUwk^a%e#^&p^&0%&0'

g Á

© Eª©m

q/lv1b® Á Á Ád'yo1'7f-pq.(1'%a-t%ed1utqU7

^&'%&C1b^&^e %em%&'%e%&C1b^[qE1-%a 9/2' g Á Õª805 g y4~z|7m/2

-f(7<1C`k1(qE1bd1p-0%e n0'7^e YÏm<1^¯L7%e%&C1b^-%e %&|7?p0__^&1b-%&|%e-|L''L^&0%&0'L/w%a7k^a%e#^&p%&(1'4

:[; )[; ?GÕB6NNPDEI ZI<V

z|7k-0 <%e¡%e¡1('1C`P%ev1u%&<1^^&%ep^&1b-f('1-0%&8pq.70?%e(t-^1C 7'770^e4rz|7t^&0%&0'L%&c-^1C -oL7o1^[(1w-%e%&_00%eY%&

Í Á Щ 3

o Í 0^e Í Ð Í Í Eª©8«8

R)

pb27<1b.70%&MqUk^&1p7<17~#_^e¼bq9#0%&'t1c-0%&%&0qU0^$Ïm<18%e k%e8c70|1'(8q.7^&[¤y "_0o7k^a n^ecq.7%ec%&p1--1Yv18o(7%&-^1C 4c^a %e(-^1C -% %AqU|1c1 <k%el%&21#01_^&pk-#d7(1^&%C1b%&L1^&7<1u70^&-('%e(7p^e'81%e7 %el70^&-d_A^&¯ Í Ã /w7 Ã %&r70-%ev1bq[7_0` _$%eo7<1b|-%e1t%e|8%&1^&^a dv18R`w70c/w7^&o^e 7o%e|L#"%e8|%&%&0^&0-%&'%e42z|7?%&p1^&(1#_^& q.13%&0%eo-^&1R qUp%e0<%ao(1_Pxp^&%e®o7?%&7(1^#07(P-^e4t¹2$c7-% %"o%&]-0^1C Pc_A/l¬/l#"%e8%ef70^&0%&0'Y#^1bk1<%ab4.z|7P0qU~7t%e'^&1~%&70(1^[#7(P-^Õ $/l?1/w%a

Í Á Ð © Í

Eª©88

_8 ¦%em'1b%e'f7- %& %eC1-¨q-%e^a 6y`b1^&<1u%&0'f7%e8'1^qUk0^104<^&'%&C1b^0^&/l-(tk0^e%e#^e 70%&r-^&1C 8/w7%&v7%&rC1-d1u7w^& m_8 3 ° 01^e^&R/jqU~70-0%&^1u%&Yq^&%&'7m~`p-o7ty$#<1%&nqW7s%e`4

z|7t1^-^1C 1^e'11C %&|70? qW7^&%e'L-^&1R n1-70?'%&o-^1C ¬-0t7t^&0'~#1b7n^&'7qUw1- <y-¡1C 4.z|70%&w-^&1C %&

Á

Ð

° <

Eª8)8

<|7?%e(#^etC1q7%&'^1|%e7d1b^W#7?/w%a7n/2Y%ed1b' Ð P%&w7?1qU|_A7%ed1'4.z|7mw70-0% %"t%e%&c-^1C P_A/lf70t/l%&(1'2%&|'%a`n_8

Ð Á

° < © Ð Á ° 0

Ð Ð Eª8$T

<|y01#^e %aq Á ) £©©(1b- Á 0 07

Ð Á rÐ

-1R P Eª8

pb7<1u7L_%e'78o%&(1' [7LqU7tqU½7L^&08 W/w%&^&^7<1C`^&-^&1R 1-7m1%e`L4dz|7dp!bq|+.Ïm¯Õª8PTc?70(%ed1'#11b%&]3(#00L7`^&P%a f-%e#A%&fqU 7^&%e'dÏP1b%e[ 10-]Ïm%ec®mR/w^&-0'qr_A7 f1- <4z|7¡(%e--^eo%&-0qr+.Ïm¯Õª8PTwÏm%ep1(#"#%e?`^&P%a -%&#"%&[ <_00p7-70%eq d%&wbp0-0-[4|+.%a7w`%&31f_At-3L<-n7__^e?18 w%eqW7%e(-^&1R YC1n_"tC1-[4

pR/l` 1(0%eqU(17c1---3L70?^e(P-^C1n_%1bw7-%e`- 4~z|7%aqUd1w7c%e8P-p1-0^1C #0#A%&1^ Ð Í </w7%ev7¡1y^&%&®bt18`¡^e4z|7%ec1ypd1^M#<1bcbq7?'(y%e%&t-^&1R 1b-¡%&0170%&(1't#<11b%e4qt1b^&^&R/l-¡qU "7^&1'#<1b1b%&]Ïm%&c7<1bc7k-%ev1b_Akd1^e^& "1-]qU®mR/w6-7%eq 7%&oC10t7<1b %ecP_%&'4Lz|7m 70 t-%e`-§qU­1^&t%&t1##Ap^&%e(%aC4|¹2$c_8 n(1%&'(_"b7f7%ed1'#<1b1b%&1-f7#"#%e?`^&P%a -%e#A%& 0C1YC1bo1-|qUl70c&%"y|qW1k%aqU¶(1l74lz|7p`^e$%e

R)8

-10 0 10 20 300

25

50

Day of June 98

Mag

nific

atio

n

M%e'4 ª$4 %&'78n0`¬qU7 \ ~c y`8¡«u! \ )0 o7R/w%&0'È70§7<1##¡%e(1'%a<C1b%&d#P--n_m 1%&t%&0'4

-%e#A%& [%&-0^1C ¡1-- %&§1'^&ql7^&%e''81^&1uP ¡%e)8 ° 07<1C`_"C1-[ <'%e`P%e' Á b)< o®mÈ \ #A Uz μ91$" <1b#7<±«))©m4

7p^e7<1C`?_"f0-3-%&0 ?LT ° )«)k'%a`c$ $ (3 ®m¿ \ #A o¡Îo$v71®9 A1u#79±b0TPR8~1-f¹~)8$C« ° ª8k'%e`p ! ®mÈ \ #A E¹2%&'' aÓ& <1b#79±«0T«y4r2k_%&0%&'k7^e'%e` Á 8<,o®m¿ \ #" 4

:[;[; +@ B¦B6N8SROuGÕH rNPV@N$@

5j7¬7^&%e'd1bo-%e%&_$%&¡%&obt P(%e 7` ](#0^&%&1b-¡%&(1'#<1bk1¦0^eC43<_%&<1b ¬#"%&8Y^e MyP^e §7%e'76(1'%a<C1u%&oC1b%&^e%&wC1¡Pp/l^e^ %¬78cq7(1%e3^e%&'(`8C4z|70%&71^e-3Y(#Ayv1^1bc^&%e'78`o%&37 \ ~c $#"%&8 1p-%&-§%e¡^ePv® aÓ.R$ # 0 <zw¹~k <zw¹~ 1 1b#7<±«)8PRª 3y4

R)«

M%e'4ª8$4 c%&%&¡1-(1'%a<C1u%&fqrqE1%emc_^&_<1v®m'-¬'81^1T0%ep_m ]1dqU'0-^e|/w%e7qE1t(1w-%a 7R/wn_m 7t#%&0®d71-%&0'4

:[;¯; NPI rNPV@GÕV¯F

+`¡/w7f7qE1?d1w-%e n%&p1^a/~1C Pp^e7<1 g A(71?0dk^a%e#^&%&(1' %at%&t%&^&^#"%e_^&nC1b7Ld1t-%&%e_0%&]%e¬7L^&0_8 -0 P%e'37#<1b¨qw-%e%&?%&67Y%ed1'bqwP0(kqE1b%&8k_<1bv®P'0-Z'1^1u$%e4¡¹2170('81^&1u$%&t1b#"#0%e_^e P0--[ MC1§(17-¦8ql7%&_%&'780-%&%e_0%&43z|70Y'81^&1u$%&/w%&^e^_Ad^&%e'78^e (1'0%e<-6_8 ¦1b¨18/w7%ev7'1^&^a 31bt_"kC1b-[ _A17%ek_%&'780o%ec®mR/w[4k¹20o%e]'1^70%ed1b'~/w%e^&^_Atd1b'%e-(o%&0-0%&%&71f1b70 91b-n7%&Ò# !/w%&^e^[_"o71b(cR`~$-0-n'%&lY70c®8 4rq¯70c_<1v®m'-'81^&1u$%&2-k0|7<1C`t1bm (%&8%&0%&#qU-§%&m1b%e[ [C1C1771t_8 ¡v1®m%e'Y71C`1'^&^e%&#0%&%a q7qE1%emw_1v®m'0-3'1^1u$%e4

z|7k(1'0%e<1b%e3(1b%an%ep7k%&8`d1u%inq.70'1-%&8cq.7k- <y%&¡/w%e7#Ay%&(1'#A%e%e[ 1b-]7L- <y%&¬%eo##"%e<1^¯70'1-0%&8tq70k%&-^1C 4r!P%&w7w--%e`b1b%e`|q7|%&~-^1C k%er1 P(%&2d1b%i 7wd1b'%eC1b%&(1b%a %e P(%&31L/2^&^Õ4 z|7%& P(y%e3",]d1u%i 7<17n%&-0#A-8(#Am P/w7%&v7Y/lcC1bdv1®b?_"7c1'^epq7v1u%&7<1b~-0%1'<1^&%r7(1b%a" 1-37¡/w%e?7?/l%e'8`b1^&0bq.7k(1'0%e<1b%ed1b%i 1bL Ð v4z|7

R)

1b A/w70%&v7f%e7¸q7%&'8`b1^& Aq '%e`k Ð y4w¹lC1b71b%&p1^&70c q70c-%1b'<1^9^&8~q70cd1u%i" P/w7%ev7'%e`27`b1^eq " ° $ /w7%ev7¦%&##"%e<1^370d0qE1d(1-0%e M/ld<-67<1b Á g 43!$f%aq2/lC1b6-y(%e<1 /2(C1¦-0%&7dqE1((1?-%a 4n¹20 <1^&^a ]C1b?_"-y(%e-n_AC1bt/2-¢ ®mR/¥7t0^&0-3_%e'78qW70b4~T/l` A/l?1-y(%e " Ð $ 10- " $ qU 7t70C14lz|7t'1-%e8wq %&|'%a`3_8

-

- " 3 ° $ " " $t° $ 3

Á 1 " Ð $ 3 " ° 1 " $ 3 $ 1 " $ 3 " Ð 1 " Ð $ 3 $ Eª8ª8

z|7m1^&%&0C1lk_0%&<1b%&dq¯7o'1-%e8|q¯7o708p^&^e%&#0%&%a L#P--_8 Y70o71C1bY_"-Yky~70c'1b-%&m2q[7c0qE1cd1b2-0%e d1-d7%&lC1_A%em'1b--y(%ec70?(1w-%e%&_00%e(P-^ek7t0v1%e8 -tL7t#A%&_%e^&%e (q1--%e'1%aqU d1w7C4

` %&#^&py01#^&oqW(1|-0%&<1u%&%e'71|/2^&-_Ac<-70?1C`1b'v1b'8%1^9^e^&%e#0%e%e q70%&(1'l1%e^&p1b~1-%&0 ?1-1b!$!d^&4Mz|7o%&(1'/w%&^e^_An ° oÁ °

Y%e(c/w%&-o%&]7Lv1b'8%1^-0%&%&]71%&7L1b-%1^

-%ey%e[ Ad7%&p71cC1(mc-%&0 1b-¡7k7k(1p8v1b%&-f/w%e7%&

70%&^&obqM1-%&0

y µ Á @ Á

«

Eª8b©m

<w1#"%&8wd1b|^& lÁ <1b-n7t#A-%e'((1~qUk0^1k%&

Á

©

Eª8

/w7%ev7¬%e-% %mt_A1k7'1-%e8cq /w%e7]#"o1-%ec%e-% %8t%ef7k/lC1b42¹l7qUk^1bcC1n_At/w%en1

y µ Á

«

3 Eª88

#0#^e P%&0'¡7Yv7%eÏP0L¡70^&0 \ !"Rb©4 ° ))83A1b7^&(1 aÓwÕ1bb#79±b©8)8)$T_0v1b%&-1(1c^&%&0%a 31b%eq @, Á « @, 4L¹2$ 1b%& aÓ.Õ1bb#079±«)8«8~'y , Á ) , qUp70k#A^e \ !$)ª)8 ° TP 10-pP®m1 aÓ E1b#79±8PR)l' @, Á R«)9 @, qU|7^e2^Cª8« ° 8$ <70t%e|'71^[(1|^&#"-%&8L^ew('%e` Á 4

R)

*,+.-0/21-3.456%&'78C <))8