Lecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation

Transcription

1 Lctur Rlc nutrnos mpratur at nutrno dcoupln and today Effctv dnracy factor Nutrno mass lmts Saha quaton Physcal Cosmoloy Lnt 005

2 Rlc Nutrnos Nutrnos ar wakly ntractn partcls (lptons),,,,,,, typcal ractons n p But somtms usd as nrc nam for wakly ntractn partcls Physcal Cosmoloy Lnt 005

3 h cross scton for nutrno ntracton s vry small m n K h tm scal for ntracton s vn by t n n ( ) v 0.70 a k From last lctur For Frmons for on spcs 70 6 m Physcal Cosmoloy Lnt 005

4 assum v=c t s -[] For ~ a fw K (prsnt day tmpratur of th Unvrs) ths s much, much larr than a Hubbl tm oday, nutrnos ar dcoupld Physcal Cosmoloy Lnt 005

5 Whn dd ths nutrno dcoupln happn? Compar ntracton tm to th a of th Unvrs: At arly tms th Unvrs was a radaton domnatd. Frdmann quaton R R 8 G rad,0 R R 0 ak squar root dr dt R 8 G rad,0 R R 0 Rarran dt 8 G R rad,0 0 R dr Physcal Cosmoloy Lnt 005

6 Physcal Cosmoloy Lnt 005 R R R R G t r rad,0 H s 0. r 0 0 r rad,0 H G t.7 MV K 0 st 0. 0 H r H E t t t t Intrat to t th Hubbl tm 0 and ρ rad,0 ar known from th CMB

7 Rcall from lctur Nutrnos dcoupl bfor + / - annhlaton k m c 0.5 MV 50 9 K So thy mss out on th corrspondn nry nput lo z + / - annhlaton at z = 0 =.95 K lo t Physcal Cosmoloy Lnt 005 Howvr, ths backround has not bn drctly dtctd yt!

8 At hh nry many partcls ar prsnt whch hav dffrnt tmpraturs. It s thus convnnt to dfn an ffctv dnracy factor * and us as a rfrnc otal nry dnsty for all partcls * ( ) c a * bosons 8 frmons 7 Physcal Cosmoloy Lnt 005

9 Physcal Cosmoloy Lnt 005 *s ) ( a s and frmons bosons * 8 7 s and smlarly for dnsty, wth factor ¾ nstad of 7/8

10 Bfor th quark-hadron transton ( > ~0 K) thr ar photons, 8 Gluons, W +, W -, Z 0, 6 Quarks, Lptons, Hs (?) * =06.75 * dcrass wth cosmc tm as th numbr of rlatvstc spcs dcrass. At z=0:, 6 nutrnos.7 K.95 K 7.95 * assumn that nutrnos ar stll rlatvstc Physcal Cosmoloy Lnt 005

11 0 5 K 0 K 0 9 K h voluton of * () as a functon of tmpratur n th SU() C SU() L U() Y thory. Physcal Cosmoloy Lnt 005

12 Hstory of th Unvrs B Ban Physcal Cosmoloy Lnt 005

13 Nutrno mass lmts In th standard modl of partcl physcs nutrnos should b masslss but GUs allow a fnt mass. h bst constrants on th nutrno mass com from cosmoloy and astrophyscs. Numbr dnsty of nutrnos: n ( ) 0.70 a k 6 nutrno spcs.95 K Physcal Cosmoloy Lnt 005

14 crt H 0 / 8 G H n 0 m c / 8 G h m c 9.5 V From df alaxy clustrn/structur formaton obsrvatons w hav f 0. m mat.6 V bttr than constrants by bst laboratory xprmnts Physcal Cosmoloy Lnt 005

15 Supr-Kamokand nutrno xprmnt Physcal Cosmoloy Lnt 005

16 Kamokand II and Supr-Kamokand hs s a Japans solar nutrno dtcton xprmnt. Ornally usd a tank of 000 tons of pur watr surroundd by photo-multplr tubs. Was latr upradd to us 5 tms as much watr. Whn a nutrno scattrs lctrons t producs Crnkov lht whch can b dtctd. Dtctor s also snstv to th drcton of th ncomn nutrno. hs xprmnt dtcts about half th numbr of nutrnos prdctd by th standard solar modl. Physcal Cosmoloy Lnt 005

17 Nutrno oscllatons In th standard modl of partcl physcs nutrnos hav zro mass. hs s no lonr blvd to b th cas Non-zro mass that a nutrno cratd wth a spcfc flavour can latr b masurd to hav a dffrnt flavour. As a nutrno travls th probablty of t bn masurd as a spcfc typ vars. hs varaton s calld nutrno oscllaton. h obsrvd numbr of solar nutrnos s sn as vdnc for nutrno oscllatons (th mssn nutrnos hav oscllatd nto a dffrnt typ) and thrfor nutrnos hav mass. Frst vdnc for physcs byond th standard modl of partcl physcs. Physcal Cosmoloy Lnt 005

18 What s masurd s m m 0 0 V and m m 0 V hs ar only masurmnts of mass dffrncs btwn th dffrnt spcs. If th mass of th most massv nutrnos s of th sam ordr as th larr mass dffrnc thn 0 V m Physcal Cosmoloy Lnt 005

19 Equlbrum abundancs n th non-rlatvstc lmt h Saha quaton Consdr th racton X Y Z Enrtcs: m X c m Y c m Z c B -[] whr B s th chan n bndn nry Physcal Cosmoloy Lnt 005

20 Physcal Cosmoloy Lnt 005 Equlbrum forward and rvrs chmcal potntals ar qual -[] Z Y X 0 ) ( ~ ~ ) ( ) ( k E p d p n ~ c p c m E In th last lctur w had

21 Physcal Cosmoloy Lnt 005 In th non-rlatvstc lmt: ~ c m p m c E 0 ) ( ~ ~ ) ( ) ( m k m k p k m c p d p n -[] ) ( ) ( ) ( k m c m k n

22 Physcal Cosmoloy Lnt 005 k B z y x z y x z y x m m m k n n n hs s calld th Saha quaton. Rcall assumptons: qulbrum, non-rlatvstc lmt Can us [], [] and [] to drv