Cosmology. Outline. Relativity and Astrophysics Lecture 17 Terry Herter. Redshift (again) The Expanding Universe Applying Hubble s Law

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1 Csmlgy Csmlgy Rlativity and Astrphysics ctur 17 Trry Hrtr Outlin Rdshit (again) Th Expanding Univrs Applying Hubbl s aw Distanc rm Rdshit Csmlgical Principl Olbrs Paradx A90-17 Csmlgy A

2 Csmlgy Rdshit Astrnmrs din th rdshit, z, an bjct as: Nt that 1 z bs bs z mit bs mit bs bs 1 v 1 v I th rdshit is knwn w can slv r th vlcity th bjct. This givs 1 z 1 v rl 1 z 1 Quasars hav bn masurd t vry high rdshits. Fr instanc, a quasar masurd t hav z = 4.897, th abv quatin givs a vlcity (rlativ t th spd light), v rl = 0.944! bs mit bs rl rl 1/ A90-17 Csmlgy 3 Rdshit at lw vlcitis At lw vlcitis z 1 v 1/ rl rl rl rl rl 1 v rl 4 Ignring trms gratr than linar in v rl, v v v 1 v z v rl Astrnmrs typically us th cnvntinal vlcity rathr than n rlativ t th spd light. This thn bcms z vcnv c Fr narby bjcts (galaxis) this apprximatin wrks wll. A90-17 Csmlgy 4 A90-17

3 Csmlgy Early Astrnmical Histry Sliphr (~191) nticd that spiral nbula shwd almst prdminantly rdshits. By 195 h had radial vlcitis r 40 galaxis Hubbl usd th 100-inch tlscp n Mt. Wilsn t masur distancs t 18 galaxis Fund linar rlatin btwn incrasing rdshit and incrasing distanc, nw knwn as Hubbl s law H d v cnv ~ cz Hubbl und that th Univrs is xpanding! Th gratr th distanc, th highr th rcssin vlcity A majr gal HST was t masur H accuratly. Currntly, H ~ 70 km/s/mpc Otn usd is H = 100 h km/s/mpc = (10 10 yrs) -1 h A90-17 Csmlgy 5 Hubbl s law rcssin vlcity Rcssin vlcity is prprtinal t distanc: v cnv = H. d H ~ 70 km/sc/mpc galaxy distanc A90-17 Csmlgy 6 A

4 Csmlgy Csmlgy Csmlgy is th study th structur and vlutin th univrs. On vry scal bsrvd s ar th univrs shws structur: stars rm star clustrs and galaxis galaxis rm galaxy clustrs and suprclustrs, and larg structurs A90-17 Csmlgy 7 Distributin Galaxis n th Sky A90-17 Csmlgy 8 A

5 Csmlgy Galaxy Distributin A90-17 Csmlgy 9 arg scal structur Structurs ~ 00Mpc in siz ar sn. This is much lss than th mst rmt QSOs which ar ~ 4000 Mpc distant. Nt this is stimatd rm th tim r light t travl rm th QSO t us nt strictly crrct. Th mst xtnsiv survys cvr nly ~ 1/1000 th bsrvabl univrs! ik trying t dtrmin th apparanc th arth rm a map Rhd Island. A 300 Mpc cub anywhr in th univrs cntains ~ 100,000 galaxis (xcluding aint dwar llipticals and irrgulars). Th ttal numbr galaxis is rughly galaxis Bttr stimats giv galaxis A90-17 Csmlgy 10 A

6 Csmlgy Th Csmlgical Principl Csmlgists mak tw assumptins knwn as th csmlgical principl: 1. Th univrs is hmgnus. smth n th largst scals. Th univrs is istrpic. lks th sam in vry dirctin I a igur is istrpic rm mr than n pint, it must als b hmgnus Hmgnus but nt istrpic Istrpic but nt hmgnus A90-17 Csmlgy 11 Dp Galaxy Simulatin Nt: Th Univrs is nt hmgnus and istrpic but it is in a statistical sns (that is, n avrag). A90-17 Csmlgy 1 A

7 Csmlgy Thr is n cntr t th univrs! Rdshit rsulting rm th Hubbl lw is tn call th csmlgical rdshit. Hubbl s law is vry spcial. I w ar galaxy A, th vlcitis ar: A B What d ppl n galaxy B s? A B Th sam xpanding univrs! A90-17 Csmlgy 13 Olbrs Paradx Fr a static, unirm dnsity, ininit univrs th sky shuld b bright! Evrywhr yu lk yu shuld s a star. W can cmput what t xpct r such a univrs. Supps w hav surcs luminsity,, ccurring thrughut spac at a dnsity,. has units #/Mpc 3 (r smthing similar). What is ttal lux w wuld s rm ths bjcts. t us lk at a small rgin spac a distanc r rm us. r d dr r d r d A small vlum, dv = dr (r d), cntain a numbr surcs, dn, givn by th dnsity tims th vlum: dn = dv => dn = r dr (d) = r dr d Th lux pr slid angl (radianc), di, w s rm this small vlum is givn by d dn di r dr dr d 4 r d 4 r 4 S that whn w intgrat vr all spac (distancs) w can s that this gs t ininity i r gs t ininity. d I d 4 dr 0 0 A90-17 Csmlgy 14 A

8 Csmlgy Olbrs Paradx Answr: Th univrs is nt ininit du t its init ag. It is nt unchanging in tim. W can alrady s that i th Univrs is init in siz (and/r ag) thn r ds nt g t ininity. Hwvr, th xpansin th Univrs intrducs tw cts du t rdshit (th Dpplr ct): Rdshiting mvs phtns t lngr wavlngths s phtns hav lss nrgy (E = h = hc/) Als, du t tim dilatin n rcding galaxis phtns ar mittd at a slwr rat A90-17 Csmlgy 15 Flux-rdshit rlatinship: Cnsidr irst a Nwtnian univrs, i.. n which is lat. Th lux,, r a surc luminsity,, lcatd a distanc d away is: 4 d I th surc is mving away rm us, th tim is dirnt in th bsrvrs (rquncy, ) ram rlativ t th mittrs (rquncy, ) ram,.g. dt dt 1 z W als hav th act that th phtns ar shitd in rquncy, again by th actr (1+z). Th bth hav th ct dcrasing th bsrvd lux,.g. r a mving surc 4 d (1 z) A90-17 Csmlgy 16 A

9 Csmlgy Flux-rdshit rlatinship: This is kay i w ar bsrving all th lux rm a giv surc, hwvr, in cass practical intrst w bsrv th surc vr a init bandwidth. S w hav d 4 d (1 z) Nw rm ur prvius rsult d 1 d z d ik B d = B d S that 4 d (1 z) W culd qually hav wrk in spac. This givs 4 d (1 z) 3 A90-17 Csmlgy 17 K-crrctin W ar almst dn, hwvr, it is imprtant t nt that th wavlngth th surc w bsrvd dpnds n rdshit. And hnc n its lux in that prtin th spctrum ccurring at shrtr wavlngths that ar rdshitd int ur bsrving band. This mans that r a givn class bjcts w wuld b bsrving a dirnt prtin th spctrum dpnding n th rdshit. T cmpar th sam intrinsic prprtis w wuld lik t nrmaliz t sm standard wavlngth. This cncpt is knwn as th K-crrctin. Such a crrctin dpnds n th spctrum th surc! A90-17 Csmlgy 18 A

10 Csmlgy Rdshitd phtns Startd at 0.5 m Rlativ lux z = 0.1 z = 1.0 W typically masur th lux bjcts thrugh a givn iltr (r bandpass). An xampl is th rd iltr at 0.9 m shwn at lt. Fr rdshitd phtns t nd up in this iltr thy must hav startd ut at a shrtr wavlngth T nd up in iltr at 0.9 m Wavlngth Nt: lux gs dwn and spctrum shits t lngr wavlngths as rdshit incrass. Fr a rdshitd bjct, th lux at th bsrvd wavlngth riginats rm shrtr wavlngth part th spctrum in th rst ram th bjct => i w want t cmpar ths t bjcts crrctly w nd t accunt r this shit sinc w will b lking at a dirnt parts th spctrum! A90-17 Csmlgy 19 K-crrctin W want th luminsity th surc in its rst ram,.g. d z 4 (1 ) S w nd t knw th spctral shap. W can writ dwn a similar xprssin r spac. I thn 4 d (1 z) 1 In prsnt day applicatins, th K-crrctin is rmally dind t includ bth a crrctin r luminsity chang as a unctin (r ) and th chang in bandwidth. A90-17 Csmlgy 0 A