An early question about the nature of the universe is known as the Olbers's Paradox: why is it dark at night?

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PHY 454 - cosmology - J. Hdbrg - 2017 Cosmology 1. Olbrs Paradox 2. Distancs 1. Standard Candls 2. Hubbl's Vlocity vs. Distanc curv 3. Hubbl Paramtr 4. Light 3. Exansion 1. Hubbl Flow 4.

1 PHY cosmology - J. Hdbrg Cosmology 1. Olbrs Paradox 2. Distancs 1. Standard Candls 2. Hubbl's Vlocity vs. Distanc curv 3. Hubbl Paramtr 4. Light 3. Exansion 1. Hubbl Flow 4. Earlir tims 1. Big Bang Imlications 5. Cosmic Microwav Background 1. Isotroy/Anisotroy 2. Olbr's Paradox Rsolution Fig. 1 A forst in Orgon An arly qustion about th natur of th univrs is known as th Olbrs's Paradox: why is it dark at night? Olbrs Paradox obsrvr Similarly, if w look in vry dirction, thr should b a star thr,... vntually. Th assumtions: 1. Th Univrs is homognous 2. Th Univrs is infinitly larg 3. Th Univrs is infinitly old Fig. 2 If th univrs is infinit, thn thr should b a star vrywhr w look - why is it dark out? Distancs Many diffrnt mthods for masuring distancs Pag 1

PHY 454 - cosmology - J. Hdbrg - 2017 Radar How long for light to travl. Examl: Lunar Lasr Ranging RtroRflctor (LRRR) on th moon. Masurs distanc to Fig.

HST Max distanc 3,000 arscs (10,000 ly) Milky way is at last 30,000 arscs in diamtr. (Andromda is about 780,000 arscs away) Fig. 4 Bssl's hliomtr By htt://www.klimaluft.

2 PHY cosmology - J. Hdbrg Radar How long for light to travl. Examl: Lunar Lasr Ranging RtroRflctor (LRRR) on th moon. Masurs distanc to Fig. 3 Goddard's Lasr Ranging Facility dircting a lasr (grn bam) Crdit: Tom Zagwodzki/Goddard Sac Flight Cntr Parallax On arth: about 100 arscs max distanc. HST Max distanc 3,000 arscs (10,000 ly) Milky way is at last 30,000 arscs in diamtr. (Andromda is about 780,000 arscs away) Fig. 4 Bssl's hliomtr By htt:// - htt:// Public Domain, htts://commons.wikimdia.org/w/indx.h? curid= Standard Candls Th flux (masurd brightnss) of an objct dnds on two things: how far away it is and its luminosity: Pag 2

PHY 454 - cosmology - J. Hdbrg - 2017 whr L is th luminosity and r is th distanc btwn sourc and obsrvr. If w hav a known valu for L, thn w can calculat r basd on th masurd flux.

If w know th distanc to som narby ons (from arallax), w can calibrat th rlationshi. Max: 30,000,000 arscs (~100 million ly) Usful for objcts in this galaxy, and a fw narby ons.

3 PHY cosmology - J. Hdbrg whr L is th luminosity and r is th distanc btwn sourc and obsrvr. If w hav a known valu for L, thn w can calculat r basd on th masurd flux. Som wll undrstood hysical rocsss can hl lock in a valu for L Chids - Variabl stars Priod of brightnss fluctuations is rlatd to aarnt magnitud, m. If w know th distanc to som narby ons (from arallax), w can calibrat th rlationshi. Max: 30,000,000 arscs (~100 million ly) Usful for objcts in this galaxy, and a fw narby ons. Ty 1A Surnova A whit dwarf in a binary systm can gain mass from th comanion until it rachs a limit, roducing an xlosion. This is a surnova. Th luminosity of th rsulting xlosion can b rdictd. Max: 1 billion ly F = L (1) 4πr 2 Fig. 5 X-ray: NASA/CXC/Rutgrs/G.Cassam- Fig. 6 Chna, J.Hughs STScI t al.; Radio: NRAO/AUI/NSF/GBT/VLA/Dyr, Maddalna & Cornwll; Otical: Middlbury Collg/F.Winklr, NOAO/AURA/NSF/CTIO Schmidt & DSS Rdshift Pag 3

PHY 454 - cosmology - J. Hdbrg - 2017 Earlir 20th cntury obsrvations of galactic sctra indicatd rd-shiftd sctral lins for most.

(narly all ar moving away from us) Slihr, galaxis, and cosmological vlocity filds, John A. Pacock Hubbl's sctra from othr galaxis.

4 PHY cosmology - J. Hdbrg Earlir 20th cntury obsrvations of galactic sctra indicatd rd-shiftd sctral lins for most. Vsto Slihr did th first masurmnts of rdshift in galactic sctra. This suggstd thy wr moving away from us. Fig. 7 Slihr's 1917 data on galaxis aarnt vlocitis. (narly all ar moving away from us) Slihr, galaxis, and cosmological vlocity filds, John A. Pacock Hubbl's sctra from othr galaxis. Hubbl was th first to corrlat th rdshifts to distanc using Chid Variabl stars outsid th Milky Way. Fig. 8 Hubbl - Th Ralm of th Nbula Fig. 9 Hubbl's Vlocity vs. Distanc curv Fig. 10 From Th Ralm of th Nbula Hubbl Paramtr Th Hubbl aramtr is just th slo of th vlocity-osition data: v = H 0 d (2) Pag 4

5 PHY cosmology - J. Hdbrg Th valu of H might dnd on tim, so w can call th Hubbl constant th valu it has today: H 0 H( t 0 ) Th currnt valu for is around 70. H 0 Fig. 11 Rvisions to th Hubbl Constant By Ewn - Own work, CC BY- SA 4.0, htts://commons.wikimdia.org/w/indx.h? curid= Light Fig. 12 A Hubbl diagram using Ty 1A surnova. (Hubbl's original lot is containd in th small rd squar in th bottom lft.) /nas Dfin rdshift as chang in wavlngth w.r.t wavlngth at tim of mission,. λ z 0 λ = λ Δλ λ (3) Exansion If vrything sms to moving away from vrything ls, thn on ossibility is that sac is just gtting biggr. r(t) = a(t)r 0 (4) Pag 5

6 PHY cosmology - J. Hdbrg whr r 0 is th saration at th currnt tim, and a(t) is a dimnsionlss function known as th scal factor. Wavlngth - scal factor rlation Thus, λ λ = 0 (5) a( t ) a( t 0 ) λ 1 + z = a( t 0 ) 1 = = (6) λ 0 a( t ) a( t ) Thus, obsrving a quasar with z = 6.4 mans w ar looking at it whn th univrs was 1 a( t ) = = (7) tims smallr. Hubbl Flow Th motion of galaxis as art of th xansion is calld th Hubbl Flow This can b distinguishd from th culiar vlocity, which would b for xaml, th motion of th Milky Way towards Andromda. Earlir tims If w run th 'film' backwards, thn arlir in tim, vrything would hav bn much closr togthr. Two otions: ithr things would b mor dnsly ackd in th bginning, or mayb thr was just lss stuff. Stady Stat Univrs Big Bang Thoris wr roosd that suggstd th univrs was non changing in fundamntal aaranc. Mayb th amount of mattr was changing ovr tim, so that th avrag dnsity of th univrs rmaind constant. Anothr otion was that th dnsity was gratr arlir in th history of th univrs. Also, th univrs would hav to b hottr too. Big Bang Imlications Pag 6

Intnsity PHY 454 - cosmology - J. Hdbrg - 2017 ~ 1 mm 1 2 3 4 5 wavlngth [mm] Fig. 13 Blackbody radiation for a tmratur of around 3 K.

7 Intnsity PHY cosmology - J. Hdbrg ~ 1 mm wavlngth [mm] Fig. 13 Blackbody radiation for a tmratur of around 3 K. Th amount of H-3 rsnt in th univrs can b usd to figur out th tmraturs ncssary in th vry arly univrs. Thn basd on th xansions rats, w can figur out a tmratur that th univrs should b at now. Rough stimats rdictd 3-5 K. If th univrs wr a blackbody, this should b convrtibl to a ak wavlngth. Cosmic Microwav Background Fig. 14 Th Holmdl Horn Antnna that Pnzias and Wilson usd to first masur th CMB. By NASA - Grat Imags in NASA Dscrition, Public Domain, htts://commons.wikimdia.org/w/indx.h? curid= Two scintists working at Bll Labs kt rcording a signal that thy thought was nois - and couldn't gt rid of not mattr what thy trid. Thy calld som collagus who wr involvd in microwav astronomy. Isotroy/Anisotroy Is it th sam vrywhr? Pag 7

PHY 454 - cosmology - J. Hdbrg - 2017 Fig. 15 Data from th first 9 Minuts of th COBE satllits mission. Astrohysical Journal, Part 2 - Lttrs (ISSN 0004-637X), vol. 354, May 10, 1990,.

8 PHY cosmology - J. Hdbrg Fig. 15 Data from th first 9 Minuts of th COBE satllits mission. Astrohysical Journal, Part 2 - Lttrs (ISSN X), vol. 354, May 10, 1990,. L37-L40 Th CMB has a diol anisotroy. This is likly du to th motion of th local grou of galaxis comard to th rst of th visibl univrs, or th Hubbl Flow. Fig. 16 Diol Anistroy COBE diol data How to mak a CMB? Start with a rally hot dns bginning: T 10 4 K. At ths tmraturs, baryonic mattr will b comltly ionizd. Any hotons will scattr of lctrons and th univrs will b oaqu. A dns, hot, and oaqu mdium will roduc blackbody radiation. Fig. 17 Th ionizd, oaqu univrs bfor rcombination Pag 8

9 PHY cosmology - J. Hdbrg As th univrs xands, th tmratur cools. Around T 3000 K, th rotons and fr lctrons combin to form nutral atoms. Now, th blackbody hotons ar fr to stram throughout th univrs. Fig. 18 Transarnt univrs aftr rcombination Cooling of th CMB Th nrgy dnsity of a hoton gas: 4σ u = ( ) T 4 (8) c and th rssur: P = u 3 (9) From th first law of thrmodynamics. dq = de + PdV (10) Sinc th univrs is homognous and isotroic, w xct thr to b no hat flow: dq = 0. Thus, w gt: de dv = P(t) dt dt Substituting u and P from abov, and taking drivativs, and simlifying: 1 dt T dt 1 dv = 3V dt sinc th volum of th univrs is roortional to th scal factor cubd: (11) (12) V (t) a(t) 3 (13) w can writ: 1 T dt dt 1 da = a dt (14) Pag 9

PHY 454 - cosmology - J. Hdbrg - 2017 which can b rxrssd as: which imlis: d d (ln T) = (ln a) dt dt (15) T(t) a(t) 1 (16) Fig.

10 PHY cosmology - J. Hdbrg which can b rxrssd as: which imlis: d d (ln T) = (ln a) dt dt (15) T(t) a(t) 1 (16) Fig. 19 NASA / WMAP Scinc Tam Olbr's Paradox Rsolution Th univrs is not infinitly old. Can't say how big it is, but only what w can s. (visibl univrs) Pag 10

The Death of Stars - II.

The Death of Stars - II. Th Dath of Stars - II. Larning Objctivs! How can w us H-R diagrams to masur th ag of star clustrs (and hnc th ag of our Univrs)?! Why do high and low mass stars volv diffrntly? How ar havy lmnts such as