Sterrekunde

Is daar 'n manier om ouderdom in te skakel in die massa-helderheidsverhouding vir sterre?

Is daar 'n manier om ouderdom in te skakel in die massa-helderheidsverhouding vir sterre?


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Ek vra my af of daar 'n manier is om die helderheid van 'n ster nie net te formuleer as 'n funksie van massa nie, maar ook op ouderdom, en indien wel, hoe die formule vir helderheid sal lyk. In die geval van die son weet ek dat dit elke biljoen jaar so 10% helderder word, maar ek betwyfel of hierdie verhouding geld vir alle massa-reekse van sterre, net soos u die formule moet aanpas vir die ligverhoudingsmassa-verhouding vir sterre. van verskillende massas.

As iemand 'n bietjie lig kan werp op hierdie saak, sal dit baie waardeer word.


Dit lyk asof u die vertikale pad van 'n ster in die Hertzsprung-Russel-diagram (HRD) is.

Die enigste probleem is dat sterre-evolusie redelik ingewikkeld is. Kyk hier na 'n paar gesimuleerde trajekte vir verskillende massas en chemiese samestellings van Bertelli et al. 2008

Veral voor en na die hoofreeks (dws gereelde vervelige waterstofverbranding) word die helderheidsevolusie uiters wisselvallig.

Uit die simulasies hierbo kan 'n mens ook onderskeie ouderdom-helderheidsverhoudings aflei (geneem uit Danchi 2013):

U kan weer sien dat die verhouding baie ingewikkeld is vir jong of ou sterre en dat dit redelik konstant is gedurende die hoofreeks. Die probleem is dat dit gedurende die grootste deel van die hoofreeks te min verander. Dus, selfs met 'n goeie massa en metaalmeting, kan u die ouderdom nie akkuraat skat net vanaf die helderheid nie. Daarbenewens is daar nog onsekerhede in ons modelle.

Nog iets wat u kan doen, is om die massa-helderheidsverhouding te probeer verbeter deur ouderdom in te sluit. Ek dink dit is ook wat die titel van u vraag impliseer. Die probleem hier is dat ons gewoonlik nie die ouderdom van 'n ster ken nie. Maar as ons dit doen, soos Rob Jeffries in sy antwoord verduidelik het, is dit in beginsel moontlik.

'N Mens dink dat dit gedoen word om die ouderdom van die helderheid te kry, is om alles in te gaan en sogenaamde isochrone in die HRD te bereken. Dit is lyne met sterre van dieselfde ouderdom, maar wisselende massas en metallisiteite en kan afgelei word van simulasies. As 'n mens dan die helderheid, temperatuur en metaal meet, kan gekyk word watter isochroon die ster in die MVD val (en dus watter ouderdom hy het). Dit is egter nog steeds onakkuraat, veral in die hoofreeks, en word meestal gedoen met 'n hele sterregroep, waar statistieke dinge vergemaklik.

Dit is egter nie my vakgebied nie, dus sal ek bly wees dat 'n werklike kundige kan bel. :)


Ek stem basies saam met ruimtebrood dat dit ingewikkeld is, maar dan is dit ook die basiese verhouding van helderheid en massa as u sterre begin insluit wat nie in die hoofreeks is nie.

As ons onsself beperk tot die hoofreeks, kan u sien dat massa die dominante veranderlike is, en dat die helderheid miskien gedurende die lewensduur van die hoofreeks met ongeveer 'n faktor twee toeneem.

Hoe kan jy dit dan in 'n vergelyking plaas? Wel sê ons het $$ L / L _ { odot} simeq 0.7 (M / M _ { odot}) ^ {a}, $$ as die basiese verband tussen ligsterkte en massa vir 'n ZAMS-ster (zero age main sequence "). Die indeks $ a $ is iets soos 3,5, maar eintlik verskil dit in verskillende massa-reekse.

Ons moet dit nou doen vermenigvuldig hierdie helderheid deur $ f (t) $, waar $ f $ is 'n ongeveer lineêre funksie van tyd $ t $. $$ f (t) simeq 1 + (t / t _ { rm ms}), $$ waar $ t _ { rm ms} $ is die totale leeftyd van die hoofreeks.

Nou kan ons 'n benadering gebruik vir die leeftyd van die hoofreeks $$ t _ { rm ms} simeq 10 ^ {10} (M / M _ { odot}) ^ {- 2.5} { rm yr} $$

Dus is ons lineêre regstellingsfaktor vir die ZAMS-helderheid $$ f (t) simeq 1 + 10 ^ {- 10} (M / M _ { odot}) ^ {2.5} t , $$ waar $ t $ is in jare en die verhouding is geldig tot aan die einde van die hoofreeks.

Om dit te beklemtoon, is dit super benaderd, en 'n meer akkurate benadering sal numeriese interpolasie van werklike sterre-modelle behels.


Is daar 'n manier om ouderdom in te skakel in die massa-helderheidsverhouding vir sterre? - Sterrekunde

Die evolusionêre reekse vir sterre word beskryf deur hul posisie op 'n grafiek genaamd die Hertzsprung-Russell (HR) -diagram. Die meeste stadiums van sterre-evolusie, wat begin met protostars, het 'n spesifieke posisie op die HR-diagram. Daar sal verwys word na die verskillende vertakkings van die hieronder genoemde HR-diagram in die beskrywings van die evolusionêre reekse vir verskillende massa-sterre wat volg.

Die periodieke tabel van die elemente is 'n rangskikking van al die bekende elemente in volgorde van toenemende atoomgetal. Die rede waarom die elemente soos in die periodieke tabel gerangskik is, is om hulle almal met hul uiteenlopende fisiese en chemiese eienskappe in 'n logiese patroon te pas. Die vertikale lyne van elemente, genaamd groepe, en die horisontale lyne van elemente, genoem periodes, is chemies dieselfde en het 'n gemeenskaplike stel eienskappe. Die elemente is ook in blokke gerangskik wat gemeenskaplikhede deel. Die rangskikking van die elemente in die periodieke tabel toon die periodisiteit en neigings van sommige eienskappe, soos elektronkonfigurasie, metalisiteit, atoomradiusse en smeltpunte. Die ligging van enige individuele element in die tabel bepaal die eienskappe en eienskappe van daardie element, asook watter soorte chemiese bindings dit vorm en chemiese reaksies wat dit sal ondergaan.

Die Hertzsprung-Russell-diagram, of HR-diagram, is die periodieke tabel van die sterre - 'n analoog van die periodieke tabel van die elemente. Daar is ontdek dat wanneer die helderheid (absolute grootte of helderheid) van sterre teenoor hul temperatuur (sterreklassifikasie) geteken word, die sterre nie lukraak op die grafiek versprei word nie, maar meestal beperk is tot enkele goed gedefinieerde streke. Die sterre binne dieselfde streke het 'n gemeenskaplike stel eienskappe, net soos die groepe, tydperke en blokke elemente in die periodieke tabel. In teenstelling met die periodieke tabel, verander die fisiese eienskappe van sterre oor tyd, en daarom verander hul posisies op die HR-diagram ook - dus kan die HR-diagram beskou word as 'n visuele plot van die sterre evolusie. Dit is 'n grafiese hulpmiddel wat sterrekundiges gebruik om sterre te klassifiseer. Van die ligging van 'n ster op die grafiek is die helderheid, spektraaltipe, kleur, temperatuur, massa, chemiese samestelling, ouderdom en evolusiegeskiedenis bekend.

90% van alle sterre beslaan die skuins band wat loop van die linkerbovenhoek (warm, helder sterre) na die onderste regterhoek (koel, dowwe sterre) van die H-R-diagram. Sterre word hoofreekssterre wanneer die proses van termonukleêre samesmelting - waterstof tot helium - stabiliseer. Hierdie sterre is in hidrostatiese ewewig - die uitwaartse stralingsdruk van die samesmeltingsproses word gebalanseer deur die inwaartse swaartekrag. Wanneer die oorgang van 'n ster na die hoofreeksster plaasvind, word die ster 'n ZAMS-ster (Zero Age Main Sequence) genoem. Die bepalende faktor waar 'n ster in die hoofreeks geleë is, is massa. Die Son is 'n G-spektraalklasster met 'n effektiewe oppervlaktemperatuur van

5800K. Aangesien die lig en massa van alle ander sterre relatief tot die son gemeet word, het die son een sonlig en een sonmassa. Die O- en B-sterre is die warmste en mees massiewe, en die K- en M-sterre is die koelste en minste massiewe sterre. Daar word soms na die O- en B-sterre verwys as vroeë reeks sterre, en die K- en M-sterre as laat volgorde sterre. Hierdie terme verwys na sterre massiewer (vroeë volgorde) as die son of minder massief (laat volgorde) as die son. Al die sterre van die sonmassa met versmelting van waterstof tot helium wat binne hul kern voorkom, neem dieselfde posisie in die hoofreeks as die son waarop hulle op daardie plek bly, met die spesifieke verhouding van temperatuur en absolute grootte totdat die waterstof in die kern uitgeput raak. en die samesmelting van waterstofkerne tot heliumkerne stop. Die massa-helderheidsverhouding vir hoofreekssterre word gedefinieer as: L / L (Son)

[M / M (Son)] 4. Alle hoofreekssterre met 'n massa kleiner as

Daar word soms na 8 sonmassas verwys as dwergsterre, met die koelste, minste massiewe sterre in die regterkantste hoek, rooi dwerge. Hoe massiewer die ster, hoe vinniger is die samesmelting, en hoe minder tyd oorbly dit in die hoofreeks. Die hoeveelheid tyd wat 'n ster aan die hoofreeks spandeer, is ook 'n funksie van sy massa en helderheid en word gedefinieer as: T (jaar) = 10 10 M / L. (Sien HR-diagram)


Inhoud

Aan die begin van die 20ste eeu het inligting oor die soorte en afstande van sterre meer beskikbaar geword. Daar is getoon dat die spektra van sterre kenmerkende eienskappe het, wat dit moontlik maak om te kategoriseer. Annie Jump Cannon en Edward C. Pickering aan die Harvard College Observatory het 'n metode van kategorisering ontwikkel wat bekend geword het as die Harvard Classification Scheme, gepubliseer in die Harvard Annals in 1901. [2]

In Potsdam in 1906 het die Deense sterrekundige Ejnar Hertzsprung opgemerk dat die rooiste sterre - geklassifiseer as K en M in die Harvard-skema - in twee verskillende groepe verdeel kon word. Hierdie sterre is baie helderder as die son, of baie flouer. Om hierdie groepe te onderskei, noem hy hulle 'reuse' en 'dwerg' sterre. Die volgende jaar het hy begin om sterregroepe te bestudeer, groot groeperings sterre wat op ongeveer dieselfde afstand geleë is. Hy het die eerste kleurstukke teenoor die helderheid van hierdie sterre gepubliseer. Hierdie intrige het 'n prominente en deurlopende reeks sterre getoon, wat hy die hoofreeks genoem het. [3]

Aan die Universiteit van Princeton het Henry Norris Russell 'n soortgelyke ondersoek gevolg. Hy het die verband bestudeer tussen die spektrale klassifikasie van sterre en hul werklike helderheid as gekorrigeer vir afstand - hul absolute grootte. Vir hierdie doel het hy 'n stel sterre gebruik wat betroubare parallakses gehad het, en waarvan baie in Harvard gekategoriseer is. Toe hy die spektraaltipes van hierdie sterre teen hul absolute omvang beplan, het hy gevind dat dwergsterre 'n duidelike verhouding gevolg het. Dit het die regte helderheid van 'n dwergster met redelike akkuraatheid voorspel. [4]

Van die rooi sterre wat deur Hertzsprung waargeneem is, het die dwergsterre ook die spektra-helderheidsverhouding gevolg wat Russell ontdek het. Die reuse-sterre is egter baie helderder as dwerge en volg dus nie dieselfde verhouding nie. Russell het voorgestel dat die "reuse-sterre lae digtheid of 'n groot helderheid van die oppervlak moet hê, en die omgekeerde geld vir dwergsterre". Dieselfde kurwe het ook getoon dat daar baie min dowwe wit sterre was. [4]

In 1933 stel Bengt Strömgren die term Hertzsprung – Russell-diagram bekend om 'n helderheid-spektrale klasdiagram aan te dui. [5] Hierdie naam weerspieël die parallelle ontwikkeling van hierdie tegniek deur Hertzsprung en Russell vroeër in die eeu. [3]

Aangesien evolusiemodelle van sterre gedurende die dertigerjare ontwikkel is, is aangetoon dat, vir sterre met 'n eenvormige chemiese samestelling, 'n verband bestaan ​​tussen die massa van 'n ster en sy helderheid en radius. Dit wil sê, vir 'n gegewe massa en samestelling is daar 'n unieke oplossing vir die bepaling van die ster se straal en helderheid. Dit het bekend geword as die Vogt-Russell-stelling wat vernoem is na Heinrich Vogt en Henry Norris Russell. Volgens hierdie stelling, as die chemiese samestelling van 'n ster en die posisie daarvan in die hoofreeks bekend is, is die massa en radius van die ster ook so. (Daar is egter later ontdek dat die stelling effens afbreek vir sterre met 'n nie-uniforme komposisie.) [6]

'N Verfynde skema vir sterreklassifikasie is in 1943 deur William Wilson Morgan en Philip Childs Keenan gepubliseer. [7] Die MK-klassifikasie het aan elke ster 'n spektraaltipe toegeken - gebaseer op die Harvard-klassifikasie - en 'n helderheidsklas. Die Harvard-klassifikasie is ontwikkel deur 'n ander letter aan elke ster toe te ken op grond van die sterkte van die waterstofspektrale lyn, voordat die verband tussen spektra en temperatuur bekend was. In volgorde van temperatuur en wanneer duplikaatklasse verwyder is, volg die spektraaltipes sterre, in volgorde van dalende temperatuur met kleure wat wissel van blou tot rooi, die volgorde O, B, A, F, G, K en M. (A populêr geheue vir die memorisering van hierdie reeks sterklasse is "Oh Be A Fine Girl / Guy, Kiss Me".) Die helderheidsklas het gewissel van I tot V, in volgorde van dalende helderheid. Sterre van helderheidsklas V het tot die hoofreeks behoort. [8]

In April 2018 het sterrekundiges die opsporing van die mees "gewone" ster (naamlik hoofreeks), met die naam Icarus (formeel MACS J1149 Lensster 1), op 9 miljard ligjare van die aarde, opgespoor. [9] [10]

Wanneer 'n protostêr gevorm word deur die ineenstorting van 'n reuse molekulêre wolk van gas en stof in die plaaslike interstellêre medium, is die aanvanklike samestelling deurgaans homogeen, bestaande uit ongeveer 70% waterstof, 28% helium en spoorhoeveelhede ander elemente, volgens massa. [11] Die aanvanklike massa van die ster hang af van die plaaslike toestande in die wolk. (Die massaverspreiding van nuutgevormde sterre word empiries beskryf deur die aanvanklike massafunksie.) [12] Tydens die aanvanklike ineenstorting genereer hierdie ster voor die hoofreeks energie deur gravitasiekrimping. Sodra dit voldoende dig is, begin sterre waterstof omskakel in helium en gee dit energie af deur 'n eksotermiese kernfusieproses. [8]


DIE KERNLEEFTYD VAN DIE SON

Ons het gesien hoe sekere atoomkerne verval ondergaan wat een kern in 'n ander omskakel. Dit blyk dat dit moontlik is om hierdie reaksies die ander rigting te laat loop. Natuurlik is die regte fisiese toestande nodig om die omgekeerde verval te laat plaasvind. Nog ander kernprosesse is moontlik, met slegs stabiele kerne. Al hierdie prosesse gaan onder die algemene naam van kernreaksies, en dit speel 'n belangrike rol in die son en ander sterre.

Daar was baie wetenskaplike vooruitgang tussen die studie van radioaktiwiteit en 'n werkbare teorie oor die produksie van sonenergie. Een van die belangrikste hiervan was die besef dat die son byna geheel en al uit waterstof en helium bestaan. Klein hoeveelhede swaarder elemente is ook teenwoordig, maar saam vorm dit slegs ongeveer 2% van die massa van die son. Hierdie ontdekking is gemaak deur Cecelia Payne-Gaposchkin en aangebied in 1925 as haar doktorale proefskrif in astrofisika aan die Radcliffe College, nou deel van die Harvard Universiteit. Payne-Gaposchkin gebruik die toenmalige veld van kwantummeganika om tot 'n baie verrassende gevolgtrekking te kom. vir die tyd. Haar proefskrif word deur baie mense steeds as die grootste Ph.D. verhandeling wat ooit op die gebied van astrofisika gedoen is.

'N Ander belangrike ontdekking wat op die produksie van sonenergie betrekking het, is 20 jaar tevore gedoen. Gepubliseer in 1905 onder die titel Zur Elektrodynamik bewegter K & oumlrper (Aan die elektrodinamika van bewegende liggame) deur Albert Einstein, destyds 'n klerk in die patentkantoor van Bern, Switserland, het die koerant die verstommende bewering gemaak (een onder verskeie) dat massa en energie onderling omkeerbaar was. Baie ander vooruitgang was ook relevant, maar ons gaan ondersoek instel na hoe hierdie twee idees die begrip van die werking van die son en ander sterre beïnvloed het.

Beskou as beginpunt die alfa-deeltjie, 4 He. Ons het hierdie deeltjie vroeër bekendgestel tydens ons bespreking van radioaktiwiteit. Die alfa-deeltjie is die mees algemene isotoop van helium. Dit bestaan ​​uit twee protone en twee neutrone. Die massas van hierdie deeltjies word in Tabel 5.2 getoon.

Tabel 5.2
DEEL PROTON NEUTRON 2 PROTONE + 2 NEUTRONE ALPHA (GEMEET) VERSKIL
Massa (10-27 kg) 1.672621637 1.674927211 6.695097696 6.64465620 0.050441496

As ons die massas van die protone en die neutrone waaruit die alfa-deeltjie optel, bymekaar tel, kom ons agter dat die alfa-deeltjie 'n massa laer het as die samestellende dele. Hierdie toevoeging is in die tabel gedoen, met die verskil in die laaste kolom. Die verskil is klein, slegs ongeveer 0,7%. Hoe kan dit tog wees dat die protone en neutrone 'n laer massa het as hulle in 'n alfapartikel versamel word as wanneer hulle alleen is? Hierdie verskil staan ​​bekend as die bindingsenergie, en dit hou direk verband met massa-energie interkonversie. Sommige van die massa van die protone en neutrone word omgeskakel na energie om 'n alfadeeltjie te skep, en daardie energie word vrygestel aan die omgewing wanneer die alfadeeltjie gevorm word. Die hoeveelheid energie word gegee deur die beroemde massa-energie-ekwivalensie van Einstein & rsquos:

waar (E ) = energie, (m ) = massa, en (c ) = die snelheid van die lig.

Hierdie energievrystelling bied 'n moontlike bron van energie vir die son. Soos blyk uit Cecelia Payne-Gaposchkin, is die oorgrote meerderheid van die son waterstof, met die meeste van die res helium. Miskien verkry die son sy energie deur die waterstof in helium om te skakel en energie in die proses te onttrek. Die algemene kernreaksie sou wees:

Hierdie soort kernreaksie, waar ligter elemente saamwerk om swaarder elemente te vorm, staan ​​bekend as kernfusie. Dit verskil van reaksies waarin swaarder elemente in kernsplitsing in ligter elemente verdeel word.

ENERGIE VAN HITROËNFUSIE

In die vorige aktiwiteit moes u gevind het dat energie kon onttrek word as ons 'n manier kon bedink om vier protone in 'n heliumkern te verander. Ons sal die bespreking van hoe dit kan gebeur, later bespaar. Vir eers sal u die kernleeftyd van die son vind en kyk of dit ooreenstem met die son se leeftyd van minstens vyf miljard jaar - die geskatte ouderdom van die aarde.

VERDER GAAN 5.4: KERNREAKSIES IN DIE SON EN ANDER STERRE

KERNENERGIE LEEFTYD VIR DIE SON

In hierdie aktiwiteit sal u skat hoeveel tyd die son kan bestaan ​​as dit aangedryf word deur die omskakeling van waterstof na helium deur kernfusiereaksies. In die kernreaksies wat ons oorweeg, word een soort atoom (waterstof) in 'n ander (helium) omgeskakel. Volg hierdie stappe om die aktiwiteit deur te werk:


Die reeks sterre massas

Figuur 5. Bruin dwerge in Orion: Hierdie beelde, geneem met die Hubble-ruimteteleskoop, toon die gebied rondom die Trapezium-sterreswerm in die stervormende streek genaamd die Orionnevel. (a) Geen bruin dwerge word in die sigbare ligbeeld gesien nie, beide omdat hulle baie min lig in die sigbare lig uitsteek en omdat hulle in die stofwolke in hierdie streek weggesteek is. (b) Hierdie beeld is in infrarooi lig geneem wat deur die stof na ons toe kan beweeg. Die vaagste voorwerpe in hierdie beeld is bruin dwerge met massas tussen 13 en 80 keer die massa van Jupiter. (krediet a: NASA, CR O'Dell en SK Wong (Rice Universiteit) krediet b: NASA KL Luhman (Harvard-Smithsonian Sentrum vir Astrofisika) en G. Schneider, E. Young, G. Rieke, A. Cotera, H. Chen, M. Rieke, R. Thompson (Steward Observatory).

Hoe groot kan die massa van 'n ster wees? Sterre massiewer as die Son is skaars. Geen van die sterre binne 30 ligjare van die son het 'n massa van meer as vier keer die van die son nie. Soektogte op groot afstande vanaf die Son het gelei tot die ontdekking van enkele sterre met massas tot ongeveer 100 keer die son, en 'n handjievol sterre (enkele uit 'n paar miljard) het massas tot 250 sonmassas. . Die meeste sterre het egter minder massa as die son.

Volgens teoretiese berekeninge is die kleinste massa wat 'n ware ster kan hê ongeveer 1/12 van die son. Met 'n & # 8220ware & # 8221 -ster bedoel sterrekundiges een wat warm genoeg word om protone saam te smelt om helium te vorm (soos bespreek in The Sun: A Nuclear Powerhouse). Voorwerpe met 'n massa tussen ongeveer 1/100 en 1/12 die van die son, kan vir 'n kort tydjie energie produseer deur middel van kernreaksies waarby deuterium betrokke is, maar hulle word nie warm genoeg om protone te versmelt nie. Sulke voorwerpe is tussen massa tussen sterre en planete en het die naam gekry bruin dwerge (Figuur 5). Bruin dwerge is soortgelyk aan Jupiter in radius, maar het massas van ongeveer 13 tot 80 keer groter as die massa van Jupiter.

Nog kleiner voorwerpe met 'n massa van minder as ongeveer 1/100 van die massa van die son (of tien Jupiter-massas) word planete genoem. Hulle kan energie uitstraal wat geproduseer word deur die radioaktiewe elemente wat hulle bevat, en hulle kan ook hitte uitstraal wat gegenereer word deur stadig onder hul eie gewig saam te pers ('n proses wat gravitasiekrimping genoem word). Die binnekant sal egter nooit die temperatuur bereik wat hoog genoeg is om enige kernreaksies te laat plaasvind nie. Jupiter, waarvan die massa ongeveer 1/1000 van die massa van die son is, is ongetwyfeld byvoorbeeld 'n planeet. Tot in die negentigerjare kon ons net planete in ons eie sonnestelsel opspoor, maar nou het ons duisende elders ook. (Ons bespreek hierdie opwindende waarnemings in The Birth of Stars en die ontdekking van planete buite die sonnestelsel.)


Is daar 'n manier om ouderdom in te skakel in die massa-helderheidsverhouding vir sterre? - Sterrekunde



Hertzsprung-Russell-diagram wat die son se evolusionêre pad toon
en helderheid op verskillende stadiums van sy evolusie


Hertzsprung-Russell-diagram wat massas en helderheid van hoofreekssterre toon

Soos hierdie figuur aantoon, is die sterre bo-aan die hoofreeks baie massief, die sterre in die middel het 'n gemiddelde massa en die sterre aan die onderkant het baie min massa.

Ons kan die verwantskap tussen massa en helderheid duideliker aantoon deur 'n massa-helderheidsdiagram vir hoofreekssterre te teken:



Massa-helderheid diagram

Soos in die diagram getoon, neem die massas en die helderheid van hoofreekssterre geleidelik toe, hoewel nie op 'n heeltemal eenvormige manier nie. Die kromme stel die werklike verband tussen massa en helderheid voor, die reguit lyn is 'n eenvoudige benadering tot die werklike verhouding. (Vir diegene wat wiskundig geneig is, kan die kurwe ook redelik eenvoudig lyk. Hou egter in gedagte dat die helderheidsgebied wat hier getoon word meer as 10 miljard keer is, en dat die massa ongeveer 1000 keer is. Om die resultate van so 'n groot aantal getalle in so 'n kompakte grafiek vereis die gebruik van log-log-koördinaatpapier. Op so 'n grafiek stel selfs 'n reguit lyn 'n eksponensiële vergelyking voor, en geboë lyne stel baie komplekse verhoudings voor.)
Die verband tussen massa en helderheid wat in die bostaande grafiek getoon word, is so belangrik vir ons begrip van die eienskappe van hoofreekssterre dat dit 'n spesiale naam kry. As ons dit deur 'n grafiek voorstel, noem ons dit die Massa-helderheid diagram. As ons dit met 'n vergelyking voorstel, noem ons dit die Massa-helderheidsverhouding (in die diagram hierbo getoon as 'n reguitlyn benadering, met die helderheid ongeveer eweredig aan die eksponensiële krag van die massa).

Die massa-helderheidsverhouding
Soos in die grafiek hierbo getoon, wissel die helderheid van die hoofreekssterre eweredig met 'n mate van krag van hul massas. Vir die grootste deel van die reeks sterremassas is die proporsionaliteit die 3,5 krag van die massa, wat beteken dat as die massa verdubbel, die helderheid ongeveer 11 keer toeneem, of 'n bietjie afronding, ongeveer 10 keer. As gevolg hiervan kan ons die helderheid van verskillende sterre skat deur die massa te verdubbel (of te halveer) en die helderheid met 10 te vermenigvuldig (of te deel). Die tabel hieronder toon hoe dit werk:

Aan die hoë kant van die massaskaal verander die helderheid stadiger as wat hier aangedui word, en 'n 1000000 sonligsterkte Hoofreeksster sou eintlik ongeveer 100 sonmassas wees in plaas van 64 sonmassas, maar as ons in ag neem dat die helderheidsgebied hier 10000 miljoen keer is en die massa-massa ongeveer 1000 keer, is dit opmerklik dat so 'n eenvoudige berekening so byna akkuraat is.

Die hoofreeksleeftyd van sterre
Die verband tussen helderheid en massa hou ernstige gevolge in vir die leeftyd van die hoofreekssterre. Die brandstof wat sterre laat skyn, is hul massa (of meer spesifiek die massa waterstof in die kern van die ster), en sterre met meer massa het meer brandstof om te verbrand, dus jy kan verwag dat hulle langer sal hou as sterre met minder massa. Maar die tempo waarteen die brandstof moet verbrand, is eweredig aan die helderheid, en helderder sterre moet dus nie so lank hou as wat swakker is nie. Die verhouding tussen 'n ster se leeftyd en die leeftyd van die son word gegee deur hoeveel meer brandstof hy het, gedeel deur hoeveel vinniger hy die brandstof verbrand. Aangesien hoofreekssterre, wat twee keer so helder is, tien keer vinniger brand (twee keer die massa wat tien keer die helderheid lewer, soos hierbo aangedui), verbrand die brandstof net ongeveer 'n vyfde (2 / 10) so lank. As gevolg hiervan kan ons die tabel hierbo wysig om die lewensduur van die sterre in te sluit. (Opmerking: In hierdie tabel word die lewensduur afgerond, aangesien die helderheid hierbo slegs ongeveer korrek is. Selfs die hoofreeksleeftyd van die Son, wat ongeveer 12 miljard jaar is, word afgerond tot 10 miljard jaar, om die getalle eenvoudig te hou. Onthou ook dat diegene wat nie in die Verenigde State is nie, op hierdie webwerf slegs 'n duisend miljoen is, en 'n triljoen slegs 'n miljoen miljoen.)

Aangesien die helderheid wat hier getoon word slegs benader is, sou die lewensduur slegs benader wees, selfs al was daar geen ander komplikasies nie, maar vir die sterre met die laagste massa is daar 'n bykomende komplikasie. Die leeftyd van sterre soos die son en sterre met 'n hoër massa is net so 'kort' soos dit is omdat slegs die brandstof in hul kerne verbrand word terwyl dit op die hoofreeks is. As die son al sy brandstof teen die huidige koers kon verbrand, kan dit ongeveer 100 miljard jaar duur. Dit duur net ongeveer 10 miljard jaar, want net die sentrale deel van die son is warm genoeg om kernfusie te ondersteun. Dieselfde geld vir al die sterre, en dus word die brandstof in almal in die middel "verbrand". Maar vir sterre waarvan die evolusiepad min of meer reguit afbeweeg na die hoofvolgorde tydens hul vorming, reik die konvektiewe sone (of konvektiewe omhulsel) aan die buitekant van die ster diep in die kern van die ster en as die brandstof in die kern opgebruik word vars brandstof van buite af in die kern gery. As gevolg hiervan verbrand die sterre wel al die brandstof deur die ster terwyl dit hoofreekssterre is, alhoewel die werklike verbranding slegs in die middel plaasvind. Dit verhoog die lewensduur van sterre van 1/4 en 1/8 sonmassa met ongeveer 'n ander faktor van 8 tot onderskeidelik 2 triljoen jaar en 10 triljoen jaar. Die sterre van 1/16 sonmassa sou nog langer hou, maar soos bespreek op die bladsye oor stereldood, word sterre van daardie lae massa waarskynlik nooit warm genoeg om kernverbranding te ondersteun nie, dus het hulle glad nie 'n leeftyd van die hoofreeks nie .
Nou wat beteken dit? As massiewe sterre nie baie lank duur nie, dan moet enige helder massiewe sterre wat ons sien, relatief onlangs "gebore" (gevorm) wees. In werklikheid moes die mees massiewe sterre gister volgens astronomiese standaarde gebore wees. Selfs die minste massiewe sterre wat in die sterre-tabel massiewer is as die son, sterre met twee sonnemassas, het 'n leeftyd van minder as die helfte van die ouderdom van die sonnestelsel. Dit beteken dat as die son nog in die sterretros was waarin dit gevorm het, dit een van die helderste sterre in daardie groep sou wees. Al die sterre wat oorspronklik helderder as dit was, van net 'n bietjie helderder tot 'n miljoen keer helderder, sou al dood wees. Hulle dooie hulke sou nog steeds rond wees, maar hulle sou of waarneembaar flou of net skaars helder genoeg wees om met groot teleskope te sien.
Aan die ander kant het die sterre wat 'n laer massa het as die son, baie, baie langer lewens as die son. Alhoewel sterre soos die son al vroeg in die geskiedenis van die heelal gevorm het (tussen 12 en 15 miljard jaar gelede) al dood sou wees, sou elke ster met ongeveer die helfte van die sonmassa wat nog ooit was gevormde sou nog net so helder skyn (of miskien moet ons net so vaagweg sê) soos altyd, want hul lewensduur is almal baie langer as die ouderdom van die Heelal.

Waarom helder sterre skaars is
Selfs wanneer sterretrosse die eerste keer ontstaan, is die helder sterre nie so veel soos die flouer sterre nie, want die helderder sterre benodig meer massa, en al sou 90% van die massa van die groep in die helderste sterre wees, sou u nie soveel kry nie baie daarvan, aangesien elkeen soveel massa opgebruik, terwyl die massa van ongeveer 10% wat tot sterre met lae massa gevorm het, baie sterre kan word omdat elkeen nie veel massa benodig nie. Maar daarbenewens sterf die helder sterre baie vinnig uit, so na 'n rukkie daal hul aantal tot nul, terwyl die dowwe sterre feitlik vir ewig hou, en hulle getal bly so groot soos toe hulle die eerste keer gevorm het.


Standaard gloeilampe

Ons bespreek in Celestial Distances die groot frustrasie wat sterrekundiges ervaar toe hulle besef dat die sterre in die algemeen nie standaard is nie bolle. As elke gloeilamp in 'n groot ouditorium 'n standaard gloeilamp van 100 watt is, moet die lampe wat vir ons helderder lyk, nader wees, terwyl diegene wat dowwer lyk, verder moet wees. As elke ster 'n standaardligsterkte (of wattage) gehad het, sou ons hul afstande op dieselfde manier kon aflees op grond van hoe helder dit vir ons lyk. Helaas, soos ons geleer het, kom geen sterre of sterrestelsels in 'n helderheid van standaarduitgifte nie. Desondanks het sterrekundiges op soek na voorwerpe daarbuite wat op een of ander manier soos 'n standaard gloeilamp optree — wat dieselfde intrinsieke (ingeboude) helderheid het, waar hulle ook al is.

'N Aantal voorstelle is gemaak vir watter soorte voorwerpe effektiewe standaard gloeilampe kan wees, insluitend die helderste superreussterre, planetêre newels (wat baie ultravioletstraling afgee) en die gemiddelde bolvormige groep in 'n sterrestelsel. Een voorwerp blyk besonder nuttig te wees: die tipe Ia supernova. Hierdie supernovas behels die ontploffing van 'n wit dwerg in 'n binêre stelsel (sien The Evolution of Binary Star Systems) Waarnemings toon dat supernovas van hierdie tipe almal bykans dieselfde helderheid bereik (ongeveer 4,5 × 10 9 LSon) by maksimum lig. Met so 'n geweldige helderheid is hierdie supernovas op 'n afstand van meer as 8 miljard ligjare opgespoor en is dit dus veral aantreklik vir sterrekundiges as 'n manier om afstande op groot skaal te bepaal (Figuur 2).

Figuur 2: Tik Ia Supernova. Die helder voorwerp links onder in die middel is 'n tipe Ia-supernova naby sy piekintensiteit. Die supernova oorskry maklik sy gasheerstelsel. Hierdie uiterste toename en helderheid help sterrekundiges om Ia supernova as standaard gloeilampe te gebruik. (krediet: NASA, ESA, A. Riess (STScI))

Verskeie ander soorte standaardbolle wat oor groot afstande sigbaar is, is ook voorgestel, insluitend die algehele helderheid van byvoorbeeld reuse-elliptiese vorms en die helderste lid van 'n sterrestelsel. Tipe Ia-supernovas is egter die akkuraatste standaard gloeilampe en dit kan gesien word in sterre sterrestelsels as die ander soorte kalibrators. As we will see in the chapter on The Big Bang, observations of this type of supernova have profoundly changed our understanding of the evolution of the universe.


AST Final Exam

A scientific theory cannot be accepted until it has been proven true beyond all doubt.

A scientific theory must make testable predictions that, if found to be incorrect, could lead to its own modification or demise.

A scientific theory must explain a wide variety of phenomena observed in the natural world.

A scientific theory should be based on natural processes and should not invoke the supernatural or divine.

retrograde motion of planets

non-uniform motion of sun, west to east, along ecliptic in 1 yea

motion of planets west to east compared to stars

motion of sky east to west in 24 hours

It held that the planets moved along small circles that moved on larger circles around the Earth.

It placed the Sun at the center so that the planets' apparent retrograde motion was seen as the Earth passed each one in its orbit.

It varied the motion of the celestial sphere so that it sometimes moved backward.

It held that the planets moved along small circles that moved on larger circles around the Sun.

You, Earth, solar system, Milky Way Galaxy, Local Group, Local Supercluster, universe

You, Earth, Milky Way Galaxy, solar system, Local Group, Local Supercluster, univers

You, Earth, solar system, Local Group, Local Supercluster, Milky Way Galaxy, univers

You, Earth, Local Group, Local Supercluster, solar system, Milky Way Galaxy, universe

it depends on the month of the year

constellations are group of stars bound by gravity

constellations reflect the cultures of the people who created them

we can divide the sky into constellations

the relative positions of the stars within a constellation can change over very long periods of time

All particles in the rings orbit their planet at the same speed and with the same period

Rings are always located closer to a planet's surface than any large moon

Individual ring particles closer to a planet orbit faster than particles farther out

All 4 giant planets have rings

Jupiter's greater mass compresses it more and increases its density.

Saturn's rings make the planet look bigger.

Saturn is further from the Sun, thus cooler, and therefore less compact.

Saturn has a larger proportion of hydrogen and helium than Jupiter, and is therefore less dense.

is much higher than on Earth

shows an extreme change with the seasons.

is much lower than on Earth.

is about the same as on Mercury.

the Moon is between the Sun and the Earth.

the Earth is between the Moon and the Sun.

the Sun is between the Moon and the Earth.

the Sun moves temporarily out of the ecliptic.

create light and dark bands.

cause Jupiter's magnetic field to ripple.

produced the ring system discovered by Voyager.

all the other four answers are correct

the temperature of the object by matching the overall spectral shape to a blackbody curve.

the line-of-sight velocity by observing Doppler shifting of the spectral lines.

the pressure of the gas in the emitting region due to broadening of the spectral lines.

The Sun would rotate faster than it does now

The Sun would rotate slower than it does now

The rotation of the Sun will stay the same

The Sun's angular size in the sky will stay the same

The rotational period is longer.

The orbital period is longer.

The rotational period varies with the Moon's phase.

Its rotation is retrograde, it rotates in direction opposite to the other planets

It rotates faster than any Jovian planet

It rotates at the same rate as the Earth

It rotates in synchronism with Mercury

A small amount of mass can be turned into a large amount of energy.

Mass can be turned into energy, but energy cannot be turned back into mass.

It takes a large amount of mass to produce a small amount of energy.

You can make mass into energy if you can accelerate the mass to the speed of light.

Earth is catching up with and passing Mars in their respective orbits.

Mars is getting closer to the Sun.

Mars is moving around the Sun in the opposite direction from which Earth is moving around the Sun.

Earth and Mars are on opposite sides of the Sun.

More massive stars live much shorter lives than less massive stars.

More massive stars live slightly shorter lives than less massive stars.

More massive stars live much longer lives than less massive stars.

More massive stars live slightly longer lives than less massive stars.

X-rays if the matter was dense

Between the orbits of Mars and Jupiter

Between the orbits of Earth and Mars

Between the orbits of Jupiter and Saturn

Between the orbits of Venus and Earth

The F8V star is cooler than the Sun.

The Sun is hotter than the K2III star.

The A5I star is hotter than both the Sun and the K2III star.

The K2III star is cooler than the F8V star, which is cooler than the A5I star.

They have lower temperatures than the photosphere of the Sun.

They have low rotation rates.

They are storm systems like those on the Jovian planets.

Planetary nebula/white dwarf formation is more common.

Supernovae are more common.

They both occur in about equal numbers.

their masses are lower than the combined mass of other bodies in their orbits

they orbit too far from the Sun

they are all irregular in shape

they are predominantly icy in composition

very few sunspots were seen.

Roger "Buster" Maunder went through a batting slump.

the Earth experienced a prolonged global drought.

sea level was at its lowest point in history.

Asteroids are made of rocky material. Comets are made of icy material.

Asteroids are made of icy material. Comets are made of rocky material.

Asteroids and comets are both made of rocky and icy material, but asteroids are larger in size than comets.

Asteroids and comets are both made of rocky and icy material, but asteroids are smaller in size than comets.

is hotter than the chromosphere and heated by magnetic activity

is hotter than the chromosphere and heated by solar photons

is cooler than the chromosphere

is at the same temperature as the chromosphere

be the sites of nova and supernova explosions.

have a mass limit of 3 Msun.

never occur in a binary star system.

be composed mainly of silicon.

B: is located in the disk of the Galaxy.

C: contains a few hundred thousand members.

It is converted to energy

It is recycled back into hydrogen.

It is transformed into electrons.

remains the same, but its apparent brightness is decreased by a factor of four.

is decreased by a factor of four, and its apparent brightness is decreased by a factor of four.

is decreased by a factor of two, and its apparent brightness is decreased by a factor of two.

remains the same, but its apparent brightness is decreased by a factor of two.

Everywhere in the universe at once

At a single point in the center of the then-existing universe

Somewhere in the Virgo galaxy cluster

All of these statements are equally correct

a massive object bends light as that light passes close to the massive object.

a massive object pulls much more distant objects closer to us.

dark matter builds up in a particular region of space, leading to a very dense region and an extremely high mass-to-light ratio.

a telescope lens is distorted by gravity.

dark matter of the galaxy

massive O and B stars in the galaxy

HII regions of the galaxy

The halo stars and globular clusters are distributed in a roughly spherical region surrounding and centered on the disk the Sun is located roughly 2/3rd to halfway out from the center in the plane of the disk.

The globular clusters are distributed in a roughly spherical region surrounding and centered on the disk the Sun resides roughly at the center of the disk, which also contains the halo stars.

The halo stars and globular clusters are distributed in a roughly spherical region surrounding and centered on the disk the Sun resides at the edge of the disk.

The halo stars and globular clusters are distributed in a roughly spherical region surrounding and centered on the disk the Sun resides roughly 2/3rd to halfway out from the center, well away from the plane of the disk.


19.3 Variable Stars: One Key to Cosmic Distances

Let’s briefly review the key reasons that measuring distances to the stars is such a struggle. As discussed in The Brightness of Stars, our problem is that stars come in a bewildering variety of intrinsic luminosities. (If stars were light bulbs, we’d say they come in a wide range of wattages.) Suppose, instead, that all stars had the same “wattage” or luminosity. In that case, the more distant ones would always look dimmer, and we could tell how far away a star is simply by how dim it appeared. In the real universe, however, when we look at a star in our sky (with eye or telescope) and measure its apparent brightness, we cannot know whether it looks dim because it’s a low-wattage bulb or because it is far away, or perhaps some of each.

Astronomers need to discover something else about the star that allows us to “read off” its intrinsic luminosity—in effect, to know what the star’s true wattage is. With this information, we can then attribute how dim it looks from Earth to its distance. Recall that the apparent brightness of an object decreases with the square of the distance to that object. If two objects have the same luminosity but one is three times farther than the other, the more distant one will look nine times fainter. Therefore, if we know the luminosity of a star and its apparent brightness, we can calculate how far away it is. Astronomers have long searched for techniques that would somehow allow us to determine the luminosity of a star—and it is to these techniques that we turn next.

Variable Stars

The breakthrough in measuring distances to remote parts of our Galaxy, and to other galaxies as well, came from the study of variable star s. Most stars are constant in their luminosity, at least to within a percent or two. Like the Sun, they generate a steady flow of energy from their interiors. However, some stars are seen to vary in brightness and, for this reason, are called variable stars. Many such stars vary on a regular cycle, like the flashing bulbs that decorate stores and homes during the winter holidays.

Let’s define some tools to help us keep track of how a star varies. A graph that shows how the brightness of a variable star changes with time is called a light curve (Figure 19.9). Die maximum is the point of the light curve where the star has its greatest brightness the minimum is the point where it is faintest. If the light variations repeat themselves periodically, the interval between the two maxima is called the period of the star. (If this kind of graph looks familiar, it is because we introduced it in Diameters of Stars.)

Pulsating Variables

There are two special types of variable stars for which—as we will see—measurements of the light curve give us accurate distances. These are called cepheid and RR Lyrae variables, both of which are pulsating variable stars . Such a star actually changes its diameter with time—periodically expanding and contracting, as your chest does when you breathe. We now understand that these stars are going through a brief unstable stage late in their lives.

The expansion and contraction of pulsating variables can be measured by using the Doppler effect. The lines in the spectrum shift toward the blue as the surface of the star moves toward us and then shift to the red as the surface shrinks back. As the star pulsates, it also changes its overall color, indicating that its temperature is also varying. And, most important for our purposes, the luminosity of the pulsating variable also changes in a regular way as it expands and contracts.

Cepheid Variables

Cepheids are large, yellow, pulsating stars named for the first-known star of the group, Delta Cephei . This, by the way, is another example of how confusing naming conventions get in astronomy here, a whole class of stars is named after the constellation in which the first one happened to be found. (We textbook authors can only apologize to our readers for the whole mess!)

The variability of Delta Cephei was discovered in 1784 by the young English astronomer John Goodricke (see John Goodricke). The star rises rather rapidly to maximum light and then falls more slowly to minimum light, taking a total of 5.4 days for one cycle. The curve in Figure 19.9 represents a simplified version of the light curve of Delta Cephei.

Several hundred cepheid variables are known in our Galaxy. Most cepheids have periods in the range of 3 to 50 days and luminosities that are about 1000 to 10,000 times greater than that of the Sun. Their variations in luminosity range from a few percent to a factor of 10.

Polaris , the North Star, is a cepheid variable that, for a long time, varied by one tenth of a magnitude, or by about 10% in visual luminosity, in a period of just under 4 days. Recent measurements indicate that the amount by which the brightness of Polaris changes is decreasing and that, sometime in the future, this star will no longer be a pulsating variable. This is just one more piece of evidence that stars really do evolve and change in fundamental ways as they age, and that being a cepheid variable represents a stage in the life of the star.

The Period-Luminosity Relation

The importance of cepheid variables lies in the fact that their periods and average luminosities turn out to be directly related. The longer the period (the longer the star takes to vary), the greater the luminosity. This period-luminosity relation was a remarkable discovery, one for which astronomers still (pardon the expression) thank their lucky stars. The period of such a star is easy to measure: a good telescope and a good clock are all you need. Once you have the period, the relationship (which can be put into precise mathematical terms) will give you the luminosity of the star.

Let’s be clear on what that means. The relation allows you to essentially “read off” how bright the star really is (how much energy it puts out). Astronomers can then compare this intrinsic brightness with the apparent brightness of the star. As we saw, the difference between the two allows them to calculate the distance.

The relation between period and luminosity was discovered in 1908 by Henrietta Leavitt (Figure 19.10), a staff member at the Harvard College Observatory (and one of a number of women working for low wages assisting Edward Pickering, the observatory’s director see Annie Cannon: Classifier of the Stars). Leavitt discovered hundreds of variable stars in the Large Magellanic Cloud and Small Magellanic Cloud , two great star systems that are actually neighboring galaxies (although they were not known to be galaxies then). A small fraction of these variables were cepheids (Figure 19.11).

These systems presented a wonderful opportunity to study the behavior of variable stars independent of their distance. For all practical purposes, the Magellanic Clouds are so far away that astronomers can assume that all the stars in them are at roughly the same distance from us. (In the same way, all the suburbs of Los Angeles are roughly the same distance from New York City. Of course, if you are in Los Angeles, you will notice annoying distances between the suburbs, but compared to how far away New York City is, the differences seem small.) If all the variable stars in the Magellanic Clouds are at roughly the same distance, then any difference in their apparent brightnesses must be caused by differences in their intrinsic luminosities.

Leavitt found that the brighter-appearing cepheids always have the longer periods of light variation. Thus, she reasoned, the period must be related to the luminosity of the stars. When Leavitt did this work, the distance to the Magellanic Clouds was not known, so she was only able to show that luminosity was related to period. She could not determine exactly what the relationship is.

To define the period-luminosity relation with actual numbers (to kalibreer it), astronomers first had to measure the actual distances to a few nearby cepheids in another way. (This was accomplished by finding cepheids associated in clusters with other stars whose distances could be estimated from their spectra, as discussed in the next section of this chapter.) But once the relation was thus defined, it could give us the distance to any cepheid, wherever it might be located (Figure 19.12).

Here at last was the technique astronomers had been searching for to break the confines of distance that parallax imposed on them. Cepheids can be observed and monitored, it turns out, in many parts of our own Galaxy and in other nearby galaxies as well. Astronomers, including Ejnar Hertzsprung and Harvard’s Harlow Shapley, immediately saw the potential of the new technique they and many others set to work exploring more distant reaches of space using cepheids as signposts. In the 1920s, Edwin Hubble made one of the most significant astronomical discoveries of all time using cepheids, when he observed them in nearby galaxies and discovered the expansion of the universe. As we will see, this work still continues, as the Hubble Space Telescope and other modern instruments try to identify and measure individual cepheids in galaxies farther and farther away. The most distant known variable stars are all cepheids, with some about 60 million light-years away.

Voyagers in Astronomy

John Goodricke

The brief life of John Goodricke (Figure 19.13) is a testament to the human spirit under adversity. Born deaf and unable to speak, Goodricke nevertheless made a number of pioneering discoveries in astronomy through patient and careful observations of the heavens.

Born in Holland, where his father was on a diplomatic mission, Goodricke was sent back to England at age eight to study at a special school for the deaf. He did sufficiently well to enter Warrington Academy, a secondary school that offered no special assistance for students with handicaps. His mathematics teacher there inspired an interest in astronomy, and in 1781, at age 17, Goodricke began observing the sky at his family home in York, England. Within a year, he had discovered the brightness variations of the star Algol (discussed in The Stars: A Celestial Census) and suggested that an unseen companion star was causing the changes, a theory that waited over 100 years for proof. His paper on the subject was read before the Royal Society (the main British group of scientists) in 1783 and won him a medal from that distinguished group.

In the meantime, Goodricke had discovered two other stars that varied regularly, Beta Lyrae and Delta Cephei , both of which continued to interest astronomers for years to come. Goodricke shared his interest in observing with his older cousin, Edward Pigott, who went on to discover other variable stars during his much longer life. But Goodricke’s time was quickly drawing to a close at age 21, only 2 weeks after he was elected to the Royal Society, he caught a cold while making astronomical observations and never recovered.

Today, the University of York has a building named Goodricke Hall and a plaque that honors his contributions to science. Yet if you go to the churchyard cemetery where he is buried, an overgrown tombstone has only the initials “J. G.” to show where he lies. Astronomer Zdenek Kopal, who looked carefully into Goodricke’s life, speculated on why the marker is so modest: perhaps the rather staid Goodricke relatives were ashamed of having a “deaf-mute” in the family and could not sufficiently appreciate how much a man who could not hear could nevertheless see.

Go to https://www.bslzone.co.uk/watch/deaf-history/deaf-history-john-goodricke to see a short video on the life and work of John Goodricke, which is part of the “Deaf History” series and set up so both hearing and hearing-impaired viewers can enjoy it.

RR Lyrae Stars

A related group of stars, whose nature was understood somewhat later than that of the cepheids, are called RR Lyrae variables, named for the star RR Lyrae, the best-known member of the group. More common than the cepheids, but less luminous, thousands of these pulsating variables are known in our Galaxy. The periods of RR Lyrae stars are always less than 1 day, and their changes in brightness are typically less than about a factor of two.

Astronomers have observed that the RR Lyrae stars occurring in any particular cluster all have about the same apparent brightness. Since stars in a cluster are all at approximately the same distance, it follows that RR Lyrae variables must all have nearly the same intrinsic luminosity, which turns out to be about 50 LSon. In this sense, RR Lyrae stars are a little bit like standard light bulbs and can also be used to obtain distances, particularly within our Galaxy. Figure 19.14 displays the ranges of periods and luminosities for both the cepheids and the RR Lyrae stars.


Astronomy Exam Study

A) is attributed to the gravitational force of black holes.

B) is slowing the expansion of the universe.

C) was suggested by the unexpected rotation speeds of galaxies.

A) a massive non-luminous cloud of material that surrounds the galaxy, providing the dominant source of
gravity in our galaxy.

B) a disproven super-gravity concept once thought to be possible, but contradicted by evidence.

C) a halo component curiously absent in most others galaxies which astronomers have examined.

A) were made in fusion reactions in the core of the Sun.

B) were made from hydrogen and helium interactions in
galactic gas clouds.

C) were generated in hydrogen and helium interactions in the Big Bang.

A) because the stars in the constellations move so slowly—typically about the speed of a snail—that their
motions are not noticeable

B) because the stars in the constellations are not moving

C) because the stars in the constellations all move at the same speeds and in the same directions, so they
don't change their relative positions

A) Nearly every atom from which we are made was once inside of a star.

B) The overall chemical composition of our bodies is about the same as that of stars.

A) the portion of the universe that is not hidden from view by, for example, being below the horizon

B) the portion of the universe that can be seen by the naked eye

C) that portion of the universe that we can see in principle, given the current age of the universe

B) you, Earth, solar system, Local Group, Local Supercluster, Milky Way Galaxy

A) usually maintain an even spacing with each other, much like the planets of the solar system.

B) gradually fall inward to the inner galaxy, where they accumulate in the massive central bulge.

C) each also have their own independent motions (which we cannot easily see in the night sky) as fast as
70,000 km/hour.

A) predict when an eclipse would happen, but not necessarily what type and where it would be visible.
4

B) completely predict every lunar eclipse.

C) predict when they'd see the next total solar eclipse in their area.

A) The phase of the Moon must be new, and the Moon's orbital plane must lie in the ecliptic.

B) The phase of the Moon must be full, and the Moon's orbital plane must lie in the ecliptic.

C) The phase of the Moon must be new, and the nodes of the Moon's orbit must be nearly aligned with
Earth and the Sun.

D) The phase of the Moon can be new or full, and the nodes of the Moon's orbit must be nearly aligned
with Earth and the Sun.

A) tipped toward the Sun, 23-1/2 degrees.

B) tipped toward the galactic center, 23-1/2 degrees.

C) in a direction that traces a cone of radius 23-1/2 degrees, crossing through Polaris and Vega.

A) The Northern Hemisphere is tilted toward the Sun and receives more direct sunlight.

B) Due to Earth's tilt, the Northern Hemisphere is closer to the Sun than the Southern Hemisphere.

C) The Northern Hemisphere is tilted away from the Sun and receives more indirect sunlight.

A) Earth's rotation defines a day.
The cycle of the Moon's phases takes about a week.
Earth's orbit defines a year.
Earth's cycle of axis precession defines a month.

B) Earth's rotation defines a day.
The saros cycle of eclipses defines a month.
Earth's orbit defines a year.
Earth's cycle of axis precession takes 26,000 years.

C) Earth's rotation defines a day.
The cycle of the Moon's phases takes about a month.
Earth's orbit defines a year.
Earth's cycle of axis precession takes 26,000 years.

A) A scientific theory should be based on natural processes and should not invoke the supernatural or
divine.

B) A scientific theory must explain a wide variety of phenomena observed in the natural world.

C) A scientific theory must make testable predictions that, if found to be incorrect, could lead to its own
modification or demise.

A) Einstein's theory of relativity has been tested and verified thousands of times.

B) Evolution is only a theory, so there's no reason to think it really happened.

C) I wrote a theory that is 152 pages long.

A) A planet's mass has no effect on its orbit around the Sun.

B) More massive planets orbit the Sun at higher average speed.

C) A more massive planet must have a larger semimajor axis.

A) Both stars are moving away from me, Star A is faster than Star B.

B) Both stars are moving toward me, Star B is faster than Star A

C) Both stars are moving away from me, Star B is faster than Star A.

A) The lead spectrum peak is at a shorter wavelength.

B) The two spectra peak at the same wavelength.

C) The lead spectrum peak is at a longer wavelength.

A) the speed of our solar system orbiting the center of the Milky Way Galaxy, Earth's speed of revolution
about the Sun, Earth's speed of rotation on its axis, the speeds of very distant galaxies relative to us,
typical speeds of stars in the local solar neighborhood relative to us

B) Earth's speed of revolution about the Sun, Earth's speed of rotation on its axis, the speed of our solar
system orbiting the center of the Milky Way Galaxy, typical speeds of stars in the local solar
neighborhood relative to us, the speeds of very distant galaxies relative to us

C) Earth's speed of revolution about the Sun, typical speeds of stars in the local solar neighborhood
relative to us, Earth's speed of rotation on its axis, the speed of our solar system orbiting the center of
the Milky Way Galaxy, the speeds of very distant galaxies relative to us

D) the speeds of very distant galaxies relative to us, typical speeds of stars in the local solar neighborhood
relative to us, Earth's speed of rotation on its axis, Earth's speed of revolution about the Sun, the speed
of our solar system orbiting the center of the Milky Way Galaxy