introducción a la astrofísica · introducción a la astrofísica jorge zuluaga, 1997 tabla de...

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http://urania.udea.edu.co/sites/jzuluaga/pages/libros.rs/files/librosmrq1a/IntroduccionAstrofisicaZuluaga-TOC.html Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido Parte I. Astrofísica Estelar Capítulo 1. Parámetros físicos de las estrellas... 3 - 37 Capítulo 2. Atmósferas estelares... 38 - 79 Capítulo 3. El interior estelar... 80 - 105 Capítulo 4. Evolución estelar... 106 - 141 Parte II. Astrofísica del Medio Interestelar Capítulo 5. La observación del medio interestelar... 144 - 153 Capítulo 6. Física y química del medio interestelar... 154 - 187 Parte III. Astrofísica Galáctica Capítulo 7. La Vía Láctea... 190 - 207 Capítulo 8. Estructura y dinámica de galaxias... 208 - 233 Apéndice A... 232 - 233 http://urania.udea.edu.co/sites/jzuluaga/pages/libros.rs/files/librosmrq1a/IntroduccionAstrofisicaZuluaga-TOC.html [16/11/2009 05:38:25 p.m.]

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Page 1: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

http://urania.udea.edu.co/sites/jzuluaga/pages/libros.rs/files/librosmrq1a/IntroduccionAstrofisicaZuluaga-TOC.html

Introducción a la Astrofísica

Jorge Zuluaga, 1997

Tabla de Contenido

Parte I. Astrofísica Estelar

Capítulo 1. Parámetros físicos de las estrellas... 3 - 37 Capítulo 2. Atmósferas estelares... 38 - 79 Capítulo 3. El interior estelar... 80 - 105 Capítulo 4. Evolución estelar... 106 - 141

Parte II. Astrofísica del Medio Interestelar

Capítulo 5. La observación del medio interestelar... 144 - 153 Capítulo 6. Física y química del medio interestelar... 154 - 187

Parte III. Astrofísica Galáctica

Capítulo 7. La Vía Láctea... 190 - 207 Capítulo 8. Estructura y dinámica de galaxias... 208 - 233

Apéndice A... 232 - 233

http://urania.udea.edu.co/sites/jzuluaga/pages/libros.rs/files/librosmrq1a/IntroduccionAstrofisicaZuluaga-TOC.html [16/11/2009 05:38:25 p.m.]

Page 2: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

Page 3: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido
Page 4: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 8: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 12: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 17: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 26: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 27: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 28: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 31: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 35: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 36: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 43: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 44: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

S = B (T )λ λ 1

S = B (T )λ λ 2

S = B (T )λ λ 3

S = B (T )λ λ 4

T1

T2

T3

T4

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I v "

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θ

θ

Superficie Estelar

τλ τλs

ATMÓSFERAESTELAR

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Page 46: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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V g ? 8J=>L j g . ?¯8;=IL j . >1? g ?j g . ?¯8;=IL j . ? g ?9j g . ?¯8J=>L j

8J=>?@7UAJ7UFKC Q h97UAJMN7U[KSN=>8Iv

V g >1? g ?jJj g . ?8J=>L!Uj . >? g ? j g . ? 8J=>L!Uj V g ?8;=IL j . ? g ?j g . ?¯8J=>L j V g ?8;=IL Uj

V g >? g ?j g . ?8J=IL UjBj . ? g ?9j g . ?8J=>L!Uj V g ?8;=IL j

' McMNF|:B=>AB7UZ Q 8L Q F SPr Z5MW:B=>8+=IF ? ? g GKF ?KGKF|: Q LIG@7USW\^GKMN=>AB7_=IF =>SMWF^:J=IA;M Q AzCK=XST779:BZ~PQ 8i=IAB7js ? v Q [b:B=IFE=IZ Q 8=ISAJ=>8JGKS:<7UC Q v

>1? g ? j

? g ?j g . ? . ? p8J=IL Uj V g ?8;=IL j g bk j8CK=yFHGE=I8;:JA Q MNF|:B=>AHP=I8?@79A;:pPr LIGKSN7UAVL Q F Q LI=IASN7 Q AJZu7'CK= >?5=IFRST7 8JGK?O=IAi@LIMW=Uv%Mk =UkDCE=>:B=>AJZ5MNF@79A>? g ? Ujak&VMWL<Y@7DMNF|:B=>FK8JMWC@7UCqv@=>FohHMNAi:BGKC-CK= bk vK=I8i:°P7yC@7UC@7D? Q AIv

>? g Uj

? g ?9j g . ?¯8J=>L j V g ? 8J=IL Uj g bk j

¬%7/7UF|:B=>AJM Q A_=IL>G@7ULIMpPQ Fx=a`b?KA;=I8B7GKF@7tGKFEC@7UZ5=IF|:<7USwAJ=ISN7ULIMpPQ F=>F^:JAJ=-GKF@7/LI7UF|:BMNCK7UC\^GK=o7UCKZ5MW:B=GKF@7XZ5=ICKMWC@7V?KA;=ILIMW8B7 g SN7VMNF|:B=>FK8JMWC@7UCD=>8J?O=ILUPr @Lp7CK=ST7AB7UCKMN7ULIMpPQ FD?KA Q hU=IFKMW=IF|:B=CK=SN74=I8i:BAJ=>SNSN7|j s SN7GKFKL>M"PQ FyCK=GE=IF|:B=9vH=>8;:B7xPGKS:BMNZu7EvCK=17U[K8 Q SNGb:<7VAJ=>SN=ahU79FKLIMN7V=IF5ST7VCK=a:B=IA;ZuMWF@7UL>M"PQ F_CE=1SN74=I8i:BA;GKL>:JGKAB7 `Cc g3~c1d_tuyxc3y.yxo `uc cehoihtucos`Cccep g bqoipcko epor`ucTid_ipod_o cT`Losxo_epipc3iIors`Cc Otuhcho nLc3d_o1ehoIg1ihtudrc3orseho1

tCs~yzo sxtCy~cTorseho|1ipc3s~yzod_oipdcc.hw~c3ho 1Lg1iNo;epcicIg1svw~s~cxipgTbqwxs~yxtCyxc1y g1zehtudrc.wxoeptos~yzo c sxg.tCx`CtCdcwxs~cOtCsxors~pcxipgTbqwxs yxc3y`CtsxocT` ~htsxg wxo cTidrcv`CcLc3hoyxo`uc cep g1;bqorico epor`ucTi

Page 47: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

I v

I (0, )λ θ

I (0, /2) = aλ λπ

I (0, /2) = a + bλ λ λπ

¯MWGKAB7m bk ² $&VMN8;:JAJMW[KGKLIMpPQ FDCK=1ST7=IFK=>AJKPr 7=>FGKFuY@7UCK=1AB7UCEMT7UL>M"PQ Fy\^GK=4=>Zu=>AJ=? Q A+ST78JGK?O=IAi@LIMW=CK=ST7_=>8;:JAJ=ISWST7EkCK=a:<7USWST7UC@7CE=zSN779:BZ~PQ 8;=>AB7=>8;:B=>ST7UA>km8pPr ?KGK=>8GEF?KA Q L>=I8 QQ [E8J=IAih97ULIM Q F@7US g ST7Z5=ICKMWC@7fCK=>? g

j;jF Q 8C@79A@P7_@F@7USWZu=>F|:B=XMNFb Q AJZu7ULIMpPQ F'8 Q [KAJ=SN7_MNF Q [E8J=IAih97U[KSN=X=>8;:JAJGKLa:BGKAJ7uCK=ST7D7:BZ~PQ 8;=>AB7D=I8i:B=ISN7UAIkF=>8;: Q AJ7UCKMNLI7D=ISqh97US Q ACK= bk k¬%7UZ5=IF|:<7U[ESN=IZ5=IF|:J=_ST7A;=ISN7ULIMpPQ Ft=IF|:JAJ=!>? g

j s ?yF Q =I8X:B7UF/CKMNA;=ILa:<7'L Q Z Q 8;=yF Q :<7'=>F Hk k

7¯79AB7u§7UL>MNSWMW:<79Af=IS¯=>8;:B7U[KSN=>LIMWZuMW=IF|: Q CK=GKFK7L Q FE=a`bM"PQ F/=l`b?KS®Pr LIMW:B75=>F|:BAJ=y79Z_[@7U81Lp7UF|:JMNC@7UCE=I8V=>S)7U8:BA Q iPr 8;MNL Q MWF^:JA Q CKGKL>=GKF@78J=IA;MN='CE=8JGE? Q 8;MNL>M Q FK=>8:J=PQ A;MNLp798 s 8JMWZu?KSWMW@LI7ULIM Q FK=>8\^GK=SN=5?c=>AJZ5MW:B=>F? Q A=¡;=IZ5?KS Q A;=ICKGKL>MNA1ST7yMNF|:B=>AB79S=IFtSN75A;=IST79LIM"PQ FoL>MW:B7UC@7Ek 1F@7uCE==>SNST79879CKZuM:B=X? Q A1=;=IZ5?KS Q SN7? Q 8JMW[KMNSWMNC@7UCuCK=GKF@7yCK=I?O=IFECK=IFKL>MT75=a`b?KSPr LIM:<7_CK= ?L Q F ?CK=ST7 Q A;Z7 ) v? ?Z? ?

' M°MNF|:JA Q CKGKLIM Q Z Q 8+CKMNL<Y@7CK=I?O=IFECK=IFKL>MT7=>F bk v^GKF'?EA Q LI=I8 Q 8;MNZ5?KSN=CK=MNF|:B=>AB7UL>M"PQ Fv:BMN=>FK=1L Q Z QAJ=>8JGKS:<7UC Q v>1? g

Uj ? ZT? L Q 8 g Hk " j

¬%7CK=>?c=>FKCK=IFELIMT7GEFKLIM Q F@7US%CK=[>1? g jL Q F]=ISDP79FKGKS Q CK=>8JCK=_=>S¯\^GK=_8;= Q [K8;=IAihU7uGKF/Y@7U8B7USWMN=IF|:J=CK=>8JCK=ST78JGK?O=IAi@LIMW=/CK=/ST7n=>8;:JAJ=ISWST7 g h=>A'@GKAJ7 bk ² jlv1L Q F|:BMW=IFK=>ST7U8'LI7UF|:BMWC@7UCK=>8 ? s T?R\^GK=CK=a:B=IA;ZuMWF@7UAJ7UFu=>F PGKS:BMNZu7VMNFE8;:<79FKLIMN7L>G@7US°=I8=IS@h97US Q A+CK= ?7LIG@7USW\^GKMN=>A? Q A;GEFKCKMNCK7UC­PQ ?E:BMWLp7=IF=ISO8J=>F Q CK=ST77:BZ~PQ 8;=>AB7=I8;:J=ISN7UAIk ' Mc7U8;GKZuMWZ Q 8zSN7L Q FKCKMWLIM"PQ FuCK=V¬b¤ g ¬ Q Lp7US°¤fYK=>AJZ Q C s F@79ZuMWL\^GKMNSWMN[KA;MNGKZjavH8JGK? Q FK=>Z Q 81=>F|: Q FKL>=I8\HGE=/? ? g ! javKCE=Z Q C Q \^GK==>S L Q F Q LIMWZu=>F^: Q CK=GKF@7CK=>?c=>FKCK=IFELIMT7CK= L Q FnST7o?KA Q GKFKCKMWC@7UC PQ ?E:BMWLp7Ev F Q 8?KA Q h=>=IAJ7tCK=SN7oCK=>?c=>FKCK=>FKLIMN7]CK=¤ L Q FCKMWL<Y@7DLp7UF|:BMWC@7UCWkFL Q FKL>SNGK8;M"PQ F-ST7DZ5=ICKMWC@7_CK= >? g jlvK=IFoST7y7U?EA Q `bMNZu7ULIMpPQ F'CK=GKF@7579:JZ­PQ 8i=IAJ7y?EST7UF Q ?@79AB7USW=IST7s L Q Fn¬H¤v%F Q 8C@7-=IS+?O=IAi@S+CK=D:B=IZ5?O=IAB7:BGKAJ7U8=>F=>S+8J=IF Q CK=5ST7 Z5MN8JZu7Ek5F=>8;: Q AB79CKMNLI7oSN7MNZ5? Q A;:B7UFKLIMN7CK=F^GK=I8i:BA Q 7UF|:J=IAJM Q A7UFP79SNMN8;MN8>k

^as wxsLc ;odrd_tg3sKg1;ehoihtCg3ihoyzorg epipc3ipcv`Cc-c3`tuyzo 1~sxgLg3`Cg`CcObqw~s~d_tCg3s~c3`tuyxc1y<Lyzo.w~s~chwxLg;tud_tg3sKd_g1go;epc

Page 48: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

θ

θ

Limbo

Centro

¯MNUGKAB7! bk $@=IFfPQ Zu=>F Q CK=IS Q 8;LIGKA;=I8;LIMNZ5MN=>F|: Q CK=ISSWMNZ_[ Q =>8;:B=>ST7UA>k7=>A Q v LPQ Z Q Zu=>CKMNA>1? g

j k Q FK8;MNCP=>AJ=>8J=_SN758;MW:BGK7ULIMpPQ F]CK=ST7D@GKAJ7 bk vO=IFtSN75\^GK=8J=_YK7uAJ=>?KAJ=>8J=>F^:B7UC Q GKFK7=I8i:BAJ=>SNSN75L>G s 78JGE?c=>A;@L>MN=z=I8¯A;=I8 Q SNGK[ESN=Uv=I8i: Q =I8 GKF@7=>8;:JAJ=ISWST7f\^GK=wF Q hU=IZ Q 8L Q Z Q GKF?KGKF|: Q k G@7UFEC Q CKMWAJMWMNZ Q 8F^GK=I8i:BAJ7Z5MNAJ7UC@7V79SELI=>F|:BA Q CK=wST74=>8;:BA;=ISWST7EvSN74AB79CKMT7UL>M"PQ F\^GK=hHMN=IFE=fCK=7USNSPr :B=IFECKA@P7VGKFK7MWF|:B=IFE8JMNCK7UC=I8;?c=>LPr @Lp7Ev@=>FhHMNAi:BGKC-CK=X bk#" v@MNUG@7USq7bv

>? g ' Y P j ? Z?

7US ZuMWAB7UA1Y@7UL>MT75=IS¯[ Q A;CK= Q SWMNZ_[ Q CK=ISCKMN8;L Q 7U?@79AJ=IF|:J=_CK=_SN7u=I8i:BA;=ISNSN7EvOST7uMWF|:B=IFE8JMNCK7UC/=I8;?c=>LPr KLp7CK=ST7_AJ7UCKMN7ULIMpPQ F':B=>FKCK=IAKP7u79SqhU79S Q A>v>? g

E j ?

=IFoGKF@7y8JM:BG@79LIM"PQ F MNF|:B=>AJZ5=ICKMN7_8J=h=IA;MW@LI75\^GK=9v>? g

E j >1? g

Y P~E V j >? g

' Y P j

=I8i: Q =>8Iv=>S¯CKMW8JL Q CK=SN7u=>8;:BA;=ISWST779?@7UAJ=>LI=>A@P7'8JGE?c=>A;@L>MT7USWZu=>F^:J=Z5=IF Q 84[KA;MNSNSN7UF|:B=7US7ULI=>AJLI7UAJF Q 8X78JGoSNMWZ_[ Q k8;:J=y=>FPQ Z5=IF Q A;=ILIMW[c==ISF Q Z[KAJ=DCK= ª "aHB<a¦D38@ ª :Ha¢¯¢ ¦ ª <a a¢£U s 8JG Q [K8;=IAihU79LIM"PQ FR=>8=IS_PGKFEMNL Q LI7UZ5MNF Q =>FSN7yCE=>:B=>AJZ5MNF@79LIM"PQ F CK= >? g jlk

&V=I[O=u7UF Q :B7UAJ8;=\^GK==>S Q 8JLIGEAJ=IL>MNZ5MN=>F^: Q CK=>SSWMNZ_[ Q =I8i:B=>ST7UA>v¯\^GK='L Q AJA;=I8J? Q FKCE='7GEFn=IFPQ Zu=>F QLISN7UAB79Zu=>F^:J= Q [E8J=IAih97UC Q ? Q AV=;=>Zu?KS Q =>FR=>S)Lp798 Q CK=DF^GK=>8;:BA Q ' Q S g =IA4KGKAB7 bk jlvqF Q =I84GKF@7L Q FKLISWGK8JMpPQ F =a`bLISWGK8JMh97_CK=XST7 Q AJZu7CK= >5C@7UC@7_? Q A bk#" vb?@7UAB7ST7 Q [b:B=IFELIM"PQ FoCE=VST7L>G@7USq8;=XYKMN QGKF@78JGK? Q 8;MNLIMpPQ F58 Q [KA;=SN7V Q AJZu7X=a`b?KSPr LIM:<7XCK=1ST7CK=I8;L Q F Q LIMWC@7XGKFKLIMpPQ F fk G@7USN\^GKMW=IA Q A;Z7X\^GK=7UC Q ?E:B= vOCE=I[O=IA@P798JMN=>Zu?EAJ=?EA Q CKGKLIMWAGKF@7F>1? g j?@7UAJ7uSN75L>G@7US>? g ' Y P j >? g E jlk7GK=>CK=CK=>Z Q 8i:BAJ7UAJ8;=_\^GK=_=I8i: Q 8;=_8B79:JMN8i§7ULI=8JM ­=>8VGKF@7uGEFKLIMpPQ FtLIA;=IL>MN=IF|:J=DCK=SN7u?KA Q GKFKL>MNC@7UC©PQ ?E:BMWLp7Ev\^GK=D=IF/SN7'7U?KA Q `EMWZ79LIM"PQ Ft¬b¤ =I\^GKMh97USN=7'8JGK? Q FK=>AV\^GK=DST7u:J=IZ5?c=>AB79:JGKAB7uLIAJ=>LI=DY@79LIMT77UCK=IF|:JA Q

Page 49: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

I v |²

¯MNGEAB7! bk $ Q : Q AB79Pr 7CK=>S ' Q S=IFo=ISqhHMW8JMN[ESN=UkCK=ST7579:BZ~PQ 8;=>AB7Ev°YK=>L<Y Q \^GK==I84L>ST7UAJ7UZ5=IF|:B= Q [|hHM Q =>FtST7y8JM:BG@79LIM"PQ FCK=GKF@7u79:BZ~PQ 8;=>AB7yF Q A;Z7US k=>CKMNC@7981?EAJ=IL>MN8J7U8CE=IS Q 8;LIGKA;=ILIMWZuMW=IF|: Q CK=>S%SNMNZ[ Q 8 Q ST79AfY@7UFo8JMNC Q YE=IL<Y@7U81=IFoh97UAJMN7U8S Q FKMW:JGKCK=>8CK= Q FEC@7EkFD: Q C Q 8S Q 8)Lp798 Q 8+8J=fhU=IAJM@Lp7XSN74hU79SNMNCE=IwCE=1SN74AJ=>ST7UL>M"PQ F bk#" vS Q \^GK=CK=IZ_GE=I8;:JAB7X\^GK==ISZ Q CK=IS Q SNMWFK=p7US8JGK?EGK=I8i: Q ?@7UAB7 ?uAJ=I?EAJ=I8;=IF|:<7-GKF@7-[KGK=>F@7o7U?KA Q `bMNZu7UL>M"PQ F/7 SN7'CK=I?O=IFKCE=IFKL>MT7AJ=I7USqCK==>8;:<7yLp79F^:JMNC@79C L Q FoST7_?KA Q GKFKCEMNC@7UC PQ ?E:BMWLp7Ek+FoGKFo7U?@7UAi:<7UC Q ? Q 8i:B=IA;M Q A>vKST7h97USWMNCK=>VCK=>SZ Q CK=>S Q \^GK=>C@7UA@P7yCK=>Z Q 8i:BAJ7UC@7y7D?@7UA;:JMNAfCK=7UA;GKZ5=IF|: Q 8iPr 8JMWL Q 8>k G@7UFEC Q F Q =>8? Q 8JMW[KSN=5AJ=>8 Q Sh=>AST7o8JGK?O=IAi@LIMW=CK=ST7-=I8;:JAJ=>SNST7bv: Q C@7oMNFE Q A;Z79LIM"PQ FR8 Q [KA;=ST7oCKM AJ=>LIL>M Q F@79SNMNCK7UCuCE=4ST7MNF|:B=>FK8JMWC@7UC'=>8J?O=ILUPr @LI7_8J=4?EMN=IA;CK=Uv s S Q \^GK=4AJ=IL>MN[O=IF'F^GK=>8;:JA Q 8MWFK8;:JAJGKZ5=IF|: Q 8AJ=>8JGKS:<7CK=4GKFK78JGE?c=>AJ? Q 8JMWLIM"PQ FCK=ST7=IFK=>AJ@Pr 7?KA Q hU=IFKMW=IF|:B=CK=I8;CK=VCKMW8;:JMNF|: Q 8z?KGKF|: Q 8wCK=ST78JGK?O=IA@L>MN==I8i:B=ISN7UAIkF-=I8;:J=XLp7U8 Q F Q MNZ5? Q A;:<7? Q Aw:<7UF|: Q L Q F Q LI=>AST7=IFK=>AJ@Pr 7_\HGE=X=I8f=IZ5MW:JMNC@7=IF-GKF@7_CE=>:B=>AJZ5MNF@79C@7CKMWAJ=IL>LIMpPQ F]CK=>8JCK=DGEFt?KGKF|: Q CE=ST758JGK?O=IAi@LIMW=_=I8i:B=>ST7UA>k48VCK=F^GK=I8i:BA Q MWF|:B=IAHP=I8X79Y Q AB75L Q F Q L>=IAVSN7Lp79F^:JMNC@79C: Q :<7US+CK=u=IFK=>AJ@Pr 7\^GK=uKG s ='YK7ULIMN7]79GK=>AB7oCK=I8;CK='ST7o8JGK?O=IAi@LIMW=CK=uST7-=I8i:BAJ=>SNSN7 s \^GK=AJ=>8JGKS:<7CK=4SN7X8JGKZu7CK=>SO7U? Q A;:B==>FK=IA;¯P=>:JMNL Q CK=1ST7U8 Q FKCK7U8w\^GK=18B7USW=IFu=IFu: Q CK7U8CEMNAJ=>LIL>M Q FK=>8Ik8i:<7=IFE=IAJKPr 7 =I8i:°P7-LIG@7UF|:JMW@LI7UC@7-? Q AX=>SCK=IF Q ZuMWF@7UC Q KG Q AB7UCKMN79:BMh Q v\HGE=u8;=5CE=>@FKM Q =>FSN7'8J=>LILIMpPQ F

rorsOcT`C|3wxs~c1<o;ehipor`C`uc3Ros`uc3 1w~o `uc cep g1;bqoric;o o.QehtCors~yxo ~c3ipcbqg3ipc3iR`uc yzosxg3tCs~c3yxcd_ipg3g1;bqoricxcTwxsL1w~o`uc d_g1s~yztud_tg3syxo wxs yzodrihod_tCorseho n~c3drtCccTbqwxoric ho pceptC;b#c3droaorsO;w~cTiheho c1ItCsehoihtCg3ioso ec4wx`ehtC cors -1g3`ehwxicor`|3ic3yxtos1epoyzo eporLoipcTehwxic hotCs-QtCoriheho [`uc d_g1s~yztud_tg3s orsLd_tCg3s~c1yxc yzo;c4yzodrwxx`tCi;o1QtCs orLcTip|3g `ucdrc3sehtuyxc3yKyzoic3yxtCc1d_tg3sors or` ipc3sx|3g-Qtu;tCx`Co.xihgzdroyzos1epoyzoyztudn~c os -3g3`ehw~ipcOoepcTs owxos c d_g1OLcTic3yxcd_g1s`ucwxoO``Cor|cyzoO`Cc1 os -3g3`ehw~ipc1tCs1eporiptg1iho c1 ipor|1wx`Cc3ihorwxovo`bqorsg1OosxgKyzor` g1pd_w~ihod_tCOtCorsepgyzor` `CtvLgKhoht|1wxoc3sxtbqo;epcTsLyzg~

Page 50: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

%

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Page 51: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

I v '! !g |j

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Page 52: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

Iout

Iin

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Page 54: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

Iλο

s=0 s=s

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Espectroscopio

CUERPOABSORBENTE

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Page 55: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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m8JGKZ5MN=>FKC Q / ?nMNFKCK=>?c=>FKCKMW=IF|:B=RCK=RST7?KA Q GKFKCKMWC@7UC SNMNFE=p7US vSN7x?EA Q GKFECKMNC@79C PQ ?b:BMNLI7e8;=?KGE=ICK=R=I8;LIAJMW[KMNA ? / ? , J k m8JGKZ5MN=>FKC Q 7UCK=>Z­P7U8-?@79AB7=ISVL>GK=IA;? Q GKF@7x8JM:BG@79LIM"PQ F CK==>\HGEMNSNMW[KAJM Q :B=>AJZ Q CEMNFP7UZ5MNL Q v^Mk =Uk? ? g ! # jlv@ST7_A;=IST79LIM"PQ F-7UF|:B=IA;M Q Af\^GK=>C@7Ev>? g , J j / ? ? g ! # j

FL Q FKL>SNGK8;M"PQ F s L Q Z Q 8J=hU=4=>FST77UF|:B=>AJM Q A+=a`b?KAJ=>8JMpPQ FqvHST7AB7UCKMN7ULIMpPQ FD8B79SNMN=>F|:B=1CK=IS°LIGE=IAJ? Q:JMN=IFE=_GKF?c=>A;@S¯=I8J?O=ILa:BAJ7US g CK=>?c=>FKCK=>FKLIMN7-CE= >L Q F @cj\^GK=DA;=I?KA;=I8;=IF|:<7oST78;GK?c=>AJ? Q 8JMWLIMpPQ FCK=>S?c=>A;@S1CK=oGKF~L>GK=IA;? Q FE=IA Q L Q F~ST7/:B=>Zu?O=IAJ79:BGEAB7CK=SN7RZu79:J=IAJMN7/\HGE=t79:JAB7phHMN=I8J7SN7AJ7UCKMT79LIM"PQ F g 7U?KA Q `bMWZ7UCK7UZu=>F|:B=ST7yZuMW8JZu7_=IF]: Q CK7U8?@7UA;:J=I8Bj s CK=>S?O=IAi@S%CK=8;G Q ?@79LIMNCK7UCg =IA@GKAJ7 bk#" jlk Q A;AJ=>8J? Q FKCK=1=I8i:B=1Lp7U8 Q 7ST7V?EA Q CKGKLIL>M"PQ FyCK=GKF5=I8;?c=>L>:JA Q CK==IZ5MN8JMpPQ Fqk]PQ :B=>8J=5\HGE=5SN7 8JMW:JG@7UL>M"PQ FL Q FK8JMWCK=IAJ7UC@7Ev%?@7UAJ7 ST7 \^GK=u8;=yCK=IZ Q 8;:JA Q 7U?@7UA;=IL>=5GEF=>8J?O=IL>:JA QCK==IZ5MN8;M"PQ Fqv|L Q MNFELIMNCE=L Q F'ST78JGE?KGK=I8i:<7_=>F'ST7AJ=I8;?c=>L>:JMWh97SN= s =I8;?c=>L>:BAJ7US\^GK==I8i:<7U[KSW=IL>=4\^GK=¥7U8J=>8 g Zu79:B=>AJMN75? Q L QQ ?K7ULp7|j=IF/=>ZuMW8JM"PQ FqvO7GKF@7u:J=IZ5?c=>AB79:JGKAB7uC@7UC@7 ! # 8 Q [KA;=_S Q 81\^GK=F Q MWFKLIMWCK=XAB7UCEMT7UL>M"PQ F =l`b:J=IA;M Q A>vK?KAJ=>8J=>F^:B7UFtGKFo=I8;?c=>L>:JA Q L Q Z Q =ISCK=>8JLIA;MW: Q k 0 ? " g ]79:J=IA;MT7_Z_G s'Q ?@7ULI7|j=>Fu=>8;:B=LI7U8 Q g . ?Uj2 k)m8JGKZ5MN=>FKC Q =I\^GKMWSNMN[EAJM Q :B=IA;Z Q CKMWFP7UZ5MNL Q : Q :B7USv bk#" \^GK=ICK7Ev

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>1? ? ? g"!$# j8 CK=IL>MNA%ST7fAB79CKMT7UL>M"PQ F=>Zu=>AJ=>F^:J=z:JMN=>FK=+=IS|=I8;?c=>L>:JA Q CK=+GKFLIGK=>AJ? Q FK=>A Q 7ST7:B=>Zu?O=IAJ79:BGKAJ7CK=>SKLIGE=IAJ? Q =IFyLIGE=I8;:JM"PQ Fv|=I8CK=>LIMNA=>SK=I8;?c=>L>:JA Q CK=fST7SNGKf=>ZuM:BMNCK7=I8GEF5=>8J?O=ILa:BA Q L Q F|:BMNF^G Q k&V=XF^GK=ah Q =>SAJ=>8JGKS:<7UC Q =IZ5?Pr AJMNL Q CK=ST7D=>8J?O=IL>:JA Q 8;L Q ?qPr 7y8J=AJ=>?KA Q CKGKL>==>F=>8;:B=Lp798 Q k

bk>1? # v M k =9k)=ISL>GK=IA;? Q =I8i:°P7y[@7 F@7UC Q ? Q AfAB79CKMT7UL>M"PQ F =l`H:B=IA;M Q A&V=XF^GK=ah Q C Q 88 Q FoS Q 8f? Q 8;MN[KSW=I8fLp798 Q 8=IFo=I8i:<758JMW:JG@7UL>M"PQ F+$/10 ? "¬%7D8JM:BG@7UL>M"PQ F-=>81MWCP=IF|:JMNLp7y7 "p[qkS+=I8;?c=>L>:BA Q ?KA Q CEGKLIMWC Q =I8GKFn=>8J?O=IL>:JA Q L Q F|:BMWF^G Q k'S?KA;MNFKL>MN?@79S7U? Q A;:J=u79SL Q F|:BMWF^G Q S QY@79LI=-=ISZ5=ICKM Qts ST7tL Q F^:JAJMW[KGKLIMpPQ Fe\HGE=Y@79LI=-ST7/AB79CKMT7UL>M"PQ F=l`H:B=IA;M Q AyCK=>8B7U?K7UAJ=>LI=o? Q AySN7GK=>A;:J=79[K8 Q A;LIMpPQ Fqk8;:B7'8JM:BG@7UL>M"PQ F]AJ=I8;GKSW:B7CK=_F^GK=>8;:JA Q L Q Z5?KSW=>: Q MNF|:B=>AHP=I84C@7UC Q \^GK=D?EGK=ICK=D8;=IA7U8;MNZ5MNSN7UC@7y7SN78JM:BG@79LIM"PQ Fu\^GK=V=>FEAJ=>F|:<7UZ Q 8wL>G@7UFKC Q =I8;:JGKCKMN7UZ Q 8SN7F@79:JGKAB79SN=II7CK=ST7SNGK1=IZ5MW:JMNC@7? Q ASN7U8DLp7U?K7U8yZ­P7U8yMWF^:J=IA;M Q A;=I8DCK=-ST779:JZ­PQ 8;=IAJ7/CK=-ST7/=I8i:BAJ=>SNSN7 $-8;=IwPGKFe? Q CK=>Z Q 8_hU=IA;MW@LI7UA? Q A1=IS 7UFP7USWMN8;MN8fCK=F"p[qkfST7yAB79CKMT7UL>M"PQ F-=>ZuM:BMNCK7y? Q A=I8i:<7U8Lp7U?K7U84C Q FKCK=SN7 Q ?@7ULIMWC@7UCo=I8=IF=l`b:JAJ=>Z Q 7USW:B7EvvK7U? Q A;:<7D=>SL Q F|:BMWF^G QuQ [K8J=>A;h97UC Q =IFo=IS=>8J?O=IL>:JA Q CK=ST7D=I8i:BA;=ISNSN7Ek 0 ? "Fo=I8;:J=LI7U8 Q bk " 79C Q ?E:B7ySN7_ Q AJZu7Ev

>1? >1? # Z ? g ? . >1? # j' M8;=C@75\^GK= ? >? # =IF|: Q FKLI=>8SN7_AB7UCKMN7ULIMpPQ F =IZ5MW:JMNC@7:BMN=>FK=ST7 Q A;Z7bv

>1? >? # Z ?? . >1? #

' GE? Q FEMN=IFEC Q 7 / ?tMWFKCK=I?O=IFECKMN=>F^:J=-CK=SN7t?KA Q GKFKCKMWC@7UCPQ ?E:BMWLp7/=ISfA;=I8;GKSW:B7UC Q 7UF|:B=IA;M Q AD8;=L Q F|hbMW=IAi:B==IFqv>1? >? # Z / ? J , ? . >1? #

\^GK=_L Q AJA;=I8;? Q FECK=D7uGEFt=I8;?c=>L>:BA Q CK==>ZuMW8JMpPQ Fqk8;: Q =I8>vq8JM 8 Q [EAJ=GEFtLIGK=>AJ? Q ? Q L Q'Q ?@7UL QMWFKLIMWCK=AB7UCKMN7ULIMpPQ \^GK=:BAB79FK8J? Q A;:B75=>FK=IA;@Pr 75MNFE=>AJM Q A7uSN7u\^GK==>ZuM:B==IS LIGE=IAJ? Q =>FtLIGE=I8;:JM"PQ Fv=>F^: Q FKL>=I8SN7AJ7UCKMT79LIM"PQ F5=>Zu=>AJ=>F|:B=4CE=IS°ZuMW8JZ Q :B=IFECKA@P7vHL Q Z Q =IFu=ISOLp7U8 Q ""7Ek¯GKF=>8J?O=IL>:JA Q=>Fe=>S\^GK= 8J=-8;GK?c=>AJ? Q FK= =>SCP=I[EMNS=>8J?O=IL>:JA Q CK= SN7tAB7UCKMN7ULIMpPQ FMWFKLIMWCK=IF|:B= g 8JGE? Q FE|7UZ Q 8JS QL Q F|:BMNF^G Q j+L Q F'ST7XGK=>A;:B==IZ5MN8;M"PQ FyCK=>ScL>GK=IA;? Q vb\^GK=V78JGhU=IV=>8;:°P7 Q [O=IAJFK7UC@7? Q Az=ISO?O=IA;KSCK= / ? g h=>AKGKAB7 bk ""jak

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I

B (T )λ ο

Continuo Térmico

κλ

Pefil de absorción

Espectro de emisión resultante

¯MWGKAB7! Hk "%"$8J?O=IL>:JA Q CK=XST7_AJ7UCKMT79LIM"PQ F \HGE==>Zu=>AJ=XCE=GEFL>GK=IA;? Q L Q FAJ7UF-=IZ5MN8;M"PQ F s 8 Q [KA;==IS\^GK=MNFELIMNCE=VAB7UCEMT7UL>M"PQ F Z_G s :B=>FHGE=L Q FGEFo=>8J?O=ILa:BA Q L Q F|:JMNF^G Q k7 Q A Q :JA Q ST7UC Q 8JM8J=L>GKZ5?KSN=\HGE= ? >? # ST7uAJ7UCKMN7UM"PQ Fo=IZ5MW:JMNC@7_:J=IFKCKAKP7'GKF@7MWF|:B=IFE8JMNCK7UCC@79C@7D? Q A>v

>? >? # . / ? J , ? . >1? #

C Q FKCK=CK=F^GK=>h Q 8J=Y@7DYK=>L<Y Q SN7_8JGK? Q 8JMWLIMpPQ F-CK=MNFKCK=>?c=>FKCK=>FKLIMN75CK= / L Q F k81=I8;:J==>S%Lp7U8 Q ?@7UAJ75F Q 8 Q :JA Q 8Z~P7U8MNF|:B=>AJ=>8B7UF|:B=9kfF]=>8;:<7y8JM:BG@79LIM"PQ FSN7yAJ7UCKMN7ULIMpPQ F =IZ5=IA=>F|:B=/?KA;=I8J=>F|:<7UAKP7eL>ST7UAJ7U8'?O=IAJCEMNC@7U8 LI7UGK8J7UC@7U8-? Q A'ST7n7U[K8 Q AJLIMpPQ F CK=IS4Zu=>CKM Q g FPQ :J=I8J==>S8;MNF Q Z5=IF Q 8=IFST7-=a`b?KAJ=>8JMpPQ F?@7UAJ7>1?Uj s Q [O=IA;F@7UC@7U8? Q A=>S+?c=>A;@SzCK= / ? g h=>A@GKAJ7 bk#"x jlk)SE=>8J?O=ILa:BA QQ [E:J=IFKMWC Q 8J=>A@P7UGEF5=>8J?O=ILa:BA Q CK=79[K8 Q A;LIMpPQ Fqv|=IFD=>SK\^GK=8 Q [EAJ=f=ISbL Q F|:JMNF^G QCK=ST7uAJ7UCKMN7ULIMpPQ FMWFKLIMWCK=IF|:J=8J=8JGK?O=IA;? Q FECKA@P7UF/GEF@78J=>AJMW=_CK=CE=I?KA;=I8JM Q FK=>8X\HGE=_MNFKCEMNLp79F]ST798? Q 8JMWLIM Q FK=I8fCE=Z~P7`bMNZu7_7U[E8 Q A;LIM"PQ FoCE=ISZ5=ICKM Q k

S7UFP7USWMN8;MN8'79F^:J=IA;M Q A F Q 8 AJ=>hU=ISN7e=>F 8IPr F|:B=>8JMN8-SN7=a`b?KSNMWLp7UL>M"PQ F CE=RSN7F@79:JGKAB7USW=II7CK=ISX=>8J?O=IL>:JA QCK=RST7U8 =>8;:JAJ=ISWST7U8 $e¬%7U8oLp7U?@798oMWF|:B=IA;M Q A;=I8o7US:<7UZ5=IF|:B= Q ?@7ULp798o=>ZuM:B=>F ? Q A U7Ek GKF L Q F|:JMNF^G QCK=a:B=IA;ZuMWF@7UC Q ? Q A%GKF@71:J=IZ5?c=>AB79:JGKAB7Lp79A@P7ULa:B=IAIPr 8i:BMNLI77U8 Q LIMN7UC@7171=>SNST798 g ? Q A=¡;=IZ5?KS Q !g |j;j LIGK7UFKC Q =>8;:<7'AJ7UCKMN7ULIMpPQ Ft79:JAB7phHMN=>8B7'ST7984Lp79?@7U8XZ~P7U84=l`b:J=IA;M Q A;=I8 s :BAB79FK8J?@79AJ=IF|:J=I8 g ? X"j1CK=ST7D7:BZ~PQ 8;=>AB7EvK\^GK==I8i:<7UF7yGKF@7_:B=>Zu?O=IAJ79:BGKAJ7DMNFE=>AJM Q A s \^GK=? Q A:B7UF|: Q =IZ5MW:J=IF AB79CKMT7UL>M"PQ F L Q FZ5=IF Q AXMWF|:B=IFE8JMNCK7UC\HGE=5SN7'=IZ5MW:JMNC@75? Q AXSN7U8XLp79?@7U8XZ~P7U8X?KA Q GKFKC@7U8 g ? >1? # jav8;=5?EA Q CKGKLI=y=>S=IFfPQ Zu=>F Q CK=o7U[K8 Q AJL>M"PQ Fx8J=>SN=>L>:BMh97\^GK=-SW= MNZ5?KAJMWZu=u7USf=I8;?c=>L>:JA Q @F@7USf8;GK8yLp7UAKP7UL>:J=IAIPr 8;:JMNLp798DCK=7U[K8 Q AJL>M"PQ Fk

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Continuo de radiación exterior

κλ

Pefil de absorción

I = I - c k ( S - I )λ λο λ λ λο

I = B (T )λο λ ο

S = B (T )λο λ c

Espectro de absorción resultante

T <Tc o

¯MWGKAB7A Hk "x I$X8J?O=IL>:JA Q CK=DST7'AJ7UCKMN7ULIMpPQ F/\^GK=y=IZ5=IAJU=DCK=yGKFLIGK=>AJ? Q L Q FGKF@7-=IZ5MN8JMpPQ FtZ5=IF Q A7'ST75MNF|:B=>FK8JMWC@7UC/CK=ST7AJ7UCKMT79LIM"PQ F]MNFELIMNCE=IF|:B=9k+8i:B=D=>8X=IS¯LI7U8 Q ?K7UAB7'SN7U84LI7U?@7U8V8;GK?O=IAJM Q AJ=>8VCK=DSN779:JZ­PQ 8i=IAJ7y=>8;:J=IST79AIk .')('* ,"# - - %$&(')*+

FK7yhU=I8;=YK7UF]?KA Q CEGKLIMWC Q 79[K8 Q A;LIM Q FK=I8=>F]GKF@75LIMW=IA;:B75A;=IMpPQ Fo7USNA;=ICK=>C Q ACK=GKF@7yS Q FEMW:JGKC-CK=Q FKCK7_=I8;:B7U[KSW=ILIMWC@7_8 Q [KAJ=X=>SL Q F^:JMNF^G Q CK=XSN7SNGEV\^GK=X=IZu7UF@7CE=ISqMWF^:J=IA;M Q ACK=VST7=I8;:JAJ=>SNST7bvK7U?@79AJ=IL>=8 Q [KAJ=DCKMWL<Y Q L Q F^:JMNF^G Q S Q \HGE=DSNST79Z7UZ Q 8GKF@7 SPr FK=I7=I8;?c=>L>:BAJ7US)CK=y79[K8 Q A;LIMpPQ FqkFRSN7'AJ=>M"PQ F]CK=ST798fS®Pr FE=p7U8=>8J?O=ILa:BAB79SN=I81=ISL Q F|:BMWFHG Q 8;=CE=> Q A;Z7DL Q Z Q S Q ZGK=I8i:BAB7DSN7DKGKAB7 bk " Ek¬ST7UZu7UFKC Q ?y=>S@G Q AB7UCKMN79:BMh Q =IF/ST75S Q FEMW:JGKC]CK= Q FKC@7A@/?KA Q hU=IFKMW=IF|:B=DCK=DSN7u=>8;:BA;=ISWST7 s ?=IS+@G Q \HGE= Q [K8;=IA;h97UA;MT7UZ Q 88JM8@PQ S Q =a`bMW8;:BMW=IAJ7ST7oL Q F|:JAJMN[EGKLIMpPQ FnCK=>SwL Q F|:BMNF^G Q =IZ5MW:BMWC Q ? Q AST798AJ=>M Q FK=I8%Z~P7U8?KA Q GKFKC@7U8 CK=+ST7fZ5MN8;Z7Ev"? Q CK=IZ Q 8L Q FK8;:JAJGKMWA S Q \HGE=zA;=IL>MN[O=z=>S^F Q Z_[KA;=+CK=V<¡@<a ª8 ª l¦5£U¢ "£<: ª ?& ? g h=>A1KGKAB7 bk#" ^jlv s \^GK=8;=IAKP7uCK=7UY Q AJ75=>F]79CK=ISN7UF|:B=FHGE=I8;:JA Q ?KGKF|: Q CK=?@7UAi:BMWC@7D7DST7Y Q AB7DCK=X=I8i:BGKCEMT7UAfSN7_=I8;:JAJGKLa:BGKAJ7 s =IS7UFfP7USNMW8JMN8CK=XST798fS®Pr FE=p7U8=>8J?O=ILa:BAB79SN=I8=>8;:B=>ST7UA;=I8>k' Q [EAJ==IS=>8J?O=IL>:JA Q F Q AJZu7USWMNp79C Q CK=a@FKMWZ Q 8f=>S@a+¢ :H¢£¢<¨= 8J£-<¡@<a §J£U¢ v?|v

? " . ? ?

S?c=>A;@SCE=XST7DS®Pr FK=p7=>8Z­P7`bMWZ Q =>F8;GL>=IF|:BA Q v @ @ #s LIA;=IL>=CE=I8JCE= Y@7U8i:<7? # ?@7UAJ7DSNGK=> QCK=>LIAJ=>LI=>ACK=F^GK=ah Q Y@798;:<7 7yS Q ST79AJ Q CK=X: Q C Q =>S%7UFKL<Y Q AJ=I7USCK=ST7_SPr FK=I7F@kSMNF|:B=>AJM Q ACK=ST7DSPr FK=I7_CK=>@FE==>F=>S?KST79F Q ?& ;? J<S @]GKF P7UAJ=I7y: Q :<7US ? # C@7UC@7D? Q AIv ? #

?

" . ?

? :BAJ7tLp7UF|:BMWC@7UCCK=AJ=ISW=>h97UFKL>MT7t=>F=IS=>8;:BGECKM Q CK= SN7U8_SPr FK=I7U8=>8J?O=IL>:JAB7USW=I8DA;=ILIMW[c==ISF Q Z_[KAJ=CK=7UFKL<Y Q =I\^GKMWh97USW=IF|:B= ?-\^GK='8;='CK=a@FK= L Q Z Q =IS79FKL<Y Q CK='GEFAJ=>L>:°P79FKGKS Q CK= 7US:BGKAJ7GKFEMW:<79AJMT7

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I ²

λ

¯MWGKAB7m bk#" $ 479:JGKAB79SN=II7CK=>S°=I8J?O=ILa:BA Q CK=7U[K8 Q AJLIMpPQ FCE=GKFK7=I8i:BA;=ISNSN7=>FGKFCKMT7UUAB7UZu7VCK=KG QCK=AB79CKMT7UL>M"PQ F L Q F|:BAJ75S Q FKM:BGKC'CE= Q FKC@7Ek

F / Fλ λc

1

λ

∆λ

λo

Wλο

¯MWGKAJ7! bk " $+8;:BA;GKL>:JGKAB75CK=GKF@7DSPr FK=p7_=>8J?O=ILa:BAB79S =>FGoCKMN7UAB79Z7F Q AJZu7USNMWp7UC Q k

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Línea delgada Línea saturada Línea gruesa

F /Fλ λο

λ

¯MWGKAB7! Hk " ² $¤fMN? Q 8fCK=S®Pr FE=p7U8=>8J?O=ILa:BAB79SN=I8>k\^GK=_=>Ft=IS CKMT79AB7UZu7y=I8J?O=ILa:BAJ7US¯F Q AJZu7USNMWp7UC Q =>FKLIMW=IAJAJ7uGKFP79AJ=p75MNGK7US 7uST75CK=SN7uSPr FK=I7Ek7 Q A8JGCK=a@FKMNL>M"PQ Fv

? # " ? #

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Page 64: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 65: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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r = 2ra

r = ra

vt

v

v

Situación original

Situación equivalente

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V "

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Y M H

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Page 67: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 68: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 69: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 70: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 85: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 87: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 88: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 89: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

0 B -0 -0 ! !" " ! : $B<4b62>@?V4G=xB<47=x>QB<>@C K P\47?V>@=2> K >@PR:O47PR>Q=SV>SV:<CvuV4G=HD K 476247=a>QBC@47PRDGH47?SV>QB6^:O=R624 ?1HM CQB<>@4 Z>@BO>@C K PR4G?V>@=:<? K >QPR:<4GPR>@=N q)¥;:<?%BO47=>QB<>QC K P\47?V>Q=5B<:OYhDGSV4G=)a2CQ47?%BUDw=>Q?V>@P\YTHJ DG=6^>QSV:UDw=f:O?h8747B M C@PRDGSTDG=>@?BUDw=5C@4GB<:<=\:<47?c>@=)>@? K P\>yB<47=f:<4G?V>@=>@=C@DG=EHJ :<62F47=\:<]VBO>Z M >t=R>1SV>tC M DGB<Z M :O>@P K :<Fm4oSV>FVPR4;C@>Q=R4xZ M HJ 6^:OC@4VzSV> RDG?VSV42SV>@=\CEDGP K DGSVD2SV>_>Q? K PNDGSVD2B<DFm47=\:<]V:OB<:<SVDGSXCQ47?V=R:OSV>@PRDGSTDcq K P\4~DGPRY M 6^>Q? K 4>@?C@47? K PNDSV>>@= K DFm47=R:O]V:<BO:<STDGS zED M ?_6HDG=I>QBUDG]m47PNDwSV45at>QB7FVP\:<62>@PR4uc:<= K H47PR:OCEDG62>@? K >GzuTDGCQ>oP\>@BUDwC@: H4G?pD2BUD>QTCQ:<>@?cC@:UD2>@?V>QPRYH> K :OCED^Sc>oB<4G=FVP\4CQ>@=\47=1Z M HJ 6^:OC@47=Qq ?FVPR4G6^>QSV:<42F M >QSV>oSV>C@:OPR=\>oZ M >o>Q? M ?TD^PR>EDwC@C@:EH47?pZ M HJ 6^:OCEDF M >QSV>B<:O]>QPNDGP\=R>_SV>QB47P\SV>@?pSV> M ?c47=n: Y7P q *#D26XDG=RDSV>~C@4G6] M = K :<]cB<>?V>QC@>@=RDGPR:<DdFTDwPNDyFVPR4;S M CQ:<PBO47=9G4. : R o>@62: K :<SV47=|F47P)>QBm¥47BTCEDwSTD=\>@Y M ?VSV4=R>QPTHDF47P K DG? K 4:<Y M DwB=9G .[: R ( S q%¥:= M Fm47?V>@6247=Z M >^>QB¥47B>@= K HDuV>@CvuV4n>@? K >QPNDG62>@? K >XSV>QBC@4G6] M = K :<]cB<>1CQ47?V=\:<SV>QPNDGSV4czc= M = . : S F>QPR62: K :<P@HJ DG?2Z M >t]VPR:OB<B<DGPND_C@47?jB<Do62:<=R6^Dd:O? K >@?c=R:<SVDGSFm47P M ?F>QPEHJ 4SV4xSc> M ?V47=-: D+?V4G=@zcBO4xZ M >_>@= K D2>Q?>@? K >QPNDC@47? K PRDGSV:OC@C@:EH47?C@47?BO47=PR>QY7:<= K PR4G=DGP\Z M >@47BEH47Y7:<CQ47=@zTZ M >dF4G?V>@?nF47P.> \>Q6^FcB<4>@B¤47PR:OY7>@?SV>BUDG=~FVP\:<62>@PRDG=~C@:O8;:OB<:<@DGC@:O47?V>Q=@zVZ M >8:O>@P\47?47]h8;:UDG62>@? K >>QB6^:O=R624¥47BZ M >_CQ47?V4;C@>@6247=QzTuTDGC@> 2D+?c47=@q K PRD.SV>)B<DG=k M >@? K >Q=Sc>>Q?V>@P\YTHJ D~Z M >fk M >fCQ47?V=\:<SV>QPNDGSTD.F4GPB<47=#>@= KNM Sc:<47=\47=Sc>@BhFVP\47]VB<>Q6XDFVP\4CQ>@SIHJ DSV> M ?6^>QCEDG?c:<=R624xC@4G6AHM ?j>Q?n6 M CvuV47=.FVPR4;C@>Q=R47=.DG= K PR4wkHJ =R:OC@47=-$>QBC@47B<DGFV=\42YGPNDE8;: K DwC@:<4G?TDGB q&¤4SV4=R:O= K >@6^D¨Sc>FTDwP K HJ C M B<DG=jD MK 47Y7PRDE8: K DG? K > K :<>Q?V>[DG=R4;C@:<DGSTD M ?TD¨>@?V>QPRYVHJ DF4 K >@?VCQ:UDGByYGPNDE8h: K DGC@:O47?TDGBa M ?VD>@?c>@PRYVHJ DCQ:<?H> K :OCED K 4 K DwB.P\>@= M B K DG? K >pSc>pBUD[= M 6^DSc>p>@?c>@PRYVHJ DCQ:<?H> K :OCEDSc>pBUDw=FTDGP K HJ C M B<DG=:<?cSV:O8;:<S M DGB<>Q=@q*#Dx>@?V>QPRYTHJ DFm4 K >@?VCQ:UDGBISc> M ?nC M >@P\F42C@47?=R:O6^> K P@HJ D>@=k H>@P\:<CEDxSV>_PRDGSV:<4 / >Q= K HD2STDwSTDxF47PQz

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Page 90: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 91: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 92: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 93: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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V P 9 = M 62:<>@?cSV4_>@BT8wDGB<47P|SV> CQ47PRP\>@=RFm47?VSc:<>@? K >1Dy6^D K >QPR:UDtCQ47?2BUDyC@4762Fm47=R:OC@: H4G?xSV>~BUDy6XD K >@P\:UD1=\47BUDwPaxCQ476^FcB<> K DG62>@? K >:O47?V:OEDGSTDzhCQ47624tk M >~CEDGBOC M B<DGSV4y>@?2>@Bc> \>@62FVBO4:.Sc>.B<Dt=R>QC@C@:EH47?Iz©>@?cC@47? K PRDG6247=T?TDwB<62>@? K >wz V : T9 . : uTDG]c:UDG6247=y=R:O?V>@6o]TDGPRYG4n47] K >@?c:<SV4 M ?TD K >Q6^Fm>@PRD KNM PRD6nHJ ?c:<6^DXSV>@B)47P\SV>@?SV>2SV>@CQ>@?TDG=dSV>26^:OB<>@=SV>62:<BOB<47?c>@=SV>YGPNDGSV4G=1FTDGPRDXZ M >x4;C M P\PNDG?P\>EDGCQC@:O47?V>@=1SV>dk M =\: H47?pSV>@BuV:<SVPVH47Y7>Q?V4X>Q?,>@B|:O? K >@P\:<47P=R4GBUDGPQzca? M >@= K PR4XDG? K >QPR:<4GP.>Q= K :<6^D K :L874SV>_BUD K >Q6^Fm>@PRD KNM PNDC@>@? K PNDGB zTZ M >oPR>QFVPR>Q=R>Q? K D M ?VD^] M >Q?TDDGFVP\4Ec:O6XDwC@: H4G?9DGBf8GDwB<47PdSV> K >@PR62:<?VDGSV4Fm47P6¨H> K 4SV4G=6WHDw=oFVP\>@C@:O=R47=Qz)CEDG>j= M = K DG?VC@:<DGB<62>@? K >%F4GPSV>Q]TD\4SV>X>@= K > M 6]cPNDGB qpxL.4F M >QSV>@?Iz>Q? K 47?VCQ>@=Qzf4;C M PRPR:OPdP\>EDGCQC@:O47?V>@=dSV>Xk M =\: H47?? M C@BO>EDGPd>@?>@B:<? K >QPR:O47P^Sc>BUDG=2>@= K P\>@B<B<DG=j7z~>@= K 4?V4G=%SV> RD>@? K P\>,6XDG?c47= M ?Y7PNDE87>,FcPR47]VBO>@6^Dcz=\:1?V49=\47?B<4G=y>QTCQ:<>@? K HJ =R:O6^4G=yFVPR4;C@>Q=R47=? M C@BO>EDGP\>@=B<47=yZ M >^DGB<:O6^>Q? K DG?,>QBuV47PR?c4n>Q= K >QBUDGPQz^Z M H>^F M >@SV>2=R>QP>@? K 47?VC@>Q=t7q ? K >@=|Sc>DG]TDw?VSV47?TDwP>QB>VDw6^>Q?oSV>B<47=#FVP\4CQ>@=R4G=|? M C@BO>EDGP\>@=C@47624k M >Q? K >@=SV>5B<D.>Q?V>@P\YTHJ D.>@= K >@B<DGP@zSV>Q]>Q6^47=.PR>QC@47?c4CQ>@P M ?,DG=RFm>@C K 42k M ?VSTDG62>@? K DGB#SV>o? M >Q= K PRD%DG? K >QPR:O47P1DwPRY M 62>@? K DGC@:EH47? $C M Dw?VSV4CEDwB<C M BUDG6247=2>@B18wDGBO47P^6nHJ ?c:<624SV>,B<D K >Q6^Fm>@PRD KNM PNDcz?V>QC@>Q=NDGP\:<4¨FTDGPRD Z M >,B<47=X?tHM C@BO>@47= K >@?cYhDG?BUDw=t87>@BO4CQ:<STDwSV>@=yZ M >B<>Q=_F>QPR62: K Dw?= M Fm>@PRDGP_BUDG=y]VDGPRP\>@PNDw=Sc>2Fm4 K >@?VCQ:UDGB>@B<>QC K PR47= K HD K :<C@4Z M >B<4G==R>QFTDGPRDG?Iz McK :<BO:<EDw6^47=.DGP\Y M 62>@? K 4G=t>@? K >QPNDG62>@? K >xC@B HDw=R:<CQ47=@q3jH47624%C@DG6]V:<DX? M >@= K PR4P\>@= M B K DwSV4C M DG?VSV4:O? K PR4;S M CQ:<6247=)>@BO>@62>@? K 47=SV>@BC@4762Fm47P K DG6^:O>@? K 4_C M HDG? K :OC@4SV>B<47=f?1HM CQB<>@4G=>Q?jC@47BO:<=R:EH47?^7q> cDG62:<?c>@6247=>@= K DF47=\:<]V:OB<:OSTDGSIq

? CHDGBOC M BO4¨FVPR>QC@:<=\4§Sc>@B_FVPR4;C@>Q=R4§SV>CQ47B<:O=R:EH47? :<62FVB<:OCEDGP@HJ DFm47P> \>Q6^FcB<4¨BUD McK :<B<:OEDGCQ: H47?sSc>B<D>@C M DGCQ: H47?SV>%¥;CvuVPR4;SV:<?cY7>@P_FTDGPRDSc> K >QPR62:<?TDwP>QB8GDwB<47PySV>2BUD%k M ?cC@: H4G?SV>247?VSVDnSV>2BUDjFTDGP K HJ C M B<DPR>QS M CQ:<STDp>Q?FVPR>Q=R>Q?VC@:<DpSV>@BF4 K >@?cC@:UDwBfSc>%BUDTY M PRD 9cq q ?9B<DnY7PVHDwTC@DpSV>XB<DTY M PND 9qc9p=\>uTDGCQ> M ?TDP\>@FVP\>@=\>@? K DGCQ: H47?DGFcPR4E:<6^DGSTDoSV>QB P\>@= M B K DwSV4xSV> M ?Dw?~HDGB<:O=R:O=CQ476^4o>@= K >Gq3547624F M >QSV>47]V=\>@P8GDwPR=R>~DwB<B HJ C M DG?VSV4y> 8GDwB M DG6247=BUD1FVP\47]TDG]c:<B<:OSTDGSdSV>>@?cC@47? K PRDGP)DGB?tHM C@BO>@4t>Q?^DwB<Y5HM ?dB M YhDwP|SV>QB>@=\FTDGCQ:<4Vzh>c:O= K > M ?TDyFVPR4G]TDG]V:OB<:<SVDGSoSV:O= K :<? K DtSV> ySV>Z M >=\>~B<4t>Q?VC M >Q? K PR>.6HDG=)DGB<B<DSV>B<Dt]TDGP\PR>@PRD>@? S V S zD M ?^=R:<? K >Q?V>@PSV>@=\SV>1>QBmF M ? K 4SV>~8;:<= K DdCQB HDG=\:<CQ4dB<D>Q?V>@P\YTHJ D_= M VC@:<>Q? K >1FVDGPND= M Fm>@PRDGPSV:OCvuTD%]TDGP\PR>@PRDcq =yC@47624%=R:|>@B|?1HM C@B<>Q4jD K H476^:OC@4^F M SV:O>@PNDjD K PNDE8G>@=NDwPyBUDX]TDwPRPR>QPND%SV>oF4 K >@?VCQ:UDGB|DK PRDE87>@=dSV> M ? K HM ?V>@B z=R:O??V>QC@>Q=R:<SVDGS9SV>B<BO>@YhDwP_DB<DCQ:<6^D%SV>2BUDj6^:O=R6^Dcq = K >XC@4G?V4CGHJ SV:O=R:O6^4XaFTDGPRDGS~H4 \:OC@4xCQ476^Fm47P K DG62:<>Q? K 4xC M HDw? K :<CQ4^>Q=.CQ47?V4;C@:OSV4FVPR>QC@:<=RDG62>@? K >C@47624>@B " "$ # - " aXk M >

Page 94: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

:: !"

E

r

rN

Umax

Uint

distanciade retorno clásica

Potencial electrostático

Potencialnuclear

Función de onda exterior

Tunelización

Funciónde ondainterior

:OY M PNDM9cqu9 $ 47P\6XDY7>@?V>QPNDGBmSV>tB<Dk M ?cC@: H4G?XSV>t4G?VSTDoSV> M ?TDoFVDGP K HJ C M BUDdF M ? KNM DGBSV>1C@DGPRY7D # R >@?>@BFm4 K >@?VCQ:UDGB K HJ FV:OC@4xSV> M ?VD2CQ47B<:O=R: H4G?%? M C@BO>EDGPQqFm47P#FVPR:O6^>QPND87>@FVPR4GF M >@= K 4tFm47Py>@47P\Y7>DG624N9CQ476^4.=R4GB M CQ: H47?dDGBhFVP\47]VB<>Q6XD~SV>fBUD~FVPR4;S M CQC@:EH47?SV>_>@?c>@PRYVHJ Dx>@?BUDx>@= K P\>@B<B<DF4GPB<47=FVP\4CQ>@=\47=Sc>_k M =R: H4G?Iq# 4;SV>Q6^47=duTDGCQ>@P M ?=\>@?VCQ:<BOB<4CHDGBOC M BO4 ?c4>@BFVPR>QC@:<=\4Z M >%:O6^FVBO:<C@DGPEHJ D%PR>@=\47BO8G>@PB<Dn>QC M DGCQ: H47? SV>¥CvuVP\4Sc:<?VY7>QPvzFTDwPND_>@= K :<6^DGP)C M DwB>Q=DGuV4GPND_>@B8GDwB<47P6nHJ ?V:O6^4ySc>1BUD K >Q6^Fm>@PRD KNM PND_>@? M ?^FVBUDw=R6^DFTDGPRDxZ M > K >@?VYhDxB M YhDGP>QBFVPR4;C@>Q=R42SV>yk M =R:EH47?SV>_SV47=~?tHM C@BO>@47=Qq&¤4STDFTDGP K HJ C M B<DC M HDG? K :OCED K :O>@?V>^DG=R4;C@:<DGSTD M ?TD47?VSTDC M ahDpBO47?VY7: KNM S,>Q= K HDPR>QBUDGCQ:<47?TDwSTDjC@47?= M62476^>Q? KNM 6 BO:<?V>@DGBf M ?VDXFVPR4GFV:<>QSTDGSpCQ47PRF M =RC M BUDGPN zmF4GPB<D^uV:OF~H4 K >Q=R:O=SV>ort> PR47Y7BO:<>wzT6^>QSV:UDG? K >BUD>FVPR>Q=R: H4G?Iz

V

C M DG? K :OTC@DXSV>xDGBOY M ?TD26XDw?V>@PRD^BUD2SV:<62>@?c=R: H4G?pSV>B<D^P\>@Y7:EH47?pSV>QB|>Q=RFTDGCQ:<4%>Q?BUD2Z M >F M >QSV>x=R>QP>@?cC@47? K PRDGSTDBUDxFTDGP K HJ C M B<D>@?C M >Q= K :EH47?Iq¥:©C@4G?V=R:OSV>@PRDG6^4G=|DGuc47PND~BUD~FTDGP K HJ C M BUD~PR>QS M CQ:<STD.SV>? M >Q= K PR4tFVP\47]VBO>@6^D.Z M >=R>DwC@>@P\CEDDGB©F4 K >@?VCQ:UDGBSV:O=RFm>@PR=\47PFm4SV>Q6^4G=F>Q?V=NDwPZ M >y:<?VCQB M =\4DG? K >@=Sc>y=R: KRM DGP\=R>_D M ?TDxSV:O= K DG?VC@:<Do6 M aXF>QZ M >+?TDxSV>QBC@>Q? K PR4dSV:<=\F>QPR=\47P)BUDtFVP\47]TDG]V:OB<:OSTDGSxSV>~Z M >.=R>~>@?VC M >@? K PR>1>Q?X>QBT:<? K >QPR:<4GP'SV>.BUDt]TDGP\PR>QPND_>@=fSV:<= K :<? K DSV>^C@>@P\4na[SV>^= HM ]V: K 4F M >@Sc>X>@?cC@47? K PRDGPR=\>jDGBOB HJ DHM ?=R:O? C@4G? K DGPC@47?9B<D>Q?V>@P\YTHJ D?V>QC@>@=RDGPR:<DpFTDGPRDDGCQ>@PRC@DGPR=\>uTDG= K D S V S q # DwPNDXZ M >d>@= K 4 K >Q?VYhDXB M YhDGP~F M >@SV>Fm>@?c=NDGP\=R>Z M >dBUD^FVDGP K HJ C M BUDSV>@]m>K >Q?V>@P M ?TDj>@?V>QPRYTHJ DXZ M >BUD%DGCQ>@P\Z M >^D M ?TD%SV:<= K DG?cC@:UD^Z M >2>Q=ySV>@B|47PRSV>Q?,SV>x= M BO47?VY7: KNM SSc>rt>5P\47Y7B<:O>Gq = K DC@47?VSc:<C@:EH47?jF M >QSV>>@=RCQPR:O]V:<P\=R>_C@47624Vz

Page 95: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

0 B -0 -0 ! !" " ! :::

: R V R V

# ( # R R 3DGBOC M B<DG?VSV4x>QBI8GDwB<47PSV> Z M >=ND K :<=k DGC@>yB<DDG? K >@P\:<47P5:<Y M DwB<STDGS zc>@?cC@47? K PRDG6247=@z

V R # ( # R R# 4GP14 K PR42BUDGSV4^BUD K >Q6^Fm>@PRD KNM PRD2?c>@C@>Q=NDGP\:UDXFVDGPND2Z M >oBUDw=FTDwP K HJ C M B<DG= K >Q?VYhDG?B<D8G>@BO4CQ:<STDGS M = K DFTDGPRDDGFVPR4E:<6^DGP\=R>_D M ?TDSV:<= K DG?cC@:UD Sc>@BC@>Q? K PR42SV:O=RFm>@PR=\47P~>@= K HDSTDGSTDF4GP 9cq $z

HJI V # ( # R R: = M = K : KNM aG>@?VSc4X>@BI8wDGBO47PSV> >Q?VC@47? K PNDGSV42uTDGBOBUDG6247=fT?TDGBO6^>Q? K >Gz

HcI V # ( # R 9T R R# DwPNDdB<Dk M =\: H47?^SV>@B7:OSVPTH4GY7>@?V4X V P 7'>@=5?V>@CQ>@=NDwPR:UD M ?TD K >@62F>QPND KRM PND6nHJ ?V:<6^Dt>@= K :O6XDGSVDSV>wz

HJI V e ª . : Z M >>@= K HD2>Q? M ?n>Q? K >@P\4XDGC M >@P\SV42C@47?BUD K >@62F>QPND KRM PNDx>@= K :O6XDGSVDFVDGPNDx>@B?1HM C@B<>Q4x=R47B<DGP@q BDG? K >QPR:O47PyPNDGQ47?TDG62:<>Q? K 4VzISc>@6 M >Q= K PNDjF M >Q=@z¤SV>QT?c: K :L8wDG6^>Q? K >Gz Z M >2>Q=_F47PyBO4j6^>Q?V47=yFm47=R:O]VB<>Z M >XBO47=_FVPR4;C@>Q=R47=SV>2k M =R:EH47?? M CQB<>@DGPoDwB<:<62>@? K >@?[DB<DG=_>@= K PR>QB<B<DG=@qx*#Dj87>QPR:OVCEDGCQ: H47?[SV>QV?V: K :O8wDa47]V=\>@P8GDwC@:<4G?TDGB¤SV>Z M >>Q=yDG=@HJ ?V47=1BUD^SVDGPTHDXB<D^SV> K >QC@C@:EH47?SV>oB<47=.?V> MK PR:O?V47=tFcPR4;S M C@:OSV47=S M PNDw? K >B<4G=FVPR4;C@>Q=R47=~SV>_k M =R:EH47?IzVSc>BO47=Z M >_uTDG]VB<DGPR>Q6^4G=]VPR> 87>@62>@? K >d6HDG=~DGSV>QBUDG? K >Gq?VD8G>@f:<SV>Q? K :OVCEDGSV4>QB K :OF4Sc>fFcPR4;C@>@=\4~Z M >fSVD~B M YhDGPID~B<D>@?V>QPRYVHJ DSV>)BUDG= >@= K PR>QB<BUDw=I4C M FH>Q6^47?c47=DGuV4GPNDSV>jBO47=SV> K DGBOB<>@=d>@?¨B<4,Z M >jCQ47?VCQ:<>@P\?V>DBUD6^DG?V>QPNDCQ476^4p=R47?k M =\:<47?TDwSV47=BO47=?1HM CQB<>@4G=SV>%uc:<SVPVH47Y7>@?c4 BO47=6WHDG=oDG] M ?cSTDG? K >Q=>@?B<Dn>@= K P\>@B<B<DhtFTDGPRDpB<:O]>QPNDGP_BUD>@?V>QPRYVHJ Dp?V>QC@>@=RDGPR:<DpFTDGPRD6^DG? K >@?c>@P~BUD>Q= K P\>@BOBUDx>@?VCQ>@?VSc:<STD6^:OB<>Q=SV>_6^:OB<BO47?V>@=SV>D,+?V47=Qq B6WHDw=t=R>Q?VC@:OB<B<4jFcPR4;C@>@=\4SV>xk M =R:EH47?,Z M >F M >@Sc> K >@?V>QPB M YhDGP>@?[>@B:O? K >@P\:<47PSV>BUDG=t>Q= K PR>@BOBUDG=y>Q=DGZ M >QBm>Q?X>QBmZ M >.SV47=fFVP\4 K 47?c>@=1 ?1HM CQB<>@4G=SV>@B:<=VH4 K 4GF4_6HDG=)B<:O8;:<DG?V4ySV>QB7.:<SVPVH47Y7>Q?V4©|=R> M ?V>Q?XFTDGPRDkl476^DGP M ??1HM CQB<>@4xSc>dSV> McK >QPR:O4Vq*#DP\>@CQC@: H4G?n=\>F M >@SV>>@=\C@P\:<]V:OPSV>_BUDokl47P\6XDcz

( Z ( R Z Z>@= K D%P\>EDGCQC@: H4G?pB<:O]>QPND M ?TDX>Q?V>@P\YTHJ D2SV>W: Z M >=R>o8wDX>Q?,BUDkl47PR6^D2Sc>>@?V>QPRYVHJ D^CQ:<?H> K :<C@DSV>QB SV> McK >QPR:<4czc>@B F47=\: K PTH47?2a%>@B?V> MK PR:O?V4Vq B?V> McK PR:O?V4 Z M >t>Q?BUDdP\>EDGCQC@:EH47?j=R>tBOB<> 8GD M ?TDo>Q?VPRYVHJ D6HD :<6^DSV> z n> y z M ?VDtFTDGP K HJ C M BUD.> K P\>@6^DGSTDG62>@? K >>QB M =\:O8wDczw>@=RC@DGFTDyPNDwFV:<STDw6^>Q? K >5SV>QBT¥4GB=R:O?:<? K >QPNDGC KNM DGPC@DG=R:>Q?DG]V=R4GB McK 42CQ47?BUD6^D K >QPR:<DZ M >BO4xC@47?c= K : KNM aG>GzTSV>_624Sc4xZ M >?c42P\>EDGBO:<@D?V:O?VYHM ?,DGFm47P K >xD%B<DXB M 62:<?c47=R:OSTDGSnV?TDGB|Sc>x? M >@= K PND>@= K PR>QB<B<Dcq¥:'= M F M =\:<>@PRDG6247=tZ M >>@= K Dj>@=yB<DHM ?V:OCEDoP\>EDGCQC@: H4G?jFVPR4;S M C K 47PRDSV>y>@?V>QPRYVHJ D>@?j>QBI:<? K >QPR:O47P5=\47BUDGPQzc?V4G=587>QPEHJ Dw6^47=5>@?cklP\>@? K DGSc47=~C@47?j>QBFVP\47]VB<>Q6XD2SV>oZ M >oBUD^>Q?V>@P\YTHJ D K 4 K DGB¤Z M >>@BOBUDFVPR4 87>Q>GzI>Q?,FVPR4G6^>QSV:<4 M ?V47=n:7z n> oz Fm>@P\6^: K :<P@HJ D

Page 96: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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DGB¥47B z6XDG? K >@?V>QPB<D262:<=\6XDxB M 6^:O?V47=R:OSTDGSDGC KNM DGB zTC@47?c= M 62:<>Q?VSV4X>QB : hg SV>o= M uV:OSVPTH4GY7>@?V4^F4GPM ? K :<>Q6^Fm42SV>oDwF>Q?TDG= M ?V47=n: 6^:OB<BO47?V>@=5SV>D+?V4G=@z:<?ckl>QPR:O47P:<?VCQB M =\4XD2BUD>@STDwSZ M > K :<>@?c>dB<D8;:<STDx=\47]VPR>_B<D &:O>@P\PNDcq¥>tF M >@SV>y=\:<?V>Q6]TDGP\Y74o6247= K PNDwP5Z M > M ?TD87>@tkl4GPR6^DGSV4o>QB SV> McK >QPR:O4F4GP>@= K DFVP\:<62>@PNDPR>@DGC@CQ: H47?Iz>@= K >,F M >@SV>,k DGCQ:<B<62>@? K >nk M =\:<47?TDwPR=R>,CQ47?sB<4G=jDG] M ?cSTDG? K >Q=FcPR4 K 47?V>@=jSc:<=RFm47?V:O]VB<>Q=X>Q?A>QBt62>@SV:O462>@SV:<DG? K > M ?TDPR>@DGC@CQ: H47?Z M >>@= K HDSTDGSTDxFm47P@z

R Z ( Z BUDtP\>EDGCQC@:EH47?2DG? K >@P\:<47PF M >@SV>~BO:<]m>@PNDwP M ? K 4 K DGBVSV> M ?V47=$z $ > AZ M >~=R> McK :OB<:OEDG?FcPR:<?cC@:<FVDGB<62>@? K >FTDGPRDkl47P\6XDwP>@Bkl4 K H47? qf3547?XB<D>Q?V>@P\YTHJ DZ M >tDGFm47P K D_>@= K DoPR>@DGC@CQ: H47?XDdBO47=:7zn> FVPR4;S M CQ:<SV4G=>@?ABUD¨DG? K >@PR:O47P%=\>CQ47?V=R:OY M >Q? M ?c47= cz ª n> z~Z M >[D M ?A=R47?A:<?c= M TCQ:<>Q? K >@=FTDGPRD¨>FVB<:OCEDGPjB<D:<B M 62:<?TDGCQ: H47?1C@47?V= K DG? K >SV>@Bc¥47B;D.B<4.BUDGP\Y74Sc>5B<4G=HM B K :O6^47="$ .6^:OB<BO47?V>@= SV>D+?V4G=@q =PR>QZ M >@PR:OSTDF M >Q=B<D4C M PRP\>@?VCQ:UDxSV>_4 K PNDG=~PR>@DGC@CQ:<47?c>@=~Z M >oDwF47P K >Q?nD M ?n6HDG=>Q?V>@P\YTHJ Dcq?VD187>@~=\>uTD1kl47P\6XDGSc4 Fm47P'BUD1DG? K >@P\:<47PPR>@DGC@CQ: H47?IzGBUDkHJ =R:<C@D1? M C@BO>EDGP|F>QPR62: K >BUD14;C M PRPR>Q?VC@:<DSV> M ?[FTDGP1SV>PR>EDwC@C@:O47?V>Q=yF47=\:<]VBO>@=QzSV>xBUDG=1C M DGBO>@=yB<D%6WHDG=1FVPR47]VDG]VB<>C $7g >@?bBUDw=yC@47?VSc:<C@:O47?V>Q=SV>QB?1HM CQB<>Q4o=R4GBUDGPNCQ47PRP\>@=\F47?cSV>yDoDwZ M >@B<B<Dd>Q?%BUD_C M DwB z;>@= K >t?1HM CQB<>@4=R>k M =R:O47?TD_C@47?%4 K PR4d:<SH>Q? K :<CQ4FTDGPRDkl47PR6^DGP M ?c4^? M > 874XSc>@B6HDG=~DG] M ?cSTDG? K >:<=VH4 K 47Fm4xSV>M7>QB<:O4VzVDG=@HJ z

Z Z V ( >@= K DPR>@DGC@CQ: H47?>@=DGB K DG62>@? K >1>QTCQ:<>@? K >aj>Q?n>QB<B<D=R>_F M >QSV>dBO:<]m>@PRDGP M ? K 4 K DGBISV> M ?c47=:9 n> oq71Dw= K D[>@= K >F M ? K 4 B<D[>Q?V>@P\YTHJ D K 4 K DGB~B<:<]m>@PRDGSTD,>@?BUDG= 9P\>EDGCQC@:O47?V>@=^SV>@=\C@P\: K Dw=X>@=^>@? K 4 K DGB~SV>M ?V4G= . Z $ &$7Z :59( ( R qW*#D>Q?V>@P\YTHJ D K 4 K DGBBO:<]m>@PNDwSTD%F4GP>Q= K >XC@:OC@BO4SV>xP\>EDGCQC@:<4G?V>@=Qz>@?,BUDw=tZ M >x=R>xCQ47?h8:O>@P K >@?b>Q? K 4 K DwB ?1HM CQB<>@4G=1SV> 7.:<SVPVH47Y7>@?c4j>@? M ?b?1HM CQB<>@4XSV>7>QB<:O4VzhF M >QSV>tuTDGCQ>@P]VPR:OB<BUDwPDGB¥47B z;CQ47?X= M B M 6^:O?V47=R:OSTDGS2DGC KNM DGBTaCQ47?V= M 6^:O>@?VSV4oDGFm>@?TDG=>@BB:hgSV>QB7.:<SVPVH47Y7>Q?V4SV:<=\F47?c:<]VBO>tF4GP M ?pFm>@P@HJ 4;SV4xSV> :x6^:OB 62:<B<BO47?V>Q=SV>D,+?V47=Qz M ? K :<>Q6^Fm4xSV>_=R47]cPNDFTDGPRDx> FVB<:OCEDGPB<D>@= K DG]V:OB<:OSTDGSj=R4GBUDGP>Q?nBO47=HM B K :<6247= $ x6^:OB<BO47?V>@=SV>D,+?V47=Qq >@= K >2C@47? M ? K 4nSc>^P\>EDGCQC@:<4G?V>@=_=R>2B<>xSVD>QB?V476]VP\>SV>83(& "$ * - *, - 3(& "$ ab>@=d>@BOBUDjBUDPR>Q=RFm47?V=NDw]VB<>2F4GPdB<DFcPR4;S M C@CQ: H47?SV>2BUD6XDEa74GPdFTDwP K >2SV>2BUD>@?V>QPRYVHJ DBO:<]m>@PRDGSTDjF4GP? M >@= K P\4j¥47B q71Dw]HJ DG6247=fSV:<Cvuc4xZ M >tBUDoP\>EDGCQC@:EH47?%>@?jB<DoZ M >t>QB =\>yC@47?h8;:<>QP K >1SV:<P\>@C K DG62>@? K >t>Q? Fm47PB<Dk M =\: H47?CQ47? M ?b?1HM CQB<>@4^:<SH>Q? K :<CQ4%4;C M P\PR>>QB= $7g¢SV>xB<DG=8G>@C@>Q=@q B8:%$7g PR>Q= K DG? K >x>@B F M >QSV>>@?cC@47? K PRDGP M ??1HM CQB<>@4[SV> FTDwPND[kl4GPR6^DGP M ?W?1HM CQB<>Q4SV> zZ M >nSV>@=\F M H>Q=jSV> M ?TD=\>@PR:O>C@4G?V4CQ:<STDxSV>_P\>EDGCQC@:<4G?V>@=~C@4G?VS M CQ>T?VDGB<62>@? K >_DxB<Dxkl4GPR6^DGC@:EH47?%SV> M ??tHM C@BO>@4SV> q :<= K >F M >@= M ?VDbPRDG6^DDGSV:OC@:<4G?TDGBfSV>BUDCEDwSV>@?TD,F F¨Z M >FcPR4;S M C@:O>@?VSc4 M ?TD,>@?V>QPRYVHJ D,=R:<62:<B<DGPDXB<D^FVP\4S M C@:<SVDXF4GP1BUD2PNDG6^D^FcPR:<?cC@:<FVDGB zC@4G?VS M CQ>> cDGC K DG62>@? K >DwB62:<=\6^42PR>Q= M B K DGSV4XZ M >>@= K DHM B K :<6^Dcq*#4G=SV> K DGB<BO>@=SV>_BUDw=PR>EDwC@C@:O47?V>Q=.Z M >ykl47P\6XDw?B<DG=SV:O= K :<? K DG=PRDG6^DG=SV>_BUDC@DGSV>@?VD2F Fn=\>FVP\>@=R>Q? K DG?n>@?BUDTY M PRD 9cq q g mKoe_8hKfk yehdehgJhwCo h r_gchKwB_vdp_^ilz hwr_8gchKwyei?b _^ihwrkKwi?_hfvfbckdp_ww?_ r_v_hg se_vfspkr_mKoe_w?kddp_f_vwlhjilbckKwdzoefgc_^kw,r_yehilhil_vhgubctvhigch zopgu`?b hi?_hfvfbzkdKdzoefgc_^kw,mop_wezkKgukw?kdkKi hKrk_^d_vw?_"yehjir_=il_vhKf^fbckde_vw

Page 97: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

0 B -0 -0 ! !" " ! ::9

1 1 2 +H + H H + e + ν1 - 1 2H + e + H H + ν

1 2 3H + H He + γ

3 4 7He + He Be + γ

7 - 7Be + e Li + ν

7 1 4Li + H 2 He 8 4 +B 2 He + e + ν

3 3 4 1He + He He + H3 1 4 +He + H He + e + ν

7 n 1 8Be + H B + γ

ppI ppII ppIII

99,6%0,4%

100%86%

14%

99,9%

100% 100%

0,1%

100%

0,00002%

:OY M PND9q $*#DxCEDwSV>@?TD2FVPR4 K H47?%fFVP\4 K H47?jaj= M =.PNDG6^DG=@q :<= K > M ?TD=\>@P\:<>tSV:O= K :<? K DoSc>tPR>@DGC@CQ:<47?V>Q=? M C@BO>EDGP\>@=Z M >yCQ47?VS M CQ>@? K Dw6]V: H>Q?jDBUD_kl47PR6^DGCQ: H47?^SV> DjFTDGP K :<P1SV> ?1HM C@B<>Q47=ySV> 7:OSVPTH4GY7>@?V4%a>@?[>@B'Z M >:<? K >@P\8G>@?V:O>@?V>^Dj6^4;SV4jSV>xC@D K DwB<:<@DGSV47PM ?9?1HM C@B<>Q4nSc> ( R q>Q= K Dp=R>QPR:<>2SV>^PR>EDwC@C@:O47?V>Q=@z'CQ47?V4;C@:<SVDG=dCQ47624p>@B $% z=\>XFVP\>@=R>Q? K DG?D K >Q6^Fm>@PRD KNM PRDG=x= M F>QPR:<4GPR>@=2DB<DG=xC@47P\PR>Q=RFm47?VSV:O>@? K >Q=XD,BUDC@DGSV>Q?TD,FVPR4 K H47? FVPR4 K H47?a9CQ476^4bBO487>QPR>Q6^47=_>Q?>QB'CEDGFIHJOKNM B<4j=R:OY M :O>@? K >FVDGPR>QC@>@?=R>QPyFVPR:O?VC@:OFTDGB<62>@? K >BUDG=1Z M >2FcPR4;S M C@>Q?B<D%>@?V>QPRYVHJ DSV>BUDG=>@= K PR>QB<BUDw=6HDG=f6XDG=\:O8wDG=fZ M >t? M >@= K P\42¥47B q ?XBUDVY M PND 9cq $_=R>tFcPR>@=\>@? K Dw?BO47=fSV> K DGB<BO>@=fSV>>@= K >C@:OC@B<4xSc>P\>EDGCQC@:O47?V>@=Qq/ >@C@4GPRSV>Q6^47=F M >Q='Z M >FTDGP K >fSV>BO4Z M >?c47=|624 K :L8wDG]TD.D>@= KNM Sc:UDGP>@B;FVPR47]cB<>@6^D~SV>5B<DY7>Q?V>@PRDGC@:EH47?SV>B<DX>@?c>@PRYVHJ DX>Q?[>QB|:O? K >@P\:<47PSV>BUDw=1>@= K P\>@B<B<DG=@z >@PND^>@B'>Q?VC@47? K PNDGPtB<D^kl47P\6XD2>@?bBUDXZ M >oSV>@Fm>@?VSIHJ D>@BFVDGPTHDG62> K PR4

Z M >DGFTDGP\>@CGHJ D,>@?BUD>@C M DGCQ: H47?SV>>@Z M :OB<:<]cPR:<4 K H>QPR62:<C@4§ Cwq 9cq q¨3jHDGB<C M B<4G=SV> K DGBOBUDGSV4G=]TDG=RDGSV47=>Q?B<DokHJ =\:<CEDSc>yBUDG=P\>EDGCQC@:O47?V>@=~? M CQB<>EDwPR>@=~SV>Q=RCQPR: K DG=Fm>@PR62: K >@?juTDwB<BUDwP5SV:OCvuTDSV>QF>Q?VSV>@?cC@:UDq BP\>@= M B K DwSV4^>Q=@zTFTDwPNDxBUDxCEDwSV>@?TDF FIz V G9 . : 5 R R X 99T (

Y7P ( = (ajFTDwPNDx>@BCQ:<C@BO423Ltz

V hª .: R 5 R R X :9 ( Y7P (= (

? >Q= K Dw=d>cFcPR>@=\:<47?c>@=@z V : a P\>@FVP\>@=R>Q? K DpB<DjklPRDGC@CQ: H47?[SV>26XDw=NDC@476]c:<?TDGSVDSV>%3DGPR]m47?V4VzL: K PTH4GY7>@?V4a 1 HJ Y7>@?V4cz|B<4G=FcPR:<?cC@:<FVDGB<>Q=d>QB<>@62>@? K 47=dZ M >X:<? K >QP\8;:<>Q?V>@?9>Q?9>@BfC@:OC@BO43Ltq

Page 98: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

:: !"

12 1 13C + H N + γ

13 13 +N C + e + ν 13 1 14C + H N + γ

14 1 15N + H O + γ

15 1 12 4N + H C + He 15 15 +O N + e + ν 15 1 16N + H O + γ

16 1 17O + H F + γ

17 17 +F O + e + ν

17 1 14 4O + H N + He

:<Y M PRD9cq $ $*#DG=~PR>EDwC@C@:O47?V>Q=.Z M >_CQ47?V= K : KRM a7>Q?p>@BCQ:<CQB<423Ltq ?WBUD[6XDEaG47PEHJ D[SV>nBUDG=2SV:O= K :O? K DG=2>@C M DGC@:O47?V>Q=%Z M >SV>Q=RC@P\:<]m>@?W>QB>Q= K DGSV49SV>pBUDb6XD K >@P\:UDb>@?W>QB:<? K >@PR:O47P >Q= K >@BUDwPZ M >fuc>@6247=>@?VCQ47? K PRDGSV4.uTDG= K D>@= K >)F M ? K 4d >QC M DwC@: H4G?Sc>f>QZ M :<BO:<]VP\:<45uc:<SVP\47= K HD K :OC@4VzC@4G?V=R>QP\8wDGC@:EH47?SV>tB<Do6XDw=NDcz>@C M DGC@:EH47?jSV>y>@Z M :OB<:O]VPR:O4 K H>QPR62:<CQ4©f>Q= K D:O6^FcB HJ CQ: K D_Sc>_DGB<Y M ?TDo6^DG?V>@PRDBUD K >@62Fm>@PND KNM PRDcq # DGPRDC@4762FVBO> K DwPo>@B5C M DGScPR4kHJ =\:<CQ4w 6^D K >Q6WHD K :<CQ4Z M >juV>@6247=CQ47?V= K P M HJ SV4,SV>QB:<? K >@PR:O47P¤>@= K >@B<DGP'uTDGCQ>k DGB K DFm47P K DG? K 4yB<Dkl47PR6 M BUDGCQ: H47?SV> M ?VDt>@C M DGC@:EH47?Z M >SV>Q=RC@P\:<]TDyB<D6^DG?V>@PRDC@4G6^4,8wDGP@HJ D,>@?>QB:<? K >QPR:O47PxSV>BUD,>@= K PR>QB<B<Db>Q= K > M ]c:<C M 4FTDwPTHDG62> K PR4Vq ?§B<DbFcPTH4w:<6^D,=R>QC@C@:EH47?>@= KNM Sc:UDGP\>@6247=>@= K >FVPR47]cB<>@6^Dcq &)o",'£ (2&'$' * 4@ y"t& 0 y" -4/E"%$|y&)/@(2& y$'a4@&?VDy8G>@~FVP\4S M C@:<SVDtBUD1>Q?V>@P\YTHJ Dt>Q?2BO47='FVP\4CQ>@=\47=)? M C@B<>@DGPR>Q=)>@?>@BVCQ>@? K P\4_SV>BUDG=|>@= K PR>QB<BUDw=@z;CH47624>@=BOB<> 8GDwSTDo>@=RD2>Q?V>@P\YTHJ DuVDG= K DB<Do= M F>QP\TCQ:<>_SV47?VSc>y>@=PNDwSV:UDGSVDxDGB > K >@P\:<47PNhq)rt>QSV:<C@DGPR>Q6^4G=>@= K D=R>QC@CQ: H47?nDxSTDGP~PR>Q=RF M >Q= K DXDx>@=RD2FVP\>@Y M ? K Dcq :<= K >@?ok M ?VSTDG62>@? K DwB<62>@? K >9FcPR4;C@>@=\47=|Sc> K PNDG?V=\F4GP K >SV>f>@?V>QPRYTHJ D.>Q?BUD~6XD K >@P\:UD-$#C@47?cS M C@CQ: H47? zPNDwSV:UDGCQ: H47?%a%C@47?h87>QC@CQ: H47?Iq B K PNDG?V=\F4GP K >oF47PC@47?cS M C@CQ: H47?,>Q=yDGZ M >QB'>@?,>QB|Z M >B<D^>@?c>@PRYVHJ DX>Q=yB<B<> 8wDGSTD^Sc> M ?,B M YhDGPDX4 K P\4>@? M ?§C M >QPRFm4Fm47P6^>QSV:<4,Sc>nB<DG=xC@47BO:<=\:<47?V>Q=x>@? K P\>nB<DG=xFTDGP K HJ C M B<DG=SV>QB.62>@Sc:<4Vq = K > K :<Fm4bSV>K PRDG?V=\F47P K >_>@=~CQ476AHM ?j>Q?n6^D K >@PR:<D>@?>@= K DGSV42=TH4GB<:<Sc4x42>Q?p4 K PR47=~DwB K Dw6^>Q? K >tSV>Q?V=R47=Qq B K PRDG?V=RFm47P K >F4GPyPNDGSV:<DGC@:EH47? K :O>@?V>B M YhDGPtC M DG?VSc4n>QBCEDG62:<?V4jBO:<]VP\>x6^>QSV:<4jSc>2BO47=tkl4 K 47?V>@=_= M Fm>@PND%>QB|CQ47PRP\>@=RFm47?VSc:<>@? K >D%BUDG=FTDGP K HJ C M BUDG=SV>@B6^>QSV:<4cz SV>624;SV4%Z M >DG? K >Q=ySV>Z M >xB<DX>@?V>QPRYVHJ D=R>@D B<BO>Q8wDGSTD,SV> M ?B M YhDGP2D[4 K P\48HJ DbC@47BO:<=\:<47?V>Q=@zBUDbPNDGSV:<DGC@:EH47?IzfC@47? M ?TD 6^DEa747P2B<:O]>QP K DGS¨SV>6248;:O6^:O>@? K 4VzPR>@DGB<:OEDbSV:<CvuV4 K PNDw]TD\4Vq B K PRDG?V=\F47P K >nF47P^PNDGSc:UDGCQ: H47? K :O>@?V>nB M YhDwP^>Q?W6^>QSV:<4G=

Page 99: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 101: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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§ 4Corteza Exterior Corteza Interior

Interior

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00.03 R

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§ 52

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§56

Eje de rotación

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Page 146: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 151: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 152: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 192: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 193: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

FI ^

Centro inferido de la distribuciónde cúmulos

Cúmulos observados

Posición relativadel Sol

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~ Ca+v>A-G>A'?@H1I%?-GMR')-g/.;8L?+.>[7r;=%?*,+X;y;/X;8MN'?-G>:-G-0%?*,'?-0%C7:9<;(/.;8-0>[7<9:-,/./.;PO;=9A+X;=J)/.-T1IJ)>:-09[PO;=LB;y-0%-0/f*b')35'?/.14-,>oL?-,/1I9AL?-0%(L?-Y/X;4L?+.>[7r;=%?*,+X;43t+2>:3t;4;=/f*b'?35'?/21?hp>:-Y-0%?*,'?-0%C7<9:;)hf@Z1=9#-,/f3yb-s7<1RL?1;=%C7<-,9:+21I9t/.;gL?+2>A7<;=%?*0+.;g;g-0>A7:- b'?/7<+.3#1?\ E^1=%?1a*,+.LB;G>:'L)+.>A7<;=%?*,+X;G6l@H1I>:+2*0+Qb1I%(@)9:-0*,+.>:;]>:1IJ)9:-T/.;JH1P=-0LB;*,-0/.-,>A7:-lz L?+29:-0*,*0+Qb1I%-0% /.;gMN'?->:--,%?*0')-0%C7<9:;CCaUB;=@?/2-,6(@?'?L?1-,/X;=JH1I9:;=9o'?% 3t;=@B;g-0%-0/-0>A@B;=*0+218L?-T/.;g3t;=%?-,9<;g*,1I3#1]>:-kL?+.>[7<9:+2J?'Fbc ;=%E/21I>t*b'?35'?/21I>t1=J?>:-,9APO;=L?1I>z PI-,9|BjI'?9:; a\ s\$&/&9:-,>:'?/7r;=L?1@H1I9v-0/&-,%?*01=%N7:9<;=L)1?h/2-K@Z-,9:3#+27:+b1o-,>A7<;=J?/.-,*0-,9MN'?-n/.1=>v*b'?35'?/21I>x>A-#L)+.>A7:9:+2J?'Fbc ;O%L?-3t;=%?-09:;;O@?9:11Ga+.3t;=LB;=3#-0%C7:--,> e b-,9:+.*0;-,%o7<1I9A%?1;'?%t*0-0%C7:9:15MN'?--0>A7<;=JB;;'?%?1=>` @Z*L?-0>AL?-"-,/Ca1I/R-0%KL)+.9:-,*0*,+b1I%_;"/X;*01I%?>[7<-,/X;=*,+b1I%5L)- C);=j=+27r;O9:+.1)h e 1=9:3t;=%?L?1'?%K>:+2>A7<-,3o;MN'?-^7<-,%Fbc ;'?%5L?+Qb;=3t-s7<9A1*0-,9:*0;=%?1T;Y/.1I>n~ @H*=\V$&/ Ca1I/@H-09:L)-090bc ;W;O>Qbc >:'g@?9:+Pa+2/.-,jI+X;=L?;o@Z1=>:+.*,+b1I%G-0%g/X;43w;=/X;:Ga+.;o64'?%B;PR+.>A+b1I%V3Eb;=>u@?9A-0*0+2><;nL?-v/X;K3t;=%?-,9<;5*01=3t1n-0>[7r;=J?;=%WL)+27<9A+.J?')+.LB;=>i/X;=>u-,>A7:9:-0/2/X;=>u-,%-0>A7:-j=+.jC;=%C7:-0>:*,1>:+2>A7:-03t;KPR+Qb1#/.;5/.'?SO\$&/N+.%?*,9:-0+2J?/.-6q;=J?9:')@)7<1@Z-,9 e -,*0*0+21I%B;=3#+.-,%C7<1fL?-p%R')-0>A7:9<;=>7ab-,*0%?+2*Q;=>1IJ?>A-09[P=;O*0+.1=%B;=/.-,>F6wL?-0/R;=%fb;O/.+.>A+.>7<- b1I9:+2*01L?-#/.1I>v9A-0>A'?/27<;=L?1I>q@Z1=9v-0/./.;=>v@?9A1PR+2>A7<1=>0h/.-KUB;=%g@Z-,9:3#+27:+.L?1V;O/;=>A7:9:1 e bc >:+.*,1L?-0/&@?9A-0>A-0%C7<-UB;=*,-09A>:-t;'?%B;+.L?-0;35')6@?9A-0*,+.><;VL?-K/21VMN'?-t-,>v%N'?-0>[7<9<; 3q;O/X;:Ga+X;a\6Ca;=JZ-,3t1=>vJ?+.-,%GMN'?-n-,/./X;-,>'?%g*01I%:9A')%N7:1WL)-t-,>A7<9A-0/2/X;=>,h%N'?JH-0>qL?-#jC;=>v64@Z1=/2PI16UB;O>A7r;Y'?%B;3t+2>A7:-09:+21I><;V3t;O7<-,9:+.;+.%CPR+.>:+2J?/.-z 3t;O7:-09:+.;_1I>A*0'?9:;CshBMN'?-q>:-wL?+2>A7<9A+.J?'a6I-0%Y@?9A+.%?*,+.@B;=/23t-,%C7<-"-,%W/.; e 1I9:3t;5L?-w'?%YL?+.>A*01#;=@?/.;=%B;=L)1KL?-;=/29:-0L)-0L?1I9pL?- @H*=hRL?1I%?L)-"-0/ Ca1=/H1R*0')@B;'?%?;@H1I>:+2*0+b1=% hN%?1_*,-0%C7<9:;=/ hR;')%?1I> @Z*L?-0/H*0-,%C7<9:1)h6YMN'?-5-0>[7 b;9A1aL?-0;=LB;#L?-5'?%TU?;=/.1tL?-_*b')35'?/.1=>jI/21IJ?'?/.;=9:-,>0h *0'a6C;L?+2>A7<9A+.J?')*0+b1=%k-0>3b;O>"1o3#-0%)1I>-0> e b-09A+.*Q;t*01I%'?%kL?+b;=3#-,7:9:1#>:+23t+2/X;=9f;=/L?-,/L?+2>:*01)h9:1RL?-0;=L?1;t>:'TPI-,S=h >A-0j^b'?%k/.1o9A-,P=-0/X;O%/X;=>3b;O>9:-,*0+2-0%C7<-,>1IJ)>:-09[PO;=*0+21I%?-0>fL?-w'?%Y>:')@Z-,9:UB;=/21nL?-w3o;O7:-09A+X;51I>A*0'?9:;)\;x-0L)+.*Q;O9:-03#1I> -,/C@?9:-,>:-,%N7:-^*0;=@Fbc 7:'?/.1`;f-,>A7:'?L?+X;O9L)-p3t;=%?-,9<;`3Eb;=>F1f3t-,%?1I>L?-s7r;=/2/X;=LB;i/X;`-0>[7<9A'?*,7:'?9<;z 3#1I9 e 1I/.1Ij?bc ;C6oL?+.%fb;O3t+2*Q;L)-v%R')-0>A7:9<;\3w;=/X;:Ga+.;)ha/215MN'?-v%?1I>u>A-09[Pa+29Bb;5-,%Y/21I>`*0;=@Fbc 7:'?/.1=>^9:-,>A7Bb;=%C7<-0>,h@B;=9:;n;=JZ1=9:LB;=9^L?-w3o;=%)-09<;53Eb;=>ujI-,%?-09:;=/F-0/-0>A7:'?L?+21tL?-v1O7<9:1=>u>:+.>[7<-,3o;=>u>A+.3#+./.;=9:-,>0ha;n/21I>uMN'?-w@Z1=9

Page 194: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

~

50 Kpc

Posicióndel Sol

DISCO GALÁCTICO

Disco delgado

Disco Grueso

ABULTAMIENTOCENTRAL

HALOGALÁCTICO

Centrogaláctico

2 Kpc

8 Kpc

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Page 199: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 200: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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% ] J I ~

Velocidadradial

Velocidadtangencial

90o 180o 270o l

Velocidadrelativa al Sol

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~ & - & ~ - Q 'F Q:RYS 'F

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F /Fλ λο

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% : ' V

A

B

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CentroGaláctico

Sol

ÓrbitaSolar

Rmin

Ro

Velocidadradialrelativa alSol

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Page 209: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 210: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 211: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 218: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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Page 231: Introducción a la Astrofísica · Introducción a la Astrofísica Jorge Zuluaga, 1997 Tabla de Contenido

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