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Promenne Hvezdy Masarykova univerzita Pˇr´ırodovˇedeck´afakulta Ustav´ teoretick´efyziky a astrofyziky Uvod´ do studia promˇenn´ych hvˇezd ZdenˇekMikul´aˇsek,Miloslav Zejda Brno 2013 Vyd´anov r´amciprojektu Inovace v´yukyaplikovan´efyziky na Pˇr´ırodovˇedeck´efakultˇe Masarykovy univerzity (CZ.1.07/2.2.00/15.0181) v operaˇcn´ımprogramu Vzdˇel´av´an´ıpro konkurenceschopnost (VK) { 2.2 Vysokoˇskolsk´evzdˇel´av´an´ı c 2013 Masarykova univerzita ISBN 978-80-210-6241-2 OBSAH 3 Obsah Historie a metody v´yzkumu 1 Uvod´ 11 1.1 Definice . 11 1.2 V´yznamstudia promˇenn´ych hvˇezd. 11 2 Historie a souˇcasnostv´yzkumu promˇenn´ych hvˇezd 12 2.1 Prehistorie sledov´an´ıpromˇenn´ych hvˇezd . 12 2.2 Prvn´ıvˇedeck´apozorov´an´ı . 12 2.3 Zaˇc´atkysystematick´ehostudia . 13 2.4 V´yzkumpromˇenn´ych hvˇezdv 19. a 20. stolet´ı . 15 2.4.1 Vizu´aln´ıfotometrie . 16 2.4.2 Nevizu´aln´ıfotometrie . 18 2.4.2.1 Fotografick´afotometrie . 18 2.4.2.2 Fotoelektrick´afotometrie . 18 2.4.2.3 Kˇrem´ıkov´a\ fotometrie . 19 " 2.4.3 Spektroskopie . 20 2.4.4 Druˇzicov´apozorov´an´ı. 21 2.5 Typy promˇenn´ych hvˇezd . 22 2.6 Brno a promˇenn´ehvˇezdy. 25 3 Pozorov´an´ıpromˇenn´ych hvˇezd 27 3.1 Astronomick´afotometrie . 27 3.1.1 Z´akladn´ıpojmy a vztahy . 27 3.1.2 Rozloˇzen´ıenergie ve spektru hvˇezdy . 31 3.1.2.1 Z´aˇren´ıACT.ˇ Efektivn´ıteplota. Spektrofotometrie . 31 3.1.2.2 Barevn´eindexy . 33 3.1.3 Fotometrick´esyst´emy . 35 3.1.3.1 Historick´efotometrick´esyst´emy . 37 3.1.3.2 Johnson˚uvmezin´arodn´ısyst´ema jeho rozˇs´ıˇren´ı . 38 3.1.3.3 Str¨omgren˚uvsyst´em uvby(β)............... 39 3.1.3.4 Dalˇs´ısouˇcasn´efotometrick´esyst´emy . 42 3.1.3.5 Standardizace fotometrick´ych syst´em˚u . 43 3.1.4 Extinkce a jej´ıeliminace . 44 3.1.4.1 Optick´atlouˇst'ka a extinkce . 44 3.1.4.2 Mezihvˇezdn´aextinkce . 45 3.1.4.3 Atmosf´erick´aextinkce . 47 3.2 Astronomick´apolarimetrie . 49 3.2.1 Stokes˚uvvektor . 50 3.2.2 Polarizace z´aˇren´ıkosmick´ych objekt˚u. 52 3.2.3 Polarimetrick´apozorov´an´ı . 52 3.3 Astronomick´aspektroskopie . 53 3.3.1 Charakteristiky spekter . 54 4 OBSAH 3.3.2 Z´akladn´ıpojmy . 55 3.3.3 Vzhled spektra . 59 3.3.4 Co lze vyˇc´ıstze spektrogram˚u. 62 3.4 Zdroje pozorovac´ıch dat o promˇenn´ych hvˇezd´ach . 63 3.4.1 Vlastn´ı,pˇrevzat´aa archivn´ıpozorov´an´ı. 63 3.4.1.1 Vizu´aln´ıodhady . 63 3.4.1.2 Fotografick´apozorov´an´ı . 64 3.4.1.3 Fotoelektrick´apozorov´an´ı . 64 3.4.1.4 CCD pozorov´an´ı . 65 3.4.2 Soudob´epˇrehl´ıdkov´eprojekty . 66 3.4.2.1 Pozemsk´eprojekty . 66 3.4.2.2 Kosmick´epˇrehl´ıdky . 69 3.4.3 Virtu´aln´ıobservatoˇr . 71 Zpracov´an´ıpozorov´an´ıpromˇenn´ych hvˇezd 4 Regresn´ıanal´yza 74 4.1 Uvodem´ .................................... 74 4.1.1 Regresn´ımodel . 74 4.1.2 Zd˚uvodnˇen´ımetody nejmenˇs´ıch ˇctverc˚u. 76 4.2 Metoda nejmenˇs´ıch ˇctverc˚u. 77 4.2.1 Hled´an´ıˇreˇsen´ımetodou nejmenˇs´ıch ˇctverc˚u. 77 4.2.2 Krit´eria´uspˇeˇsnostimodelov´an´ı . 80 4.2.2.1 Statistika modifikovan´ych odchyleke ~i ........... 80 2 2 2 4.2.2.2 Sumy χ ; χµ a rozptyl proloˇzen´ı s ............ 81 4.2.2.3 Testov´an´ıregresn´ıch model˚upomoc´ıO-C diagram˚u. 81 4.2.2.4 Informaˇcn´ıkrit´eria AIC, AICc a BIC . 82 4.2.3 Odhad nejistot jednotliv´ych mˇeˇren´ı . 83 4.3 Line´arn´ıregrese . 84 4.3.1 Line´arn´ıregrese uˇzit´ımmaticov´ehopoˇctu. 85 4.3.2 Nejistoty parametr˚umodelu a pˇredpovˇed´ı . 87 4.3.3 Z´akladn´ıregresn´ımodely - aplikace line´arn´ıregrese . 88 4.3.3.1 Pr˚umˇern´ahodnota . 89 4.3.3.2 Pˇr´ımka jdouc´ıpoˇc´atkem . 89 4.3.3.3 Proloˇzen´ıobecnou pˇr´ımkou . 90 4.3.3.4 Proloˇzen´ıˇcasov´ych ˇradpolynomem . 91 4.3.3.5 Proloˇzen´ıˇcasov´ych ˇradharmonick´ympolynomem . 91 4.3.4 Zobecnˇen´ıline´arn´ıregrese I - vektorov´az´avisl´apromˇenn´a. 92 4.3.5 Zobecnˇen´ıline´arn´ıregrese II - v´ıcenez´avislepromˇenn´ych . 92 4.4 Neline´arn´ıregrese . 95 4.4.1 Linearizace neline´arn´ıch regresn´ıch model˚u. 95 4.4.1.1 Odhad nejistoty okamˇzik˚uextr´em˚u. 96 4.5 Robustn´ıregrese . 96 4.5.1 Vlastn´ımetoda robustn´ıregrese . 98 OBSAH 5 5 Anal´yzaˇcasov´ych ˇrad 100 5.1 Z´akladn´ıpojmy a ´uvahy . 100 5.1.1 Svˇeteln´akˇrivka . 100 5.1.2 Casˇ pozorov´an´ı . 101 5.2 Periodicita promˇennosti . 103 5.2.1 Pˇr´ıˇciny zmˇenperiody periodicky promˇenn´ych hvˇezd. 103 5.2.1.1 Pulzuj´ıc´ıhvˇezdy . 103 5.2.1.2 Rotuj´ıc´ıhvˇezdy. 104 5.2.1.3 Interaguj´ıc´ıdvojhvˇezdy . 105 5.2.1.4 LiTE a apsid´aln´ıpohyb . 106 5.2.2 Epocha, f´aze,f´azov´afunkce a okamˇzit´aperioda . 107 5.2.3 Z´akladn´ıdvouparametrick´ymodel { line´arn´ıefemerida . 108 5.2.4 Modely s pozvoln´ymizmˇenamiperiody promˇennosti. 108 5.2.4.1 Pˇr´ıklady. 109 5.2.4.2 Diskuse. Prost´ytˇr´ıparametrick´ymodel periody . 111 5.2.5 Modely s margin´aln´ımizmˇenamiperiody . 112 5.2.5.1 Kubick´ymodel zmˇenperiody . 112 5.2.5.2 LiTE . 113 5.3 Periodov´aanal´yzaokamˇzik˚uextr´em˚u. 113 5.3.1 Reˇsen´ımetodouˇ nejmenˇs´ıch ˇctverc˚u. 116 5.3.1.1 Nejistoty jednotliv´ych okamˇzik˚uextr´emu . 117 5.3.1.2 Urˇcov´an´ıparametr˚uline´arn´ıch regresn´ıch model˚u. 118 5.3.2 Standardn´ıurˇcov´an´ıokamˇzik˚uextr´em˚u. 118 5.3.3 Prost´emodely svˇeteln´ych kˇrivek . 119 5.3.4 Precizn´ıurˇcov´an´ıokamˇzik˚uextr´em˚usvˇeteln´ych kˇrivek . 120 5.4 Pˇr´ım´aperiodov´aanal´yza. 122 5.4.1 Popis metody . 123 5.4.2 Virtu´aln´ıO-C diagram . 124 5.5 Fenomenologick´emodely f´azov´ych kˇrivek . 125 5.5.1 Rotuj´ıc´ıhvˇezdys fotometrick´ymiskvrnami . 125 5.5.2 Z´akrytov´edvojhvˇezdy . 127 5.5.3 Spektroskopick´apromˇennost. 130 5.6 Simult´ann´ımodelov´an´ınestejnorod´ych zdroj˚uf´azov´einformace . 130 5.7 Hled´an´ıperiod. Periodogramy . 131 5.7.1 Metody minimalizace f´azov´ehorozptylu . 133 5.7.2 Periodogramy jako aplikace metody nejmenˇs´ıch ˇctverc˚u. 133 5.7.2.1 Line´arn´ıregrese a jej´ın´astroje . 133 5.7.2.2 Varianta I - suma ˇctverc˚uodchylek . 134 5.7.2.3 Varianta II - Lombova-Scargleova metoda . 135 5.7.2.4 Varianta III - sign´al/ˇsum . 136 5.7.3 Sloˇzitˇejˇs´ısituace . 136 5.7.3.1 Dlouhodob´ytrend . 137 5.7.3.2 Multiperiodick´ezmˇeny . 137 5.7.4 Zd´anliv´eperiody (aliasy) . 137 5.7.4.1 Faleˇsn´eperiody . 138 6 OBSAH Fyzika promˇenn´ych hvˇezd 6 Promˇennostperiodicky promˇenn´ych hvˇezd 142 6.1 Rotuj´ıc´ıpromˇenn´ehvˇezdy . 142 6.1.1 Asf´erick´ehvˇezdy . 142 6.1.2 Skvrny na hvˇezd´ach . 143 6.1.2.1 Slunce a hvˇezdysluneˇcn´ıhotypu . 144 6.1.2.2 Typ FK Comae Berenices . 145 6.1.2.3 Typ RS Canum Venaticorum { skvrnit´ıpsi . 145 6.1.2.4 Typ BY Draconis . 149 6.1.2.5 Chemicky pekuli´arn´ı(CP) hvˇezdy. 149 6.1.3 Magnetick´epole . 152 6.1.3.1 Pulsary . 152 6.2 Dvojhvˇezdy . 155 6.2.1 Z´akrytov´epromˇenn´ehvˇezdy . 155 6.2.2 Svˇeteln´ekˇrivkyz´akrytov´ych dvojhvˇezd . 157 6.2.3 Kˇrivkyradi´aln´ıch rychlost´ı. 162 6.2.4 Tˇesn´einteraguj´ıc´ıdvojhvˇezdy . 164 6.2.5 V´yznamv´yzkumu z´akrytov´ych dvojhvˇezd . 166 6.2.6 Nez´akrytov´edvojhvˇezdy . 167 6.3 Pulzuj´ıc´ıpromˇenn´ehvˇezdy. 168 6.3.1 Radi´aln´ıpulzace . 168 6.3.2 Mechanismus pulzac´ı . 172 6.3.3 P´asnestability a jeho interpretace . 173 6.3.4 Z´avislostperioda–z´aˇriv´yv´ykon a jej´ıvysvˇetlen´ı . 176 6.3.5 Pulzace radi´aln´ıi neradi´aln´ı.M´odypulzac´ı . 178 6.3.6 Helioseismologie a astroseismologie . 181 6.4 Typy pulzuj´ıc´ıch promˇenn´ych hvˇezd. 183 6.4.1 Klasick´ecefeidy . 183 6.4.2 Hvˇezdytypu W Virginis . 185 6.4.3 RR Lyrae . 186 6.4.4 Hvˇezdytypu δ Scuti . 187 6.4.5 Hvˇezdytypu γ Doradus . 188 6.4.6 Rychle osciluj´ıc´ıpekuli´arn´ıhvˇezdy . 189 6.4.7 Hvˇezdytypu β Cephei . 190 6.4.8 SPB . 190 6.4.9 Pulzuj´ıc´ıb´ıl´ıtrpasl´ıci. ..
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