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Third Bodies Or Magentic Activity in Binary Stars ?

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Third Bodies Or Magentic Activity in Binary Stars ? TMHMA FUSIKHS, PANEPISTHMIO PATRWN TOMEAS JEWRHTIKHS, UPOLOGISTIKHS FUSIKHS KAI ASTROFUSIKHS EIDIKH EREUNHTIKH ERGASIA GIA TO METAPTUQIAKO DIPLWMA EXEIDIKEUSHS « TrÐta S¸mata ή Μαγνητική Δραστηριόthta se διπλά αστρικά συστήματa ;» KwnstantÐnoc Zèrbac A.M.: 1050804 Epiblèpousa: E.-P. Qristοπούλου, EpÐkourh Καθηγήτρια PanepisthmÐou Patr¸n Πάτρα, 2018 Περιεχόμενα i Περιεχόμενα Katάλοgoc Σχημάτwn . iv Katάλοgoc Piνάκων . xi PerÐlhyh .................................. 1 Abstract ................................... 4 Κεφάλαιo 1 Troχιακά qarakthriστικά dipl¸n sustημάτwn . 6 1.1 To Πρόβλημα twn Δύο Σωμάτwn . 6 1.2 Μορφή Troχιάς . 10 1.2.1 Λύσειc twn Exis¸sewn KÐnhshc . 10 1.2.2 ExÐswsh Troχιάς . 11 1.3 ExÐswsh Kepler ............................. 17 1.3.1 EpÐlush ExÐswshc Kepler ................... 20 1.4 Troχιακά stoiqeÐa . 21 1.4.1 Troχιακή (Fwtομετρική) kai Γωνιακή Φάsh . 23 1.4.2 Kuklikèc kai 'Ekkentrec Troqièc . 24 1.4.3 Sqèsh troqiak¸n stoiqeÐwn me thn oλική sτροφορμή kai e- nèrgeia . 26 BibliografÐa KefalaÐou 1 . 29 Κεφάλαιo 2 Γεωμετρικά qarakthriστικά dipl¸n συστημάτwn 30 2.1 Ενεργό Βαρυτικό Δυναμικό - Δυναμικό Kopal . 31 2.2 Montèlo Roche ............................. 37 2.3 Morfoloγική Taxiνόμηση Dipl¸n Συστημάτwn . 42 2.4 Συστήματa Upeρεπαφής τύπου W UMa . 49 2.4.1 Γενικά Qarakthriστικά . 49 2.4.2 To παράδοξο tou tύπου W ................... 50 2.4.3 Δομή kai Εξελικτικά Σενάρια . 51 2.5 Antαλλαγή kai Metαφορά Μάζας . 55 2.5.1 DeÐkthc AktÐnac - Μάzac . 56 2.5.2 Metαφορά Μάζας (RLOF)................... 62 2.5.3 Ap¸leia Μάζας . 64 BibliografÐa KefalaÐou 2 . 70 Περιεχόμενα ii Κεφάλαιo 3 TrÐta s¸mata ή μαγνητική δραστηριόthta se διπλά αστρικά συστήματa .................... 74 3.1 Eiσαγωγή . 74 3.2 Metabolèc sto διάγραμμα O-C ..................... 76 3.2.1 Διόρθωση Astroνομικής EfhmerÐdac . 76 3.2.2 FusikoÐ mhqanismoÐ metaboλής περιόδου . 77 3.3 'Uparxh trÐtou s¸matoc γύρω από to διπλό σύστημα (Light-Time Effect).................................. 83 3.3.1 H exÐswsh tou Light-Time Effect (LITE) . 83 3.3.2 Kriτήρια iσχύος tou LITE ................... 89 3.3.3 Mèjodoi anÐqneushc pollapl¸n συστημάτwn . 90 3.3.4 H statiστική twn pollapl¸n συστημάτwn . 93 3.4 Μαγνητική δραστηριόthta sto διπλό σύστημα . 95 3.4.1 O mhqaniσμός Applegate .................... 95 3.4.2 Energeiakèc apaiτήσειc tou mhqaniσμού Applegate . 99 3.4.3 EpÐdrash tou mhqaniσμού Applegate sto διάγραμμα O-C . 102 BibliografÐa KefalaÐou 3 . 108 Κεφάλαιo 4 Teqnikèc efarmoγής thc μεθόδου elaqÐstwn tetrag¸nwn kai ektÐmhshc abebaiotήτwn . 113 4.1 Diaforikèc diorj¸seic (Differential Corrections) . 114 4.2 Mèjodoc Levenberg-Marquardt . 117 4.3 H mèjodoc Nelder-Mead Downhill Simplex . 120 4.4 Mèjodoi prosdioriσμού oλικού elaqÐstou kai abebaioτήtwn . 125 4.4.1 Σάρωση sto q¸ro twn λύσεων (Heuristic Scanning) kai Dia- tαραχή paramètrwn (Parameter Kicking) . 126 4.4.2 Mèjodoc Bootstrap . 128 4.4.3 Μαρκοβιανή alusÐda Monte Carlo kai o αλγόριjmoc Metropolis- Hastings .............................129 4.4.4 GenetikoÐ Αλγόριjmoi . 139 BibliografÐa KefalaÐou 4 . 146 Κεφάλαιo 5 Ανάλυση kai melèth metaboλής περιόδου dipl¸n ekleiptik¸n συστημάτwn . 150 5.1 To apoqwrismèno σύσthma NSVS 14256825 wc υποψήφιo gia thn ύπαρξη trÐtou s¸matoc (LITE) . 150 Περιεχόμενα iii 5.1.1 To profÐl tou astèra . 150 5.1.2 Ανάλυση tou διαγράμματoc O-C . 152 5.1.3 Συμπεράσματa . 162 5.2 H perÐptwsh tou apoqwrismènou συστήματoc NSVS 07826147 . 164 5.2.1 To profÐl tou astèra . 164 5.2.2 Ανάλυση tou διαγράμματoc O-C . 165 5.2.3 Συμπεράσματa . 174 5.3 To ainiγματικό σύστημa υπερεπαφής TZ Boo . 175 5.3.1 To profÐl tou astèra . 175 5.3.2 Ανάλυση tou διαγράμματoc O-C . 176 5.3.3 Συμπεράσματa . 191 BibliografÐa KefalaÐou 5 . 193 Παράρτημα ................................. ix PÐnakec χρόnwn elaqÐstou fwtός . ix Anaforèc Σχημάτwn . xi Katάλοgoc Σχημάτwn iv Katάλοgoc Σχημάτwn 1.1 Barukenτρικό σύσthma suntetagmènwn ενός διπλού susτήματoc sw- μάτwn. 6 1.2 Σχηματική αναπαράσtash βαρυκεντρικής troχιάς ενός διπλού susτήμα- toc. To βαρύκεντρο eÐnai shmeiwmèno kai brÐsketai sthn estÐa κάθε èlleiyhc. 13 1.3 Σχετική troχιά ενός diplού συστήματoc (me ton èna astèra sthn κύρια estÐa) kai βασικά stoiqeÐa thc èlleiyhc. 14 1.4 Qarakthristikèc gwnÐec ελλειπτικής troχιάς wc απόρροια twn gew- metrik¸n sqèsewn tou κύκλου kai thc eggegrammènhc èlleiyhc. H sqèsh metαξύ twn epifanei¸n κύκλου kai èlleiyhc pou sar¸nei to aktinikό διάνυσμα apoteleÐ kai thn ousÐa thc exÐswshc Kepler. 18 1.5 Απεικόnish tou troχιακού epipèdou se sqèsh me to epÐpedo tou oura- νού (epÐpedo xy). O άξοnac z antistoiqeÐ sthn eujeÐa παρατήρησης (me shmeÐo ekkÐnhshc to z = −∞) kai oi treic qarakthristikèc gwnÐec orÐzoun ton prosanatoliσμό tou troχιακού epipèdou. O θετικός άξοnac x orÐzei thn κατεύθυνση tou βόρεiou ouράνιou πόlou. 22 2.1 GewmetrÐa tou probλήματoc tri¸n σωμάτwn. H αρχή twn αξόnwn brÐsketai sto βαρύκεντρο tou διπλού συστήματoc en¸ to σύστημα suntetagmènwn peristrèfetai me γωνιακή συχνόthta w. 32 2.2 GewmetrÐa tou προβλήματoc tri¸n σωμάτwn me αρχή twn αξόnwn ston astèra μάζας m1............................. 34 2.3 Diatομή twn isodunamik¸n epifanei¸n sto troχιακό epÐpedo ενός διπλού susτήματoc astèrwn me λόgo μάζας q = 0.4. Ta shmeÐa Lagrange L1,L2,L3 brÐskontai sthn eujeÐa pou en¸nei ta kèntra twn astèrwn, en¸ ta L4,L5 brÐskontai sthn κορυφή iσόπλευρων trig¸nwn me βάσειc thn eujeÐa twn kèntrwn. 40 2.4 Isodunamikèc epiφάνeiec Roche. Ta kèntra twn astèrwn brÐskontai sta shmeÐa O kai S antÐstoiqa, en¸ to shmeÐo G antistoiqeÐ sto βαρύκεντρο. Ta shmeÐa L1,L2 eÐnai emfanèc όti antistoiχούν se shmeÐa tομής touc. 41 Katάλοgoc Σχημάτwn v 2.5 H τιμή tou barυτικού δυναμικού F συναρτήσει thc απόσtashc ka- tά μήκος thc eujeÐac pou en¸nei ta kèntra twn astèrwn. Βαθειά πηγάδια δυναμικού περιβάλλoun ton astèra O kai ton astèra S kai sth metαξύ touc απόσtash to δυναμικό laμβάνει mègisth τιμή sth jèsh x = L1. Stic άκρες υπάρχουν άλλα δύο mègista δυναμικού pou antistoiχούν stic jèseic L2,L3 kaj¸c o όρος tou φυγόκεντρου δυναμικού uperiσχύει stic μεγάλες apostάσειc. 41 3 2.6 H ενεργός aktÐna (1 < rL < 10 ) tou λοβού Roche συναρτήσει tou λόgou maz¸n q (0.01 < q < 10). EÐnai emfanèc όti to μικρόtero mègejoc λοβού Roche antistoiqeÐ se q = 1. 43 2.7 MorfologÐa apoqwrismènou susτήματoc (AD Boo) kai h καμπύλη (τύπου Algol) fwtometrÐac tou. Me mplè qr¸ma orÐzontai oi epi- φάνειες twn astèrwn, me κόκκιno qr¸ma h εσωτερική επιφάνεια La- grange kai me μαύρο qr¸ma h εξωτερική επιφάνεια Lagrange. Sthn ka- μπύλη fwtometrÐac to mplè qr¸ma antistoiqeÐ sth συνθετική καμπύλη kai to κόκκιno sta πειραματικά shmeÐa. Ta σχήματa dhmiουργήθηκαν me to logiσμικό Binary Maker 3.0 (Bradstreet and Steelman, 2002). 44 2.8 MorfologÐa hmiapoqwrismènou συστήματoc (DL Cyg) kai h καμπύλη (τύπου β Lyrae) fwtometrÐac tou. 45 2.9 MorfologÐa sυστήmatoc se υπερεπαφή (AW UMa) kai h καμπύλη (τύπου W UMa) fwtometrÐac tou. 46 2.10 MorfologÐa συστήματoc se διπλή επαφή (RZ Sct) kai h καμπύλη fwtometrÐac tou. 47 2.11 H sqèsh περιόδου - deÐkth qr¸matoc gia ta diplά susτήματa uperepa- φής τύπου W UMa. 'Oso μικρόterh h perÐodoc tou susτήματoc tόσο pio exeligmèna ta mèlh tou. EÐnai qarakthrisτικό όti ta susτήματa τύπου W, pou shmei¸nontai me ×, brÐskontai kurÐwc sthn κάτw arisτερά perioχή tou διαγράμματoc, h opoÐa antistoiqeÐ se μικρόterec περιόδους kai jermokrasÐec. Ta susτήματa τύπου A shmei¸nontai me κύκλο kai eÐnai pio exeligmèna kaj¸c emfanÐzontai se μεγαλύτε- rec περιόδους kai υψηλόterec jermokrasÐec. Ta dedomèna gia thn katασκευή tou διαγράμματoc sullèqjhkan από ton Mochnacki (1985). 52 Katάλοgoc Σχημάτwn vi 2.12 H sqèsh tou θερμικού (ζth.) kai δυναμικού (ζdyn.) deÐkth aktÐnac- μάζας gia astèrec ηλιακού τύπου sthn αρχή thc κύριας akoloujÐac (ZAMS). O δεξιά katακόρυφος άξοnac (q(ζ)) antistoiqeÐ ston krÐsimo λόgo maz¸n (μάζα astèra pou gemÐzei to λοβό Roche / μάza συνοδού) kai gia tic timèc tou opoÐou iσχύει ζL = ζ, me to ζ na antistoiqeÐ se perÐptwsh διατήρησης μάζας kai troχιακής stroformής katά th metαφορά μάζας. 59 3.1 Διάγραμμα O-C από dedomèna tou 1982 gia to σύσthma BW Vul.H mesaÐa perioχή antistoiqeÐ se μηδενική klÐsh eujeÐac kai epomènwc se swstό upologiσμό thc περιόδου tou susτήματoc. H πάνω pe- rioχή antistoiqeÐ se θετική klÐsh eujeÐac kai άρα h perÐodoc tou susτήματoc eÐnai μεγαλύτερη από thn perÐodo pou χρησιμοποιήθηκε gia thn kataskeuή tou διαγράμματoc, en¸ gia thn κάτw perioχή h αρνητική klÐsh upodhl¸nei th χρήση μεγαλύτerhc περιόδου από thn πραγματική. 78 3.2 Metabolèc sta διαγράμματa O-C tri¸n ekleiptik¸n susτημάτwn e- xaitÐac diaforetik¸n fusik¸n mhqanism¸n pou λαμβάνοun q¸ra sto σύσthma. 82 3.3 Ελλειπτική troχιά tou εκλειπτικού susτήματoc (E) exaitÐac thc ba- ρυτικής allhlepÐdrashc me trÐto s¸ma. Sto shmeÐo O brÐsketai to βαρύκεντρο twn tri¸n σωμάτwn από to opoÐo περνάει to epÐpedo tou ουρανού tèmnontac thn troχιά sta shmeÐa 1,3. H eujeÐa dCa apoteleÐ thn tομή tou troχιακού epipèdou me to παράλληλο epÐpedo proc tou ουρανού kai to opoÐo apèqei απόσtash αesinωsini.H klÐsh tou troχιακού epipèdou me to epÐpedo tou ουρανού eÐnai χάρin 0 eukolÐac Ðsh me i = 90o. Κάθε stiγμή h απόσtash z tou εκλειπτικού susτήματoc metαβάλλετai από ton paratηρητή me apotèlesma thn periοδική metaboλή twn χρόnwn elaqÐstou fwtός sto διάγραμμα O-C. 84 Katάλοgoc Σχημάτwn vii 3.4 Qarakthriσμός thc περιόδου se διάγραμμα lόgou maz¸n kai fasmati- κού τύπου δευτερεύοntoc astèra gia 101 διπλά εκλειπτικά susτήματa τύπου Algol. Me × apotup¸nontai όsa antikeÐmena qarakthrÐzontai από auxomeÐwsh thc περιόδου katά periοδικό τρόπο, en¸ ta σύμ- bola /, \ kai - upodhl¸noun αύξηση, meÐwsh kai stαθερή perÐodo antÐstoiqa. To σύμβοlo thc teleÐac antistoiqeÐ se όσα antikeÐmena den μπόρεσε na exaqjeÐ sumpèrasma wc proc th metaboλή thc peri- όδου. EÐnai emfanèc όti kuklikή metaboλή περιόδου emfanÐzoun μόno ta susτήματa me δευτερεύοnta astèra metagenèsterou φασματικού τύπου tou F5............................... 96 4.1 Pijanèc gewmetrikèc τροποποιήσειc ενός τετράεδρου simplex katά th διάρκεια miac επανάlhyhc. H katάλληλη allhlouqÐa epanalhptik¸n βημάτwn kai άρα gewmetrik¸n tropoποιήσεων ja èqei wc apotèlesma th surrÐknwsh tou simplex, dhlaδή, th σύγκλιsh thc μεθόδου sto ελάχιsto thc συνάρτησης elaqistopoÐhshc.
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