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Yöntemi Kullanilarak W Uma Yildizlarinin Salt Parametrelerinin Bulunmasi

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Yöntemi Kullanilarak W Uma Yildizlarinin Salt Parametrelerinin Bulunmasi ANKARA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ YÜKSEK LİSANS TEZİ ÇIKARIM (INFERENCE) YÖNTEMİ KULLANILARAK W UMA YILDIZLARININ SALT PARAMETRELERİNİN BULUNMASI Tenay SAGUNER ASTRONOMİ VE UZAY BİLİMLERİ ANABİLİM DALI ANKARA 2007 Her hakkı saklıdır Prof Dr. Ethem DERMAN danışmanlığında, Tenay SAGUNER tarafından hazırlanan “Çıkarım (Inference) Yöntemi Kullanılarak W Uma Yıldızlarının Salt Parametrelerinin Bulunması” adlı tez çalışması 24/ 09 / 2007 tarihinde aşağıdaki jüri tarafından oy birliği/ oy çokluğu ile Ankara Üniversitesi Fen Bilimleri Enstitüsü Astronomi ve Uzay Bilimleri Dalın’da YÜKSEK LİSANS TEZİ olarak kabul edilmiştir. Başkan: Prof. Dr. Rikkat CİVELEK Orta Doğu Teknik Üniversitesi, Fizik A.B.D. Üye: Prof. Dr. İ. Ethem DERMAN Ankara Üniversitesi Fen Fakültesi Astronomi ve Uzay Bilimleri A.B.D. Üye: Yrd. Doç. Dr. Birol GÜROL Ankara Üniversitesi Fen Fakültesi Astronomi ve Uzay Bilimleri A.B.D. Yukarıdaki sonucu onaylarım. Prof. Dr. Ülkü MEHMETOĞLU Enstitü Müdürü ÖZET Yüksek Lisans Tezi ÇIKARIM (INFERENCE) YÖNTEMİ KULLANILARAK W UMA YILDIZLARININ SALT PARAMETRELERİNİN BULUNMASI Tenay SAGUNER Ankara Üniversitesi Fen Bilimleri Enstitüsü Astronomi ve Uzay Bilimleri Anabilim Dalı Danışman: Prof. Dr. İ. Ethem DERMAN Bu çalışmada, W UMa türü sistemlerin salt parametrelerini hesaplayabilmemizi sağlayan ikincil yöntemlerden “Çıkarım” yöntemi yeni ve güncel evrim modelleri kullanılarak geliştirilmiş ve son hali ile tayfsal gözlemleri bulunmayan, sadece fotometrik olarak gözlenmiş sistemlerin salt parametrelerini belirlemek amacı ile kullanılıp kullanılamayacağı tartışılmıştır. Yöntemi geliştirmek için kullanılan evrim modelleri, ‘convective core overshooting” ve donukluk için daha güncel değerleri esas alan modellerdir. Yöntemi denetlemek için hem tayfsal hem de fotometrik gözlemleri bulunan ve salt parametreleri oldukça duyarlı bir şekilde hesaplanmış olan sistemler kullanılarak bir karşılaştırma yapılmıştır. Literatürden içlerinde henüz tayfsal gözlemleri bulunmayan sistemlerinde bulunduğu ve yöntemin test edilmesi için kullanılan sistemler dışında 102 geç tür (F-G-K) W UMa sistemi için salt parametreler “Çıkarım” yöntemi ile hesaplanmıştır. Son olarak da bu çalışmada kullanılan ikincil yöntem sayesinde 171 sistem için bulunan salt parametreler arasındaki ilişkilere bakılarak W UMa türü yıldızların evrimsel konumları tartışılmıştır. 2007, 83 sayfa Anahtar Kelimeler: W UMa, Salt Parametreler, Evrim Modelleri, Çıkarım Yöntemi ABSTRACT Master Thesis DETERMINATION OF THE ABSOLUTE STELLAR PARAMETERS FOR W UMA TYPE SYSTEMS WITH USING THE INFERENCE METHOD Tenay SAGUNER Ankara University Graduate School of Natural and Applied Sciences Department of Astronomy and Space Sciences Supervisor: Prof. Dr. I. Ethem DERMAN In this work, we present the Inference Method that is a minor method for determine the absolute parameters of W UMa type systems. We improve the method with using more current and advanced evolutionary models and discuss the usage of determining the absolute stellar parameters of systems which have no spectral observations, only have photometric solutions. The enhanced method based on a new evolutionary star model, takes into considiration of ‘convective core overshoot’ and improve opacities with recent developments. We make a comparasion between the parameters derived by the method and the parameters derived by combined photometric and spectroscopic solutions. We determine the absolute stellar parameters of 102 late type (F-G-K) W UMa systems with Inference method. Most of these systems have no spectral observations in literature and additional of the systems that we use for test the method. And investigate the relations between the absolute parameters which we determine by using the minor method that we present in this work.for discuss the evolutionary status of W UMa type systems. 2007, 83 pages Key Words: W UMa, Absolute Parameters, Evolutionary Models, Inference Method ii TEŞEKKÜR Yüksek lisans çalışmalarımı yönlendiren, araştırmalarımın her aşamasında engin bilgi, öneri ve yardımlarını esirgemeyen, bir gökbilimci, bir bilim insanı olarak beni en iyi şekilde yetiştirmeye çalışmasının yanı sıra bir birey olarak da gelişmeme, kendimi bulmama yardımcı olan, hayatımı değiştiren, tanıma ve birlikte çalışma fırsatı bulabildiğim için büyük bir onur duyduğum, bir insanın sahip olup olabileceği en muhteşem danışman olan sayın hocam Prof. Dr. Ethem DERMAN’a, yüksek lisansım süresince her konuda bana yardımcı olan, hiçbir sorumu yanıtsız bırakmayan sayın Yahya DEMİRCAN’a , Yrd.Doç.Dr. Birol GÜROL’a ve Doç. Dr. Selim Osman SELAM’a, çok daha hırslı bir insan olmamı sağlayan sayın Doç. Dr. Berahidtin ALBAYRAK’a, ne zaman odasına gitsem beni güleryüzle karşılayan, bilemediğim bir sorum, içinden çıkamadığım bir durumum olduğunda her zaman bana yardımcı olan sevgili hocam Gökhan GÖKAY’a, yüksek lisans odasında birlikte çalışmaktan çok büyük zevk aldığım, mutluluk duyduğum ve çok sevdiğim arkadaşım Zahide TERZİOĞLU’na, odamızı varlığı ile şenlendiren Gülhan GÜLNAZ’a, lisans ve yüksek lisansım süresince varlığı ve arkadaşlığı ile bana güç veren bitanecik Dicle ÖZDEMİR’e, farklı okullarda olsak da yüksek lisansım süresince her konuda bana yardımcı ve destek olan canım arkadaşım Mehtap ÖZBEY’e, hayatıma bir anlam kazandıran, kendimi yeniden tanımamı sağlayan, ihtiyacım olduğu her anda yanımda bana destek olan sevgili Barış MADRAN’a, bütün hayatım boyunca bana maddi ve manevi destek olan, aldığım bütün kararları sonuna kadar destekleyen ve her durumda yanımda olan dünyanın en mükemmel ANNE’sine ve BABA’sına. Kayıtsız şartsız sevgisi ve güveni ile hayatımı çekilir kılan, bir ablanın sahip olabileceği en harika, en güzel kardeşi Simay SAGUNER’e en içten ve en derin duygularla teşekkür ederim. Tenay SAGUNER Ankara, Eylül 2007 iii İÇİNDEKİLER ÖZET ............................................................................................................................... i ABSTRACT ....................................................................................................................ii TEŞEKKÜR ...................................................................................................................iii SİMGELER DİZİNİ………………….……...……………………………….……….vi ŞEKİLLER DİZİNİ………..……………...……………………………………….......vi ÇİZELGELER DİZİNİ…..………………………………...………………………….ix 1. GİRİŞ....……..…………….………………………………………………………….1 2. YÖNTEM…...……..…………………………………………………………..……11 3. ÇIKARIM YÖNTEMİ İLE SALT PARAMETRELERİN ELDE EDİLMESİ...............................................................................................................15 4. YÖNTEMİN DENETLENMESİ VE GELİŞTİRİLMESİ…....…............………21 4.1 Yöntemin Geliştirilmesi...…..........…………………………………………...…..25 4.2 Örnek Sayısının arttırılması...........………..………………………………...…...33 5. ÇIKARIM YÖNTEMİ İLE HESAPLANMIŞ SALT PARAMETRELER.........49 6. TARTIŞMA VE SONUÇ...........…………………………………………………...50 KAYNAKLAR…………...…………………………………………………………....61 EKLER .............................................................................................................................. EK 1 Rucinski et al. (2003,2004,2005,2006)Sistemlerine İlişkin Bu Çalışmada Kullanılan Parametreler ve Bu Sistemler İçin Çıkarım Yöntemi ile Hesaplanmış Salt Parametreler...........................................................................70 EK 2 Düşük Sıcaklıklı 69 Çift Yıldız Sistemine Ait Fiziksel Parametreler Ve Bu Sistemler İçin Çıkarım Yöntemi İle Hesaplanmış Salt Parametre Değerleri İle Yakut Ve Eggleton (2005)’de Verilen değerleri..........................72 EK 3 Literatürden Derlenen 102 adet W UMa Türü Çift Yıldız Sistemine İlişkin Dönem ve Işık Eğrisi Analizleri Sonucunda Bulunmuş Parametreler İle Bu Sistemler İçin Çıkarım Yöntemi İle Hesaplanmış Salt Parametreler ...............................................................................................77 ÖZGEÇMİŞ ...……………………...……………………………................................83 iv SİMGELER DİZİNİ a(RΘ) Yörünge Yarı-Büyük Eksen Uzunluğu G Gravitasyon sabiti (G = 6,672*10 −8 cm 3 gr −1 sn −2 ) L (Toplam) Sistemin Toplam Işınım Gücü 33 −1 L Θ Güneş’in Işınım Gücü (L Θ =3,90*10 erg sn ) L 1 ( L Θ ) Sistemin Birinci Bileşeninin Işınım Gücü L 2 ( L Θ ) Sistemin İkinci Bileşeninin Işınım Gücü l1 Sistemin Birinci Bileşeninin Kesirsel Işınım Gücü l2 Sistemin İkinci Bileşeninin Kesirsel Işınım Gücü M (Toplam) Sistemin Toplam Kütlesi 33 M Θ Güneş’in Kütlesi ( M Θ = 1,99*10 gr) M 1 ( M Θ ) Sistemin Birinci Bileşeninin Kütlesi M 2 ( M Θ ) Sistemin İkinci Bileşeninin Kütlesi P Θ Güneş’in Dönemi ( P Θ = 86400 sn) P(gün) Sistemin Dolanma Dönemi 10 R Θ Güneş’in Yarıçapı (R Θ = 6,96*10 cm) R 1 ( R Θ ) Sistemin Birinci Bileşeninin Yarıçapı R 2 ( R Θ ) Sistemin İkinci Bileşeninin Yarıçapı r 1 Sistemin Birinci Bileşeninin Kesirsel Yarıçapı (=R1/a) r 2 Sistemin İkinci Bileşeninin Kesirsel Yarıçapı (=R2/a) o T 1 ( K) Sistemin Birinci Bileşeninin Etkin Sıcaklığı o T 2 ( K) Sistemin İkinci Bileşeninin Etkin Sıcaklığı q (M2/M1) Sistemin Kütle Oranı σ Stefan-Boltzman Sabiti (σ =5,67*10 −5 erg cm −2 K −4 sn −1 ) k Kesirsel Yarıçap (=r2/r1) v ŞEKİLLER DİZİNİ Şekil 3.1 Logaritma toplam kütle-toplam ışınımgücü düzleminde EF Boo (q=0.534) sistemine ait Kepler Konumu ve Evrimsel Konumu (2 GY)...........15 Şekil 4.1 Z=0.0169 ve 5 GY için Vandenberg Evrim Modeli (1985) kullanılarak Çıkarım yöntemi ile hesaplanan toplam kütle değerinin karşılaştırılması………………………………………………........22 Şekil 4.2 Z=0.0169 ve 5 GY için Vandenberg Evrim Modeli kullanılarak hesaplanan toplam ışınımgücü için karşılaştırma............................................23
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