FORMATION OF LOW-MASS X-RAY BINARIES BY VASSILIKI KALOGERA Ptychio, Aristotle University of Thessaloniki, 1992 M.S., University of Illinois at Urbana-Champaign, 1994 THESIS Submitted in partial fullfilment of the requirements for the degree of Doctor of Philosophy in Astronomy in the Graduate College of the University of Illinois at Urbana-Champaign, 1997 Urbana, Illinois UNKVER§RTY OF KiLJJliNOKS A 1r UMANA-<CJHAMJFAKGN GRADUATE COLLEGE DEPA RT MENTAL FORMAT A PPR OVAL THIS IS TO CERTIFY THAT THE FORMAT AND QUALITY OF PRESENTATION OF THE THESIS SUBMITIED BY Vassi Uki Kalogera ASONEOFTHE REQUIREMENTS FOR THE DEGREE OF__ D_oc_t_o_r_of_P_h_i_lo_s_o_p_hY _________ _ IS ACCEPTABLE TO THE Department of Astronomy Full Name of Department, Division or Un.it ~d!A~ !Jlav /C/, /tf 17 Departmental Representative date ofAppr<JVal FORMATION OF LOW-MASS X-RAY BINARIES Vassiliki Kalogera, Ph. D. Department of Astronomy University of Illinois at Urbana-Champaign, 1997 Ronald F. Webbink, Advisor Low-mass X-ray binaries (LMXBs) are bright X-ray sources that consist of a compact object (neutron star or black hole) accreting from a low-mass companion that fills its Roche lobe and tidally loses mass. A study of the origin and properties of such systems formed in the Galactic disk is presented, involving the statistical modeling of the evolution of a primordial ensemble of binaries through evolutionary stages until the onset of the X-ray phase. For the completion of this study, understanding of the effects of supernova explosions on orbital dynamics, as well as knowledge of the binary characteristics of nascent LMXBs are required. Observational evidence exists in support of the idea that kicks are imparted to neutron stars at their birth. In Chapter 2, we develop an analytical method for study- ing the effect of asymmetric supernova explosions on the orbital dynamics of a binary population with initially circular orbits. We derive expressions for the distribution of systems over post-SN orbital separations, eccentricities, and center-of-mass velocities, and study their dependence on the kick and binary characteristics. This analysis is a necessary tool for population studies of binaries that experience supernova explosions. In Chapter 3, we study the binary properties of nascent LMXBs and find the donor masses and orbital separations to be constrained by the requirement for stability of mass transfer and for the age of the systems to be shorter than the age of the Galaxy. We also show that super-Eddington mass transfer allows relatively massive donors to remain in hydrostatic and thermal equilibrium, and that observed long-period LMXBs with evolved donors as well as ultra-short-period LMXBs with hydrogen deficient donors must have survived a phase of super-Eddington mass transfer. Formation of LMXBs has been suggested to occur when primordial binaries with iii extreme mass ratios evolve through a common envelope phase and the exposed helium core subsequently explodes as a supernova. In Chapter 4, we identify the complete set of structural and evolutionary constraints on the properties of LMXB progenitors and we show that (i) their orbital separations are restricted to a narrow range, and (ii) short-period LMXBs are formed only if kicks are imparted to neutron stars at birth. We perform population synthesis calculations using a semi-analytical method which offers major advantages in terms of statistical accuracy and computational efficiency. Using the results of an extensive parameter study we show that the predicted birth rates essentially reflect the choice of the - mostly unknown - characteristics of the primordial binary population, while the properties of nascent LMXBs are primarily determined by stability and age constraints and the efficiency of angular momentum losses. The random natal kicks imparted to neutron stars weaken the dependence of the results on pre-SN evolution and prevent us from distinguishing between formation paths that involve a common-envelope phase. In light of the importance of neutron stars kicks in LMXB formation, we propose a new evolutionary path, the direct-supernova mechanism, which does not invoke common-envelope evolution. Instead, the required small post-SN binary orbits are achieved because of a kick velocity of appropriate magnitude and direction relative to the pre-SN orbital velocity. The efficiency of this new mechanism strongly depends on the average kick magnitude, and can account for one third of the LMXB population for kicks of,...., lOOkms-1. ·More importantly, the direct-supernova path provides the only natural way for the formation of binary millisecond pulsars in very long period orbits. iv To Demetris v ACKNOWLEDGMENTS From the beginning through the completion of my graduate studies, my thesis advisor, Ron Webbink, played a crucial role. I am grateful to him for he taught me everything I know about single and binary stellar evolution, and he guided me with patience through my first steps in my thesis research. He has always been able to keep an essentially perfect balance between providing advice, help, and direction, and, at the same time, allowing me the freedom and independence I needed to grow as a researcher. I would like to thank him for being supportive and understanding, not only when progress was made, but also when problems arose. I am also thankful for the trust and confidence he showed in me since very early in my studies, offering me the the opportunity to participate in numerous international meetings and present my thesis work. He also encouraged me to expand my research interests, take upon other projects unrelated to my thesis, and develop collaborations with people here and also outside UIUC. Most of all, I value and respect his views and sensible attitude towards scientific research, his choice of problems based on intellectual curiosity and also the fun and satisfaction associated with it, and his scientific and personal integrity in dealing with political issues and in interacting with colleagues. I could never have made it through the past five years, if it were not for the love and continuous support from my husband, Demetris Psaltis. It has been wonderful and exciting to be able to share both my scientific and private life with him. At times when things were far from easy and my self-confidence was low, it was his belief in me and his unique way of completely understanding me that kept me on my feet. I hope that we will keep sharing our dreams and love and we will eventually solve the "two-body" problem in Astronomy! Finding myself before graduation, 9,000 kilometers away from my homeland, I cannot help but think about my parents, George and Jiannoula. I realize that my vi decision to leave Greece has been, in a way, incomprehensible to them and has caused them much pain that they do not deserve. This is why I appreciate even more the fact that they never attempted to prevent me from following the path I chose, and have always been patient and supportive to me. In my academic life here at UIUC, I was fortunate enough to interact and collabo­ rate with several other distinguished and wonderful people. Apart from giving me the opportunity to expand my research interests to other areas, these collaborations also functioned as "healthy breaks" from my thesis research. Working with Fred Lamb was a memorable experience and also taught me a great deal about "fast-lane" re­ search as well as the sense of scientific clarity and accuracy. I am also grateful for his help and psychological support during an extremely rough period in late Spring 1996, and for often providing advice over the past few years. Also, working and interacting with Gordon Baym and Icko Iben has been a thrilling and fun experience. Finally, I very much appreciate having the chance to attend classes offered by Dimitri Mihalas and Telemachos Mouschovias, which greatly advanced my graduate level education. I would also like to thank Chris Fryer for an exciting and spontaneous collabora­ tion, which soon became a warm friendship. I hope it will last for years to come. Life in the Astronomy department and more importantly in Urbana-Champaign has been made enjoyable thanks to many wonderful friends, with whom I shared many laughs, drinks, and, at times, our bitterness about life in Urbana. I will never forget the regular weekly ASTRO 500 meetings at local bars (which resulted from Demetris', Sean's, Ram's, and my persistence) with Sean Points, Robert Gruendl, Scott Teare, Gail Conway, Dimitri Mihalas, Silvia Zane, Paschalis Paschos, Jeff Veal, Ram Rao, Ian Barton. These meetings were not only fun and relaxing, but also helped me keep my sanity (although I know that Chris, Robert, Sean and Scott would doubt that I have it!) all these years; I will definitely miss them. Also, I highly appreciated Sean's efforts to bring an espresso machine to the department, the perfect excuse Vll for spontaneous, daily, fun, and noisy coffee breaks! Finally, many thanks go to the morning coffee and lunch break crews, to You-Hua Chu and John Dickel for the always refreshing chats, and Icko Iben for the most melodic whistle. Outside the Astronomy community, life was made easier especially the first few years I was in Urbana, by having a few more good friends, some from my college years, Nikos Konstantinidis, Stefania Lampoura, Costas Karafasoulis, Jiannis Alexandrou, with whom I remain in almost daily e-mail contact, but also friends here in the States, whose presence eased the strong nostalgia for Greece, John Giapintzakis, Thekla Halouva, Natassa Psalti, George Evangelidis, Leonidas Tsetseris, Paschalis Paschos, Hara Papathanassiou, and Philippos Papadopoulos. Thinking about my choices in Astronomy, I feel the need to thank three people at my undergraduate school (Aristotle University of Thessaloniki), who are very special to me: Jiannis Seiradakis, Stavros Avgoloupis, and George Kolovos.