Spectropolarimetric analysis of circumstellar mass flows by Kenneth Wood Thesis submitted to the University of Glasgow for the degree of Ph.D. Department of Physics and Astronomy, The University, ©Kenneth Wood Glasgow G12 8QQ. September 1993. ProQuest Number: 13834104 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 13834104 Published by ProQuest LLC(2019). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346 GLASGOW UNIVERSITY L 1 B R A R Y _ Sum m ary Polarimetry is not a difficult subject. Unfortunately, as it is a second order effect (typical stellar polarisations are of the order of a few percent), in many undergraduate courses on stellar atmo­ spheres and the interstellar medium it is either ignored entirely or mentioned as an aside if there is time at the end of the course. Through this lack of teaching no standard introductory texts on the subject have been adopted and many student’s experience of polarimetry is the intense and rather obscure mathematical formulation of the Stokes parameters presented in Chandrasekhar’s book on radiative transfer. As a result most theoreticians and observers embark upon research careers with the knowledge that there exist four Stokes parameters, but unaware of their physical significance or diagnostic potential. For these reasons I have devoted the first chapter of this thesis to giving a brief introduction to the subject of polarimetry and its astronomical applications. The parameters required to study polarised radiation - the Stokes parameters - are presented mathematically and their physical interpretations in terms of sums and differences of intensity components of the radia­ tion field are outlined. Following on from a summary of sources of polarised radiation in astronomy the theoretical analysis predicting the “broad-band” polarisation from the optically thin Thomson scattering extended envelopes surrounding hot single stars is presented. Chapters 2, 3, 4 and 5 extend this theoretical framework to treat the problem of line polarisa­ tion through scattering of unpolarised stellar lines in moving atmospheres. Due to the complexity of polarised radiative transfer this problem has not been treated in a systematic fashion before and the few theoretical investigations to date were built around existing radiative transfer codes which did not allow the basic physical processes contributing to the line polarisation to be iso­ lated. While the theory presented in these chapters is much simpler than a full blown radiative transfer approach it clearly demonstrates the role of scattering and Doppler redistribution, due to the scatterer’s motion, in the production of spectropolarimetric line profiles. It is further shown that adopting this approach allows determination of the inclination, velocity and density structure of circumstellar discs from analysis of the scattered spectropolarimetric line profiles - informa­ tion which cannot be determined from spectrometry alone. At the end of Chapter 5 an outline is given as to the future work required to develop a comprehensive theoretical understanding of stellar line polarisation, noting at each stage the effects on the resulting line profiles of the various ammendments to the theory. Temporal variations in the continuum polarisation of Be stars have been observed to occur over a wide range of timescales and have been attributed to variations in the shape or rate of stellar mass loss which changes the number of scattering electrons in the stellar envelope. With this interpretation of the polarimetric variations Chapter 6 illustrates a method for determining these episodic mass loss functions from analysis of polarimetric and absorption line strength data during the outbursts. The formulation of the equations in this chapter as an inverse problem was the initial problem suggested to me by my supervisor, John Brown, and the background reading I did on circumstellar polarisation while working on this problem led me to investigate the line polarisation variations presented in the previous chapters. The stellar wind speeds considered in the above chapters were such that any relativistic effects could be ignored. However, Chapter 7 considers the scattering of radiation off relativistic electrons yielding a very simple result for the degree of scattered polarisation involving the aberrational angle. This is part of an on-going investigation into polarisation from scattering in relativistic jets, which I am conducting in collaboration with John Simmons, of which the initial results are presented. The research presented in the thesis was conducted by myself or in collaboration with other members of the Glasgow Astronomy Group. The mass loss inversion, Chapter 6, and part of Chapter 2 have been published in Astronomy & Astrophysics and their references are, Brown J.C., Wood K., 1992, Astron. Astrophys., 265, 663 Wood K., Brown J.C., Fox G.K., 1993, Astron. Astrophys ., 271, 492 iii Acknowledgements This thesis was conducted under the supervision of Professor John Brown in the Department of Physics and Astronomy at the University of Glasgow and funded by the United Kingdom Science and Engineering Research Council (SERC). The work I have conducted would not have been possible without the advice and support of John Brown. His encouragement to contact and visit departments conducting research relevant to my own has been of great benefit and I would like to thank him for all the travel opportunities he gave me. Throughout my Ph.D. research I have constantly sought the advice of all members of the Astronomy group and I would like to thank them all for their patience, in particular John Simmons who suggested and guided me through the work in Chapter 7 and Geoff Fox, now at the University of Wisconsin, with whom I had many discussions regarding line polarisation. Over the three years of the Ph.D. I made several research and conference visits to the USA and Canada. These would not have been possible without the encouragement from John Brown and financial support of the SERC and the Physics and Astronomy Department at Glasgow. I also appreciate the warm welcome extended to me by members of the Astronomy Departments in Madison and Montreal during my visits there. Contents S u m m a r y ____________________________________________________________________________ i Acknowledgements_________________________________________________________________ iii Chapter 1 Astronomical polarisation ____________________________________________ 1 1.1 Introduction ............................................................................................................................................ 1 1.2 The Stokes parameters of polarised radiation .............................................................................. 2 1.3 Production of polarised radiation in astronomy ............................................................................ 5 1.3.1 Scattering 5 1.3.2 Synchrotron radiation 7 1.3.4 Interstellar polarisation 7 1.4 Polarisation from optically thin circumstellar envelopes ..........................................................9 1.4.1 General formalism 10 1.4.2 Unpolarised point source, axisymmetric envelope 13 1.4.3 Depolarisation factor for a finite spherical source 15 1.4.4 Occultation effects 15 1.4.5 Other continuum opacity sources in an optically thin envelope 16 1.4.6 How valid is the single scattering theory ? 18 1.5 Conclusions ..........................................................................................................................................20 Chapter 2 Spectropolarimetric line profiles from optically thin discs _________ 21 2.1 Introduction ..........................................................................................................................................21 2.2 Observations ........................................................................................................................................21 2.3 Theory ...................................................................................................................................................25 2.3.1 Polarisation in rotationally broadened spectral lines 25 2.3.2 Optical depth effects in a moving circumstellar envelope 27 2.3.3 Line scattering in an expanding envelope 28 2.4 Effects of electron bulk velocity on scattered line profiles ....................................................... 29 2.5 Scattering of monochromatic radiation ......................................................................................... 31 2.5.1 Pure disc rotation 32 2.5.2 Pure disc expansion 36 2.5.3 Rotation and expansion 42 2.6 Non-monochromatic source .............................................................................................................. 45 2.6.1 Pure disc rotation 46 2.6.2 Pure disc expansion 48 2.6.3 Disc expansion and rotation 49 2.7 General determination of disc inclination .....................................................................................54 Chapter 3 Inversion of Thomson scattered