Diplomarbeit Differential emission measures and elemental abundances of stellar coronae vorgelegt von Carolin Liefke Hamburger Sternwarte Universit¨at Hamburg Hamburg Oktober 2005 Titlepage: An image of coronal loops over the eastern solar limb obtained with the TRACE satellite on 6 November 1999 at 2:30 UT in the 171 A˚ bandpass that includes prominent emission lines of Fe ix and Fe x, corresponding to a characteristic plasma temperature of about 1×106 K. Image taken from http://vestige.lmsal.com/TRACE/POD/TRACEpodarchive.html Zusammenfassung Wasserstoff ist das h¨aufigste Element im Universum. In der uns vertrauten baryonischen Materie macht es einen Massenanteil von etwa 73% aus, gefolgt von Helium mit etwa 25%. Alle weit- eren Elemente mussen¨ sich die restlichen 2% teilen, die h¨aufigsten unter ihnen sind wiederum Kohlenstoff, Stickstoff, Sauerstoff und Eisen. Nicht nur fur¨ uns Menschen und das Leben auf der Erde sind aber genau diese Spurenelemente von essentieller Bedeutung. Sie haben auch einen erheblichen Einfluß auf die physikalischen Eigenschaften der Sterne, besonders auf die in ihnen stattfindenden radiativen Prozesse. Be- merkbar machen sich die Metalle dann wieder in den beobachteten Spektren, wo sie ihre Spuren in Form von Absorptions- oder Emissionslinien hinterlassen. Dementsprechend ist es m¨oglich mithilfe dieser Linien die genauen H¨aufigkeiten der einzelnen Elemente zu rekonstruieren. Eine solche Elementh¨aufigkeitsanalyse ist allerdings nicht trivial, sie erfordert die genaue Ken- ntnis der physikalischen Prozesse, die an der Entstehung der Spektrallinien beteiligt sind, sowie die Bedingungen unter denen sie entstehen. In der Korona, der ¨außersten Atmosph¨arenschicht eines sonnen¨ahnlichen Sterns, werden Temperaturen von mehreren Million Kelvin bei gleichzeitig relativ geringen Dichten erreicht. Das Spektrum der Korona ist vorrangig im R¨ontgenbereich beobachtbar, es ist dominiert von Emissionslinien der schwereren Elemente. Hochaufl¨osende R¨ontgenspektroskopie mit Hilfe der Satelliten Chandra und XMM-Newton hat in den letzten Jahren die Untersuchung der Spektren stellarer Koronen in bislang unerreichter Genauigkeit erm¨oglicht. Zur Modellierung des Koronaspektrums werden Informationen wie Temperatur, Dichte oder Druck ub¨ er das koronale Plasma, das diese Linien aussendet, ben¨otigt. Diese Parameter lassen sich allerdings nicht direkt beobachten und werden durch das differentielle Emissionsmaß DEM zusammengefaßt. Es verknupft¨ den gemessenen Fluß in einer Linie direkt mit der Elementh¨aufig- keit und den atomaren Daten, die die Linie charakterisieren. Es gilt daher, zun¨achst das differentielle Emissionsmaß unabh¨angig von den H¨aufigkeiten der Elemente zu bestimmen. In dieser Arbeit wurden zwei entsprechende Methoden angewandt, bei denen das differentielle Emissionsmaß mithilfe von h¨aufigkeitsunabh¨angigen Verh¨altnissen von Linien jeweils desselben Elementes bzw. ausschließlich mit Eisenlinien ub¨ er Polynome ver- schiedener Ordnungen angen¨ahert wird. Im Anschluß wurden mit diesem differentiellen Emis- sionsmaß die gemessenen Linienflusse¨ der zugrundeliegenden Linien synthetisiert und somit die entsprechenden koronalen Elementh¨aufigkeiten bestimmt. Diese Methode wurde auf mehrere Datens¨atze verschiedener Sterne angewandt. Vergleiche des jeweils ermittelten differentiellen Emissionsmaßes und der daraus resultierenden Elementh¨aufig- keiten mit entsprechenden Daten aus der Literatur zeigen eine gute Ub¨ ereinstimmung. 3 Abstract Hydrogen is not only the simplest and lightest but also by far the most frequent element in the universe. In the baryonic matter we are familiar with it amounts to a mass fraction of about 73%, followed by helium with approximately 25%. The remaining elements, summarized by astrophysicists as "metals", have to share the residual 2%. From these, the most abundant are carbon, nitrogen, oxygen and iron. These trace elements are not only of vital importance for life on earth, they also have a serious influence of the physical properties of stars, especially on radiative processes running inside. The metals become later visible in observed spectra, where they leave their marks as absorption or emission lines. It is thus possible to reconstruct the precise abundances of the indivual elements from these lines. Such an analysis of the elemental abundances is nontrivial though, a detailed knowledge of the physical processes and underlying conditions determining the formation of the spectral lines is required. Hence it is not surprising that in recent years even for the Sun, which can be considered as well-known and comparatively easy to study, on occasion revised numbers { sometimes noticeably deviating from the previous ones { for the abundances of individual elements have been released. A corresponding analysis of stars other than the Sun is much more difficult, there is however clear evidence that their abundances only seldom correspond to the solar values. In the corona, the outermost atmospheric layer of a solar-like star, temperatures of several million Kelvin and comparatively low densities are reached. The coronal spectrum is primarily observable in X-rays, it is dominated by emission lines of the heavier elements. High-resolution X-ray spectroscopy with the Chandra and XMM-Newton satellites presently enables the analysis of stellar coronae with unrivaled accuracy. Parameters like temperature, density or pressure of the coronal plasma emitting these emission lines determine the modeling of a coronal spectrum, they are however not directly observable. Instead, they were combined to the soo-called differential emission measure DEM, that connects measured line fluxes directly with the elemental abundance and the atomic data characterizing the line emissivity. The differential emission measure has thus to be determined independently of the abundances. In this study I applied two methods that approximate the DEM with polynomials of different orders. One approach makes use of abundance-independent line ratios of lines originating from the same element, the other makes use solely of iron lines. Subsequently, the measured line fluxes are reproduced with the underlying DEM and thus the coronal elemental abundances are determined. This method was applied to several datasets of different stars. A comparison of the differential emission measure and the resulting abundances with corresponding data from the literature shows a good agreement. 4 Contents Zusammenfassung 3 Abstract 4 1 Introduction 7 1.1 The corona of the Sun . 7 1.2 Coronae of other stars . 11 2 The physics of stellar coronae 14 2.1 Magnetic fields and coronal heating . 14 2.2 X-ray emission from coronal plasmas . 16 2.2.1 Line emission . 17 2.2.2 Continuum emission . 21 2.3 Coronal abundances . 22 3 High-resolution X-ray spectroscopy with Chandra and XMM-Newton 24 3.1 Chandra . 25 3.1.1 The High-Energy Transmission Grating Spectrometer HETGS . 26 3.1.2 The Low-energy Transmission Grating Spectrometer LETGS . 27 3.2 XMM-Newton . 28 3.2.1 The European Photon Imaging Camera EPIC . 29 3.2.2 The Reflection Grating Spectrometer RGS . 30 4 Modeling abundances and differential emission measure 32 4.1 Data processing . 32 4.2 Line fitting with CORA . 33 4.3 The lines used in this study . 35 4.3.1 H-like Ly α lines and He-like resonance lines . 35 4.3.2 Iron lines . 39 4.3.3 Interstellar absorption . 44 4.4 Continuum measurements . 45 4.5 Differential emission measure from ratios of H-like to He-like lines . 46 4.5.1 Implementation . 47 4.5.2 Abundance determination . 49 4.6 Differential emission measure from iron lines . 50 5 Results and discussion 52 5.1 Stability of the fit . 52 5.2 Influence of constraints and initial conditions . 53 5.2.1 Initial values of the polynomial coefficients . 53 5.2.2 Constraining the slopes of the DEM at the temperature boundaries . 54 5.3 Quality of the DEM fit and the deduced abundances . 55 5 5.4 Error analysis . 56 5.5 Open issues and possible improvements . 58 6 Individual stars 59 6.1 The zero-age main sequence star AB Dor . 61 6.1.1 The HETGS dataset ObsID 16 . 61 6.1.2 The LETGS dataset ObsID 3762 . 67 6.1.3 The RGS dataset ObsID 0123720301 . 71 6.1.4 Combined datasets . 76 6.2 Algol, the eclipsing binary . 82 6.2.1 The HETGS dataset ObsID 604 . 83 6.2.2 The LETGS dataset ObsID 2 . 88 6.2.3 The RGS dataset ObsID 0112880701 . 92 6.2.4 Combined datasets . 96 6.3 AU Mic, a young active M-dwarf . 102 6.3.1 The HETGS dataset ObsID 17 . 102 6.3.2 The RGS dataset ObsID 0111420101 . 106 6.3.3 Combined datasets . 109 6.4 UX Ari, an RS CVn system . 113 6.4.1 The HETGS dataset ObsID 605 . 113 6.4.2 The LETGS dataset ObsID 597 . 118 6.4.3 The RGS dataset ObsID 0111390301 . 122 6.4.4 Combined datasets . 125 A The fit dem routine 131 Bibliography 145 6 1 Introduction 1.1 The corona of the Sun The Sun has been observed from time immemorial. Many ancient cultures were aware of its importance for life on earth; the life of the people was centered on the daily recurrence of the Sun and the cycle of seasons. The Sun therefore embodied a divine power and was regarded with awe. Even in Christian Europe up to the end of the middle ages it was a symbol for the perfection of creation and had to be unblemished and unchanging. Thus early observations of sunspots being visible with the naked eye at sunrise or sunset perished or were forgotten. The invention of the telescope early in the 17th century led, among other things, to definite observations of sunspots. Many scientists of that time, e.g. Galileo Galilei, saw the dark spots in front of the solar disc, but there was disagreement about the nature of this phenomenon. Was it perhaps an illusion, feigned by the telescope? While Galilei was already convinced that the spots were structures on the solar surface, the Jesuit Christoph Scheiner at first thought to see shadows of a planet by then unknown to pass by the Sun.