Unveiling Accretion Disks - Physical Parameter Eclipse Mapping of Accretion Disks in Dwarf Novae

Unveiling Accretion Disks -
Physical Parameter Eclipse Mapping
of Accretion Disks in Dwarf Novae

Dissertation

by

Sonja Vrielmann

Universitäts-Sternwarte Göttingen

Mai 1997

Zusammenfassung

Diese Arbeit stellt eine neue Tomographiemethode vor die Bedeckungstomographie in physikalischen Parametern (Physical Parameter Eclipse Mapping). Sie ist entwickelt um die Struktur von Akkretionsscheiben in kataklysmischen Veränderlichen direkt in Form der grundlegenden physikalischen Parameter zu kartieren.
Kataklysmische Veränderliche sind enge Doppelsternsysteme in denen Materietransfer von einem der Sterne typischerweise ein Hauptreihenstern zum anderen einem weißen Zwerg stattfindet und zu der Ausbildung einer Akkretionsscheibe führt. Akkretionsscheiben sind von generellem Interesse in der Astrophysik da sie in einer Vielzahl von Objekten mit Masseneinfall auftreten wie z.B. aktiven galaktischen Kernen und jungen stellaren Objekten. Bedeckende kataklysmische Veränderliche sind ideale Laboratorien um solche Akkretionsprozesse zu untersuchen da mit Veränderung der Bahnphase unterschiedliche Teile der Scheibe sichtbar werden.

Die Tomographiemethode basiert auf der klassischen Bedeckungstomographie welche durch die Anpassung an Bedeckungslichtkurven Intensitätsverteilungen in der Akkretionsscheibe rekonstruiert. Diese Rückprojektion benutzt einen Maximum Entropie Algorithmus der die einfachste Lösung auswählt die mit den Daten kompatibel ist. In meiner neuen Methode sind die Intensitätsverteilungen durch die Verteilungen physikalischer Parameter ersetzt. Dazu wird ein spezifisches Modellspektrum benutzt um einen Satz von Bedeckungslichtkurven in verschiedenen Wellenlängen anzupassen. Das Spektrum wird je nach untersuchtem Objekt und seinem Zustand zur Zeit der Beobachtung ausgewählt.

Die vorliegende Arbeit zeigt durch die Anwendung auf synthetische Daten da die neue Methode in der Lage ist gegebene Parameterverteilungen zu reproduzieren. Dies gilt unter der Voraussetzung da die Parameter Werte im Parameterraum annehmen die außerhalb von Regionen mit Mehrdeutigkeiten liegen. Zwei Versionen mit einfachen Modellspektren wurden getestet. Prinzipiell läßt sich die Methode jedoch mit beliebigen Modellspektren anwenden.

Die neue Methode wird auf zwei reale Datensätze der Zwergnovae IP Pegasi im Ausbruch und HT Cassiopeiae im Ruhezustand angewendet. Trotz der einfachen Annahmen hinsichtlich der zugrundeliegenden Modellspektren können die Beobachtungen relativ gut reproduziert werden. Die Analysen führen zu Verteilungen der Temperatur und im Fall der optisch dünnen Akkretionsscheibe von HT Cassiopeiae zusätzlich der Oberflächendichte.

Zusätzlich werden Emissionslinien von HT Cassiopeiae mit der klassischen Bedeckungstomographiemethode analysiert um Intensitätsverteilungen zu rekonstruieren. Der Vergleich mit Intensitätsverteilungen im Kontinuum zeigt da in der erwarteten Weise die Emissionslinien im Außenbereich der Scheibe in Absorptionslinien im Inntenteil übergehen.

Abstract

This work presents a new tomography algoithm the Physical Parameter Eclipse Mapping method. It has been designed to reconstruct the structure of accretion disks in cataclysmic variables in terms of the basic physical parameters.

Cataclysmic variables are close interacting binaries in which mass transfer from one of the stars typically a main sequence star to the other star a white dwarf proceeds via an accretion disk around the white dwarf. Accretion disks are of general importance in astrophysics since they occur in a number of objects with mass accretion like active galactic nuclei and young stellar objects. The eclipsing cata clysmic variables are ideal systems to study such accretion process since with the varying orbital phase different parts of the accretion disk can be viewed.

The tomography method is based on the classical Eclipse Mapping algorithm which yields intensity distributions in the accretion disk by fitting the observed eclipse light curve. In order to avoid ambiguities this back projection is using a maximum entropy algorithm with selects the smoothest solution still compatible with the data. In my new method the intensity distributions are replaced by distributions of physical parameters using a specific theoretical model spectrum to fit a set of eclipse light curves at various wavelengths. The spectrum is chosen according to the type of cataclysmic variable under investigation and its state at the time of observation.

This work shows through application to synthetic data that with such an approach given distributions in physical parameters can be reproduced as long as the parameters assume values in the parameter space outside of regions where ambiguities arise. Versions with two simple models are tested but in principle this method can cope with any given model spectrum.

The Physical Parameter Eclipse Mapping method is applied to two sets of real data of the dwarf nova IP Pegasi on decline from outburst and HT Cassiopeiae in quiescence. In spite of the simple assumptions regarding the applied models good fits to the observations are achieved leading to reconstructed distributions of the temperature and for the optically thin accretion disk in HT Cassiopeiae additionally the surface density.

In addition emission lines of HT Cassiopeiae are analysed with the classical Eclipse Mapping method to reconstruct intensity distributions. The comparison to continuum light distributions shows that the emission lines in the outer parts of the disk transform into absorption towards the disk centre.

Contents

1 Preface

2 Accretion in Cataclysmic Variables
2.1 Cataclysmic Variables
2.2 The observations
2.2.1 The accretion disk
2.2.2 The white dwarf
2.2.3 The boundary layer
2.2.4 The bright spot and the gas stream
2.2.5 The red star
2.2.6 The outburst state
2.3 Theories of accretion phenomena
2.3.1 The viscosity
2.4 The outbursts
2.4.1 The Disk Instability model
2.4.2 The Mass Transfer Burst model
2.4.3 DI model vs. MTB model

3 IP Peg and HT Cas
3.1 The "puzzling" system IP Pegasi
3.1.1 A Dwarf Nova in the spotlight
3.1.2 The spectral appearance
3.1.3 The primary component
3.1.4 The secondary component: The red star
3.1.5 Setting the scene
3.1.6 The eclipses
3.1.7 Summary of the disk parameters
3.2 The "Rosetta Stone" HT Cassiopeiae
3.2.1 An unusual Dwarf Nova
3.2.2 The spectral appearance
3.2.3 The primary component
3.2.4 The secondary component: The red star
3.2.5 Setting the scene
3.2.6 The eclipses
3.2.7 Summary of the disk parameters

4 Eclipse Mapping
4.1 Tomography methods
4.2 Theory
4.2.1 The Entropy
4.2.2 The initial and the default image
4.2.3 Fit to the observations
4.2.4 Illustration of the MEM algorithm
4.3 Images of accretion disks
4.3.1 IP Peg & HT Cas
4.3.2 The general picture

5 Eclipse Mapping in Emission Lines
5.1 Emission Line Mapping of HT Cas
5.2 Discussion

6 Physical Parameter Eclipse Mapping
6.1 The new idea
6.2 Description of the method
6.2.1 Polar grid
6.2.2 Spherical white dwarf
6.2.3 White Dwarf spectra
6.2.4 The uneclipsed component
6.2.5 Use of a grid of model spectra
6.2.6 Use of passband response functions
6.3 Physical Models
6.3.1 Black body
6.3.2 A uniform LTE slab model

7 Application of the method to synthetic data
7.1 Test of the Temperature Mapping
7.2 Comparison with classical Eclipse Mapping
7.3 LTE-slab-version
7.3.1 Study of the model
7.3.2 Test of the LTE slab version
7.3.3Discussion

8 Application of the method to real data
8.1 IP Peg on decline from outburst
8.1.1 Optically thick accretion disk
8.1.2 Discussion
8.1.3 Comparison to the results from Bobinger et al
8.1.4 Comparison to the superoutburst light curve from HT Cas
8.2 HT Cas in quiescence
8.2.1 Optically thick disk in quiescence
8.2.2 Optically thin solution
8.2.3 Discussion
8.2.4 Fitting the white dwarf simultaneously
8.2.5 Fit with different distances
8.2.6 Comparison to Wood Horne & Vennes
8.3 Further improvements of the method

9 Discussion 

List of astronomical constants
List of Figures
List of Tables
References

So turning twisting round and round
for all your life as times pass by
no string holds you and neither ground
the only reason: Dance or Die.

Chapter 1

Preface

When we see the stars flickering above us so far away that we see no possibility to ever reach them ourselves we might wonder how the astronomers have found out so much about the universe. The only information we get from the stars and galaxies is the light that we see either with our naked eye or with telescopes of various kinds. But just this radiation contains a huge amount of information about the physical structure of the universe and physical processes occuring within.

Still we have the wish to get a picture from the stars as if taken by a photo grapher from close by for the last verification of the truth of our models. This work is aimed at getting such a closer look at a certain kind of astronomical object the accretion disks¹ in close interacting binaries by producing spatially resolved images. The following Chapter 2 introduces the reader to the objects under investigation the cataclysmic variables. The most interesting phenomenon the accretion of matter through a disk is described by current theoretical models. Chapter 3 reviews two such systems the dwarf novae IP Peg and HT Cas summarizing the information available on them. For the understanding of the following Chapters this information is not essential and the Sections may be skipped. Chapter 4 explains the Eclipse Mapping method the algorithm on which my new method is based. Therefore it is necessary to understand the principles of this classical method. In Chapter 5 I describe the application of this classical method to eclipse light curves in emission lines of the system HT Cas.

The idea of the Physical Parameter Eclipse Mapping method is presented in Chapter 6. In order to interpret real data with confidence it is very important to understand the behaviour of the method when applied to synthetic data as described in Chapter 7. Finally in Chapter 8 the application of the method to observations from the dwarf novae IP Pegasi in outburst and HT Cassiopeiae in quiescence is described. The last Chapter 9 summarizes the thesis and discusses the derived results.

Chapter 2 

Accretion in Cataclysmic Variables

The accretion disks I have investigated are found in cataclysmic variables (CVs). In the following sections I will give a brief overview of the properties of this type of system describe some of the accretion phenomena and review current theories of the physical processes responsible for them. Comprehensive reviews were given e.g. by la Dous (1989) or Warner (1995).

2.1 Cataclysmic Variables

It is generally accepted that cataclysmic variables are close binaries undergoing mass transfer. They contain a late (close to) main sequence star filling its Roche lobe the secondary star which loses mass and an accreting white dwarf. At the inner Lagrangian point where all forces balance matter can easily transgress from the Roche lobe filling star into the Roche lobe of the white dwarf. Angular momentum conservation Coriolis forces and viscosity force the matter into quasi circular orbits around the central object. By largely unknown processes angular momentum is carried outwards by a small fraction of matter causing the remaining matter to spiral inward towards the white dwarf. Since the matter flow from the secondary is (more or less) permanent a luminous disk of matter is formed around the central object the accretion disk.

In this accretion disk the matter loses gravitational energy which is (partly) transformed into radiation leading to a light source which is often brighter than the white dwarf. Only in eclipsing systems the white dwarf can sometimes be distinguished by pronounced steps in the ingress and egress of the light curve. The matter transmitted from the red dwarf star into the Roche lobe of the white dwarf hits the accretion disk at its edge some way from the line combining the two stars in the direction of rotation. Here the kinetic energy of the stream matter in (almost) free fall is partly dissipated and a shock is produced which locally heats up the disk material and leads to a prominent emitting source the bright spot².

[...]

1 Though throughout the thesis I stick to the British spelling rather than the American, I make one exception for pure symmetry. The word disk.

2 Reading the literature in the field of cataclysmic variables one stumbles over the term used for this spot. Some authors call it hot spot while more recently is is rather called bright spot. Since the temperature of this spot is not necessarily very high I also keep to the expression bright spot.