85-XX ASTRONOMY AND ASTROPHYSICS (For celestial mechanics, see 70F15)
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Institute
Eta Carinae
(2018)
The exceptional binary star Eta Carinae has been fascinating scientists and the people in the Southern hemisphere alike for hundreds of years. It survived an enormous outbreak, comparable to a supernova energy-wise, and for a short period became the brightest star of the night sky. From observations from the radio regime to X-rays the system's characteristics and its emission in photon energies up to ~ 50 keV are well studied today. The binary is composed of two massive stars of ~ 30 and ~ 100 solar masses. Either star drives a strong stellar wind that continuously carries away a fraction of its mass. The collision of these winds leads to a shock on each side of the encounter. In the wind-wind-collision region plasma gets heated when it is overrun by the shocks. Part of the emission seen in X-rays can be attributed to this plasma. Above ~ 50 keV the emission is no longer of thermal origin: the required plasma temperature exceeds the available mechanical energy input of the stellar winds. In contrast to its observational history in thermal energies observational evidence of Eta Carinae's non-thermal emission has only recently built up. In high-energy gamma-rays Eta Carinae is the only binary of its kind that has been detected unambiguously. Its energy spectrum reaches up to ~ hundred GeV, a regime where satellite-based gamma-ray experiments run out of statistics. Ground-based gamma-ray experiments have the advantage of large photon collection areas. H.E.S.S. is the only gamma-ray experiment located in the Southern hemisphere and thus able to observe Eta Carinae in this energy range. H.E.S.S. measures gamma-rays via electromagnetic showers of particles that very-high-energy gamma-rays initiate in the atmosphere. The main challenge in observations of Eta Carinae with H.E.S.S. is the UV emission of the Carina nebula that leads to a background that is up to 10 times stronger than usual for H.E.S.S. This thesis presents the first detection of a colliding-wind binary in very-high-energy gamma-rays and documents the studies that led to it. The differential gamma-ray energy spectrum of Eta Carinae is measured up to 700 GeV. A hadronic and leptonic origin of the gamma-ray emission is discussed and based on the comparison of cooling times a hadronic scenario is favoured.
In the here presented work we discuss a series of results that are all in one way or another connected to the phenomenon of trapping in black hole spacetimes.
First we present a comprehensive review of the Kerr-Newman-Taub-NUT-de-Sitter family of black hole spacetimes and their most important properties. From there we go into a detailed analysis of the bahaviour of null geodesics in the exterior region of a sub-extremal Kerr spacetime. We show that most well known fundamental properties of null geodesics can be represented in one plot. In particular, one can see immediately that the ergoregion and trapping are separated in phase space.
We then consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer. Therefore the topological structure of the trapped set on the celestial sphere of any observer is identical to that in Schwarzschild.
We discuss how this is relevant to the black hole stability problem.
In a further development of these observations we introduce the notion of what it means for the shadow of two observers to be degenerate. We show that, away from the axis of symmetry, no continuous degeneration exists between the shadows of observers at any point in the exterior region of any Kerr-Newman black hole spacetime of unit mass. Therefore, except possibly for discrete changes, an observer can, by measuring the black holes shadow, determine the angular momentum and the charge of the black hole under observation, as well as the observer's radial position and angle of elevation above the equatorial plane. Furthermore, his/her relative velocity compared to a standard observer can also be measured. On the other hand, the black hole shadow does not allow for a full parameter resolution in the case of a Kerr-Newman-Taub-NUT black hole, as a continuous degeneration relating specific angular momentum, electric charge, NUT charge and elevation angle exists in this case.
We then use the celestial sphere to show that trapping is a generic feature of any black hole spacetime.
In the last chapter we then prove a generalization of the mode stability result of Whiting (1989) for the Teukolsky equation for the case of real frequencies. The main result of the last chapter states that a separated solution of the Teukolsky equation governing massless test fields on the Kerr spacetime, which is purely outgoing at infinity, and purely ingoing at the horizon, must vanish. This has the consequence, that for real frequencies, there are linearly independent fundamental solutions of the radial Teukolsky equation which are purely ingoing at the horizon, and purely outgoing at infinity, respectively. This fact yields a representation formula for solutions of the inhomogenous Teukolsky equation, and was recently used by Shlapentokh-Rothman (2015) for the scalar wave equation.
The solar activity and its consequences affect space weather and Earth’s climate. The solar activity exhibits a cyclic behaviour with a period of about 11 years. The solar cycle properties are governed by the dynamo taking place in the interior of the Sun, and they are distinctive. Extending the knowledge about solar cycle properties into the past is essential for understanding the solar dynamo and forecasting space weather. It can be acquired through the analysis of historical sunspot drawings. Sunspots are the dark areas, which are associated with strong magnetic fields, on the solar surface. Sunspots are the oldest and longest available observed features of solar activity.
One of the longest available records of sunspot drawings is the collection by Samuel Heinrich Schwabe during 1825–1867. The sunspot sizes measured from digitized Schwabe drawings are not to scale and need to be converted into physical sunspot areas. We employed a statistical approach assuming that the area distribution of sunspots was the same in the 19th century as it was in the 20th century. Umbral areas for about 130 000 sunspots observed by Schwabe were obtained. The annually averaged sunspot areas correlate reasonably well with the sunspot number. Tilt angles and polarity separations of sunspot groups were calculated assuming them to be bipolar. There is, of course, no polarity information in the observations. We derived an average tilt angle by attempting to exclude unipolar groups with a minimum separation of the two surmised polarities and an outlier rejection method, which follows the evolution of each group and detects the moment, when it turns unipolar as it decays. As a result, the tilt angles, although displaying considerable natural scatter, are on average 5.85° ± 0.25°, with the leading
polarity located closer to the equator, in good agreement with tilt angles obtained from 20th century data sets. Sources of uncertainties in the tilt angle determination are discussed and need to be addressed whenever different data sets are combined.
Digital images of observations printed in the books Rosa Ursina and Prodromus pro sole mobili by Christoph Scheiner, as well as the drawings from Scheiner’s letters to Marcus Welser, are analyzed to obtain information on the positions and sizes of sunspots that appeared before the Maunder minimum. In most cases, the given orientation of the ecliptic is used to set up the heliographic coordinate system for the drawings. Positions and sizes are measured manually displaying the drawings on a computer screen. Very early drawings have no indication of the solar orientation. A rotational matching using common spots of adjacent days is used in some cases, while in other cases, the assumption that images were aligned with a zenith–horizon coordinate system appeared to be the most likely. In total, 8167 sunspots were measured. A distribution of sunspot latitudes versus time (butterfly diagram) is obtained for Scheiner’s observations. The observations of 1611 are very inaccurate, but the drawings of 1612 have at least an indication of the solar orientation, while the remaining part of the spot positions from 1618–1631 have good to very good accuracy. We also computed 697 tilt angles of apparent bipolar sunspot groups, which were observed in the period 1618–1631. We find that the average tilt angle of nearly 4° does not significantly differ from the 20th century values.
The solar cycle properties seem to be related to the tilt angles of sunspot groups, and it is an important parameter in the surface flux transport models. The tilt angles of bipolar sunspot groups from various historical sets of solar drawings including from Schwabe and Scheiner are analyzed. Data by Scheiner, Hevelius, Staudacher, Zucconi, Schwabe, and Spörer deliver a series of average tilt angles spanning a period of 270 years, in addition to previously found values for 20th-century data obtained by other authors. We find that the average tilt angles before the Maunder minimum were not significantly different from modern values. However, the average tilt angles of a period 50 years after the Maunder minimum, namely for cycles 0 and 1, were much lower and near zero. The typical tilt angles before the Maunder minimum suggest that abnormally low tilt angles were not responsible for driving the solar cycle into a grand minimum.
With the Schwabe (1826–1867) and Spörer (1866–1880) sunspot data, the butterfly diagram of sunspot groups extends back till 1826. A recently developed method, which separates the wings of the butterfly diagram based on the long gaps present in sunspot group occurrences at different latitudinal bands, is used to separate the wings of the butterfly diagram. The cycle-to-cycle variation in the start (F), end (L), and highest (H) latitudes of the wings with respect to the strength of the wings are analyzed. On the whole, the wings of the stronger cycles tend to start at higher latitudes and have a greater extent. The time spans of the wings and the time difference between the wings in the northern hemisphere display a quasi-periodicity of 5–6 cycles. The average wing overlap is zero in the southern hemisphere, whereas it is 2–3 months in the north. A marginally significant oscillation of about 10 solar cycles is found in the asymmetry of the L latitudes. This latest, extended database of butterfly wings provides new observational constraints, regarding the spatio-temporal distribution of sunspot occurrences over the solar cycle, to solar dynamo models.