FYSAST Examensarbete 15 hp Juni 2010 Magnetic Fields of Massive Stars Andreas Lundin Institutionen för fysik och astronomi Department of Physics and Astronomy Abstract Magnetfält i Massiva Stjärnor Magnetic Fields of Massive Stars Teknisk- naturvetenskaplig fakultet Andreas Lundin UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 This paper is an introduction to the subject of magnetic fields on stars, with a focus on hotter stars. Postadress: Basic astrophysical concepts are explained, including: Box 536 751 21 Uppsala spectroscopy, stellar classification, general structure and evolution of stars. The Zeeman effect and how Telefon: absorption line splitting is used to detect and 018 – 471 30 03 measure magnetic fields is explained. The properties Telefax: of a prominent type of magnetic massive star, Ap- 018 – 471 30 00 stars, are delved into. These stars have very stable, global, roughly dipolar magnetic fields theorized to Hemsida: have been captured during star formation and http://www.teknat.uu.se/student maintained throughout their lifetime. Different approaches to making models of the magnetic field of massive stars are explained, in particular the oblique rotator model. Finally, the use of the oblique rotator model is illustrated by finding possible field structures that would reproduce magnetic field observations of the star HD 37776. Handledare: Oleg Kochukhov Ämnesgranskare: Oleg Kochukhov Examinator: Kjell Pernestål FYSAST Contents 1 Stellar Spectroscopy 2 1.1 Spectroscopy . 2 1.2 Classification of Stellar Spectra . 3 2 Stellar Structure 4 2.1 Stellar Energy Sources . 4 2.2 Stellar Structure . 5 3 Stellar Evolution 6 3.1 Formation of Stars . 6 3.2 Main Sequence . 7 3.3 Post Main Sequence . 8 4 Diagnosing Stellar Magnetic Fields 9 4.1 Atom in a Magnetic Field . 9 5 The Zeeman Effect 9 5.1 Polarization Properties . 10 5.2 Observing Polarization in Stellar Spectral Lines . 11 5.3 Measuring Ap Star Magnetic Fields . 13 5.4 The Weak-Line Approximation . 14 5.5 The Weak-Field Approximation . 14 6 Ap Stars 14 6.1 Basic Characteristics of Magnetic Ap Stars . 14 6.2 Simple Models of Ap Stars . 15 7 Advanced Modeling 16 8 Recent discoveries 18 9 Magnetic Field Origin and Evolution 18 10 Finding the Field Structure of the Star HD 37776 20 1 1 Stellar Spectroscopy 1.1 Spectroscopy Before the invention of spectroscopy, stars could at most be described by dis- tance, brightness and movement. Information about chemical composition, surface temperature, and pressure was thought to be out of reach. In spectroscopy the light from a source is split so that individual wave- lengths can be observed, using for example a prism or a diffraction grating. Kirchhoff's laws describes what is seen in the resulting spectrum de- pending on the source: • A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines • A hot, diffuse gas produces bright spectral lines (emission lines) • A cool, diffuse gas produces bright spectral lines (absorption lines) These can be explained by the following concepts from quantum me- chanics: hc • The wavelength of a photon depends on its energy, λ = E • Atoms and molecules have discrete energy levels on which electrons can exist. • A photon can be absorbed by an atom or molecule if the photon carries energy equal to the exact amount needed for an electron to move to a higher level. • An excited atom or molecule can emit photons with energy equal to the difference between the levels when an electron moves down to a lower level. • A black body emits a continuous spectra of radiation, which only de- pends on the temperature. The spectrum produced by the detectable layer of the photosphere vaguely resembles a black body. If the light were to pass undisturbed, the spectrum would look just like the one for a black body with the temperature of the photosphere. But since the gas will become less dense and less hot further out, photons will be absorbed in the characteristic wavelengths of the gas. Gas may also emit light on some wavelengths. 2 The resulting spectrum from a star will therefore be a black body spec- trum with many dips or peaks. These are called spectral lines. The intensity of specific spectral lines are proportional to the concentra- tion of the corresponding atoms. It is thus possible to analyze the chemical composition of the outer layers of stars where the surface temperature is determined. 1.2 Classification of Stellar Spectra It was discovered early that different stars have different spectra, and several ways to classify were used. The system that is widely used today is the Harvard classification, which is a temperature sequence "O B A F G K M" were O is the hottest and M the coldest. These are then divided in subgroups by a number between 0 and 9, were 0 is the hottest. Stars to the left of the sequence are called early-type stars and those to the right are called late-type stars. The Sun is a type G2 star. Stars with different temperatures have absorption- and emission-lines of different strengths. The amount of a certain transition depends on the statistical distribution of electrons on energy levels in the atoms, and with increasing temperature comes more and higher states of excitation. Addi- tionally, different states of ionization changes the number of energy levels, thus explaining why hotter stars have fewer lines in their spectra. An atom's stage of ionization is denoted by a roman numeral after the atomic symbol. For example, H I is neutral hydrogen and He II is singly ionized. When a star is in equilibrium and burning hydrogen in its core, a phase that take up most of the stars lifetime, there is for the majority of stars a relation between luminosity and temperature. Stars that fit this relation and are in the stable hydrogen burning phase are therefore called main sequence stars. The relation between luminosity and temperature is usually represented in a so called Hertzsprung-Russel diagram, se figure 1. 2 Stellar Structure 2.1 Stellar Energy Sources When parts of a star contract under the force of gravity, potential energy is released. According to the virial theorem about half of this energy is radiated from the surface of the star while the other half heats up the contracting matter. Although this happens throughout the life of the star, it is only worth as an energy sources in the context of star formation. 3 Figure 1: Hertzsprung-Russel Diagram Figure taken from http://www.le.ac.uk/ph/faulkes/web/stars/r st overview.html Hydrogen is fused into helium by the proton-proton chain or the CNO cycle. The pp chain start occurring at temperatures of 4 million K, while the CNO cycle starts at 13 million K. CNO starts to dominate at 17 million K and its energy output increases faster with temperature. Thus CNO dominates in hotter stars more massive than 1.3 solar masses. The triple alpha process fuses helium nuclei into carbon. It starts to become effective at temperatures over 100 million K. In massive stars with even higher temperatures and densities several fusion processes occur; carbon burning, neon burning etc. 2.2 Stellar Structure The structure and evolution of stars are in large part dependent on the ways in which energy is transported from the core to the surface. As in any physical system, heat travels in the direction of lower temperature. In large parts of most stars, heat is transported by radiation being emitted 4 and reabsorbed repeatedly. In some parts though, the temperature drops so fast that instabillities occur where large chunks of matter with a different density move between layers. This is called convective motion. The distribution of convective layers depends on the mass of the star and has an important role in the way the star evolves. Stars with less than 25% sun masses are convective throughout since the temperature drops relatively fast on the small radius. As mass increase the convective zone begins further and further out, but still goes all the way out to the surface. At one solar mass, the convection is limited to 3% of the mass, extending about 30% of the radius. At a mass slightly higher than one solar mass, convection almost completely disapperas. Now when mass increases further, convection appears in the core, and extends further the more massive the star is. The distribution of convective zones at different mass is schematically illustrated in figure 2. Figure 2: Structure of ZAMS stars. The horizontal axis indicate the loga- rithm of mass in solar units, the vertical axis indicate the position in the star expressed in the fraction of the mass inside a particular radius. The cloudy areas indicate convection. The two solid curves show the positions where the distance r to the center is 0.25 and 0.5 times the surface radius. The dashed curves show the positions interior to which 50% and 90% of the stellar luminosity is generated. Figure is taken from article [9] Outside the interior region is the stellar atmosphere. The photosphere is the thin layer where the density is low enough that photons can leave the star 5 without being reabsorbed on the way, and is usually on the distance from the center that is considered to be the stars radius. It is the temperature of the photosphere that is considered to be the surface temperature or the effective temperature of the star. What is above the photosphere differs significantly between hot and cool stars. Cool stars, A7 or colder with effective temperatures below 7500 K, have a chromosphere where the temperature is between 7000 and 20 000 K.