«Sigillum Universitatis Ludovici Maximiliani MHD numerical simulations in a cosmological context Dissertation der Fakult¨t f¨ r Physik au ...»
Sigillum Universitatis Ludovici Maximiliani
MHD numerical simulations
in a cosmological context
Dissertation der Fakult¨t f¨ r Physik
Dissertation of the Faculty of Physics
der Ludwig-Maximilians-Universit¨t M¨ nchen
at the Ludwig Maximilian University of Munich
f¨ r den Grad des
for the degree of
Doctor rerum naturalium
vorgelegt von Federico Andr´s Stasyszyn
aus C´rdoba, Argentina
M¨ nchen, 15.03.2011 u Sigillum Universitatis Ludovici Maximiliani
1. Gutachter: Prof. Dr. Simon D. M. White
2. Gutachter: Prof. Dr. Harald Lesch
Tag der m¨ ndlichen Pr¨ fung: 27.05.2011 u u
Date of the oral exam:
Contents Contents I Zusammenfassung VII
IX I Introduction 1 1 Astrophysics and Magnetic Fields 3
1.1 Extragalactic physics basics.......................... 4
1.2 Observation of Magnetic Fields........................ 9 1.2.1 Synchrotron Emission......................... 9 1.2.2 Faraday rotation............................ 10 1.2.3 Zeeman Splitting............................ 11 1.2.4 Polarization of Optical Starlight.................... 12
1.3 Magnetic ﬁeld in galaxy clusters........................ 13
1.4 Large scale magnetic ﬁelds in the Universe..
Magnetic ﬁelds in the Universe are found in almost all studied environments. In particular, their presence in the inter-galactic medium and in the intra-cluster medium is conﬁrmed by diﬀuse radio emission as well as by observations of Faraday Rotation Measures towards polarized radio sources within or behind the magnetized medium.
Besides the observations, their dynamical importance in astrophysical systems is poorly constrained, therefore there are still plenty of processes in which the role of magnetic ﬁelds are not fully understood.
Astrophysical systems are complex and highly nonlinear. Therefore, numerical simulations have demonstrated to be a useful tool to study those problems. However, the inclusion of magnetic ﬁelds in numerical implementations is not easy to achieve.
Mainly because of the diﬃculties to keep the ∇ · B constraint low, and to have a stable implementation in diﬀerent circumstances.
We study and developed a cosmological MHD code in SPH. We study diﬀerent possible schemes to regularize the magnetic ﬁeld, and avoid instabilities. Those schemes included the use of Euler potentials to build the magnetic ﬁeld, as well as cleaning schemes for the numerical ∇ · B errors.
We studied the magnetic ﬁeld evolution in the context of cosmological structure formation of galaxy clusters. We compare diﬀerent numerical schemes leading us to the conclusion that the ∇ · B terms do not drive the evolution and growth of the magnetic ﬁeld in galaxy clusters. We made synthetic rotation measure maps and study the reversals of the magnetic ﬁeld in comparison with observations. The comparison between observations and high resolution simulations, suggests that the physics may be described by a multi scale turbulence model. This means that the turbulent dynamo driven by the cosmological cluster formation process works eﬀectively, reproducing basic properties from observations, even to details shown in structure functions and converging to the observation when we increase the resolution. We clearly demonstrates that using advanced schemes together with very high resolution allow to probe the properties of the ICM.
Additionally, we investigate the magnetic ﬁelds and their relation with the cosmic structure in which they are embedded. In general, the observed rotation measure signal is strongly dominated by denser regions (e.g. those populated by galaxy clusters and groups), and in unclear how is their transition to low density regions, because there is diﬃcult to acquire direct magnetic ﬁeld information of those regions.
Therefore statistical tools, such as correlation functions have to be used. To do so, we use cosmological simulations and try to mimic all the possible observation biases to constrain actual measurements. We ﬁnd that the shape of the cross-correlation function using a normalized estimator (in absence of any noise or foreground signal) nicely reﬂects the underlying distribution of magnetic ﬁeld within the large scale structure.
However, current measurement errors suppress the signal in such a way that it is impossible to relate the amplitude of the cross-correlation function to the underlying magnetization of the large scale structure (Stasyszyn et al., 2010).
Since early in history, humans were attracted to magnetic ﬁelds due to their ‘magical’ nature. Aristotle was the ﬁrst who scientiﬁcally approached magnetism in a discussion with Thales around 625 BC in Greece.
“The lodestone makes iron come or it attracts it” is one of the earliest references of magnetism in literature is in a book from the 4th century BC, titled Book of The Devil Valley Master. 14 centuries later, the Chinese scientist Shen Kuo (1031-1095) described the concept of magnetic needle and how it can improve the navigation accuracy. By the XII century the Chinese were known to have huge exploration and merchant ﬂeets using the lodestone compass to orientate.
In 1187, Alexander Neckham was the ﬁrst in Europe to describe the compass and its use for navigation. Later on, in 1269, Peter Peregrinus De Maricourt wrote the Epistola de magnete, the ﬁrst extant treatise describing the properties of magnets. The properties of magnets and the dry compass were discussed by Al-Ashraf, a Yemeni physicist, astronomer and geographer, in 1282.
In 1600, William Gilbert published De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth), in which he describes many of his experiments with an earth model called the terrella. From his experiments, he concluded that the Earth is magnetic itself and that this is the reason compasses point north (previously, some believed that it was the pole star, Polaris, or a large magnetic island on the north pole that attracted the compass).
The discovery of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Oersted, professor at the University of Copenhagen, when by accident he observed that an electric current could inﬂuence a compass needle (nowadays this is called Oersted’s experiment). After that, scientists from that epoch put eﬀort in discovering new properties from these interactions. In 1865, James Clerk Maxwell was able to compile all the phenomenological insights found to the epoch, into the socalled Maxwell’s equations, unifying electricity, magnetism and optics in the theory of electromagnetism. He compiled a set of 14 integral equations, which are not easy to use.
Oliver Heaviside, 20 years later, re-formulated these equations in the vectorial form and using partial derivatives, and which we nowadays use. In 1905, Albert Einstein used these
4 CHAPTER 1. ASTROPHYSICS AND MAGNETIC FIELDSlaws of electromagnetism in motivating his theory of special relativity, requiring that the laws held true in all inertial reference frames.
While humankind was discovering this ‘new’ phenomena, in nature several living beings already made use of it. Animals like sharks and rays are able to feel the ﬁeld lines propagating in salty water by indirectly feeling the ﬁeld’s force using particular receptors.
Birds are also known to sense magnetic ﬁelds, it helps them to orient themselves in their seasonal trips. Another example is the Chiton, a primitive marine mollusc, that has teeth coated with magnetite. It is believed that this aids them in their homing behaviour, perceiving magnetic ﬁelds for orientation. In other biological kingdoms, some bacteria are capable of synthesizing magnetite and using it to ﬁnd out at which level from the surface of the water they are, as to stay at the correct depth where there is less oxygen, allowing them to survive easily. Also there are plenty of insects and other species which have tracers for magnetite and it is believed that they use them for orientation. However, it is still unclear how these senses work in the majority of the cases.
The understanding of the role of magnetic ﬁelds in nature contrasts with the open enigma that remains regarding magnetic ﬁelds in astrophysics. The way magnetic ﬁelds sustain or generate themselves in astrophysics is an open issue. As an example, most theories explaining Earth magnetic ﬁeld agree that it should be imprinted from the protoplanetary stages of the solar system, but how it survived afterwards given the proper timescales of this system is still unknown. Additionally, the primordial magnetic ﬁeld in the proto-planetary disc is linked to the star formation process that created the Sun, which supports the existence of magnetic ﬁeld in such processes and scales. We have good measurements of the magnetic ﬁeld on earth, in laboratories and even from the Sun. In general we rely on indirect methods to infer them (see section 1.2), this makes it diﬃcult to observe them in large scales. Besides the observations, their dynamical importance for many astrophysical systems is poorly constrained, therefore there are still plenty of processes in which the role of magnetic ﬁelds are not fully understood.
In the next sections we will ﬁrst describe brieﬂy the astrophysical background of the objects that we plan to study. Then, how galactic and extragalactic magnetic ﬁelds can be estimated and brieﬂy summarize how they are embedded in those objects and on the largest scales of the Universe. We will also spent some time on numerical simulations that have shown to be useful to study this astrophysical problems. Finally, we summarize the discussion on magnetic ﬁelds which we address in more detail within the next chapters.
For a detailed discussion on extra-galactic magnetic ﬁeld, dynamo eﬀects and observations we refer the reader to Kronberg (1994), Beck et al. (1996), Moss and Shukurov (1996) and Widrow (2002). A detailed review on numerical simulations and clusters within a cosmological context can be found in Borgani and Kravtsov (2009).
1.1 Extragalactic physics basics The most common state of ordinary matter in the Universe is plasma, i.e. atoms are separated and free protons, electrons and other particles ﬁll the space. Outer space is the best vacuum environment that we are aware of, it is ﬁlled with approximately one Hydrogen atom per cubic meter on cosmological scales, and about 5 particles per cubic meter in Earth neighborhood. Therefore, in general astrophysical plasmas in the Universe can be characterized as dilute plasmas, except to the small fraction present inside stars
1.1. EXTRAGALACTIC PHYSICS BASICSand other compact objects. There is no net charge of these plasma and charges can move almost freely, justifying an “Ideal” treatment of the Magnetohydrodynamical regime (see appendix A where we derive the corresponding equations). Hence, electric ﬁelds are negligible and matter and magnetic ﬁelds are strongly coupled.
A consequence from the laws of Magnetohydrodynamics (see appendix A) is that magnetic ﬁelds need a source of any kind to sustain themselves. Space is permeated with magnetic ﬁelds, and is electrically neutral given the high conductivity of the plasma, not allowing to have large dynamos from electric currents.
The way magnetic ﬁelds evolve in time, coupled with the dynamics of baryons, growing or vanishing (never completely) in some regions is an open issue. It is unclear whether complex mechanisms are needed, such as galactic dynamos, super-nova explosions, or just a gentle baryon ﬂow to recover the magnetic ﬂux to the measured values (see section 1.2).
Magnetic ﬁelds are tightly coupled with baryons, and thus to the structures that build the Universe. But, how those structures assembled? The current knowledge in cosmology is based on the so-called standard cosmological model. In this scenario, soon after the “big bang“, the main constituents of the Universe were radiation and matter that, during the early stages, were in thermodynamical equilibrium yielding to emission of energy with black-body spectrum that we still observe today 1. The presence of density and energy disomogeneities capable of growing under gravitational instabilities is fundamental for the structure formation process. Nowadays the presence of primordial ﬂuctuations of the order of 10−5 the mean density is well established from the CMB experiment. In more quantitative terms, one can deﬁne a density contrast δ(x, t), as a function of the cosmic time and spatial position ρ(x, t) − ρb (t) δ(x, t) ≡, (1.1) ρb (t) being ρ(x, t) the density at point x and instant t and ρb (t) the background mean density as function of time. Probably these ﬂuctuation originated in the very early phases of the Universe undergoing an exponential expansion (“inﬂation”), becoming the actual seeds of structure formation. When these small over-densities are present, they can grow only if the gravitational forces are stronger than the pressure or dispersion forces.
A simple linear evolution would predict present-day structures with density contrasts δ ∼ 10−2 (Peebles, 1980). Nevertheless, we observe over-densities (i.e. galaxies) with δ ≫ 1, meaning that their evolution must have been strongly nonlinear. Additionally, once structure growth proceeds and enters an advanced stage, the diﬀerent accretion process and histories particular of each halo make the whole picture more complex, even possibly implying that baryons physics can modify the pure gravitational interaction (Pedrosa et al., 2010).