Galactic dynamics reveals Galactic history Author: Ana Hočevar Advisor: dr. Tomaž Zwitter Department of Physics, University of Ljubljana March 18, 2006 Abstract Galaxy formation theory which predicts canibalism is challenged. An effective method for discovering galactic streams as relicts from the formation of the Galaxy is presented. We turn to angular momentum phase-space and search for evidence of past merging events. The Galactic potential is presented in which simulations of satellite galaxy disruption are described in an attempt to discover the origin of the streams we detect. 1
Contents 1 Introduction 3 2 Galaxy formation 3 2.1 Consequences of a merging event........................... 3 3 6D information 4 4 Searching for galactic streams 5 4.1 Methods for detecting streams............................ 5 4.1.1 Integrals of motion............................... 5 5 Discovering the origin of a galactic stream 7 5.1 The gravitational potential of the Galaxy...................... 7 5.2 Simulations of dwarf galaxy disruption........................ 8 6 Conclusions 9 2
1 Introduction Galaxies besides being important in their own right, also serve as immense laboratories to study the laws of physics in extreme conditions and their formation is closely related to the properties of the early Universe. Here the focus will be on the dynamics of our Galaxy in an attempt to investigate the consequences of past merging events. Today it is believed that galaxies were built up after gravitational amplification of smaller fluctuations, followed by merging of precursor structures [1], [2]. The stars that make up the bulge and halo of the Milky Way today were probably building blocks of those precursor structures and with appropriate methods one hopes to find evidence of past merging events in present distribution of halo stars. Investigation of these galactic streams and finding proof of such events is important for our understanding of galaxy formation. However merging events are not only a thing of the past as can be seen on Figure 1. In view of the theory of galaxy formation interactions seen today between galaxies are a natural extension of their formative years. For example the Sagittarius dwarf galaxy is now in the process of Figure 1: The interacting galaxies NGC 4038 & NGC 4039 (the Antennae galaxies). [3] merging into our Galaxy. Furthermore M31 (the Andromeda galaxy), which is the neighbour of the Milky Way at a distance of about 700kpc, is approaching us at 100km/s. In about 10 10 years our Galaxy and M31 will probably collide [4]. 2 Galaxy formation The formation of galaxies is still one of the most active research areas in astrophysics. Theoretical arguments and many observations suggest that initial conditions imposed in the early universe, together with gravitational instability, result in a universe where the small mass fluctuations collapse and in time merge into progressively larger structures. Several merging events probably occured in the formation of a galaxy such as the Milky Way. How to find evidence of a process of this kind? 2.1 Consequences of a merging event A collision between two galaxies would have devastating consequences for the gas in both systems, however stars would due to low star density not collide with one another. Star density for the commonest stars in the solar neighbourhood is for example approximately 20 pc 2. These 3
stars have radii smaller than R max = 4.4 10 10 cm. Therefore the fraction of the area of the galactic disk that is filled with stars is of order 10 14 [4]. Instead, interactions between stars will be gravitational in nature, thus the distribution and dynamics of the stars will radically change. We only deal with a small satellite galaxy merging into a large galaxy. Collision of two equal size galaxies is a different mattter. When a satellite galaxy (for example Sagittarius dwarf galaxy) is merging into a larger galaxy (the Milky Way), a net gravitational force on it, called dynamical friction, opposes its motion. A stream of material is being stripped off from the satellite galaxy, releasing stars that freely move in the gravitational potential of the larger galaxy. As time goes on, these streams of stars get smeared out and we are left with a task of finding out which stars belong to the former satellite galaxy and which do not. 3 6D information First we should take a look at the properties of stars which we need for this discussion. When talking about the dynamics of a system it is logical that we need stars s positions (3D for each star) and their velocities (3D for each star). Dealing with a disklike galaxy like the Milky Way it is natural to work with cylindrical coordinate system with the galactic center in the origin (Figure 2). The radial coordinate r increases outward, the angular coordinate θ is pointed in Figure 2: Cylindrical coordinates. The center of the Galaxy is in the origin. the direction of the rotation of the galaxy and the vertical coordinate z increases to the north. The corresponding velocity components are labeled v R = dr dt v θ = r dθ dt v z = dz dt Our observations are however performed on Earth and need to be transformed to a galactic coordinate system with its origin on the Sun and from this system to the cylindrical coordinate system with the galactic center in the origin. For this we take that the solar galactocentric distance is R = 8.0 kpc and the orbital speed of the Sun is v θ = 220 km/s. Once we obtain all 6D information (r, θ, z, v R, v θ, v z ) for each star we want to investigate, the question is how to determine whether this star is a part of a stream of debris. (1) 4
4 Searching for galactic streams Identifying debris ought to be easier in samples in which the interaction of stars with the disk is minimized. Spiral arms which are a distinguishing feature of disklike galaxies have giant molecular clouds (GMCs) that significantly redistribute angular momentum. These dense portions of interstellar medium can contain several million M, thus the GMC s gravitational influence strongly disturbs an orbit of a star passing by. That makes galactic streams that interact with Figure 3: Due to giant molecular clouds spiral arms distort stellar orbits, which is very inconvinient for us. That is why it is better to focus on the stars of the halo, which pass through the disk twice in their orbit and are not influenced by spiral arms as much as the stars of the disk are. [5] GMCs almost impossible to find. That is why it is recomended to examine metal-poor stars which can rise far above the disk, thus halo stars. 4.1 Methods for detecting streams Several methods investigating merely the velocity vectors of stars or only stars positions have proved to be inefficient. It is true that when the disruption of a satellite galaxy begins, streams are visible. However after the disrupting satellite circles around the center of the Galaxy a few times, such strong angular correlations on the sky are no longer visible. Debris is spread all around the sky as seen on Figure 4. So where does characteristic clustering manifest itself in the debris that we observe after many galactic orbits? 4.1.1 Integrals of motion We can consider a satellite galaxy as an ensemble of particles that fly into the potential of our Galaxy, which is almost axisymmetric. Writing down the Lagrangian for a particle in such a galactic potential: L = T V (2) 5
Figure 4: A galactocentric sky projection of a simulated satellite disruption. The debris is scattered around, thus detecting a stream only with position information about a star, is practically impossible. [6] L = 1 2 m(ṙ2 + r 2 θ2 + ż 2 ) V (r, z) (3) θ is obviously a cyclic coordinate and we know that in such potential the z component of the angular momentum and the energy are integrals of motion. These quantities are conserved, which means that initial clumping in the phase space remains present even after disruption. Although the magnitude of the angular momentum vector is not fully conserved for this kind of potential (only z component is), it evolves preserving a decent degree of coherence as shown on Figure 5, where numerical simulations show strong clumping before and after disruption. Of course one could argue that the Galactic potential is surely not static when the process of Figure 5: The graph on the left displays the initial distribution of particles in the angular momentum space for a few satellites. There is obvious clumping and each clump represents a satellite. The graph on the right shows that clumping remains visible even after disruption despite slight dispersion. [6] galaxy formation is taking place. The early process must have been violent and the potential is certainly not static nor is it axisymmetric. Therefore there will be no clumping reflected in angular momentum space from that early stage. However, if this violent stage happened during the first few Gyrs, the objects falling later preceive a fairly static Galaxy and the method works. 6
That seems to be the case since there have been successful discoveries of galactic streams using this method. Even though the real galactic potential is not flawlessly axisymmetrical, actual observations of satellite debris (Helmi, White & Zeeuw 1999) show this expected clumping in angular momentum phase space (Figure 6). By using this method it has also been shown (Navarro, Helmi & Freeman 2004) that Arcturus, Figure 6: Observations of the distribution of nearby halo stars in angular momentum phase space show a clump at J z aproximately 1200kpc km/s and J aproximately 2000 kpc km/s. This points to the fact that these star belong to a galactic stream.[1] one of the brightest stars in the sky, belongs to the debris of a disrupted satellite [9]. The space of integrals is therefore the place to look for evidence of merging events (Helmi et al.). This method is very powerful since the computation of the angular momentum does not involve any detailed knowledge of the Galactic potential. Even more, the number of clumps represents the total number of merging events. However if the number of disrupted satellites is large, there is a large chance of superposition of events in the phase space. In such a case more sophisticated analysis is needed. 5 Discovering the origin of a galactic stream When a galactic stream is discovered the question of its origin occurs. Once a stream is identified, we can fit it with an orbit or a simulated stream in a given Galactic potential and determine the properties of the original satellite galaxy which after disruption produced the observed stream. 5.1 The gravitational potential of the Galaxy The morphology of the Galaxy implies the Galactic potential. The Milky Way consists of a galactic halo, a disk and a bulge as shown on Figure 7. Thus we describe the potential including three components, which all together must reproduce an accurate rotation curve for the Galaxy. Here is a possible representation of such a potential [7]: a dark logarithmic halo a Miyamoto-Nagai disc Φ halo = v 2 haloln(r 2 + d 2 ) (4) GM disk Φ disk = r 2 + (a + (5) z 2 + b 2 ) 2 7
Figure 7: Morphology of the Galaxy. [8] and a Hernquist bulge where parameters are listed in the table below. Φ bulge = GM bulge r + c (6) d v halo M disk a b M bulge c 12 kpc 131.5 km/s 10 11 M 6.5 kpc 0.26 kpc 3.4 10 10 M 0.7 kpc Therefore the Galactic potential is: Φ g = Φ halo + Φ disk + Φ bulge (7) 5.2 Simulations of dwarf galaxy disruption The question is how to determine the properties of the progenitor system which merged into the Galaxy and produced the observed stream. The one thing we need is 6D information about each star that is a part of a stream today. Each star moves according to Newton s laws of motion, thus we are able run numerical simulations of movement for the stars of the stream in the Galactic potential. Equations of motion for each star at r are simply: d r dt = Φ g (8) 8
in cylindrical coordinates is written down as: Φ g = dφ g dr e r + 1 dφ g r dθ e θ + dφ g dz e z (9) Each component (radial, angular and vertical) is numerically simulated independently for each star. That allows us to determine the average properties of the stream: orbital radii at apocentre and pericentre, the maximum height above the plane and the approximate radial period [1], [9]. These properties constrain the orbit of the progenitor. Then a stellar system describing the predisruption progenitor is modeled. Once these properties are constrained numerical simulation of the satellite galaxy and it s distruption in performed. The challenge is to fit the parameters of the modeled progenitor in a way that the stream which it generates is similar to the actual observed stream. Such simulations were successfuly done for the galactic stream found in the solar neighbourhood. The data shows that the progenitor was a stellar system similar to dwarf spheroidals with core radii R of 0.5-0.65 kpc [1]. 6 Conclusions Searching for evidence of past merging events has proven to be effective in the angular momentum phase-space. It is there that obvious clumping is detected and streams are identified. After finding a stream, numerical simulations of motion in the Galactic potential reveal the origin of the stream. Examining the substructure of the halo is in progress and even more will be done when GAIA, RAVE and other surrveys provide the needed 6D information for stars. There is an exciting time ahead of us, when observations together with simulations described here will finally explain the formation and evolution of galaxies. 9
References [1] A. Helmi, S. D. M. White, P. T. de Zeeuw, H. Zhao, Debris streams in the solar neighbourhood as relicts from the formation of the Milky Way, Nature 420, 53 (1999) [2] B. W. Carrol, D. A. Ostlie, An Introduction to Modern Astrophysics, Addison-Wesley Publishing Company, Inc. 1996 [3] http://hubblesite.org/newscenter/newsdesk/archive/releases/1997/34/image/ [4] J. Binney, S. Tremaine, Galactic dynamics, Princeton University Press, 1994 [5] http://www.astro.virginia.edu/class/oconnell/astr130/im/mw-topview-fwalter.jpg [6] A. Helmi, H. Zhao, T. de Zeeuw Detecting Halo Streams with GAIA, The Third Stromlo Symposium: The Galactic Halo, APS Conference Series 165, 125 (1999) [7] A. Helmi, S. D. M. White, Simple dynamical models of the Sagittarius dwarf galaxy, Monthly Notices of the Royal Astronomical Society 323, 529 (2001) [8] http://www.bibliotecapleyades.net/imagenescosmos/cosmosdivine7-2.jpg [9] J. F. Navarro, A. Helmi, K. C. Freeman, The extragalactic origin of the Arcturus group, The Astrophysical Journal 601, L45 (2004) [10] R. J. Tayler, Galaxies: structure and evolution, Cambridge University Press, 1993 10