Simulations of normal spiral galaxies

Mon. Not. R. Astron. Soc. 344, 358–384 (2003) Simulations of normal spiral galaxies Roelof Bottema Kapteyn Astronomical Institute, PO Box 800, NL-9700 AV Groningen, the Netherlands Accepted 2003 March 10. Received 2003 February 24; in original form 2002 April 12 ABSTRACT Key words: galaxies: evolution – galaxies: fundamental parameters – galaxies: general – galaxies: kinematics and dynamics – galaxies: spiral – galaxies: structure. 1 INTRODUCTION It is now well established that substantial amounts of dark matter are needed to explain flat rotation curves in the outer regions of spiral galaxies. However, the amount of dark matter present in the inner, luminous region of a galaxy is not well determined. Does a spiral galaxy conform to the maximum disc hypothesis (van Albada & Sancisi 1986; Salucci, Ashman & Persic 1991; Sellwood & Moore 1999), which states that the luminous part should be scaled up as much as possible? Or is the maximum rotational contribution of the disc to the total rotation around 63 per cent? The latter is derived from observations of disc stellar velocity dispersions (Bottema 1993, 1997) or suggested by a statistical analysis of rotation curve shapes in relation to the compactness of discs (Courteau & Rix 1999). When discs obey the 63 per cent criterion, their mass-to-light ratio is half that of the maximum disc case, but the disc still dominates in the inner two to three scalelengths. A rotation curve analysis generally  E-mail: allows a maximum disc rotational contribution anywhere between 50 and 90 per cent (van der Kruit 1995). The above-mentioned velocity dispersion measurements have only been performed for a dozen galaxies and the analysis depends on the not well-determined ratio of disc scalelength to scaleheight. As observations are not yet conclusive, numerical simulations of spiral galaxies may give clues regarding the disc-to-halo mass ratio. The spiral structure of galaxies has eluded astronomers for a long time. Is it a quasi-stationary density wave (Lin & Shu 1964, 1966) or is it a temporal phenomenon excited by internal or external disturbances and then swing amplified (Goldreich & Lynden-Bell 1965; Toomre 1981)? Or is it some kind of combination of these factors, such as swing amplified density waves? Until now theory and observations have been inconclusive. To compound matters, there is the ‘antispiral theorem’ (Lynden-Bell & Ostriker 1967), which states that spiral structure cannot develop in a system governed by a time-reversible description. Consequently, spiral arms cannot exist in an isolated pure stellar galaxy. Some kind of non-time-reversible action is needed, such as external forcing or gas dissipation. The need for the latter mechanism is confirmed observationally; in  C 2003 RAS Results from numerical simulations of normal isolated late-type spiral galaxies are presented; specifically, the galaxy NGC 628 is used as a template. The method employs a TREESPH code including stellar particles, gas particles, cooling and heating of the gas, star formation according to a Jeans criterion and supernova feedback. A regular spiral disc can be generated as an equilibrium situation of two opposing actions: on the one hand, cooling and dissipation of the gas; on the other hand, gas heating by the far-ultraviolet field of young stars and supernova mechanical forcing. The disc exhibits small- and medium-scale spiral structure of which the multiplicity increases as a function of radius. The theory of swing amplification can explain, both qualitatively and quantitatively, the emerging spiral structure. In addition, swing amplification predicts that the existence of a grand-design m = 2 spiral is only possible if the disc is massive. The simulations show that the galaxy is then unstable to bar formation, confirming the result of Ostriker & Peebles. The occurrence of this bar instability is further investigated. A general criterion is derived for the transition between a stable and an unstable bar, depending on the disc mass contribution and the on-disc thickness. It seems that bar stability barely depends on the presence of gas. A detailed quantitative analysis is made of the emerging spiral structure and a comparison is made with observations. This demonstrates that the structure of the numerical isolated galaxies is not as strong and has a larger multiplicity compared with the structure of some exemplary real galaxies. It is argued that the suggestion of Kormendy & Norman holds, i.e. that a grand design can only be generated by a central bar or by tidal forces resulting from an encounter with another galaxy. Simulations of normal spiral galaxies  C 2003 RAS, MNRAS 344, 358–384 on a Jeans criterion. They do not impose the Schmidt law a priori, but it is the result of a more fundamental process. Their scheme is therefore expected to hold for a broad range of physical conditions. It is well known that in a real galaxy young stars and SF regions exert a definite action on the ambient ISM. The fierce radiation heats the gas and supernova (SN) action stirs up the ensemble of gas clouds. This SF feedback maintains an equilibrium state of the ISM. When simulations lack such a feedback a catastrophic gas cooling occurs, forming supergiant cloud complexes (Shlosman & Noguchi 1993). Therefore, in the numerical calculations an SF feedback prescription is also needed. As mentioned above, Elmegreen & Thomasson (1993) made a numerical study of isolated galaxies to specifically investigate spiral structure, more or less as a function of the disc-to-halo mass ratio. They find for a ‘rather massive’ disc a grand-design m = 2 structure, which lasts for several rotation periods. For substantially less massive discs the spiral structure becomes flocculent. Though their investigation is very interesting it contains several caveats. The main one is that the development of a bar is prevented in at least two ways. First, by using an artificial Q barrier in the inner regions. Secondly, the disc is stabilized by a large softening length (Romeo 1994) that has to be used to perform the two-dimensional simulations. Therefore, it is expected that the results of Elmegreen & Thomasson only partially apply to a real galaxy. Results in the present paper differ from the study of Elmegreen & Thomasson mainly relating to the development of a bar in massive discs. My original intention was to investigate what happens to the morphology of a normal galaxy when the ratio of disc to dark matter changes. Inevitably, during the research other and additional problems emerged that necessitated a somewhat broader scope. Nevertheless, this paper still focuses on the global properties and global morphology of a galaxy and does not aim to go into specific details. Besides the above-mentioned mass ratio another defining parameter for a galactic disc is the value of the stellar velocity dispersion, or more or less equivalently, the thickness of the disc. In addition effec (...truncated)