Morphology, photometry and kinematics of N-body bars — I. Three models with different halo central concentrations

Mon. Not. R. Astron. Soc. 330, 35–52 (2002) Morphology, photometry and kinematics of N-body bars – I. Three models with different halo central concentrations E. Athanassoula1P and A. Misiriotis1,2 1 Observatoire de Marseille, 2 Place Le Verrier, F-13248 Marseille Cedex 4, France University of Crete, Physics Department, PO Box 2208, 710 03 Heraklion, Crete, Greece 2 Accepted 2001 October 8. Received 2001 July 23 A B S T R AC T Key words: methods: numerical – galaxies: kinematics and dynamics – galaxies: photometry – galaxies: structure. 1 INTRODUCTION A bar is an elongated concentration of matter in the central parts of a disc galaxy. Within this loose and somewhat vague definition fit a number of very different objects. Thus, different bars have very different masses, axial ratios, shapes, mass and colour distributions. They can also have widely different kinematics. Several observational studies have been devoted to the structural properties of bars and/or to their morphology, photometry and kinematics, thus providing valuable information on these objects and on their properties. Many N-body simulations of the evolution of disc galaxies have witnessed the formation of bars. Most studies have focused on understanding what favours or hinders bar formation. Not much work, however, has been done on the ‘observable’ properties of N-body bars. This is quite unfortunate because such studies are necessary for the comparison of real and numerical bars. In fact, P E-mail: q 2002 RAS several observational studies have taken an N-body simulation available in the literature and have analysed it in a way similar to that used for the observations in order to make comparisons (e.g. Kormendy 1983; Ohta, Hamabe & Wakamatsu 1990; Lütticke, Dettmar & Pohlen 2000). Although this is very useful, it suffers from lack of generality, as the specific simulation may not be appropriate for the observational question at hand, and as it does not give a sufficient overview of the alternative properties N-body bars can have. Here we will approach the comparisons between real and N-body bars from the simulation side, giving as wide a range of alternatives as possible, while making an analysis as near as possible to that used by observers. We hope that in this way our work will be of use to future observational studies and will provide results for detailed comparisons. An obvious problem when comparing N-body bars to real bars is that simulations trace mass, while observations give information on the distribution of light. The usual way to overcome this hurdle is to assume a constant M/L ratio. This assumption should be adequate for the inner parts of galaxies (e.g. Kent 1986; Peletier & We discuss the morphology, photometry and kinematics of the bars which have formed in three N-body simulations. These have initially the same disc and the same halo-to-disc mass ratio, but their haloes have very different central concentrations. The third model includes a bulge. The bar in the model with the centrally concentrated halo (model MH) is much stronger, longer and thinner than the bar in the model with the less centrally concentrated halo (model MD). Its shape, when viewed side-on, evolves from boxy to peanut and then to ‘X’shaped, as opposed to that of model MD, which stays boxy. The projected density profiles obtained from cuts along the bar major axis, for both the face-on and the edge-on views, show a flat part, as opposed to those of model MD which are falling rapidly. A Fourier analysis of the face-on density distribution of model MH shows very large m ¼ 2, 4, 6 and 8 components. Contrary to this, for model MD the components m ¼ 6 and 8 are negligible. The velocity field of model MH shows strong deviations from axial symmetry, and in particular has wavy isovelocities near the end of the bar when viewed along the bar minor axis. When viewed edge-on, it shows cylindrical rotation, which the MD model does not. The properties of the bar of the model with a bulge and a non-centrally concentrated halo (MDB) are intermediate between those of the bars of the other two models. All three models exhibit a lot of inflow of the disc material during their evolution, so that by the end of the simulations the disc dominates over the halo in the inner parts, even for model MH, for which the halo and disc contributions were initially comparable in that region. 36 E. Athanassoula and A. Misiriotis 2 S I M U L AT I O N S We have made a large number of simulations of bar-unstable discs, three of which we will discuss in this paper. Each is characteristic of a class of models, other members of which will be discussed in Paper II. In order to prepare the initial conditions we basically followed the method of Hernquist (1993), to which we brought a few improvements, described in Appendix A. The density distribution of the disc is given by   Md 2 z rd ðR; zÞ ¼ expð2R/hÞ sec h ; ð1Þ 4ph 2 z0 z0 that of the bulge by rb ðrÞ ¼ Mb 1 ; 2pa 2 rð1 þ r/aÞ3 ð2Þ and that of the halo by rh ðrÞ ¼ M h a expð2r 2 /r 2c Þ : 2p3=2 r c r 2 þ g 2 ð3Þ In the above, r is the radius, R is the cylindrical radius, Md, Mb and Mh are the masses of the disc, bulge and halo respectively, h is the disc radial scalelength, z0 is the vertical scale thickness of the disc, a is the scalelength of the bulge, and g and rc are scalelengths of the halo. The parameter a in the halo density equation is a normalization constant defined by pffiffiffi a ¼ {1 2 p expðq 2 Þ½1 2 erfðqފ}21 ; ð4Þ where q ¼ g/r c (cf. Hernquist 1993). In all simulations we have taken M d ¼ 1, h ¼ 1 and have represented the disc with 200 000 particles. The halo mass, calculated to infinity, is taken equal to 5, and rc is always taken equal to 10. The halo mass distribution is truncated at 15. The disc distribution is cut vertically at zcut ¼ 3z0 and radially at half the halo truncation radius, i.e. Rcut ¼ 7:5. The velocity distributions are as described by Hernquist (1993) and in Appendix A. The first two fiducial models that we will discuss at length here have very different central concentrations. For the first one we have taken g ¼ 0:5, so that the halo is centrally concentrated and in the inner parts has a contribution somewhat larger than that of the disc. As the mass of the disc particles is the same as that of the halo particles, the number of particles in the halo is set by the mass of the halo within the truncation radius (in this case, roughly 4.8) and in this simulation is roughly equal to 963 030. We will hereafter call this model the ‘massive halo’ model, or, for short, MH. For the second model we have taken g ¼ 5, so that the disc dominates in the inner parts. The halo is represented by 931 206 particles. We will hereafter call this model the ‘massive disc’ model, or, for short, MD. Both the MH and MD models have no bulge. In order to examine the effect of the bulge, we will consider a third fiducial model, which is similar to MD but has a b (...truncated)