Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 2 October 2018 (MN LATEX style file v2.2) Short-term dynamical evolution of grand-design spirals in barred galaxies Junichi Baba⋆ Earth-Life Science Institute, Tokyo Institute of Technology, 2–12–1 Ookayama, Meguro, Tokyo 152–8551, Japan. Accepted 2015 September 22. Received 2015 September 22; in original form 2015 July 30 ABSTRACT We investigate the short-term dynamical evolution of stellar grand-design spiral arms in barred spiral galaxies using a three-dimensional (3D) N-body/hydrodynamic sim- ulation. Similar to previous numerical simulations of unbarred, multiple-arm spirals, we find that grand-design spiral arms in barred galaxies are not stationary, but rather dynamic. This means that the amplitudes, pitch angles, and rotational frequencies of the spiral arms are not constant, but change within a few hundred million years (i.e. the typical rotational period of a galaxy). We also find that the clear grand-design spi- rals in barred galaxies appear only when the spirals connect with the ends of the bar. Furthermore, we find that the short-term behaviour of spiral arms in the outer regions (R > 1.5–2 bar radius) can be explained by the swing amplification theory and that the effects of the bar are not negligible in the inner regions (R < 1.5–2 bar radius). These results suggest that, although grand-design spiral arms in barred galaxies are affected by the stellar bar, the grand-design spiral arms essentially originate not as bar-driven stationary density waves, but rather as self-excited dynamic patterns. We imply that a rigidly rotating grand-design spiral could not be a reasonable dynamical model for investigating gas flows and cloud formation even in barred spiral galaxies. Key words: method: numerical — galaxies: kinematics and dynamics — galaxies: spiral — galaxies: structure 1 INTRODUCTION self-gravitating hydrodynamic simulations in fixed barred potentials (e.g. Sanders & Huntley 1976; Sanders 1977; Spiral arms in disc galaxies can be classified into three cat- Huntley et al. 1978; Sormani et al. 2015). This theory ex- egories: grand-design, multiple-arm, and flocculent spirals plains the physical mechanism responsible for the formation arXiv:1509.07239v2 [astro-ph.GA] 1 Oct 2015 (Elmegreen & Elmegreen 1987). Grand-design spiral arms of the spirals in barred galaxies in terms of closed orbits are large-scale coherent, symmetric, two-armed patterns of the gas (see also Wada 1994): the spiral arms in barred (e.g. NGC 628), whose number fraction is more than 50% galaxies are regarded as kinematic density waves (i.e. crowd- in nearby spiral galaxies (Grosbøl et al. 2004; Kendall et al. ing of gaseous closed orbits) driven by an external barred 2011). Observations show that grand-design spirals are as- potential. However, spiral arms in observed barred galaxies sociated with bars or companions (Kormendy & Norman are composed of not gas but stars; therefore, theories based 1979; Seigar & James 1998; Kendall et al. 2011), suggesting on stellar dynamics are required for investigating the origin that a bar or companion is essential in forming a grand- of spiral arms in barred galaxies. design spiral in a disc galaxy. In barred spiral galaxies, the grand-design spirals extend from the ends of the bars. Furthermore, although some studies found little or no cor- relation between bar strengths and spiral arm strengths (Durbala et al. 2009; Kendall et al. 2011), other studies On the other hand, the ‘invariant manifold theory’ is an- have found correlations (Block et al. 2004; Salo et al. 2010). other bar-driven spiral theory (Romero-G´omez et al. 2006, These observations, therefore, suggest that bars drive grand- 2007; Athanassoula et al. 2009a,b, 2010) and has been devel- design spirals with the same pattern speed as the bars. oped from stellar orbital theories in fixed barred potentials This ‘bar-driven spiral hypothesis’ has been promoted (Danby 1965). Essentially, the back-bones of barred spirals by the ballistic closed-orbit theory, which is based on non- are bunches of untrapped stars escaped from unstable La- grangian points L1 and L2 close to the ends of the bar. This means that stars should move along the arms rather ⋆ E-mail:[email protected]; [email protected] than across the arms (Athanassoula 2012). This behaviour c 0000 RAS 2 J. Baba is completely different from the quasi-stationary1 density Minchev et al. 2012). Recently, Roca-F`abrega et al. (2013) wave theory, which predicts that stars should traverse the performed N-body simulations of pure stellar barred spi- arms but would stay longer in the arm than in the inter-arm ral galaxies and analysed the spiral rotation frequency region (Lin & Shu 1964). Furthermore, the manifold theory from selected snapshots where the spiral amplitude is predicts a rigidly rotating spiral arm with a similar pat- above 70% of the maximum amplitude; they concluded tern speed to that of the bar (i.e. Ωspiral Ωbar) and that that the spiral rotation frequency approaches the bar’s ≃ stronger bars should have more open spirals compared to rigid body rotation in barred galaxies with the incre- weaker bars (Athanassoula et al. 2009b). Recently, Struck ment of bar strength. On the other hand, Baba et al. (2015) extended the classical epicyclic orbit approximation (2009) performed N-body/hydrodynamic simulations of a to the ‘p-ellipse’ orbit approximation (Struck 2006) and pro- barred spiral galaxy and suggested that the spiral arms posed that ensembles of eccentric resonant orbits excited in are not rigidly rotating patterns but transient recurrent Lindblad zones can provide a backbone for generating kine- patterns (i.e. dynamic spirals), and these results are sim- matic bars and spiral waves. Furthermore, Struck (2015) ilar to those obtained from multiple arm spiral galaxies showed that some resonant eccentric orbits have a similar (Sellwood & Carlberg 1984; Fujii et al. 2011; Wada et al. appearance to invariant manifold orbits. 2011; Grand et al. 2012b; Baba et al. 2013; D’Onghia et al. The manifold theory and eccentric resonant orbits the- 2013). Grand et al. (2012a) also found that spiral arms in ory, however, do not consider the self-gravity of stars, despite barred galaxies are dynamic patterns whose rotation fre- the fact that the self-gravity of stellar discs plays an essential quencies decrease with the radius in such a way that the role in the dynamical evolution of spirals via the (non-linear) rotation frequency is similar to the rotation of stars. swing amplification mechanism (Sellwood & Carlberg 1984; In this study, to address the short-term (e.g. a few Carlberg & Freedman 1985; Fujii et al. 2011; Baba et al. hundred million years) behaviour of grand-design spirals 2013; D’Onghia et al. 2013; D’Onghia 2015). The swing am- in barred spiral galaxies, we performed a three-dimensional plification mechanism, proposed by Toomre in 1981, oper- (3D) N-body/hydrodynamic simulation of a Milky-Way-like ates through a combination of three aspects, i.e. the shear- barred spiral galaxy. This paper is organized as follows. We ing flow, epicyclic motions, and the disc self-gravity, in disc describe the galaxy model and our numerical simulation galaxies2. Because the amplification is most efficient around methodologies in Section 2. In Section 3, we present our the corotating radius (e.g. Shu 1992), prominent spiral arms results concerning the short-term behaviour of grand-design tend to have differentially rotating patterns, which almost spirals in the barred galaxy and effects of the bar on spiral follow the galactic rotation at every radius (Ωspiral Ω; dynamics. Finally, we summarize our results in Section 4. ≃ Baba et al. 2013). Besides, the pitch angles are expected Long-term (e.g. 10 Gyr) behaviour of spirals in barred ∼ to depend on the shear rates of galactic discs (Fuchs 2001; galaxies, as well as effects of a ‘live’ dark matter (DM) halo, Baba et al. 2013; Michikoshi & Kokubo 2014). will be presented in a forthcoming paper (M. S. Fujii et al. For investigating the origin of grand-design spirals in preparation). in barred galaxies, N-body and N-body/hydrodynamic simulations are required, and several preliminary numer- ical studies have been proposed. However, the studies 2 NUMERICAL SIMULATIONS AND have not reached a consensus about the dynamics of ANALYSIS barred spirals. Some numerical simulations of barred spi- ral galaxies have shown that the bar and spiral arm are We performed a 3D N-body/hydrodynamic simulation rigidly rotating patterns with different pattern speeds, and of a Milky Way-like galaxy with an N-body/smoothed they are independent patterns (Sellwood & Sparke 1988; particle hydrodynamics (SPH) simulation code ASURA-2 Rautiainen & Salo 1999) or are coupled via non-linear in- (Saitoh & Makino 2009, 2010). In this study, we focus on teractions (Masset & Tagger 1997; Rautiainen & Salo 1999; the dynamical evolution of spiral arms in a simulated barred spiral galaxy, while detailed studies on spatial distributions of the interstellar medium (ISM) around spiral arms as well 1 In general, the word stationary or steady means ‘not moving.’ as the structures of the ISM/clouds and their galactic en- However, in this context, this word indicates that density waves vironmental dependences are separately discussed in Baba, do not propagate radially and that instead they propagate az- Morokuma-Matsui & Egusa (2015a) and Baba, Morokuma- imuthally with a single pattern speed. See Bertin & Lin (1996) Matsui & Saitoh (2015b), respectively. for further discussion on the concept of quasi-stationary density waves. 2 The term ‘swing amplification’ is used to express the ampli- 2.1 Numerical methods fication process, which combines the shearing flow, epicyclic mo- tions, and disc self-gravity, regardless of whether the process is The self-gravities of stars and SPH particles were calculated a linear or nonlinear phenomenon.