TESTING THEORIES IN BARRED SPIRAL GALAXIES Eric E. Mart´ınez-Garc´ıa Instituto de Astronom´ıa,Universidad Nacional Aut´onomade M´exico, AP 70-264, Distrito Federal 04510, Mexico. [email protected] ABSTRACT According to one version of the recently proposed \manifold" theory that explains the origin of spirals and rings in relation to chaotic orbits, galaxies with stronger bars should have a higher spiral arms pitch angle when compared to galaxies with weaker bars. A sub-sample of barred- spiral galaxies in the Ohio State University Bright Galaxy Survey, was used to analyze the spiral arms pitch angle. These were compared with bar strengths taken from the literature. It was found that the galaxies in which the spiral arms maintain a logarithmic shape for more than 70◦ seem to corroborate the predicted trend. Subject headings: galaxies: kinematics and dynamics | galaxies: spiral | galaxies: structure | galaxies: kinematics and dynamics 1. INTRODUCTION by the manifolds. This approach has been studied by two different groups of people. Spiral arms in barred galaxies have been ex- One of those groups (Romero-G´omez et al. plained in the past as density waves (e.g., Kor- 2006, 2007; Athanassoula et al. 2009a,b, 2010), chagin & Marochnik 1975) or spiral waves that considers a continuous flow of orbits along the result from the crowding of gas orbits (Huntley et manifolds emanating from L or L . When spi- al. 1978). Kaufmann & Contopoulos (1996) in- 1 2 rals form, stars move away from the corotation voked for the first time the need for chaotic orbits in a radial movement (Athanassoula et al. 2010), as building blocks of spirals near the end of the and material is needed to replenish the mani- bar. In the Kaufmann & Contopoulos (1996) mod- folds. One prediction of this \manifold theory" els, regular orbits dominate the main structure of (or \Lyapunov tube model"), not accounted for in the bar and the outermost portions of spiral arms. the density wave scenario, is that stronger bars The inner portions of spiral arms are supported by should have more open spirals as compared to chaotic orbits. Recently it has been proposed that weaker bars, i.e., the spiral arms pitch angle1 chaotic motion can support the spirals in barred- should increase with bar strength (Athanassoula spiral systems. The new theory proposes that un- et al. 2009b). This kind of correlation was previ- arXiv:1109.3470v3 [astro-ph.CO] 14 Oct 2011 stable Lagrangian points (L or L ) near the end 1 2 ously predicted by Schwarz (1984), although for of the bar are the sites where chaotic orbits are gas arms driven by a bar perturbation. guided by invariant \manifolds", and are the ori- gin of spirals and (inner and outer) rings (Voglis & Another view of the \invariant manifold the- Stavropoulos 2006a; Patsis 2006; Romero-G´omez ory" (Voglis et al. 2006b,c; Tsoutsis et al. 2008, et al. 2006; Voglis et al. 2006b,c; Romero-G´omez 2009) considers the locus of all points with initial et al. 2007; Tsoutsis et al. 2008, 2009; Athanas- conditions at the unstable manifolds that reach a soula et al. 2009a; Harsoula & Kalapotharakos local apocentric (or pericentric, see Harsoula et 2009; Athanassoula et al. 2009b, 2010; Contopou- 1 los & Harsoula 2011). In this scenario the spiral The angle between a tangent to the spiral arm at a certain point and a circle, whose center coincides with the galaxy's, dynamics are coupled to the bar, and are driven crossing the same point. 1 al. 2011) passage, i.e., the apsidal sections of the al. (2004) investigated the relation between the manifolds. In this scenario, there is no need for amplitude of the spirals with the pitch angle in the replenishment of material to obtain long-lived non-barred and weakly barred galaxies. spirals (see, e.g., Efthymiopoulos, C. 2010). Both One prediction of the density wave theory (Hozumi views of the \invariant manifold theory" predict a 2003, see x6.1) entails that different pitch angles trailing spiral pattern for strong perturbations and are expected for spirals when observed in different similar pattern speeds for the bar and spiral, i.e., bands (e.g., optical versus near-infrared [NIR]). bar spiral Ωp = Ωp . However, in the view of Voglis et According to Athanassoula et al. (2010), the \in- al. (2006b,c) and Tsoutsis et al. (2008, 2009), the variant manifold theory" predicts that stars of \azimuthal tilt" of the spiral response (Tsoutsis different ages will be guided by the same mani- et al. 2009), i.e., the difference between the bar's fold, and no difference between the winding of the major axis and the Lagrangian points L1 or L2 at spirals is expected. the moment of the onset of the spiral, determines In this paper, we will investigate whether the how open the spiral arms will be. In this case, the predictions of pitch angles are observed for real pitch angles are smaller than the ones predicted galaxies, or not. Two methods were applied for by Athanassoula et al. (2009b) and become even this purpose: the \slope method" (Section 4.1), smaller for pure bar models when the \azimuthal which is especially good for determining how long tilt" is not taken into account (C. Efthymiopoulos, the logarithmic shape is maintained for spiral private communication 2011). arms, and the \Fourier method" (Section 4.2), Patsis et al. (2010) describe one more dynami- which was used to determine the \dominant" pitch cal mechanism that supports spiral arms through angle inside a given annulus for each object. stars in chaotic motion. They propose this mech- anism by describing the spiral arms of the barred- 2. GALAXY SAMPLE spiral NGC 1300. Together with the bar, these spiral arms are inside the corotation and are not related to the presence of unstable Lagrangian The initial galaxy sample consists of 104 galax- points and the associated families of periodic or- ies classified as Fourier bars in Laurikainen et bits. This alternative mechanism may be linked to al. (2004). The data were acquired from the some range of pitch angles of spiral arms encoun- Ohio State University Bright Galaxy Survey (OS- tered in barred-spiral systems. UBGS) (Eskridge et al. 2002). From this initial Do manifolds drive spiral dynamics in barred sample, it was found that only 84 objects present galaxies? Or are the dynamics driven by the spiral-like features. Nevertheless, not all the ob- bar? The bar may drive the dynamics, affecting jects are suitable for this kind of study due to the spiral amplitude locally, as reported by Salo asymmetries, e.g., short, faint, or ragged spiral et al. (2010) (see also Block et al. 2004) and arms, or prominent rings. The following criteria previously discarded (or weakly corroborated) by were established in order to obtain a sample, in- other authors comparing bar strength to spiral cluding objects with a morphology candidate to arm strength (Buta et al. 2009; Durbala et al. be explained by \chaotic" spirals. 2009; Seigar & James 1998). Bars driving the dynamics would imply an accordance with (lin- 1. The spiral arms must remain logarithmic, ear) density wave theory. These spirals may be a i.e., with a constant pitch angle (i), at least continuation of the bar mode, or an independent for 50◦ in the azimuthal range, α.2 This was mode coupled to the bar (e.g., Tagger et al. 1987; verified with the \slope method" (see Sec- Masset & Tagger 1997). In the \Lyapunov tube tion 4.1). The lower limit value of α was cho- model", the strength of the bar affects the pitch sen according to Figure 4 in Athanassoula et angle of the spirals, but not its amplitude. The al. (2009b), where the manifold loci remain amplitude of the spirals depends on how much ma- terial is trapped by the manifolds, although, the 2Although the spiral arms may extend further in the disk amplitude of the spirals should in general decrease with a varying pitch angle, i.e., different slopes in a ln r versus θ map. outward (Athanassoula et al. 2010). Grosbøl et 2 logarithmic (for the adopted model param- The predicted trend in Athanassoula et al.'s eters) and maintain a \nearly" logarithmic (2009a) \manifold models" requires the strength geometry up to ∼ 100◦. We consider that of the bar at the radius of the Lagrangian points the manifold loci and the density maximum L1 or L2. It should be mentioned that for these along the spirals coincide. According to Pat- models the self-gravity of the spirals was not taken sis (2006), spirals supported by chaotic par- into account. On the other hand, the addition of ticles may extend up to π=2 radians. Vari- the spiral potential in Tsoutsis et al.'s (2009) mod- ations of α toward larger angles will be dis- els shifts the positions of the Lagrangian points L1 cussed in Section 6. or L2 both in the radial and azimuthal directions. The strength of the bar can be obtained from 2. The object presents two spiral arms visually the Laurikainen et al. (2004) radial profiles of the connected to the bar. perturbation strength. Laurikainen et al. (2004) 3. No prominent inner rings (near the bar's used the gravitational torque method (Combes & end) are present.3 Ring structures are con- Sanders 1981; Buta & Block 2001; Block et al. nected to the bar on both sides. The pitch 2002) taking care of the artificial bulge stretch (see angle definition as applied in this investiga- also Speltincx et al. 2008). The perturbation tion only refers to spiral arms. A dependence strength is calculated as of the inner ring shape on bar strength has been investigated by Grouchy et al.