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LJMU Research Online LJMU Research Online Font, J, Beckman, JE, Querejeta, M, Epinat, B, James, PA, Blasco-Herrera, J, Erroz-Ferrer, S and Perez, I INTERLOCKING RESONANCE PATTERNS IN GALAXY DISKS http://researchonline.ljmu.ac.uk/id/eprint/959/ Article Citation (please note it is advisable to refer to the publisher’s version if you intend to cite from this work) Font, J, Beckman, JE, Querejeta, M, Epinat, B, James, PA, Blasco-Herrera, J, Erroz-Ferrer, S and Perez, I (2014) INTERLOCKING RESONANCE PATTERNS IN GALAXY DISKS. Astrophysical Journal: Supplement Series, 210 (1). ISSN 0067-0049 LJMU has developed LJMU Research Online for users to access the research output of the University more effectively. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LJMU Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. The version presented here may differ from the published version or from the version of the record. Please see the repository URL above for details on accessing the published version and note that access may require a subscription. For more information please contact [email protected] http://researchonline.ljmu.ac.uk/ The Astrophysical Journal Supplement Series, 210:2 (30pp), 2014 January doi:10.1088/0067-0049/210/1/2 C 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A. INTERLOCKING RESONANCE PATTERNS IN GALAXY DISKS J. Font1,2, J. E. Beckman1,2,3, M. Querejeta1,4,B.Epinat5,P.A.James6, J. Blasco-herrera7,8, S. Erroz-Ferrer1,2,andI.Perez´ 9 1 Instituto de Astrof´ısica de Canarias, c/ V´ıa Lactea,´ s/n, E-38205, La Laguna, Tenerife, Spain; [email protected], [email protected], [email protected] 2 Departamento de Astrof´ısica. Universidad de La Laguna, Tenerife, Spain 3 Consejo Superior de Investigaciones Cient´ıficas, Spain 4 Max-Plack-Institut fur¨ Astronomie, Konigstuhl¨ 17, D-69117 Heidelberg, Germany; [email protected] 5 Laboratoire d’Astrophysique de Marseille, Universite´ d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Juliot-Curie, F-13388 Marseille Cedex 13, France; [email protected]. 6 Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Warf, Birkenhead, CH41 ILD, UK; [email protected] 7 Department of Astronomy, University of Stockholm, AlbaNova, SE-10691, Stockholm, Sweden 8 Instituto de Astrof´ısica de Andalucia, CSIC, Apdo. 3004, E-18080 Granada, Spain: [email protected] 9 Departamento de F´ısica Teorica´ y del Cosmos, Universidad de Granada, Spain; [email protected] Received 2013 January 25; accepted 2013 October 11; published 2013 December 11 ABSTRACT We have developed a method for finding dynamical resonances in disk galaxies using the change in sense of the radial component of the in-plane velocity at a resonance radius. Using simulations we show that we would expect to find these changes at corotation radii with a weaker effect at the Lindblad resonances. The method works well with observations at high spectral and angular resolutions, and is suited to the analysis of two-dimensional velocity fields in Hα from Fabry–Perot spectroscopy. We find clear indications of resonance effects in the disk velocity fields of virtually all of the 104 galaxies. The number of resonance radii detected ranges from one to seven, with a median of four. The frequency curves Ω, Ω ± κ/2, Ω ± κ/4 against radius for all the galaxies led us to discover a pattern in over 70% of the sample: given two pattern speeds, say Ω1 and Ω2,theOLRofΩ1 coincides with the corotation of Ω2, and the inner 4:1 resonance of Ω2 coincides with the corotation of Ω1. Although the second coincidence has been predicted, a prediction of this double coincidence is not found in the literature. This pattern is found once in 42 of the galaxies, twice in a further 26, three times in 5, and even four times in 1 galaxy. We also compute the ratio of corotation radius to bar length where we have sufficient image quality, finding a mean value of 1.3, and a shallow increase toward later type galaxies. Key words: galaxies: fundamental parameters – galaxies: kinematics and dynamics – galaxies: spiral – galaxies: structure – techniques: interferometric Online-only material: color figures, figure set 1. INTRODUCTION smaller radius). Following from this it has become standard to attempt to determine whether a bar is a fast rotator or a slow Density wave theory (Lindblad 1961; Lin & Shu 1964) has rotator by estimating whether its corotation radius is less than been the basis for the analysis of the dynamics of disk galax- 1.4 times the bar length (fast rotators) or greater than this value ies. This theory has the virtue that it can explain the universal (slow rotators). As this property has been linked to the presence presence of well formed spiral arms containing major star form- of dark matter halos, whose dynamical friction has been pre- ing complexes, although stochastic formation and reformation dicted to slow down the angular speed of the bar on timescales of arms has been proposed as a rival model (Gerola & Seiden much less than a Hubble time (Weinberg 1985; Hernquist & 1978). It also has the virtue that it predicts observable phenom- Weinberg 1992; Tremaine & Ostriker 1999) the search for a ena, both morphological and kinematic, and can therefore be reliable way to determine corotation has taken on cosmological tested. The underlying first order models, based initially on col- relevance (see also Debattista & Sellwood 2000; Sellwood & lective stellar dynamics in the potential of either axisymmetric Debattista 2006). Added to this, in a recent article Foyle et al. (for unbarred models) or not axisymmetric (for barred models) (2011) presented observational evidence that spiral arms may disks, yield a set of common features which have been widely not be long-lived, which would cast some doubt on the applica- discussed in both the theoretical and the observational liter- bility of density wave models to galactic structure in general. ature. These are the Lindblad resonances, the 4:1 resonances, Adhering to the conventional view that spiral structure re- and corotation, defined using the properties of the rotation curve quires an explanation based on at least a fairly stable density and the oscillating frequency of a test star under a small per- wave system, and supported by numerous simulations which turbation within the gravitational field of the disk. In particular show that bars should be stable, albeit evolving, configurations the corotation radius, defined as the radius at which the density (and indeed supported by the well-established observational re- wave angular pattern speed coincides with the angular speed sult that some two thirds of disk galaxies have bars or oval of the material in the disk, has been a parameter whose value distortions, Marinova & Jogee 2007) there have been many has been sought via a combination of observations and theo- studies over the years designed to measure the pattern speed of retical modeling. This corotation radius has been quantitatively density wave systems associated with galactic bars. One of the predicted for barred galaxies. The basic models of Contopoulos best known, due to Tremaine & Weinberg (1984) combines the (1980) suggested that corotation should be close to the ends of stellar surface density distribution from photometric imaging the dominant bar of a galaxy (and for stability reasons not at a with line of sight velocity distribution, via long slit spectra 1 The Astrophysical Journal Supplement Series, 210:2 (30pp), 2014 January Font et al. parallel to the bar major axis. It was used successfully on corotation radii, and for the barred galaxies of their sample used NGC 936 (Merrifield & Kuijken 1995), on five SB0 galaxies the radius closest to, and just larger than, the bar length, to by Aguerri et al. (2003), and Corsini (2011) presented results derive the pattern speed associated with the bar. However they on 18 galaxies using this technique. It is based on clear and well also postulate that in some cases the end of the bar is not at understood principles, but has two drawbacks which make it corotation, but at the outer Lindblad resonance, in which case difficult to extend to large samples of galaxies: it is applicable corotation is at a smaller radius than the bar length, and the to stellar populations where interstellar dust does not obscure bar is considered “superfast.” In any case they claimed that the the stellar emission, so it works less well on late type galax- presence of resonance patterns in the full sample of galaxies ies, and more importantly, the spectral measurements require should be considered evidence for the persistence of density rather long exposures, particularly in the outer disk, thus re- wave systems in galaxy disks. stricting the numbers of objects observable in practice. As it It is interesting to note that predictions of multiple pattern relies on the continuity of the emitting sources, opinion is di- speeds can be found in the literature dating back decades. They vided on whether it can also be applied using measurements of appeared in the output of N-body simulations of Sellwood the interstellar gas. Nevertheless, Zimmer et al. (2004) applied & Sparke (1988), who found bars and spirals in the same it to CO emission line maps of three galaxies, while Rand & galaxies rotating with different pattern speeds; similar behavior Wallin (2004) applied it to five more. Hernandez et al. (2005) was derived by Rautiainen & Salo (1999).
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