A direct test of density wave theory in a grand-design spiral galaxy


The exact nature of the arms of spiral galaxies is still an open question1. It has been widely assumed that spiral arms in galaxies with two distinct symmetrical arms are the products of density waves that propagate around the disk, with the spiral arms being visibly enhanced by the star formation that is triggered as the passing wave compresses gas in the galaxy disk1,2,3. Such a persistent wave would propagate with an approximately constant angular speed, its pattern speed ΩP. The quasi-stationary density wave theory can be tested by measuring this quantity and showing that it does not vary with radius in the galaxy. Unfortunately, this measurement is difficult because ΩP is only indirectly connected to observables such as the stellar rotation speed4,5,6. Here, we use the detailed information on stellar populations of the grand-design spiral galaxy UGC 3825, extracted from spectral mapping, to measure the offset between young stars of a known age and the spiral arm in which they formed, allowing a direct measurement of ΩP at a range of radii. The offset in this galaxy is found to be as expected for a pattern speed that varies little with radius, indicating consistency with a quasi-stationary density wave, and lending credence to this new method.

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Fig. 1: UGC 3825 and its star-formation tracers used here.
Fig. 2: Derived pattern speed ΩP(r) for UGC 3825.

Data availability

Integral field spectroscopy data of UGC 3825 are available as part of data release 14 of the SDSS38. The specific data that support the plots within this paper and other findings of this study are an updated version of these data, and will be made publicly available as part of SDSS data release 15, which will be described in a separate paper by the MaNGA collaboration in early 2019 (Aguado et al., manuscript in preparation). In the meantime, the data used here are available from the corresponding author upon reasonable request.


  1. 1.

    Dobbs, C. & Baba, J. Dawes review 4: spiral structures in disc galaxies. Publ. Astron. Soc. Aust. 31, e035 (2014).

    ADS  Article  Google Scholar 

  2. 2.

    Lin, C. C. & Shu, F. H. On the spiral structure of disk galaxies. Astrophys. J. 140, 646 (1964).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    Bertin, G. Dynamics of Galaxies (Cambridge Univ. Press, Cambridge, 2014).

  4. 4.

    Tremaine, S. & Weinberg, M. D. A kinematic method for measuring the pattern speed of barred galaxies. Astrophys. J. Lett. 282, L5–L7 (1984).

    ADS  Article  Google Scholar 

  5. 5.

    Font, J. et al. Resonant structure in the disks of spiral galaxies, using phase reversals in streaming motions from two-dimensional Hα Fabry–Perot spectroscopy. Astrophys. J. Lett. 741, L14 (2011).

    ADS  Article  Google Scholar 

  6. 6.

    Beckman, J. E., Font, J., Borlaff, A. & Garca-Lorenzo, B. Precision determination of corotation radii in galaxy disks: Tremaine–Weinberg versus Font–Beckman for NGC 3433. Astrophys. J. 854, 182 (2018).

    ADS  Article  Google Scholar 

  7. 7.

    Lin, C. C. & Shu, F. H. On the spiral structure of disk galaxies, II. Outline of a theory of density waves. Proc. Natl Acad. Sci. USA 55, 229–234 (1966).

    ADS  Article  Google Scholar 

  8. 8.

    Kalnajs, A. J. The Stability of Highly Flattened Galaxies. PhD thesis, Harvard Univ. (1965).

  9. 9.

    Toomre, A. Group velocity of spiral waves in galactic disks. Astrophys. J. 158, 899 (1969).

    ADS  Article  Google Scholar 

  10. 10.

    Bertin, G., Lin, C. C., Lowe, S. A. & Thurstans, R. P. Modal approach to the morphology of spiral galaxies. I. Basic structure and astrophysical viability. Astrophys. J. 338, 78 (1989).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    Bertin, G. & Lin, C. C. Spiral Structure in Galaxies: A Density Wave Theory (The MIT Press, Cambridge, 1996).

  12. 12.

    Zhang, X. N-body simulations of collective effects in spiral and barred galaxies. Astron. Comput. 17, 86–128 (2016).

    ADS  Article  Google Scholar 

  13. 13.

    Egusa, F., Sofue, Y. & Nakanishi, H. Offsets between Hα and CO arms of a spiral galaxy, NGC 4254: a new method for determining the pattern speed of spiral galaxies. Publ. Astron. Soc. Jpn 56, L45–L48 (2004).

    ADS  Article  Google Scholar 

  14. 14.

    Tamburro, D. et al. Geometrically derived timescales for star formation in spiral galaxies. Astron. J. 136, 2872–2885 (2008).

    ADS  Article  Google Scholar 

  15. 15.

    Egusa, F., Kohno, K., Sofue, Y., Nakanishi, H. & Komugi, S. Determining star formation timescale and pattern speed in nearby spiral galaxies. Astrophys. J. 697, 1870–1891 (2009).

    ADS  Article  Google Scholar 

  16. 16.

    Gonzalez, R. A. & Graham, J. R. Tracing the dynamics of disk galaxies with optical and infrared surface photometry: color gradients in M99. Astrophys. J. 460, 651 (1996).

    ADS  Article  Google Scholar 

  17. 17.

    Puerari, I. & Dottori, H. A morphological method to determine corotation radii in spiral galaxies. Astrophys. J. Lett. 476, L73–L75 (1997).

    ADS  Article  Google Scholar 

  18. 18.

    Martnez-Garca, E. E., González-Lópezlira, R. A. & Bruzual-A, G. Spiral density wave triggering of star formation in SA and SAB galaxies. Astrophys. J. 694, 512–545 (2009).

    ADS  Article  Google Scholar 

  19. 19.

    Martnez-Garca, E. E. & González-Lópezlira, R. A. Signatures of long-lived spiral patterns. Astrophys. J. 765, 105 (2013).

    ADS  Article  Google Scholar 

  20. 20.

    Verley, S. et al. The AMIGA sample of isolated galaxies. V. Quantification of the isolation. Astron. Astrophys. 472, 121–130 (2007).

    ADS  Article  Google Scholar 

  21. 21.

    Pettitt, A. R., Tasker, E. J., Wadsley, J. W., Keller, B. W. & Benincasa, S. M. Star formation and ISM morphology in tidally induced spiral structures. Mon. Not. R. Astron. Soc. 468, 4189–4204 (2017).

    ADS  Article  Google Scholar 

  22. 22.

    Hart, R. E. et al. Galaxy Zoo: comparing the demographics of spiral arm number and a new method for correcting redshift bias. Mon. Not. R. Astron. Soc. 461, 3663–3682 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Bundy, K. et al. Overview of the SDSS-IV MaNGA survey: mapping nearby galaxies at Apache Point Observatory. Astrophys. J. 798, 7 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Conroy, C. Modeling the panchromatic spectral energy distributions of galaxies. Annu. Rev. Astron. Astrophys. 51, 393–455 (2013).

    ADS  Article  Google Scholar 

  25. 25.

    Kennicutt, R. C. Jr. Star formation in galaxies along the Hubble sequence. Annu. Rev. Astron. Astrophys. 36, 189–232 (1998).

    ADS  Article  Google Scholar 

  26. 26.

    Meidt, S. E., Rand, R. J. & Merrifield, M. R. Uncovering the origins of spiral structure by measuring radial variation in pattern speeds. Astrophys. J. 702, 277–290 (2009).

    ADS  Article  Google Scholar 

  27. 27.

    Hart, R. E. et al. Galaxy Zoo and SPARCFIRE: constraints on spiral arm formation mechanisms from spiral arm number and pitch angles. Mon. Not. R. Astron. Soc. 472, 2263–2279 (2017).

    ADS  Article  Google Scholar 

  28. 28.

    Baba, J., Morokuma-Matsui, K. & Egusa, F. Radial distributions of arm-gas offsets as an observational test of spiral theories. Publ. Astron. Soc. Jpn 67, L4 (2015).

    ADS  Article  Google Scholar 

  29. 29.

    Blanton, M. R. et al. Sloan Digital Sky Survey IV: mapping the Milky Way, nearby galaxies, and the distant universe. Astron. J. 154, 28 (2017).

    ADS  Article  Google Scholar 

  30. 30.

    Yan, R. et al. SDSS-IV MaNGA IFS galaxy survey: survey design, execution, and initial data quality. Astron. J. 152, 197 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    Drory, N. et al. The MaNGA integral field unit fiber feed system for the Sloan 2.5 m Telescope. Astron. J. 149, 77 (2015).

    ADS  Article  Google Scholar 

  32. 32.

    Law, D. R. et al. Observing strategy for the SDSS-IV/MaNGA IFU galaxy survey. Astron. J. 150, 19 (2015).

    ADS  Article  Google Scholar 

  33. 33.

    Law, D. R. et al. The data reduction pipeline for the SDSS-IV MaNGA IFU galaxy survey. Astron. J. 152, 83 (2016).

    ADS  Article  Google Scholar 

  34. 34.

    Wake, D. A. et al. The SDSS-IV MaNGA sample: design, optimization, and usage considerations. Astron. J. 154, 86 (2017).

    ADS  Article  Google Scholar 

  35. 35.

    Smee, S. A. et al. The multi-object, fiber-fed spectrographs for the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey. Astron. J. 146, 32 (2013).

    ADS  Article  Google Scholar 

  36. 36.

    Yan, R. et al. SDSS-IV/MaNGA: spectrophotometric calibration technique. Astron. J. 151, 8 (2016).

    ADS  Article  Google Scholar 

  37. 37.

    Gunn, J. E. et al. The 2.5 m Telescope of the Sloan Digital Sky Survey. Astron. J. 131, 2332–2359 (2006).

    ADS  Article  Google Scholar 

  38. 38.

    Abolfathi, B. et al. The fourteenth data release of the Sloan Digital Sky Survey: first spectroscopic data from the extended Baryon Oscillation Spectroscopic Survey and from the second phase of the Apache Point Observatory Galactic Evolution Experiment. Astrophys. J. Suppl. 235, 42 (2018).

    ADS  Article  Google Scholar 

  39. 39.

    Lintott, C. J. et al. Galaxy Zoo: morphologies derived from visual inspection of galaxies from the Sloan Digital Sky Survey. Mon. Not. R. Astron. Soc. 389, 1179–1189 (2008).

    ADS  Article  Google Scholar 

  40. 40.

    Lintott, C. et al. Galaxy Zoo 1: data release of morphological classifications for nearly 900,000 galaxies. Mon. Not. R. Astron. Soc. 410, 166–178 (2011).

    ADS  Article  Google Scholar 

  41. 41.

    Vazdekis, A. et al. Evolutionary stellar population synthesis with MILES—II. Scaled-solar and α-enhanced models. Mon. Not. R. Astron. Soc. 449, 1177–1214 (2015).

    ADS  Article  Google Scholar 

  42. 42.

    Kroupa, P. The local stellar initial mass function. In Dynamics of Star Clusters and the Milky Way (eds Deiters, S. et al.) 187 (Conference Series Volume 228, Astronomical Society of the Pacific, 2001).

  43. 43.

    Girardi, L., Bressan, A., Bertelli, G. & Chiosi, C. Evolutionary tracks and isochrones for low- and intermediate-mass stars: from 0.15 to 7 M sun, and from Z=0.0004 to 0.03. Astron. Astrophys. Suppl. Ser. 141, 371–383 (2000).

    ADS  Article  Google Scholar 

  44. 44.

    Cappellari, M. & Emsellem, E. Parametric recovery of line-of-sight velocity distributions from absorption-line spectra of galaxies via penalized likelihood. Publ. Astron. Soc. Pac. 116, 138–147 (2004).

    ADS  Article  Google Scholar 

  45. 45.

    Cappellari, M. Improving the full spectrum fitting method: accurate convolution with Gauss–Hermite functions. Mon. Not. R. Astron. Soc. 466, 798–811 (2017).

    ADS  Article  Google Scholar 

  46. 46.

    Cid Fernandes, R., Mateus, A., Sodré, L., Stasińska, G. & Gomes, J. M. Semi-empirical analysis of Sloan Digital Sky Survey galaxies—I. Spectral synthesis method. Mon. Not. R. Astron. Soc. 358, 363–378 (2005).

    ADS  Article  Google Scholar 

  47. 47.

    Asari, N. V. et al. The history of star-forming galaxies in the Sloan Digital Sky Survey. Mon. Not. R. Astron. Soc. 381, 263–279 (2007).

    ADS  Article  Google Scholar 

  48. 48.

    Cardelli, J. A., Clayton, G. C. & Mathis, J. S. The relationship between infrared, optical, and ultraviolet extinction. Astrophys. J. 345, 245–256 (1989).

    ADS  Article  Google Scholar 

  49. 49.

    Blanton, M. R., Kazin, E., Muna, D., Weaver, B. A. & Price-Whelan, A. Improved background subtraction for the Sloan Digital Sky Survey images. Astron. J. 142, 31 (2011).

    ADS  Article  Google Scholar 

  50. 50.

    Gerssen, J., Kuijken, K. & Merrifield, M. R. The shape of the velocity ellipsoid in NGC 488. Mon. Not. R. Astron. Soc. 288, 618–622 (1997).

    ADS  Article  Google Scholar 

  51. 51.

    Fukugita, M. et al. The Sloan Digital Sky Survey photometric system. Astron. J. 111, 1748 (1996).

    ADS  Article  Google Scholar 

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This work makes extensive use of the Starlight and pPXF spectral fitting tools, both of which are freely available. The Starlight project is available at http://www.starlight.ufsc.br/ and is supported by the Brazilian agencies CNPq, CAPES and FAPESP, and by the France-Brazil CAPES/Cofecub programme. pPXF was created and is maintained by M. Cappellari and is available at http://www-astro.physics.ox.ac.uk/~mxc/software/. The table-matching tool TOPCAT (available at http://www.star.bris.ac.uk/%7Embt/topcat/) was also used in this work. Several Python tools were also essential for this research. Astropy is a community-developed core Python package for Astronomy available at http://www.astropy.org/. Scipy is an open-source scientific computing package available at http://www.scipy.org/. The figures were generated using matplotlib, available at https://matplotlib.org/. This publication uses data generated via the Zooniverse platform, the development of which is funded by generous support, including a Global Impact Award from Google, and a grant from the Alfred P. Sloan Foundation. This publication has been made possible by the participation of almost 6,000 volunteers in the GZ:3D project on https://www.zooniverse.org/. Funding for the SDSS-IV has been provided by the Alfred P. Sloan Foundation, US Department of Energy Office of Science and Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah. The SDSS web site is https://www.sdss.org/. SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration, including the Brazilian Participation Group, Carnegie Institution for Science, Carnegie Mellon University, Chilean Participation Group, French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam, Max-Planck-Institut für Astronomie (Heidelberg), Max-Planck-Institut für Astrophysik (Garching), Max-Planck-Institut für Extraterrestrische Physik, National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University and Yale University. We are grateful for access to the University of Nottingham High Performance Computing facility, without which the spectral fitting work done here would not have been possible in any reasonable timeframe.

Author information




M.R.M. conceived the idea. T.G.P. developed the method and obtained the results. A.A.-S. and M.R.M. supervised the work, and led the main analysis and interpretation alongside T.G.P. K.B.W. calculated the kinematic parameters of UGC 3825 and discussed the implications of the results. K.L.M. and C.M.K. devised, implemented and provided output from the GZ:3D spiral-arm mask project. N.D., K.L.M., A.-M.W., K.B.W. and many others within the SDSS community obtained the MaNGA IFU data, developed reduction and analysis code, continue to maintain software and hardware, and performed many other tasks necessary for the running of a large collaboration. All authors discussed the results and contributed to the final manuscript.

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Correspondence to Thomas G. Peterken.

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Peterken, T.G., Merrifield, M.R., Aragón-Salamanca, A. et al. A direct test of density wave theory in a grand-design spiral galaxy. Nat Astron 3, 178–182 (2019). https://doi.org/10.1038/s41550-018-0627-5

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