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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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.

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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


  1. School of Physics and Astronomy, The University of Nottingham, Nottingham, UK

    • Thomas G. Peterken
    • , Michael R. Merrifield
    •  & Alfonso Aragón-Salamanca
  2. McDonald Observatory, The University of Texas at Austin, Austin, TX, USA

    • Niv Drory
  3. Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth, UK

    • Coleman M. Krawczyk
    •  & Karen L. Masters
  4. Department of Physics and Astronomy, Haverford College, Haverford, PA, USA

    • Karen L. Masters
  5. School of Physics and Astronomy, University of St Andrews, St Andrews, UK

    • Anne-Marie Weijmans
  6. University of California Observatories, University of California, Santa Cruz, Santa Cruz, CA, USA

    • Kyle B. Westfall


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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.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Thomas G. Peterken.

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