Skip to main content Accessibility help
Hostname: page-component-99c86f546-cxxrm Total loading time: 0.826 Render date: 2021-11-27T18:31:04.735Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Dynamics of secular evolution

Published online by Cambridge University Press:  05 September 2013

James Binney
Oxford University
Jesús Falcón-Barroso
Instituto de Astrofísica de Canarias, Tenerife
Johan H. Knapen
Instituto de Astrofísica de Canarias, Tenerife
Get access



The material in this article was presented in five hours of lectures to the 2011 Canary Islands Winter School. The School's theme was ‘Secular Evolution of Galaxies’ and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and chemical evolution, so these topics are avoided here. The material starts with an account of the connections between isolating integrals, quasiperiodicity and angle-action variables – these variables played a prominent and unifying role throughout the lectures. This leads on to the phenomenon of resonant trapping and how this can lead to chaos in cuspy potentials and phase-space mixing in slowly evolving potentials. Surfaces of section and frequency analysis are introduced as diagnostics of phase-space structure. Real galactic potentials include a fluctuating part that drives the system towards unattainable thermal equilibrium. Two-body encounters are only one source of fluctuations, and all fluctuations will drive similar evolution. The orbit-averaged Fokker-Planck equation is derived, as are relations that hold between the second-order diffusion coefficients and both the power spectrum of the fluctuations and the first-order diffusion coefficients. From the observed heating of the solar neighbourhood we show that the second-order diffusion coefficients must scale as ˜ J1/2. We show that periodic spiral structure shifts angular momentum outwards, heating at the Lindblad resonances and mixing at corotation. The equation that would yield the normal modes of a stellar disk is first derived and then used to discuss the propagation of tightly wound spiral waves.

Publisher: Cambridge University Press
Print publication year: 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Arnold, V. I. (1978), Mathematical Methods of Classical Mechanics, New York: Springer
Aumer, M., Binney, J. J. (2009), MNRAS, 397, 1286
Bell, E. F., Zucker, D. B., Daniel, al. (2008), ApJ, 680, 295
Belokurov, V., Zucker, D. B., Evans, N. al. (2006), ApJ, 642, 137
Binney, J. (1982), MNRAS, 201, 1
Binney, J. (2010), MNRAS, 210, 2318
Binney, J., Lacey, C. (1988), MNRAS, 230, 597
Binney, J., Tremaine, S. (2008), Galactic Dynamics, Princeton: Princeton University Press
Gradshteyn, I. S., Ryzhik, I. M. (1965), Tables of Integrals, Series and Products, New York: Academic Press
Kaasalainen, M., Binney, J. (1994), PhRvL, 73, 2377
Kalnajs, A. (1977), ApJ, 212, 637
Lin, C. C., Shu, F. H. (1966), Proc. Nat. Sci., 55, 229
McConnachie, A. W., Irwin, M. J., Ibata, R. al. (2009), Nature, 461, 66
Merritt, D., Valluri, M. (1999), AJ, 118, 1177
Read, J., Evans, N. W. (1998), MNRAS, 300, 106
Rix, H.-W., Zaritsky, D. (1995), ApJ, 447, 82
Sellwood, J. A. (2008), in Formation and Evolution of Galaxy Disks, J. G., Funes, S. J., and E. M., Corsini, eds., ASP Conf. Ser., 396, p.241
Sellwood, J. A., Binney, J. J. (2002), MNRAS, 336, 785
Sellwood, J. A., Kahn, F. D. (1991), MNRAS, 250, 278
Sparke, L. S., Sellwood, J. A. (1988), MNRAS, 231, 25
Spitzer, L., Schwarzschild, M. (1953), ApJ, 118, 106
Sridhar, S., Touma, J. (1996), MNRAS, 279, 1263
Toomre, A. (1964), ApJ, 139, 1217
Toomre, A. (1969), ApJ, 158, 899
Toomre, A. (1981), in The Structure and Evolution of Normal Galaxies, S. M., Fall & D., Lynden-Bell, eds., Cambridge: Cambridge University Press, p. 111
van Kampen, N. G. (1955), Physica, 21, 949
Wielen, R. (1977), A&A, 60, 263
Cited by

Send book to Kindle

To send this book to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats

Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats