The Kinematics and Dynamics of Galactic Rings
The Physics of Resonance
The physics involved in resonance entails the differential rotation of a galaxy's bar with respect to particles in the the disk of the galaxy. Put simply, it is the value of the bar pattern angular velocity in relation to the angular frequency of circular rotation and the radial epicyclic frequency of every star and dust cloud in the disk of the galaxy. The epicycles are actually closed elliptical orbits of material in the disk of the galaxy that are precessing around the central region of the galaxy. How fast a bar pattern rotates determines what kind of resonance you end up with in a galaxy. If the bar pattern speed is fast enough then it is believed that it can push a spiral out to the Outer Lindblad Resonance (OLR). If OLR is in the visible disk then it may lead to ring and pseudoring formation. The three major resonances relevant to ring formation are:
Outer Lindblad Resonance (OLR)
Inner Lindblad Resonance (ILR)
Inner 4:1 Ultraharmonic Resonance (UHR)
Figure 1. The OLR subclass of outer pseudorings
Figure. 2. Schematic showing the relative shapes, sizes, and major-axis orientations of all of the bar and ring features of NGC 3081, including the "dimples" in the outer R1 ring feature. Here "nr" refers to the nuclear ring, and "nb" to the nuclear (secondary) bar. Axes are labeled in arcsecond offsets relative to the nucleus. North is at the top, and east is to the left.
Image and description source:
A HUBBLE SPACE TELESCOPE STUDY OF STAR FORMATION IN THE INNER RESONANCE RING OF NGC 3081 by R. Buta et al.
Other important types of resonance are
corotation (CR) and the
outer 4:1 resonance. In corotation (CR) the periodic rate of rotation of the bar is equal to the angular frequency of circular rotation of the disk. In the outer 4:1 resonance the periodic rate of rotation of the bar is equal to the angular frequency of circular rotation plus 1/4 of the radial epicyclic frequency.
Figure 3. Corotation resonace (CR)
If you read nothing else on this subject, at the very least, read
Galactic Rings by R. Buta and F. Combes. I consider this a must-read. (very highly recommended)
Another paper worth reading is the following:
Title:
The Morphology of Barred GalaxiesAuthors: Buta, R.
Journal: Barred galaxies. Astronomical Society of the Pacific Conference Series, Volume 91; Proceedings of a conference held at the University of Alabama; Tuscaloosa; Alabama; 30 May - 3 June 1995; San Francisco: Astronomical Society of the Pacific (ASP #91); |c1996; edited by R. Buta, D. A. Crocker and B. G. Elmegreen, p.11
Bibliographic Code: 1996ASPC...91...11B
TABLE I. Summary of notation for ring and lens phenomena (below) from the paper (above),
Galactic Rings by R. Buta and F. Combes.
| TABLE I. Summary of notation for ring and lens phenomena |
| Feature symbol |
| nr | nuclear ring |
| nr' | nuclear pseudoring |
| r | inner ring |
| rs | inner pseudoring |
| R | outer ring |
| R' | outer pseudoring |
| R1 | Type 1 OLR subclass outer ring |
| R1' | Type 1 OLR subclass outer pseudoring |
| R2' | Type 2 OLR subclass outer pseudoring |
| nl | nuclear lens |
| l | inner lens |
| rl | inner ring/lens |
| L | outer lens |
| RL | outer ring/lens |
Here's a wonderful paper written by Dr. Ronald Buta et al on a study done with the Hubble Space Telescope of the inner resonance ring of NGC 3081. Even though the paper's focus is on this one galaxy, it gives the reader a much more in-depth understanding of the kinematics and dynamics of inner rings in general. Admittedly, it's a little technical, but well worth reading.
A HUBBLE SPACE TELESCOPE STUDY OF STAR FORMATION IN THE INNER RESONANCE RING OF NGC 3081.
The Origins of Spiral Arms
Hydrodynamic Modeling
How Two, Three and Four Arms Are Created
by a Single Galactic Bar
The Origins of Spiral Arms - translated by Charles Danforth, University of Colorado
Figure 1. By aligning a series of concentric elliptical (2/1) orbits, a bar can be produced (a). If each ellipse is given an azimuthal offset proportional to r
½, the effect is a two armed spiral of orbits (b). A set of (3/2) orbits produces a three armed spiral (c) and (4/1) produces a four armed pattern (d).
The above illustration is from
The Origins of Spiral Arms by Charles Danforth, University of Colorado.
Star-Forming Nuclear Rings in Spiral Galaxies
Here's a paper entitled
Star-Forming Nuclear Rings in Spiral Galaxies.pdfExamples of the Application of the Notation for Ring
and Lens Types to Actual Images of Galaxies
I realize that this is a lot to swallow all at once. So, I have provided a couple of examples of objects, each with a very sophisticated classification using feature symbols from Table I. There is a summary of notation for ring and lens phenomena below. But, I have also included "alternative" classifications from both NED and SIMBAD, which are considerably simpler, to give you a better idea of what you may come across in Galaxy Analysis. Thank you for reading.
Eric
NGC 3081
RA=9:59.5, Dec=-22:50
Classifications: (R1R2')SAB(r,nr)0/a
Alternative ClassificationsSIMBADBasic data: Seyfert 1 Galaxy*
Morphological type S0:r
NEDClassifications: (R_1)SAB(r)0/a Sy2*
*SIMBAD and NED seem to be in disagreement on whether this is a Seyfert 1 or a Seyfert 2 galaxy.
NGC 2273
RA = 6:50.1, Dec. = +60:51
Classifications: (RR)SB(rs)a Sy2
Alternative ClassificationsSIMBADBasic data: Seyfert 2 Galaxy
Morphological type SBa
NEDClassifications: SB(r)a: Sy2
The thumbnails (below) are more examples of ring and pseudoring classifications.
