Differential Galactic Rotation
General Description
This simulation illustrates the model of galactic rotation proposed by
Jan Oort in 1927. In Oort's model most of the mass of the galaxy is
concentrated at the center. Stars move in circular orbits around the
center, with orbital speeds that are inversely proportional to the
square root of their distance from the center. Oort realized that
this model produced a specific pattern of radial velocities in the
stars near the sun, and that this pattern matched the observational
data fairly well. The simulation is intended to illustrate both
Oort's model and the resulting pattern in the radial velocities. The
simulation can also depict the so-called "high-velocity" stars, which
are stars that have very low orbital speeds around the galactic center
and therefore have high speeds relative to the sun.
One window depicts stars (including the sun) orbiting counterclockwise
around the galactic
center as seen from above the galactic North pole. The velocity
vectors of the stars can be displayed, and stars near the sun can be
highlighted. Another window shows the highlighted stars (and,
optionally, the high-velocity stars) in the region
near the sun. The radial velocity and relative velocity vectors for
these stars can be displayed. Finally, a plot of radial velocity
versus galactic longitude (using either the modern longitude system in
which the galactic center is at longitude 0, or the pre-1958 system
with the galactic center at longitude 325 degrees) can be shown. The plot can display data for
the highlighted stars, the high-velocity stars, and two sets of
Cepheid variables studied by Alfred Joy in 1939. Using the Cepheid
period-luminosity relation Joy found distances to these stars that fit
with the distances derived from Oort's rotational model, provided that
the apparent magnitudes of the stars were corrected for interstellar
absorption. The user can explore the simulation and then determine
which group of Cepheid variables is more distant from the sun.
Galaxy Frame
This frame shows stars orbiting the galactic center from a perspective
above the North galactic pole.
- Galaxy Options Menu
- Show Velocity Vectors: show the velocity vectors for all
stars.
- Show Relative Motion Near Sun: display a new window
depicting the relative motion of stars in the solar neighborhood.
- Show Plot of Radial Velocity vs. Longitude: display a
new window with a plot of radial velocity vs. longitude for
the stars near the sun.
- Show "High-Velocity" Stars: show a set of stationary
stars that do not orbit the galactic center.
- Keep Colors Fixed: force all stars to retain their
original coloring, even if they move into or out of the
solar neighborhood. This option allows the user to see how
a group of stars gets pulled apart into a spiral pattern by
differential rotation.
- Visual Elements
- Cyan point: galactic center.
- Orange point/arrow: our Sun and its velocity vector.
- White points/arrows: stars and their velocity vectors.
- Green points/arrows: stars in the solar neighborhood (or
stars that started in the solar neighborhood, if colors are
fixed) and
their velocity vectors.
- Pink points: "high-velocity" stars (these stars do not
move, so they have no velocity arrows).
- Controls
- Play/pause button: play or pause the simulation.
- Step button: advance the simulation by one time step.
- Reset button: reset the simulation to its initial state.
- # of stars: number of stars shown in the simulation. To
change this value type a new value into the text box, hit
return, and then hit the Initialize button.
- Initialize button: read in the input for the # of stars
and initialize the simulation.
- r_min: The minimum distance from the sun for stars
included in the solar neighborhood (in units of the sun's
distance from the galactic center).
- r_max: The maximum distance from the sun for stars
included in the solar neighborhood (in units of the sun's
distance from the galactic center).
Solar Neighborhood Frame
This frame shows the stars in the solar neighborhood (as defined by
r_min and r_max above) in the sun's rest frame.
- Solar Neighborhood Options Menu
- Show Radial Velocity Vectors: show arrows depicting the radial
velocities of stars relative to the sun.
- Show Relative Velocity Vectors: show arrows depicting the
velocities of stars relative to the sun.
- Visual Elements
- Orange point: the sun.
- Green points: stars in the solar neighborhood.
- Magenta arrows: velocities of regular stars relative to
the sun.
- Cyan arrows: velocities of "high-velocity" stars
relative to the sun.
- Red/blue arrows: radial velocities of stars relative to
the sun (red for motion away from the sun, blue for motion
toward the sun).
- Yellow arrow: points toward the galactic center.
Radial Velocity Plot Frame
This frame shows a plot of the radial velocity of stars vs. their
galactic longitude.
- Plot Options Menu
- Use Old (Pre-1958) Longitude System: use the pre-1958
longitude system in which the longitude of the galactic center was
325 degrees. [In the modern system the longitude of the galactic
center is defined to be zero.]
- Show Max/Min Curves: show theoretical curves based on Oort's
model for stars at distances of r_min and r_max (see above) from the
sun.
- Show Star Data: display the data points for stars in the solar
neighborhood and high-velocity stars (if included).
- Show Joy's Group 2: show data for Group 2 Cepheid variables
from Joy's 1939 paper.
- Show Joy's Group 3: show data for Group 3 Cepheid variables
from Joy's 1939 paper.
- Visual Elements
- Red/blue points: data for stars in the solar neighborhood
(red for positive radial velocity, blue for negative radial
velocity).
- Pink points: data for high-velocity stars.
- Black curve: theoretical curve for stars at a distance
of r_max from the sun. [Note: this curve shows a series
approximation to the exact result. This approximation is accurate
up to about r_max=0.5, but will deviate noticeably from the exact
result for larger values of r_max.]
- Green curve: theoretical curve for stars at a distance
of r_min from the sun (subject to the same limitations as the r_max
curve).
- Black squares: data for Joy's Group 2 Cepheids.
- Magenta squares: data for Joy's Group 3 Cepheids.
Todd K. Timberlake (ttimberlake@berry.edu)