Formation of a tidal stream

## Formation of a tidal stream

Movie of the formation of a tidal stream (28 MB) <a href="stream_movie.mp4">Movie of the formation of a tidal stream</a> (28 MB) <br>

#### Doomed love.

The movie above shows a simple simulation of the formation of a single tidal stream as a small galaxy (we'll call it "Tiny") merges with a large one (that we'll call "Bertha"). Here is a key to understanding the movie:

• The movie is looking down on the merger from above, or up from below if you prefer, at the plane in which most of the action is taking place. This is really a projection of a 3D system, of course, but we have chosen the vantage point to yield most of the information about the interaction. The x- and y-axes are centered on Bertha's center, with distances measured in units of kiloparsecs. The kiloparsec is a nice tractable unit for studying galactic interactions: the disk of our galaxy, the Milky Way, is about 30 kpc across and the Sun is about 8 kpc from its center[0].

• Bertha is invisible in the movie [1], but you can see her influence on Tiny! The simulation makes some assumptions about Bertha: she's spherically symmetric, her mass density varies with the distance from the center according to a particular formula, and she contains so much more mass than Tiny that we can assume this formula is constant during the merger - that is, the gravitational force of Tiny on Bertha can be ignored (but not the other way round). To give you an idea of Bertha's size, about half of her mass is inside the red circle.

• The white dots are a sampling of Tiny's stars [2]. Each "star" feels the gravitational pull from the other stars in Tiny, as well as Bertha's gravitational pull. Both of these are different for stars at different positions (remember that Bertha's mass density varies with the distance from the center, so her gravitational pull does too). Tiny starts to come apart when the difference between Bertha's pull on his near and far sides is larger than the pull of his stars on each other. This difference in the gravitational force is the same thing that causes tides on the Earth (in that case it's the Earth's oceans that get differentially pulled by the Moon and Sun) so we call the process "tidal disruption."

• The initial orbit of Tiny around Bertha is almost, but not quite, circular. In cases like this, Tiny's disruption is rather gradual---the closer Tiny gets to Bertha, the stronger the tides, but since their closest approach (pericenter) is not much different from their farthest separation (apocenter), the tidal disruption proceeds at a nearly constant rate. The stars that have been tidally stripped from Tiny form a long arc around Bertha [3] that almost, but not quite, traces Tiny's orbit.

• The first stars to be stripped from Tiny are the ones around his edges, because these stars feel the weakest pull from Tiny and the largest tidal difference from Bertha. In fact there is a characteristic distance from Tiny's center, called the tidal radius, within which stars are safe from being tidally stripped. The tidal radius depends on the mass ratio of the two galaxies and the distance between them; it's shown as a green circle around Tiny's center of mass. The smaller the circle, the stronger the tides. You'll see that it shrinks a bit as Tiny gets closer to Bertha: for orbits that get sufficiently close to Bertha's center the tidal radius can be zero, which means that Tiny will be entirely disrupted: no stars are safe!

[0] Okay, okay, I know you want to know what that is in light years, but trust me---it won't help with a sense of scale. 1 kpc = 1000 pc = 3260 light years (or so). Now what are you going to do? The point is to compare to things you know the size of already - in this case, the diameter of our galaxy and the position of the Sun in it are good yardsticks. If those things were more precisely defined, astronomers would measure distances in units of the solar distance and/or the milky way's diameter instead of any of these units (actually, they already do anyway, even though those things aren't that well measured!). The only reason we use parsecs is because of how some astronomical distances are measured.

[1] If Bertha weren't invisible, you wouldn't be able to see the stream formed by Tiny except perhaps at Bertha's edges---Tiny contains far fewer stars than Bertha (in this case, several thousand times fewer!), and they are spread quite thinly over time as Bertha's tides rip Tiny apart, so the stream of stars from Tiny is usually fainter than the background from Bertha.

[2] Actually, the white dots are simulation particles that are used to track approximately what the stars in the region right around a particular dot location would do. Each white dot has a mass equivalent to about ten thousand stars, so you can think of each one as tracking the collective behavior of that many stars. We do this because to simulate each star in Tiny with one particle would take much longer (more than 10,000 times longer!), and isn't that much more informative in this particular case because we've made so many other simplifying assumptions.

[3] Actually two arcs: one made of stars that orbit around Bertha faster than Tiny's main bulk (the "leading arm") and one of stars that orbit slower (the "trailing arm").