Walk on water: reflections on dynamical friction
Or: how to stop a galaxy with nothing to push on, part 2
Author’s note: this post continues a post from two weeks ago. I’ve included an edited version of the first part for completeness, but have also indicated where the new material starts below!
Do you know what happens when two galaxies smash into each other at a typical collision speed of nearly one million miles per hour?
Surprisingly little, actually. At least at first. In the words of my graduate dynamics textbook, they "simply pass through one another like ghosts." Gotta love a good dynamics ghost.
The reason for this is actually pretty straightforward: galaxies are mostly empty space. If you were to shrink the sun to the size of a basketball in Chicago, the nearest star to it would be on the other side of the planet, somewhere in Hawaii. Now what are the odds of hitting another basketball thrown randomly from outer space? Very much not good. The balls will basically never collide. So too with a galaxy - the stars pass each other like ships on opposite sides of the planet, alone and distant in the night.
But that’s not the end of the story. Because these passing stars, as if of their own accord, all slow down. Which is its own sort of surprise. On earth we slow down because of contact: our sled grates along the ground or our parachute catches the wind - trillions upon trillions of molecules pushing back on our bodies, staying our fall. But in space their’s no contact, no appreciable density of particles to slow the fall. The closest stellar pass might be trillions of miles, that is to say light years, away. And yet, the stars slow down. Over long periods of time dramatically, altering the course of their orbits, eventually bringing galaxies back together again to setting into one larger galaxy, derailed and stopped. Effectively braked. So, the question for today: why does that happen? How do you pump the brakes in space? What allows galaxies to come together, and then pause, and stay a while?
Allow me to introduce you to the fascinating, if confusing, advanced astrophysical idea of dynamical friction. Dynamical friction - a special process that slows the stars of colliding galaxies – the stickiness that makes galaxies come back to each other, like lassoed bulls or uncertain lovers. Don’t let its name fool you: it’s very different from regular friction, which makes sleds stop and gears grind: though dynamical friction has a similar slackening effect, it requires no contact, no roughness of surfaces, no sliding or squealing or great carpet burns.
It’s a slowing force that arises not from any ground, but instead from the motions (that is, the dynamics) of the surrounding stars.
Here’s the idea: an object like a star, black hole, or star cluster from galaxy #1, passes through the spaced out stars in galaxy #2. The stars in galaxy #2 are gravitationally attracted toward the object like scattered ducklings to a mother duck - stars above it move down toward it, and stars below it move up toward it. This means that after it passes, there’s a higher density of stars behind the object - a crowd of stars in its wake (see Figure 1).
[Author’s note: Part Two - the new material - starts here!]
Now the key to dynamical friction is this: it’s impossible for the object not to be affected by the crowd behind it. The large number of stars directly behind the object exert a gravitational tug on the object that pull on it from behind, slowing it down. Said again, the pull from the higher density crowd is larger than the collective pull from any of the other stars; the crowd pulls back on the object, affecting its motion, slowing it down. It’s like the difference between walking by yourself and walking with a group: I’m a power walker on my own, but when I’m walking with a group I pace myself, feeling the effect of their presence, moving slower so as to not be too far out in front, wanting to stay part of the fun. The effect of the group is to slow us all down.
Which makes me wonder the extent to which people also suffer from dynamical friction. I think I certainly do. I started this substack earlier this year, and dove into it with reasonable confidence and gusto. I had maybe 5 subscribers, and no reputation to worry about. Since then my subscriber list has expanded and the work I’ve posted has set some expectations: my readers, and mine. It’s interesting how quickly the addition of new followers makes it harder to post. I feel the weight of readership, the drag of collecting expectations. It gives me a little tug of empathy for famous people, I suppose. I like to think others opinions of me shouldn’t matter, wouldn’t pull. And yet, if the crowd wants something, can I not give it to them? Consider the costs if I don’t respond.
My first year as a professor, moving through the great sea of student critics, trying to please them, trying to get it all right, Eminem and Beyoncé produced a single together describing their struggles with their following crowds. “Walk on water,” they feel the people saying. Be perfect. “I walk on water, but I ain’t no Jesus” Beyoncé sings. “I walk on water, but only when it freezes.” Emenim comes in trying to explain further, the sound of ripping paper an accent to the words. “Will this step just be another misstep / To tarnish whatever the legacy, love or respect, I've garnered?” he asks.
A legacy, I see, means chains attached. Eminem writes of trying to write more: “Into the dark, I plummet” … “Why are the expectations so high?”
I remember thinking how much I resonated with this song. Not as a famous person – I’m certainly no Eminem or Beyoncé – but I’m still often slave to what I think others think. I still want you to love me, dear reader. I want my friends to think highly of me, my mom to be proud. I like to pretend I’m a rock, an island, who doesn’t care about what the rest of you all human beings surrounding me think. But physics doesn’t care how much I pretend. The crowds we attract pull back, no matter how hard we try to get away, how tightly we squeeze our eyes shut. I guess you don’t have to be famous to understand Beyoncé’s desperate plea:
I'm only human, just like you I been making my mistakes, oh if you only knew I don't think you should believe in me the way that you do 'Cause I'm terrified to let you down, oh If I walked on water, I would drown
My take away here is less about fame and meeting expectations, but more just an acknowledgement that as we move through our lives we respond to the impact of those around us. Not unlike gravity, the closer objects tend to pull most strongly. Not unlike gravity, the more objects flow in a certain direction, the more I’m drawn that way. And not unlike stars in space, though most stars never touch, their impact is still felt. Each star is dynamic, moving, changing, rocketing through three dimensional space, its motions intertwined with those of each other.
Which makes me think it’s worth noting that dynamical friction is a subtle effect. There are other forces at play in mergers that are easier to see, like shock waves between gas particles and giant tidal streams. But though dynamical friction appears subtile, it is present, and strong. I think of George Bailey in the classic Christmas movie It’s a Wonderful Life. In the movie he considers jumping off a bridge because he’s so fed up with the direction of his life – the ways he feels trapped and without purpose or impact in a small town. A mulled-wine loving angel named Clarence shows George what the town would look like if he’d never been born. And we see that without George his friend would have been in jail for a simple misunderstanding, his brother dead from a moment’s misjudgment. Homes closed, businesses changed.
I remember (not really intentionally) brokering a relationship between two of my friends in high school. They’d both talk to me about their feelings, I’d invite them both to parties, and suggest they might talk about things more (“yeah, he might be receptive to that.”). They’ve now been married for a decade, and have two small kids. Perhaps that would have happened anyway. But then again, who knows?
Because like it or not, our lives create a ripple behind us. A friend said to me the other day: privilege is not noticing my wake. Which made me pause. A little touch, from him to me. And in reflection, my friend has a point. How is it that the more well connected we are the less we notice the soft power we have, and reciprocally, the buoying strength of our supporting network?
These ripples might penetrate deeper than we think. One of my friends noted to me that it’s not just what we see on the surface. After reading an early draft of this piece, she wrote the following: “I wonder if our memories form a sort of dynamical friction as we pass through life and this is the pull we feel to go back, reflect and get nostalgic for the past. Memories are weird. We like to think of them as factual and carved in stone, but they are actually very dynamic. They get pruned and reshaped and recast. Perhaps this is why we can get nostalgic for periods of life that were, at the time, actually experienced as quite humdrum or even stressful. Our brains prune out all the ‘space’ in between, leaving a denser cluster of memories that pulls us backwards.”
I sense that she’s right. We all have to live with ourselves, and the bright stars of our past. It’s like the long gray haired man at my former church who was in a band 30 years ago, and couldn’t stop sharing when he found out I was a musician of sort. Like old rockers always living their glory days, aren’t we all.
Yet, then again, I don’t think nostalgia is the whole of it. While we might think of this friction as a drag, a slowing force that holds us back, perhaps we might too notice that these memories, these people — whatever the analogy we use — anchor us. As we age we learn where we stand. Sure, we are still moving, we still change. But sometimes the dynamics behind us provide a sort of stability, saving us from the ravage of rocketing through space with no place to be — giving us a little nudge, a little sense of direction, a place to land. For our wedding one of our guests made us a hand-knit wall hanging that says, in big bold letters, “You Are Home.” It hangs by our door now, a lovely reminder of home the place, yes, but also home the constellation of people around me. Home, the great “cloud of witnesses,” which, as the writer of Hebrews suggests, allows us to run the race set out before us.
So in the balance dynamical friction doesn’t seem particularly good or bad. It’s just the way that it is for merging galaxies. It’s a fact for close interactions of celestial objects, which, I suppose, in some sense, we all are.