Thread by @Astropartigirl

An interesting fact about my research on Self-interacting dark matter (SIDM) is that this type of particle dark matter requires a velocity-dependent cross-section to explain observations on both small and large scales. Now, let's unpack what all this jargon actually means!

The standard paradigm of dark matter, the type that successfully explains everything we see in the Universe today, like the things encoded in the Cosmic Microwave Background that tell us about dark matter, large-scale structure like clusters of galaxies, is Cold Dark Matter (CDM)

More specifically, CDM is not only cold, but also *collisionless*: this means that dark matter particles don't interact with each other at all, in the way that, say, billiard balls do. So they pass each other without seeing each other at all, while billiard balls might collide.

That's generally what CDM is. When we simulate the Universe with CDM, we get back precisely the Universe we observe today on large scales. But notice I said *on large scales*, ie galaxy clusters, and larger. When we zoom in, however, we find problems.

When we zoom in, that is to say we look at small scales. Not the giant galaxy cluster scale dark matter halos, but the smaller ones, like dwarf galaxy halos. Here, CDM simulations give us dwarf halos that have *way too much* stuff in their centers compared to observations.

Other issues arise as well, like the number of these satellite halos (dwarf galaxies are satellite galaxies of galaxies the size of the Milky Way and Andromeda, which together form the Local Group), but let's focus on the overly dense cores as this plays into why SIDM exists.

Using CDM successfully gives us back a Universe that looks like the one we live in in every way *except* when we zoom in and look at dwarf scale halos (the dark matter halos dwarf galaxies live in). This has been a known problem for a long time. So physicists knew something's up.

Physicists then asked the question: how do we resolve the mismatch we see in dwarf scale halos produced by CDM simulations so that they match the halos that the dwarf galaxies we observe actually live in? And here is where SIDM was born (circa the year 2000)!

Dark matter that doesn't interact (ie CDM) will form overdense regions in the cores of dwarf galaxy halos, resulting in halos that don't match observations. But what if we allow self-interactions? Kinda like billiards balls, if there are many in a region, some should scatter.

Then dense regions experience a lot of scatterings, while outer regions with less stuff won't interact at all and behave like CDM. And scatterings cause particles to exchange kinetic energy, thereby thermalizing (equilibrating) the inner region and leaving the outer untouched.

The dense regions that thermalize kinda "puff up" the core by kicking dark matter particles that are in there further out, alleviating the overdensity CDM produces and finally, matching observations!! Well, for dwarf galaxies, at least.

But when you fix one thing, you can't break another and call it a working theory. The first model of SIDM was of this type: fixed dwarf halos, messed up cluster ones. Because observations tell us cluster halos are happy living in halos that have dense cores, but dwarfs aren't.

Here's where we need to unpack the term "interaction cross-section": assume we have two balls the size of a small marble. If we launch these at each other, their cross-sectional area is small enough that they might pass each other without colliding at all.

Now, take two balls the size of basketballs. Launch these at each other, and their cross-sectional area is much larger, yielding a higher likelihood that the two will collide. An interaction cross-section can be taken (at least conceptually) in a similar way:

The larger the cross-sectional area, the higher the likelihood two particles will collide. The smaller, the less likely. It is more complicated than this (there are forces to consider and how those forces dictate the way interactions behave), but conceptually this will suffice.

Now, the cross-section required to resolve the overdensity observed in dwarf halos is much too large to explain cluster-scale halos: the same cross-section creates cluster-scale halos with centers that are not dense enough compared to observations.

(Jargon time: the overdensity in simulated CDM dwarf halos compared to observations is known as the core-cusp problem: "cuspy" halos are ones with very dense inner regions, while "cored" ones have less stuff in their centers. This will be language I'll use in an upcoming tweet)

So, using the same interaction cross-section for cluster scales produces halos that are cored, but clusters don't seem to have cores (for the most part, or at least, not appreciable ones), where cored means low density centers. Clusters are happy with cusps, ie dense centers.

But the first model had a constant interaction cross-section for SIDM which fixes dwarf halos and gives them the cored halos (lower density inner regions) they're observed to live in, but also gave clusters cores, when they're observed to be cuspy (dense inner region)!

So clearly we had a problem. Let's look at the differences between small and large scale systems: Well, smaller scales have smaller masses, so their gravitational potential is smaller. And velocities of particles will depend on the gravitational potential their in.

So then, dwarf halos with smaller masses ➡️ smaller gravitational potential ➡️ smaller velocities for particles in them.
Similarly, galaxy clusters have much larger mass ➡️ larger gravitational potential ➡️ larger velocities for particles in them.

So what if the interaction cross-section depends on velocity, such that higher velocities give smaller interaction cross-sections?! Lets picture this:

Now imagine launching two balls, but *this time*, speed matters: launch them at high speeds and the cross-sectional area decreases, thus the lesser the likelihood of a collision. Launch them at low speeds and the cross-sectional area increases, so collisions are more likely.

This is not just a thought experiment: on the particle level, forces *do* behave this way! The microscopic world is weird🙂 One example of velocity-dependent cross-section is Rutherford scattering (the wiki page is pretty good if you want to read about it) en.m.wikipedia.org/wiki/Rutherfor…

Turns out if dark matter has a velocity-dependent cross-section such that high velocities yield smaller cross-sections, we can explain dwarf scale halos and cluster scale ones. And that's what one of my research projects is establishing: velocity-dependent cross-section for SIDM!

There's still work to be done of course, but this is one of the motivations for looking at dark matter that isn't collisionless, but rather, experiences self-interactions.

Another cool implication of SIDM: if dark matter particles interact, then they do via a force we've not yet discovered. SIDM gives rise to a new... DARK FORCE!

I hope you enjoyed learning about SIDM! For an idea of the masses of dwarf galaxies and galaxy clusters (as well as much more), here is a list I made:

And here's a cool thread I wrote on how *amazingly whoa* galaxy clusters are

And yes, I've written a thread on dark matter before, so if you're down for more, here you go

And here's a Moment I made out of a thread I wrote in SIDM that's quite a bit shorter than this one, so here's your "tl;dr but i still wanna learn about SIDM"
twitter.com/i/moments/8657…

And finally, my two-part blog post on dark matter, starting with how we know it exists, and the second talks about several dark matter models (not just SIDM)!
Here's Part 1: astropartigirl.com/2018/01/01/dar…

And here's Part 2, where you can learn a bit about other dark matter models, too: astropartigirl.com/2018/01/10/dar…

And that ends today's Cosmology with the Astropartigirl. Happy Tuesday everyone! 😊

*they're (literally one of my most despised autocorrects 😑)

Important thing that's implied but not explicitly state: SIDM solves small scale probs while leaving large scales untouched (it behaves like CDM everywhere but inner regions of halos). So SIDM fixes small scale probs while preserving successes of ΛCDM cosmology on large scales.

And as I said, you can't fix one issue while breaking another. This is why SIDM is a viable dark matter model, and why I take it seriously and work on it.