All of physics is a "math model". One we attempt to falsify. And when a scientist does prove some part of the model wrong, the community leaps up in celebration and gets to working on the fix or the next.
Dark matter started as exactly a catchall designed to make the model work properly. We started with a very good model, but when observing extreme phenomenon (in this case the orbits of stars of entire galaxies), the model didn't fit. So either there was something we couldn't see to explain the difference ("dark" matter), or else the model was wrong and needed modification.
There's also multiple competing theories for what that dark matter is, exactly. Everything from countless tiny primordial black holes to bizarre, lightyear-sized standing waves in a quantum field. But the best-fitting theories that make the most sense and contradict the fewest observations & models seem to prefer there be some kind of actual particle that interacts just fine with gravity, but very poorly or not at all with electromagnetism. And since we rely on electromagnetism for nearly all of our particle physics experiments that makes whatever this particle is VERY elusive.
Worth observing that once, a huge amount of energy produced by stars was an example of a dark energy. Until we figured out how to detect neutrinos. Then it wasn't dark anymore.
In short, you're exactly right. It's a catch-all to make the math model work properly. And that's not actually a problem.
"Repeat until you think it’s correct. Hopefully other people agree with you."
Dark Energy has entered the chat.
For those with time to spare: study all you can about neutron stars (including magnetars and quark stars), then go back to "black holes" (especially their event horizons and beyond) and there's a good chance you'll feel like a lot of aspects in BH theories are mythologies written in math - all of it entertaining, nonetheless.
For those who seek extra credit, study zero-point energy before reflecting on cosmic voids, galaxy filaments, galaxies, gravitationally bound celestial systems, quantum chromodynamics and neutrinos. Then, ponder the relativity between neutron stars, zero-point energy and hadron quark sea.
The attempts to measure dark matter directly have gotten incredibly sensitive and still haven't found anything.
Yeah, it's legitimate science being done, but some people treat it as sacred and would fight you to no end because they say Dark Matter is some certainty, rather than approaching it with the proper scientific skepticism or with a statistical outlook.
For the most part believers in Dark Matter are cool, but a vocal minority practically worship it as the only possible truth.
The certainty is that there is something there, we just don't know what it is. The name "dark" anything is irrelevant.
If a new hypothetical model showed that either some far off unobserved mass(es) or the currently observable mass can have the gravitational effects that were previously explained by dark matter, or any other far off idea about the nature of gravity at large scale: then there would be evidence there is nothing there. Currently there is no evidence that something is there, just that there are forces and motions that are not understood.
"just that there are forces and motions that are not understood." - aka, there's "something" there... Doesn't have to be a physical something. You're intentionally misunderstanding or misinterpreting just to try and win points on the Internet.
I mean, they are working on adjusting Newtonian dynamics for the situations where gravity between objects is low. This would fix the model for the strange galaxy spin and where 2 stars orbit eachother.
The issue with this is there are too many unknowns as we have a (relatively) fixed point of perspective. But statistical analysis is working on reducing the impact of those unknowns, and there is likely a paper published in the next few months regarding this.
Then, I guess it's a matter of understanding why this applies. And maybe it applies because of dark matter, and it all wraps back round to an undiscovered thing.
Or, perhaps Newtonian dynamics isn't complete but has been accurate enough to withstand all our testing (like taking 9.8 as the value of G on earth, even though it varies across the globe, and the moon/sun/planets also have a miniscule impact. For everything we do on earth, 9.8 is accurate enough)
Dark matter still has strong scientific support, although still undiscovered.
Modifying Newtonian dynamics has so far been disproven.
Both are worthy of pursuing
Okay I see what you mean, the meaning of your words missed me the first time, sorry. You're saying something is happening, not necessarily that something else exists to cause it.