Does the Failure to Find Dark Matter Prove the Existence of Dark Matter?

a reply to: Arbitrageur

Sorry I'm digging this up, I hope you still attend to this?

My question is quite simple: couldn't this just be one of those situations where the sum is bigger than its parts?

Like it doesn't make much difference if you add Mercury & Venus to the gravity of the Sun, but if you look at the whole Solar system, and I mean the whole thing, with asteroids and everything with a mass in it, that the interaction adds that much to the system?

So in other words: is dark matter maybe nothing more than gravity interacting with itself?

a reply to: Arbitrageur

Since your excellent 'Ask any question you want about physics' thread has been closed, I would like to pose a question and it's about dark matter.

Vera Rubin discovered that stars on the outer edge of spiral galaxies travel at the same velocity as those closest to the central black hole. Unlike in solar systems, where the velocity of the planets slows down the further they are from the star because of the declining gravitational influence from the star. And this led to the idea of dark matter to account for the extra gravity in galaxies that visible matter can't provide.

Why then doesn't the same apply to solar systems?

Why do the planets slow down the further they are from the star, where is the influence of dark matter? Surely the planets should have uniform velocities as seen in galaxies.

originally posted by: Peeple
a reply to: Arbitrageur

Sorry I'm digging this up, I hope you still attend to this?

My question is quite simple: couldn't this just be one of those situations where the sum is bigger than its parts?

Like it doesn't make much difference if you add Mercury & Venus to the gravity of the Sun, but if you look at the whole Solar system, and I mean the whole thing, with asteroids and everything with a mass in it, that the interaction adds that much to the system?

So in other words: is dark matter maybe nothing more than gravity interacting with itself?

Your question is a bit muddled, since instead of "gravity interacting with itself" I think you mean the gravity of the planets interacting with each other or something?

The sun contains something like 99.8 to 99.9% of the mass of our solar system, we think, so if one chooses to consider the .1 to .2% of other mass to not be that important, then you won't be too far off. But the .1 to .2% of the remaining mass in the planets and other bodies in the solar system do interact. In fact, before Neptune was discovered, Uranus was the outermost planet known, and careful study showed it wasn't exactly following the laws of motion predicted by gravity from the sun and other known planets. So one astronomer calculated that there must be another planet beyond Uranus that's tugging on it, and he even predicted a location. So they searched the skies around that location and found the predicted planet, now called Neptune, in a rather stunning confirmation that Newton's laws of gravity seem to work well in our solar system.

It has little to do with dark matter except to show that no dark matter was used in those calculations.

a reply to: CJCrawley
It's really one of the best questions I've seen asked about dark matter, especially considering we are spending millions of dollars on dark matter searches here on Earth, so how does that make sense when calculations of orbits of planets in our solar system do not show any detectable amounts of dark matter?

I suspect the answer has something to do with the distribution of matter, and dark matter. OK here are some things to consider.
-Light from the sun takes 8 minutes to reach earth, and some hours to reach more distant planets in our solar system
-Light from the nearest star take about 4.25 years to reach us.

So, we can see that the distances to other stars are vast, compared to the distances in our solar system, and understanding this is part of the key to answering your question.

Now let's look at some rough mass estimates from Dr. Siegel's article on this topic
Sun Mass (kg): ~2000000000000000000000000000000
Earth Mass (kg): ~6000000000000000000000000
Estimated amount of dark matter inside Earth's orbit around the sun (kg): -10000000000000

So, that's an estimated 10 trillion kilograms of dark matter inside Earth's orbit, so you should think it should have some effect, right? But can the effect be measured? If you drop a paper clip, Newton's laws say, while the paper clip accelerates toward the Earth, the Earth also accelerates toward the paper clip. You can calculate that acceleration of the Earth, but, it's too small to measure due to other noise in the measurement and limitations of the accuracy of measuring Earth's position. Likewise with dark matter, Siegel strongly suspects the 10 trillion or so kilograms of dark matter is probably there, but like trying to measure Earth's acceleration toward the paper clip, that's simply too small a mass to be accurately measured compared to the mass of the sun and the mass of the Earth.

Now, think of the distance to the nearest star. That 10 trillion kilograms inside Earth's orbit isn't much mass in the scheme of our solar system, but what if there's 10 trillion kilograms of dark matter for every 8 light minutes between our star and the nearest star 4.25 light years away? There are lots of 8 minutes in 4.25 years. This analogy is mathematically flawed in several respects because the geometry of the dark matter halo is thought to be spherical and not disk-like such as our galaxy, and for other reasons, but mathematical accuracy aside, conceptually that's sort of the answer. To put it another way, the density of dark matter is relatively low, so in a relatively "small" region like the orbits of our planets, the total amount of dark matter doesn't add up to much, but in the much more vast distances between stars, even that low density adds up, plus we think there might be a third dimension to the dark matter, which might form a spherical halo that goes beyond the matter disk of the galaxy, sort of like this sketch:

No Evidence of Dark Matter Around the Sun

Before that link, I sort of paraphrased Ethan Siegel's explanation from 2018 (maybe not that well so you can read his original article at the prior link). But I'd be interested to know what Siegel thinks of that "No Evidence of Dark Matter Around the Sun" article, since it suggests a lower dark matter density than he postulates.

My take is, dark matter seems to be really hard to measure locally, and it probably has something to do with the way dark matter is distributed, but since it still escapes direct measurement locally, it's hard to have much confidence in our guesses of the local density of dark matter. When studies show dark matter isn't needed to explain local motions, we might infer the dark matter isn't there, but maybe it is, just in small quantities which don't add up to much locally, but do add up to significant amounts in the huge "halo" thought to surround our galaxy in the above artist's impression, but who knows if that's anywhere close to accurate? We don't really know. Dark matter is an interesting mystery, and we certainly admit we don't understand it and don't have all the answers about it, but we do have many what we think are measurements of it on larger scales, not only through galaxy rotation curves, but also though gravitational lensing measurements.

originally posted by: moebius
a reply to: Arbitrageur

From my understanding there is still a mass window for PBHs of sublunar mass 10^20 - 10^22 g as a possible dark matter candidate. They are too light to be detected by micro lensing but heavy enough to not have evaporated.

If one questions the Hawking radiation prediction, one would get a much broader mass range starting from Plank mass BHs, which would probably not be directly detectable at all.

I would think that as our instruments and methodologies (accounting for 'wobble' in celestial bodies, detecting occlusion of stars) for observing distant objects become more precise and sensitive, we will start to have better confidence in whether or not there are enough non-luminal objects on the size you're describing out in the cosmos to account for how we see the galaxies move.

Ultimately predictive theory can only answer so many questions, and if we really want to understand how it all works, we'll need to start getting out to other solar systems to start gathering some data. Of course "getting out there" is merely the stuff of sci-fi novels, unless you subscribe to the "breakaway civilization" and "secret space program" conspiracies.

a reply to: SleeperHasAwakened
I think we can do a lot from Earth, or Earth orbit, or elsewhere in our solar system like LaGrange points, as our instrumentation continues to improve.

Getting humans to other star systems may be centuries away, but the "Breakthrough Starshot" idea of sending lots of little probes isn't quite as far away, sending just miniature probes instead of humans, though that's not right around the corner either:

According to The Economist, at least a dozen off-the-shelf technologies will need to improve by orders of magnitude.