B Cosmic Rays Charge: Expect Reissner-Nordstrom Black Holes?

[William Nelso]

Cosmic rays are overwhelmingly positively charged. Hence, whatever is emitting them must be building up an enormous negative charge. So should we expect to see highly charged Reissner-Nordstrom black holes out there? Perhaps even near extremality?

 

[Vanadium 50]

Cosmic rays are overwhelmingly positively charged. Hence, whatever is emitting them must be building up an enormous negative charge.

That doesn't follow. Replace "cosmic rays" with "alpha rays" - we don't see our smoke detectors throwing off lightning bolts.

 

[William Nelso]

Are you saying that no charge at all will be built up, or that it doesn't have to be large?

 

[Vanadium 50]

How large is large? Could there be a loose electron here and there? Sure.

 

[William Nelso]

Well, let's estimate it.
Cosmic ray density is believed to be basically one per 1000 cubic meters, almost all protons (I read this here: http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/cosmic.html)

So charge density is 10^-3/m^3.
The Laniakea galaxy supercluster that we are in is approximately 160 Mpc in diameter, or 10^24m.
Its volume is therefore about 10^72 m^3.
Multiplying this by the charge density we get a total charge of
Q = 10^69.

Now, the cluster contains around 10^5 galaxies.
So there is a charge of 10^64 per galaxy.

Let's assume each galaxy contains a billion solar mass black hole at its core, and that these holes
ultimately gave rise to the cosmic rays. The compensating negative charges should then accumulate on these holes.
Is the charge enough to bring the holes to extremality?

To answer this we need the black hole mass in Planck units.
The Planck mass is 2x10^-5 g.
The solar mass is 2x10^33 g or 10^38 in Planck units.
A billion solar mass black hole therefore has mass 10^47 in Planck units.

Now 10^64 is definitely larger than 10^47.
In fact it looks like the cosmic ray charge per galaxy is seventeen orders of magnitude larger
than the maximal charge theoretically possible for a billion solar mass black hole.

This is a lot more than a loose electron here and there.

 

[William Nelso]

A simpler way to look at it is that the mass of a galaxy is about 10^45 g.
If the charge is really around 10^64 (negative), as estimated above, then there
would be charge of 10^19 per gram, or roughly one Coulomb per gram of mass.
This is clearly ridiculous since the electrostatic forces would blow the galaxy apart almost immediately.
So what is the problem here?
I assumed only two things.
A) Cosmic ray charge density is about 10^-3 per m^3.
B) Universe is overall uncharged.
Maybe the first was wrong. I don't immediately know how to get this aside from the reference that I cited at first.

 

[stefan r]

Cosmic rays are overwhelmingly positively charged. Hence, whatever is emitting them must be building up an enormous negative charge. So should we expect to see highly charged Reissner-Nordstrom black holes out there? Perhaps even near extremality?

Try this with air. Start with your palms together (or any two solid objects). There is no air in the space occupied by your hands. Now pull them apart. Is there a vacuum? The only time you get a vacuum is when you have a geometry prevents air from rushing into fill the vacuum. For example in piston. If the source emitting cosmic rays built up a negative charge then local protons would be attracted to the source (or electrons repelled into deep space).

I am not an astro-physics expert. But I believe you can explain the lack of negative charge cosmic rays with the low mass of electrons. Charged particles interact with other charged particles. An interaction that takes 0.1% of an alpha particle's energy would completely stop a beta particle if the beta had the same velocity. A Jet could be electrically neutral at a source. We would not detect the electrons because they did not make the trip, they slowed down to much on the way to be detectable, and/or they are harder to detect because they have less mass.

In general even if the sources were charged the galaxy supercluster is not going to have the charge. Positive cosmic rays sources can be randomly orientated. Two sources pointing at each other have a neutral net flow.

 

[William Nelso]

Ok, I made at least one error. The cosmic ray density 10^-3 m^-3 is intragalactic, not intergalactic.
Most of the rays are trapped in galaxies.
So I redo my estimate for a single galaxy, say the milky way, diameter 40 kpc and thickness 0.3 kpc.
This volume is less than the previous cluster volume by roughly a factor of 4000*4000*400000 = 10^13.
Hence the charge for the galaxy is 10^(69-13) = 10^56.
This is a lot less than the previous galaxy estimate of 10^64.
It still seems like a fair amount of charge, roughly 10^9 electron charges per gram.
However gravitational attraction of two gram masses is 10^12 stronger than the EM force of two electrons.
So the effect of these charges is, at most, 10^-3 weaker than gravity, and probably much less because
the negatives, wherever they are, are screened in a bath of the positives.

Still it makes me wonder, where are the negative charges? They apparently are not distributed through space
the way the positives are. So, they are attached to objects. The natural guess is they are attached
to the objects that created the rays in the first place.

Which brings me back to my original question, whether black holes that generate cosmic rays might wind
up being extremally charged as a result. I note that the total charge is still around ten orders of magnitude
larger than the extremality charge for a billion-solar-mass black hole. So if black holes are involved in
generating some of the rays, there is certainly plenty of negative charge available to extremize them.

 

[William Nelso]

... I believe you can explain the lack of negative charge cosmic rays with the low mass of electrons.

Indeed I am sure this is the reason. But regardless of reason, the fact is that positive charges are permeating space, while negative charges are not seen.
Assuming that charge is overall neutral, where are the corresponding electric charges? That is my question. And it interested me primarily because of the possibility that a lot of the charge might lie on black holes, which is interesting because highly charged black holes reach a condition called "extremality" which is a very peculiar state of matter that would be awesome to actually find. Unfortunately, even aside from my own ramblings, extremal black holes are considered unlikely since the charge decays by Schwinger pair creation. But it's still strange because the decay would emit electrons and they would have to end up someplace. SOMETHING out there ought to be carrying negative charge to compensate the cosmic ray charge.

 

[Drakkith]

SOMETHING out there ought to be carrying negative charge to compensate the cosmic ray charge.

Have you considered that perhaps any negatively charged regions end up attracting positive charges from other places (such as other cosmic rays passing nearby) and end up being neutralized or at least prevented from accumulating excessive negative charge?

 

[William Nelso]

Have you considered that perhaps any negatively charged regions end up attracting positive charges from other places (such as other cosmic rays passing nearby) and end up being neutralized or at least prevented from accumulating excessive negative charge?

Yes but that just moves the charges around. The fact remains that there is a large free positive charge in the interstellar medium, which presumably must be balanced by an equal negative charge which is attached to various kinds of matter. Since the volume of interstellar space is far greater than that of matter-containing regions, the density of negative charge in those regions must, on average, be vastly greater than the density of cosmic rays.

 

[Dr_Nate]

This question has been bothering me and a student of mine for a while now. Where are the negative charges and how did they get there?

 

[mathman]

Educated guess: Electron are scattered around much more easily than protons so they don't get very far from the source.

 

[Dr_Nate]

Educated guess: Electron are scattered around much more easily than protons so they don't get very far from the source.

This is one possibility that I'm thinking of too. But, the difficulty then becomes, like OP already mentioned, you've got a large amount of negative charge at the source. The question is then why don't astrophysicists tell us they've observed these negatively charged stellar objects? Probably because they don't exist.

Perhaps the mutual repulsion forces the electrons to travel away from the region, but then we're back at the original problem: where are the electrons?

 

[mathman]

I would

This is one possibility that I'm thinking of too. But, the difficulty then becomes, like OP already mentioned, you've got a large amount of negative charge at the source. The question is then why don't astrophysicists tell us they've observed these negatively charged stellar objects? Probably because they don't exist.

Perhaps the mutual repulsion forces the electrons to travel away from the region, but then we're back at the original problem: where are the electrons?

I believe that the scattering spreads them out and slows them down, so they are not as noticeable. Also I wonder if too much emphasis is being placed on the net charge difference observed - I don't have any details, but I suspect the total mass of cosmic rays is very small in terms of the total mass in the universe.

 

[Vanadium 50]

The calculations shown must have issues with them somewhere (and I am too lazy to search for where).

The critical density of the universe today is 10^-29 g/cm3. 5% of it is neither dark matter nor dark energy, so matter is 5 x 10^-31 g/cm3. That is 0.3 protons/m^3. The claim that cosmic rays make up 3% of this is way, way, way too high.

1. It requires 3% of all matter in the universe to have been processed through the cosmic ray generating process.
2. The momentum being carried by this many cosmic rays will dominate the motion of objects in the universe. Heck, even the recoil will dominate the motion of objects in the universe.

The IGM is largely (re-)ionized hydrogen, containing both protons and electrons, with a tiny bit of neutral hydrogen. It's hot, but not that hot: 20 kK and not 20 GK. It is simply not consistent with 3% of the mix a million times hotter.

 

[Dr_Nate]

The calculations shown must have issues with them somewhere (and I am too lazy to search for where).

The critical density of the universe today is 10^-29 g/cm3...

Well, maybe, later in the week I'll find some reliable numbers and go through the math.