class of models, the maximum plasma frequency is kind of below the typical ALMA band.
Whereas in this other class of models,
Um…
Uh, you have plasma frequencies that go, you know, to, like, 10 to the minus 2 eV, or something like that. And so that's why you don't… we don't really see…
sensitivity in the Alma frequency range in this class of models.
You could, I mean, you know, you can see that you can extend these lines
to higher frequencies, but I think they would… you can see if you just kind of extend this, they're dropping… the sensitivity is dropping very rapidly, so…
And eventually, there will just be a kinematic cut from that maximum plasma frequency.
Okay, so everything that I've mentioned up to this point, I, uh…
has assumed that axions make up 100% of dark matter. The thing that Nico was complaining about earlier, and I promise to give him some hope.
Uh, that we are not overly reliant on the dark matter, uh,
the knowing the dark matter.
abundance.
So, I've mentioned if you already have axions that are there, how can they convert to photons?
But it turns out that axions can also be produced very efficiently in
in pulsars, and to understand that, I have to go beyond the standard model of all SARS,
I told you this gold right, Julian, this equilibrium solution works.
pretty well, but it turns out that there are important, importantly, some
some localized regions in which that breaks down, in which the Gold Wright-Julian model breaks down, in a way that's very important for axions.
And these regions are called vacuum gaps, and specifically there's one of relevance, which is called the polar cap. It's this little yellow region here.
And this is at the base of the radio beam, so if I… so there are field lines here that close.
Uh, this is called a closed magnetosphere.
And there's an important length scale that I've neglected, which is the fact that because this thing is rotating,
There is kind of a causal, uh, cylinder that goes around the axis of rotation.
Which is what's called the light cylinder.
And it basically says that causality demands that I cannot have a field line
that exit the light cylinder and close, uh, and be entirely closed.
Because then I have particles that are communicating. Particles can communicate with each other along field lines,
Um, and so you can't… so these field lines that… that exit the light cylinder just are opened up.
And so what that means is that if I have particles flowing along these field lines, rather than coming back to the neutron star, they're effectively kind of
ejected from the magnetosphere.
Not exactly, there's some… a little bit more details about what happens in the equatorial region, but that's not really… I'm not gonna get…
too far into that here.
So what happens now is that if you're losing charges along this… in this open field lines,
you start to… if you don't have enough charges to screen electric fields,
Then you open up a gap region here, where E.B is non-zero.
Uh, and so this is exactly what you need for Axion production.
Uh, and so the… I won't go too much into the microphysics of what's going on, but as you open that gap,
the basic, as I mentioned, it becomes unstable to runaway electron-positron pair creation through what's called a pair cascade.
And you can see the basic steps of it here.
You have a high-energy particle,
Uh, you have a particle being accelerated along these curved field lines,
If you have a particle moving along a curved trajectory, it emits a Lar Moore radiation, or curvature radiation in this case.
And that photon, because this electron is highly boosted,
That photon will have a very high energy,
And typically, it can have energy higher than the threshold for pear production.
So, it can convert in the presence of… it hits a magnetic field and can pair-create.
And those pairs that you create emit more high-energy photons, which create more pairs, and this takes place basically until you screen the gap.
But this process is constantly… you kind of have this… this endless, uh, competition between particles flowing out along these open field lines,
create opening up this gap, and then the gap closing due to, uh…
electron-positron pair creation.
And this is something highly nonlinear physics that, in order to actually model in detail, we need simulations, and so this is something that people, you know, plasma physicists and astrophysicists are very interested in.
Because it turns out that this process that I just mentioned, uh, it was about, uh, 5 years ago that it was determined that this is
Likely, the mechanism giving rise to coherent radio emission from pulsars, this
bursty screening of
Uh, of this gap region in the magnetosphere. And so here, what I'm showing you is a plasma… what's called a PICC simulation, which is a particle and cell simulation. And what's being plotted here, so this
This simulation box is basically this region here.
this polar cap region.
And what's being plotted in the color bar here is exactly… is E dot B. It's exactly what we need for Axion production.
And you can see this, uh, what's baked into it is all of these QED processes that I mentioned.
Um, and you see that it's kind of…
you know, it has this kind of bursty, you know, non-stationary behavior,
And in the case of what they're interested in, and what astrophysicists are interested in,
This, you know, this physics launches electromagnetic waves.
And those waves are what we think are actually the coherent radio emission from pulsars. And this has been a long-standing problem
Since their discovery in…
uh, 67, I think, since pulsars were first observed in the 1960s, it's been kind of a long-standing problem.
of understanding what is the mechanism for a coherent radio emission. And in the last 5 years or so, particularly with the advancement of these
particle and cell simulations, people are starting to converge on this dynamical screening as a mechanism for radio emission.
Um, but you can… basically, this thing, you know, E.B acts as a source for axions, uh, it's like an axion charge.
And so you're radiating a bunch of axions
Uh, from this. And once you produce those axions, uh, so these are the ray tracing simulations that I mentioned earlier, you produce a bunch of axions, which are shown by these red lines here.
And then we do some, uh, some modeling of their propagation as they leave the magnetosphere, and we calculate this resonant conversion process into photons.
Uh, you know, with some detailed 3D models of the magnetosphere. I won't go into too much detail here. And out comes some radio photons.
Uh, and this is something that, uh,
You can go… so the prediction here is that pulsars would emit
Broadband radio emission?
Uh, and specifically, you know, we know they emit broadband radio emission along their axes,
But the prediction here is that they are now emitting quasi-isotropically, so everywhere along the, uh…
the, uh… the phase of the neutron star.
And if you look at the pulses, they're actually very clean between, if I look at, let's say, intensity as a function of phase,
They typically look something like this.
So they're very clean between pulses.
Uh, but the prediction here, if I have Axion emission, is that on top of this, there should be some big, uh, you know, quasi-iso… I mean, there will be some… I shouldn't say it's exactly a phase-independent, but there will be some…
uh, Axion contribution as well.
And this allows us to set constraints, because we have data that says that, you know, it's very… there is not a lot of radio emission.
Uh, in between pulses, and that allows us to set this constraint.
Uh, and so let me accelerate, because I realize that we're running low on time.
An interesting…
let's say, uh, extension of this story, so I mentioned that axions leave once they're produced, they leave and they convert to photons.
But a substantial fraction of them are produced with velocity less than the escape velocity of the neutron star, which is actually quite large. I mean, a neutron star is almost a black hole gravitationally speaking.
Its escape velocity is about half the speed of light.
And you can convince yourself that, uh, the fraction of phase space that is gravitationally bound
goes like the escape velocity cubed.
And so this tells you that about 10%, you know, 1.5 cubed is, like, 1 in 8.
About 10% of axions that are produced actually just stay there, they remain gravitationally bound. Of course, they dissipate through various processes, through, you know, as they propagate through the neutron star, they can convert into photons.
And this is something that we study in a lot of detail.
Um, let me just skip to the answer.
One of the things that happens is that as they, uh, as they undergo these orbits, some fraction of those
bound axions will convert into radiopotons.
Uh, can you go into gravitational waves, too, or no? Well, it's too…
Like, super variants, right?
You can, I think it would be very… I think it would be very suppressed. I mean, like, the couplings…
that we get to are, like, let's say 10 to the minus 14. I assume it's like a Planck-suppressed…
You know, I think there actually have been papers about this bursty pair creation. Does that radiate gravitational waves? Okay.
No, but I was thinking that, kind of like Super Radius, that you have the Axiom file, and then you have…
Because you have, like, a… instead of having your stationary e-field, you have the stationary G-feel, like, a gravitational field, so…
Yeah, you… yeah, I'll, uh, in the case of Super Radiance, they can get gravitational waves, because it's, like, the gravitational additive, right? They have different energy levels.
Okay. Yeah, in this case, it's not exactly… it's just a dense cloud. It's not really quantized in that way, uh… Well, you have two ways to… okay, you have to wait to…
Blue. One is, like, from the level transition, and the other one is from the…
The one that you said, like… Oh, just the cloud, the presence of the cloud itself? Yeah, it's a small contribution to the overall mass. Okay. That's the problem. I think it would be very hard to… yeah, yeah, it's not gonna be comparable in mass to the neutron star. Okay. And even then, like, an isolated neutron star, it's very hard to detect gravitational waves from.
You could ask questions, which I think is an interesting one. If you have a merger of two neutron stars, or a neutron star in a black hole, one of which has
you know, a cloud around it. That might give you some observable gravitational wave signal, but I haven't… I haven't actually thought too much about that.
Um, but, uh, yeah, so we propose a search, or, like, we estimate or forecast a search for these radio lines emitted specifically from the axion clouds.
Uh, and we actually see… this is with an existing radio telescopes.
Uh, that we can actually get down, uh, at… in this range to the QCD axi online.
with this telescope, I think it is, uh, if I remember right, it's Green Bank, the Green Bank Telescope in, uh…
Um, it's in West Virginia.
In West Virginia. Uh, you can get… They're only doing, like, crumple. Okay, sorry. No, that was Racebo. Okay, yeah, sorry, yeah. I hope Green Bank did it. No, no, no, no, yeah, that's right. We're shutting it down.
Yeah, so, so, and I just wanted to mention again, this… this…
series of searches is also… it's dark matter agnostic. Because you're producing your axions in the neutron star,
we think we'll be able to get down to the QCD axion line with existing telescopes. We're trying to collect data now, and then with future telescopes, I think we can really rule out, like, or…
ideally observe, a significant fraction of the, uh, the QCD axion line with something like SKA. Yes?
I won't get to Axion.
How long does it last? Yeah, that's a great question.
It depends on the orbit a little bit.
So, some of it, uh…
We find that the fastest process…
is this conversion, like, these ones with highly eccentric orbits, if they reach a…
part of the magnetosphere where the axion mass equals the plasma frequency, they can con… some fraction of them convert into radio photons.
That's one dissipation process. You can also look at, like, absorption in the neutron star itself.
Um, uh, so typically these things last…
So, it's more…
You keep pumping them in through this process, and there's a dissipation process, so eventually you reach, like, a detailed balance between pieces.
Yeah, yeah. How fast?
how… it depends a little on the coupling, but it can be as fast as…
hours to reach that equilibrium.
Once it's produced, then it's just in equilibrium. It'll last there until, you know,
But an individual actually looks reduced, and that's a lifetime. Oh, I see what you're saying. Yeah, yeah, good, good. Oh, an individual axion, yeah, good. That's a slightly different question. It will be typically the…
Uh, let's say for this axion, it would be something like…
the Axion, or the inverse axion mass.
divided by, like, the conversion probability here. So that would be, like, seconds or something.
So you're saying that the… what's the loss mechanism?
Is it absorption in the neutral store, or is it a radiation converting into photons outside?
It's… again, it depends on the orbit. If… if it, like, if it reaches…
For a typical orbit, I would say the dominant
Uh, the dominant process would probably be absorption in the neutron's dust.
Yeah, yeah. Uh…
Because most axions don't reach… have sufficiently eccentric orbits to get out there, so most of them are kind of…
uh… you know,
undergoing orbits that go through the neutron star. Now, the neutron star absorption, admittedly, we look at just
absorption through standard processes like inverse Bremstrah loan.
Because these axions are so low energy,
Uh, they are… the rates for these processes are typically suppressed by the energy of the axion divided by the temperature of the neutron star.
cubed, or something like that, because the rate of Bremsstrahlong goes, like, you know,
Omega over T.
Omega cubed.
So, typically, these processes are fairly slow.
Uh, for a typical Axion,
I would say for those ones, I would say maybe, I think, again, it depends on the coupling and all of these things, but for the couplings that we look at,
maybe hours or something.
But you, you are, you are continually injecting axions in from… you're producing them as well.
Yes. Yes, yes, exactly. So we… I actually do have a plot somewhere.
Uh, so yeah, if you, uh…
I think I have it in a supplemental side, but I can show you, we basically have…
you know, you're right, it is… it depends on the energy loss rate and the production rate, and you balance those, and that's what gives you these, uh…
these equilibrium densities that we reach.
For an individual axion, I'd have to check, I don't know off the top of my head, but this is…
you know, this thing is self-sustaining because, yes, you're losing some axions, but you're also gaining them, and those are happening at the same rate.
in equilibrary.
Right. Is it a reasonable energy, like…
Can you transfer significant amounts of energy into the neutron star?
Unfortunately not. Like, heat the neutron star or something. I think it would be hard to do so, uh…
How deep into the neutron star are they getting absorbed?
Like, right on the surface, or is it…? So, it also depends a little on the orbit. I mean, most of the orbits won't go much past, like, there's the crust and maybe the outer, uh, outer core.
Uh, fortunate, we don't try to model, like…
you know, this is something for future work. We don't try to model, like, the inner, inner part, the inner core of the neutron star. This will really only affect some small fraction of
highly, uh, radial orbit, let's say.
Um… but…
Uh… yeah, they typically get, you know, let's say order one part of the radius of the neutron star in.
Um, you know what itches?
Oh, yeah. Um…
Uh…
Yeah, but to, yeah, to answer your question, I mean, I…
The timescale will depend on various things, but what I'm showing here is the equilibrium.
This is, like, that equilibrium density that you get from balancing these two things.
Uh, and you see there's a big jump, a big drop here. These are the axions that reach
the, you know, that conversion radius where you can convert to photons. So in the inner parts here, it's dominated by absorption in the neutron star.
And the outer parts, uh, it's dominated by the equilibrium is dominated. The main dissipation process is conversion to photons, which is why you see these drops here.
More questions about this. I think this is pretty much all I…
I had, I'll kind of flash this. There are a few other things that I, uh, that I didn't get a chance to mention, uh, but if you have questions about any of the things on here, please feel free to ask, or if there are more questions, I'm happy to take them.
Take them now, okay?
If you have questions?
So it was just, like, like, eh…
coincidence that you've barely reached the QCD line?
Uh, it's not barely, right? I mean, we don't get… we don't get to DFSD, but it's not like a… You have, like, a corner there, like, okay, yeah, yeah. Oh, I think this is just a function of GBT's sensitivity. Like, most of this thing is determined by…
how sensitive the Green Bank is. That's a coincidence, though. What? It's a coincidence that you're almost… like, do you, like…
Oh, no. Is it a coincidence? I would, uh…
I mean, we mixed a statement about how long we're integrating, like, you can…
If you pick how long you integrate, you can go as low as you want.
But we are… I mean, we took a kind of standard value for assuming we were actually submitting a proposal, what is a reasonable amount of time, which is, like, a few hours or something. Maybe, I think this is with an hour. Okay. 1 or 10 hours, but it's very insensitive to that, because the…
The process goes like G to the 4, like, the production rate goes like G to the 4, or G squared, depending on whether you've reached equilibrium.
Uh, and the…
you know, the radio sensitivity goes like… or the sensitivity with integration time, SNR, goes, like, T to the half, t to the minus the half.
So, it's very insensitive to how much… if I take a thousand hours, it's not gonna look that different from this, or if I took…
you know, one minute, it wouldn't look that different.
Yeah, any other… any other questions?
Okay, if there's no more questions, let's take the speaker again.
I just