08:05:23 Thank you everyone for joining us for the key ATP fundamentals of gashes halos program, consistent with the rest of this week, we are covering the question what roles do non thermal components play and, and how different non thermal processes impact the
08:05:41 dynamics and the behavior of the circle galactic medium.
08:05:51 Today, we will be joined by Ellen's Waibel professor at University of Wisconsin, so she'll talk, and take us through the hour.
08:05:59 We encourage people to put their questions or comments or discussion rather than just in the zoom channel which is kind of the or the zoom chat, just kind of the the intuitive place to go to instead go into the slack application and go into Halo 21 week
08:06:15 three non thermal that will allow us to kind of preserve those comments and discussions, and you can do threads so if somebody asks a question and someone else knows the answer during the presentation, they can respond and start a discussion organically
08:06:29 there.
08:06:30 I.
08:07:20 Glen Rudy and Drummond fielding have set up an after party, it will not be on this, zoom, it will be on a separate zoom but the link is in the halo turbulence group.
08:07:23 So, I encourage people to to join that, particularly if they are interested in having further discussion on turbulence and its impact on the circuit galactic medium and galactic atmosphere.
08:07:36 So just a quick announcement tomorrow we will have an update on on future conversations, including the halo turbulence group, and we will have structured discussion for any discussion that we may miss this.
08:07:49 Today, this structured discussion on small groups of five to six people, so everyone really gets a chance to participate and also meet other participants in the, in the KITP program.
08:08:02 And these are, these will have topics suggested on and voted by the audience. So, you know, if you have a pet question, you can add it and hopefully other people have voted, and then that'll be the question that everyone discusses, and it seems to have
08:08:15 worked reasonably well the last couple of weeks.
08:08:19 And then tomorrow night we have trivia, which would be super fun.
08:08:22 Not, not necessarily astronomy trivia just kind of general general trivia it'll just be a fun social event, and it's free and everyone can participate.
08:08:32 So, and we're, we're deciding what the prizes are right now so hopefully there'll be some, some great prizes for the, for the winning team really good prizes, really good prices.
08:08:42 Yes. Oh man. Oh, you guys are making it.
08:08:48 Okay, so our speaker for today, I am very pleased to announce his professor Ellen's Wible from University of Wisconsin at Madison, Ellen. I you know I don't have enough positive things to say.
08:09:03 She's She's amazing. She's, she's done so, so much great work in the field kind of straddling the realm between plasma physics and astrophysics. And, you know, cosmic rays have become kind of all our mode in the last few, few years especially with the
08:09:21 application to the CGM but, but, Ellen has been working on cosmic rays, for almost the last 50 years and has really had some seminal work defining the, the direction that the field is going, her, her earliest papers were on confinement of a cosmic rays,
08:09:39 in, in the ICM but she's worked on all of the themes of this week turbulence magnetic field dynamics all sorts of things and amongst her many accolades and awards, she she's also written review papers on on the title so we couldn't think of anyone who
08:09:57 is more appropriate to give the presentation today and and notably, she she's been involved with Kitt Kitt in the past. And I found that 20 years ago, she an EVO striker led a KITP program on astrophysical turbulence, so it seemed appropriate to have
08:10:15 her back today to talk about turbulence, as well as cosmic rays magnetic fields, and the like. So, please.
08:10:23 I'm really excited to introduce our speaker for today, Ellen sidewalk.
08:10:30 Well, I can everybody hear me. Yes. Well, thank you, Cameron, so I don't know if any of you know the disruptive comedian Sarah Silverman, but he does have a little routine where she's, she's talking to a kid and she says, honey.
08:10:48 I'm already proud. All you can do is make me on proud.
08:10:52 So, Cameron.
08:10:55 With your builder.
08:10:58 Um, let, Let me, proceed. So, I'm
08:11:10 okay.
08:11:11 This.
08:11:14 Okay, so I'm going to continue in the tradition, started by paying a great talk earlier in the week on talking about nonverbal components that the Halo and the CGM.
08:11:28 I've worked with many people on aspects of this topic but the work I'll be talking about today jaws especially on the work of this subset of my collaborators.
08:11:39 My talk also won't be as, as fun as pains.
08:11:43 But I'll do my best. So, I want to say a little bit about the context that that I'm coming from. So, as, as Cameron said the role of cosmic rays and star formation feedback has has really become interesting lately.
08:11:59 And this is for, I think three reasons. One is that because cosmic rays have a relativistic equation of state. They there at bat a cooling is much slower than the cooling of thermal gas and so they can give a sustained pressure push in the self confinement
08:12:15 model of cosmic ray transport they also heat the gas coalition Leslie by exciting waves which had been absorbed by the thermal gas. And finally, they, they may behave somewhat differently from from photons so you know radiation pressure driven winds have
08:12:33 this limitation that the radiation tends to kind of squirt out through low density holes, but because cosmic rays are confined to a magnetic field which kind of ties the different phases of the interstellar medium together.
08:12:46 This tendency may be somewhat reduced. But there is this kind of looming issue, which is that cosmic ray feedback models over predict the gamma ray emission that's been detected by fer me, and other instruments, and I you know I think Phil Hawkins and
08:13:06 his group more than anyone have have brought this out, and the, the only cure, really that's been found is that if you assume that cosmic rays diffuse at with a diffusion coefficient that's significantly larger than what has been empirically derived for
08:13:24 galactic cosmic rays.
08:13:27 That's really, that seems to be the best way to solve the problem but there is kind of this tension with local cosmic ray measurements, so that that's this sort of looming uncertainty bad, I'm coming from.
08:13:38 So, with that as a background. I have kind of a dual agenda here. One is to kind of consider up a flow dominated regime neighborly machine with a strong galactic wind and asked what that contributes to magnetic fields and cosmic rays and galaxies the
08:14:06 in the universe at large and that's going to be kind of a short talk in green for both topics actually there a couple of papers that that you can look at. And then I'm going to pivot over to how cosmic ray hydrodynamic works in multi-phase gas and But
08:14:15 Hydra dynamics I just mean that you treat the cosmic rays as a fluid instead of genetically particle by particle. And I'm going to focus on bottlenecks, which were alluded to, and briefly discussed by paying on Tuesday, and have a somewhat newer development,
08:14:32 namely the role of pressure and I satrapy instability, and I'm going to expose my possibly muddled set consciousness on this and be very happy to get your input.
08:14:48 And as always, you know, we need to test these theories observation.
08:14:52 So, we know that magnetic fields are affected by galactic outflows. Here's a far infrared image of dust polar imagery from the hawk instrument on Sophia Starburst galaxies and 82 when you can see magnetic fields kind of being from a primarily in plain
08:15:14 as musical orientation, far from the center, they kind of get drawn up in these filaments and then this is actually the astronomy picture of the day from yesterday, this is NGC, 5775, showing synchrotron filaments.
08:15:31 So, the radio component of the field tends to fall off as one over r squared and the musical component tends to fall off as whatever are with distance from floods conservation.
08:15:44 And what that means is that, in a galaxy that starts with a mostly as a musical field as dis galaxies seem to have in their planes, a rotating wind will kind of go to a park or spiral like configuration and be mostly as a musical when you get long distances
08:16:02 away and the magnitude of the field will drop. And if you have a micro Gauss field at one kilo per sec. You have 10s of mind you say 10 Nat gas at 100, Kelvin parsecs.
08:16:14 What about the cosmic rays.
08:16:16 So, when cosmic rays are fairly well coupled to the background fluid, by, by scattering waves I'll talk more about this later, they obey an energy equation like this.
08:16:25 so there's a composite velocity which is the velocity of the wind in this case or the fluid velocity and the altitude speed in the plasma component of the medium.
08:16:40 And this just says that if we follow an element of fluid moving with this velocity, that the cosmic ray energy density changes due to to effects that compression or rare faction of the flow.
08:16:55 That's one and the other is a spatial diffusion.
08:17:00 And we can, we can evaluate the relative importance of these two terms by defining a sort of cosmic ray Reynolds number, which is the ratio of the characteristic diffusion time to the characteristic infection time.
08:17:17 So, in the case that will be interested in the wind is going to terminate in a shock, and RS is the radius of that shot. And there's a wind velocity and there's the diffuse activity, and if we put in Milky Way type parameters.
08:17:32 This number is about 500, which implies that cosmic rays are pretty well coupled to the gas just an empirical statement.
08:17:42 And in that case, the cosmic rays lose energy in the wind. And in the case of highly super authentic flow which is probably the most relevant case, there, the energy density just goes like the four thirds power of the gas density, which means that the
08:18:00 energy of an individual cosmic ray goes down like one of our our.
08:18:06 And so gv cosmic ray will become an MeV cosmic ray. And, in the absence of anything that revitalizes, the cosmic rays. We will be dumping all these me the cosmic rays into the CGM and I've not worked on the question whether this has any observable signature
08:18:25 but there might be an interesting question.
08:18:29 If we go to sub authentic flow, then you is basically the outing speed and in that case you can show that the cosmic ray energy density goes like road to the two thirds and this is due to energy exchange with with waves.
08:18:46 Okay.
08:18:51 So, in the diffuse of limit where RC is the cosmic ray balance numbers less than one of the cosmic rays don't lose energy but I think that that's, I think that's less likely.
08:19:04 I think the cosmic ray rattles numbers actually pretty large for galactic wins, and that means that cosmic rays lose a lot of energy as they fly out. So, can they be revitalized by the wind termination shop.
08:19:18 So the wind termination shock we've learned from the solar system here is when the dynamical pressure in the wind, which is the dominant form of pressure by the time you get far out in the flow.
08:19:32 When that becomes equivalent to the pressure of the ambient medium which I've written here as the CGM pressure. Then there's a shock transition.
08:19:42 And so we can solve this relationship for the radius of that termination shock. And it scales like this the square root of the mass loss rate times the win, win velocity divided by the CGM pressure, and this for pie here seems to sparkly symmetric win
08:20:00 but you could put in some other solid angle.
08:20:05 Whole thing square root, and if we evaluate this for sort of traditional numbers.
08:20:11 One solar mass a year 500 kilometers a second wind ambient pressure of 10 to the minus 14 and CGS, then this is about 50 kilo parsecs so we expect these termination shocks to be 5100 200 kilo parsecs from the parent galaxy.
08:20:31 Okay.
08:20:33 And the shock velocity is about the same as the wind velocity, and there are two types of shock acceleration that we could consider one is sort of classical diffuse of, it's become classical the Future Shock acceleration.
08:20:48 So here's the shock. Here our magnetic field lines that come into the shock at an angle and the tangential component gets compressed so the field lines kind of get refracted and cosmic rays scatter up and down the field lines, they gain energy when they
08:21:07 need a wave head on and they lose energy when they catch up to a wave, but because the waves are going at different speeds, basically the speed of the fluid flow upstream and downstream of the shop.
08:21:20 There's a net gain per loop and so this is first order for me acceleration, paying alluded to, second order fairly acceleration of cosmic rays by turbulence, but this is a much faster process and it's really been embraced by the cosmic ray community as
08:21:34 the main acceleration mechanism for galactic cosmic rays.
08:21:39 Because the show the magnetic field may be almost tangential to the shock, due to the different rates at which the azimuth on radio components of the field decrease, we should consider also a mechanism called shock drift acceleration which briefly works
08:21:59 like this. So, this is the plane of the fluid and the magnetic field and so the emotional electric field. The cross be is perpendicular to the plane of the screen.
08:22:12 So, in order for particles to pick up energy from that electric field, they have to be drifting out of the screen themselves. So there can be a nonzero vd.
08:22:23 And this can happen because the magnetic field has a gradient, it, it's stronger here than it is over here. And so shocked drift accelerations been studied a lot in the solar system.
08:22:35 It's also been simulated, and it may be an important process here.
08:22:41 For diffuse of shock acceleration, there's a sort of maximum rate, and I've written down this formula to show you that it scales with the strength of the magnetic field and the square of the speed of the shock, this limit is derived assuming that the
08:22:58 weights are not linear, the amplitude of the fluctuations is the same as the amplitude of the background field is so called bone diffusion.
08:23:06 And this is plenty fast enough. If you have a wind that endures for 100 or even 10 mega years to boost cosmic rays back up to gv or 10s of gv energy. So I think there's plenty of opportunity for revitalization of the cosmic ray pool.
08:23:30 And that was the subject of chats papers so this is the bustard at owl 2017. And here on the left is so this is a very simple set of models just thoroughly driven the cosmic rays or we can just think of them as, as test particles.
08:23:48 And because this is such a simple model, it's possible to run it, thousands or 10s of thousands of times. And here is, here are the cosmic ray luminosity as functions of mass loss rate and ask them tonic when velocity so the Milky Way's probably down
08:24:08 somewhere over here, where the luminosity is almost 10 to the 14th Earth's but you know for a very fast wind a very high mass loss rate, you could impact, in principle, get a very large cosmic ray luminosity.
08:24:23 And because the cosmic ray Reynolds number in the flow is very large, the cosmic rays have a very hard time making it back to the galaxy, most of them just go pouring out into the ambient medium the CGM or the AGM what, whatever it is.
08:24:40 So, if the efficiency of cosmic ray acceleration at the Galactic wind termination shock is what we think it is for galactic supernova Romans, which is about 10%.
08:24:51 You could have 10% of the wind luminosity coming out in the form of cosmic rays.
08:24:57 Okay, so here's a summary of my claims.
08:25:03 So, in the flow dominated strong galactic wind regime magnetic field is weakened tends to become as a musical, the cosmic rays lose energy by at back expansion, but they can be revitalized at the termination shock, which is about 100 kilo parsecs of order
08:25:22 hundred kilo parsecs from the center of the galaxy. And if this doesn't happen, then the CGM is is inundated by of flux of exhausted, old cosmic ray particles of MTV energies.
08:25:40 So, one disadvantage of giving this talk over zoom is that I have no idea.
08:25:48 I have no idea if anybody has any questions or if this whole thing was comprehensible so.
08:25:56 Would anyone like to give me some feedback before we move on to the next part of the talk.
08:26:04 I think it was great, but I'll leave it to our audience in case there are no like intermediate questions or or clarification.
08:26:15 And I asked question. Hi Daniel Sure. Yeah. So you mentioned this is 100 kilo per second scales, but then also depends, all the stuff on mission history, if you have stopped first, which is a very old, then potentially I assume you couldn't have terminal
08:26:34 shock way smaller with smaller radius, the NZ 106 right that yeah that's right. And actually, I'm with a very talented undergraduate, we working with Chad and me we we ran.
08:26:56 Kind of a series of Burstein models and the idea was to see if you could, you know where to shocks form can you get interactions between shocks the way you do in the solar wind, and we never actually finished that but I think it's I think it's a very
08:27:11 interesting problem and I think that these winds are highly structured and episodic star formation certainly drives that.
08:27:20 So, I can't, I can't add much to your question, other than say back that gets very interesting.
08:27:26 Thank you.
08:27:29 Hi, Ellen. This is Chris. Hi, Chris.
08:27:32 Yeah, I was just wondering if you think that the galaxy has a cosmic ray group and when. How do you account for the fact that most of the h1 that we see in the Halo is falling in.
08:27:44 Yeah, that's, um, that's a good question. So, uh, back in, oh eight with john Everett, a postdoc, we attempted to fit the soft X ray data from the inner galaxy.
08:28:03 And
08:28:03 it previously.
08:28:06 You know people have tried to fit it as a kind of a hydrostatic bowl, and did the fit and really work very well but we did get good fits, and eventually fitted the synchrotron radiation to with a rather restricted wind, which we, I think in the end we,
08:28:24 we thought that the wind would come from kind of the three kilo per sec molecular ring, where there's a lot of star formation. I don't think that there can be a wind from the solar neighborhood cosmic ray data is is also not very compatible with that.
08:28:41 But I think there is some evidence for a wind or it's compatible certainly with some observations of a sort of a thick annular when that comes from the molecular ring.
08:28:57 It can't go too far in because the Galactic potential well is too deep.
08:29:01 But, you know, we did get good fits to the synchrotron and soft X ray data in the entire galaxy.
08:29:09 Thank you.
08:29:10 Okay, wouldn't come back to that if you want.
08:29:15 Okay.
08:29:27 Yeah,
08:29:21 great talk.
08:29:23 Yeah, I just thought it might be helpful to clarify what the implications of for observable would be for flood of me the cosmic rays vs gv cosmic grace.
08:29:39 I would love.
08:29:40 I would love to think about that, by my,
08:29:47 you know, it seems to me that at some level, it would be it would become a problem.
08:29:52 But I think quantifying that, which, you know, approximately might not be that hard.
08:29:59 I would, I would love to know more about that.
08:30:03 Okay, so now I want to talk about the the bottleneck story and this is related to a whole question of cosmic ray confinement, and how cosmic rays interact in multi-phase wins.
08:30:20 So I'm going to go through a very sort of short verbal recap of the basic model. So, when the cosmic rays scattering mean free path is short, and we treat the cosmic rays as a fluid, just like they were a gas shortening free path.
08:30:41 And the scattering agents, the most important scattering agents are short wavelength and HD waves, mostly alpha brainwaves, and the most effective form of scattering is so called gyro resonance scattering, and in Jarvis and scattering particles travel
08:30:59 one wavelength of the wave in the time and takes them to do one gyro orbit.
08:31:04 So that's driver resonance.
08:31:08 And if the waves are generated by the cosmic rays themselves from the streaming instability, which I'll keep alluding to, That is the self confinement model.
08:31:18 But if the waves are there for some other reason, like a turbulent cascade, then they're extrinsic confinement, and I'm going to assume, at least for the first part that we have self confinement by the streaming instability.
08:31:32 Okay.
08:31:51 So, the cosmic rays stream down there pressure gradient, that's intuitive and the streaming instability will excite waves. So, an alpha wave it propagates up or down the field line.
08:31:51 And if we think of it as an electromagnetic wave, which it is.
08:31:56 It can be left or right certainly polarized. And so, drifting or streaming will excite waves which are propagating in the same direction as the streaming, and both circular polarization are excited and cosmic rays.
08:32:12 So, even though the, there's a bulk drift. It's very small compared to the individual random motions of cosmic rays and cosmic rays going one way will gyro residents be scattered from one circular polarization and cosmic rays going the other way will
08:32:29 scatter from the other circular polarization. So when you have waves propagating in just one direction, it's necessary to both circular polarization. To be able to scatter the cosmic rays, or put another way, linearly polarized whips.
08:32:45 Okay.
08:32:45 Now, when the coupling is strong, limited really short need free path. The cosmic ray pressure varies with the gas density, as the two thirds power of the gas density this assumes that the cost of grades have an ultra relativistic gamma equals four thirds
08:33:01 equation of state and john skilling one of the early pioneers in this field, who then went into maximum entropy pointed out back in 1971, that this picture, kind of carries the seeds of its own destruction.
08:33:20 If the gradients of cosmic ray pressure and density become anti aligned. So as long as cosmic rays are streaming down their pressure gradient and that's also down the density gradient.
08:33:32 Everything is fine, but we reach a paradox, if the if the guest NC begins to increase along the flux too. And that's because then the altitude speed goes down.
08:33:47 The cosmic ray pressure goes up, and then you have the cosmic rays streaming up their pressure gradient. And that doesn't make sense and faced with this irreconcilable contradiction of cosmic rays just kind of decoupled, and I'll show you.
08:34:05 So the first person to show this in a computation was Josh Wiener as a graduate student working with, with pain.
08:34:13 So we're going to consider this very simple problem of what happens when we have a cosmic rays source that's magnetically connected to a cloud we're going to initially assume that everything is fully ionized, and just let's just kind of see what happens.
08:34:27 So Josh did a one D calculation.
08:34:32 And so you turn on the source. And here are the.
08:34:48 And when six mega years which is about the alpha and travel time to the cloud. In, you know with the setup assumed, we get this kind of flat steady state gradient.
08:35:01 And I guess this isn't too visible. But this basically shows that the predicted invariant is indeed invariant, namely that the cosmic ray energy density goes as the gas density to the two thirds power.
08:35:14 This has no clue. When you have no cloud.
08:35:17 Okay, now here's what happens when you put in a little toy cloud. So there's this density enhancement and comet dip in the offing speed.
08:35:29 And now, as you can see that the cosmic ray pressure is increasing.
08:35:37 So the cloud is is here, and between the source and the density maximum, the cosmic ray pressure is essentially flat.
08:35:48 So this was the first numerical demonstration of a bottleneck.
08:35:54 Now, this cosmic ray pressure does a couple of things, it.
08:36:00 So when the cosmic rays reach this point here the cloud maximum, they, they reengage, and you get this VA grad p cosmic ray heating of the cloud which kind of blades it.
08:36:14 And also there's this pressure, build up behind and something that we didn't appreciate it initially but I came to recognize later, is that when you turn on the cosmic ray source, you, you create an acoustic pulse, which, if the sound speed is greater
08:36:32 than the altitude speed actually makes it to the cloud before the cosmic rays themselves do. And that gives the cloud a push.
08:36:40 And what the cosmic rays tend to do is, is stretch the cloud out and they can also set it into motion. So, if you assume that there's very efficient radiative cooling, which essentially the gates the effect of cosmic ray heating, then the cloud, begins
08:36:58 to move. And if you're thinking, gee, this is, this is crummy This is just some numerical noise, it's not it's actually sound waves bouncing back and forth within the cloud.
08:37:09 And so this led us to wonder if there could be cosmic ray driven multi-phase wins in other words of cosmic rays could push on dense clouds. In this way, paying also showed this image where you zero in on the front on the far side that separates the cloud
08:37:29 from the hotter into Cloud medium. And you can see that the cosmic ray pressure inside the cloud is is actually about twice as big as the as the gas pressure, and then the gas pressure.
08:37:43 There's a trade off the gas pressure dominates outside the cloud, and the cosmic ray pressure falls off and Josh modeled the column densities of various ions or ratios of ions in this front and compared it with some data from Bart whacker from the cost
08:38:06 Halo survey and our model actually does about as well as other models and other best model and better than, then some. So we thought this might be promising as a, as a way of explaining some of the ionization of the CGM.
08:38:25 Okay. So, in a paper that was recently put on the archive.
08:38:32 Chad.
08:38:34 Chad will show you a lot of figures from from this paper. So the first one is, is sort of a cautionary note. So a couple things are different here from what you saw before.
08:38:46 For one thing, the cloud is is weekly ionized, and so although the gas density in total goes up, the alpha and speed in the plasma which is what's relevant for cosmic rays streaming actually goes up, even though the bulk alpha, alpha and speed goes down.
08:39:03 And so this is the result of a resolution study where we start with an initial cloud profile and allow a burst of cosmic rays to act on it, and hear the, the numerical resolution is to parsecs, and here it's a quarter of a sec.
08:39:27 And you can see that the size of this pressure step is a little different. It's actually much bigger. If you resolve it enough and there's also this little thumb here, which is due to cosmic ray heating in this interface.
08:39:42 So, a quarter of a par SEC is not a fiscal length, it's a numerically dictated length, and which had found is that you need about 10 cells across the interface to get a converged solution for what the change and pressure is and how much eating there is.
08:40:01 is. And, and so on. But, um, but there is a bottleneck here.
08:40:07 Then there's some, we went into two dimensions, so the the image that Cameron used to advertise my talk with was actually created by Josh Wiener. And here's a comparison of cosmic rays inundating cloud with two different background field strengths five
08:40:24 micro Gauss. So if the field is strong enough, it's able to kind of call column eight the cosmic ray flow and not be forced to adjust to it too much you can see the field lines are mostly pretty straight and cloud here is getting a little bit stretched
08:40:40 out. But if you have a weaker field like a micro Gauss on the acoustic for runner, and the cosmic ray pressure.
08:40:50 Expand the field and sort of try to wrap it around the cloud. So you can see that the cosmic rays, really want to get past this cloud. So Chad calls it the cosmic ray obstacle course, and later I'll be talking about the consequences of this drastic change
08:41:06 in the magnetic field and even the not so drastic change in this magnetic field which is not very visible to the eye.
08:41:15 So we looked at momentum deposition, our cloud acceleration by a 30 mega year burst of cosmic rays and here's how it depends on field strength. And you can see that there's that there's kind of a sweet spot, if the, if the magnetic field is is too low,
08:41:38 if it's very high.
08:41:42 Well, Let's see this is. Yeah, so that so it's very high, it's sort of drops off quickly you don't really deposit very much momentum.
08:41:52 And it turns out that if it's not too big but not too small, but just right.
08:41:57 That's where the maximum occurs, so this is for fully ionized case and a parsley I nice case.
08:42:08 Chad also looked at what happens if you have a lot of clumps not just a single cloud. And you can see again bottlenecks very this cosmic ray front so there's a uniform cosmic cosmic ray injection across this boundary.
08:42:24 And you can see that how the cosmic rays move, and how they distort the field, really depends on where the gas density is momentum transfer.
08:42:38 Let's say too much about that.
08:42:41 So, just cycle back to this question of gamma ray emission for for a moment.
08:42:52 So,
08:42:56 on this plot are two forms of energy loss because there's collision this loss, which is the VA grad p cosmic ray term.
08:43:01 And there's the collision of loss, which is what makes gamma rays.
08:43:09 And you notice that the solutions are kind of concentrated up here.
08:43:16 These are very different transport models, these are different transport models and different clumpiness so big clumps little clubs strong clumps week clubs, strong magnetic fields week magnetic fields.
08:43:32 The total collision loss, always turns out to be about the same now it doesn't always happen in the same place. Sometimes there's more energy lost in the low density gas sometimes where the cosmic rays are spending most of their time.
08:43:47 Sometimes, most of the energy loss is in the high density gas even though the cosmic rays don't spend much time there.
08:43:52 But one way or the other things don't change very much. So, we haven't solved this problem of over, overproduction of of gamma rays, despite all this work, but I think we have learned some other things.
08:44:10 Okay, so
08:44:15 let's get back to the basic question of whether bottlenecks actually form.
08:44:20 So, if cosmic rays are coupled to the ambient medium in the regions between plasma density extreme In other words, if the self confinement models still sometimes works.
08:44:36 Then they they heat the gas and they impart momentum volumetric Lee they're coupled everywhere. But if they're not coupled. In other words, if they are bottlenecks.
08:44:47 Then the heat only the interfaces and the accelerate only the clumps. And they have very flat profiles in between the clouds, or the clumps so for the simulation that I showed you there, they are so flat.
08:45:03 So I have a series of emails with Chad, with the subject line how flat. So the cosmic Greg radiant link scale, despite the fact that the cloud is is only kill a parsecs away from the source is 100 mega parsecs the profile goes really flat.
08:45:21 So,
08:45:24 do bottlenecks actually form. I mean the.
08:45:28 We know that the fees gas in the universe is very copy and magnetic field lines tend to be random. And if bottlenecks form, whenever you have some kind of clump along the field line, then I think our whole picture of how cosmic rays propagate has to be
08:45:47 revised. So, is there anything we might have overlooked. That could couple cosmic rays, to the thermal gas, other than the streaming instability. Well, of course I wouldn't be asking that question, if I didn't have a candidate.
08:46:15 So, I'm.
08:46:05 this part of the equation of the talk a little more quantitative with some equations.
08:46:10 So let's expand the cosmic ray distribution function. So new here is the cosine of the pitch. So, mu equals one, is a cosmic ray propagating with velocity entirely along the magnetic field new equals zero entirely perpendicular.
08:46:28 So there's an isotopic part.
08:46:33 f naught.
08:46:32 And then there's a drifting part.
08:46:35 And then there's a pressure and I saw strappy party.
08:46:39 And as I said before, the drift anisotropy destabilizes waves of both circular polarization. That co propagate with the drift pressure and I saw to be will destabilize waves propagating in both directions, but with opposites circular polarization.
08:46:59 So the waves going one way, one circular polarization will be unstable the waves going the other way. The other circular polarization will be unstable in both of these cases cosmic rays going in each direction, have some unstable way that they can resonate
08:47:15 with.
08:47:17 And so I have a paper on pressure anisotropy instability, and there's much earlier paper by Alex was area and Andre Berto snack from 2006.
08:47:28 Okay.
08:47:30 So what does pressure and I saw Kirby do. So, first of all, after chugging through a lot of kinetic theory, you can write the growth rate of the pressure and I saw to be instability in a relatively simple form.
08:47:44 This should actually be the absolute value of the pressure and I soft up so the difference between the pressure in the parallel direction and perpendicular, with respect to the magnetic field.
08:47:58 Both anisotropy, or unstable, although with different circular polarization.
08:48:03 So, you can see that if the pressure and I saw trophy is awarded the l think speed over the speed of light, which is a tiny tiny number on this.
08:48:14 That can be unstable. And for those of you who've worked on the streaming instability. If you just replace this factor here by the ratio of the drift speed to the altitude speed, you get the growth rate for the streaming instability, so they're very similar.
08:48:29 They both require and I softer piece of order the altitude speed over the speed of light, which is very small.
08:48:38 Okay.
08:48:43 So, um, there are plenty of reasons why.
08:48:47 There could, you know there were all kinds of pressure fluctuations and so on in the interstellar medium.
08:48:51 But cosmic rays can can drive their own pressure on a soft up, and here's kind of a close up of one of Chad's clumps simulations that has a fairly weak magnetic field you can really see that the field lines, which you know are very straight here where
08:49:06 the cosmic rays haven't reached them yet they're, you know they're kind of bulky and bendy and kinky over here. These are just density contours here.
08:49:18 So, how does that create pressure and I saw it up. It creates pressure and I saw it up because charged particles have to so called at Vatican variance in a magnetic field that changes slowly.
08:49:32 One of them is the magnetic moment, which is basically the magnetic flux through an orbit, and the other is a longitudinal action quantity.
08:49:44 And so in a changing magnetic field. So for example, if the magnetic field is getting weaker, because it's bulging out, then the.
08:49:55 So the magnetic field is getting weaker. So the orbit will get bigger and the perpendicular momentum will get smaller. So, a weakening magnetic field tends to create a situation where the parallel pressure is greater than the perpendicular pressure.
08:50:11 If the magnetic field were contracting go the other way and bending of the field, also causes pressure, and I saw tricky.
08:50:22 Okay.
08:50:25 So, in the classic bottleneck picture. The cosmic rays are streaming along the field at the minimum amount things speed along the flux tube. So, that's not enough to excite the drift, and the drift streaming instability, but it will have an effect on
08:50:39 the growth rate when combined with pressure anisotropy. So, just to get it straight there for four waves to propagation directions, up and down, and each propagation direction, has both circular polarization so there are four possible waves.
08:51:00 And the most unstable wave is the way in which it's propagating in the same direction as the streaming, even though the streaming is not enough to destabilize it alone.
08:51:10 And it's whatever circular polarization is unstable for that particular magnetic field.
08:51:18 So that will be the wave with the fastest growth rate.
08:51:21 But that wave will not scatter all cosmic rays.
08:51:26 In order to have all cosmic rays scattered, the ones going up the field lines and down the field lines. You either have to have waves propagating linearly polarized waves propagating in both directions, or one circular polarization propagating One Direction
08:51:44 one circular polarization propagating the other direction. Or you can have waves propagating in just one direction, but both polarization are present.
08:51:54 So it's frequently assumed in plasma physics that when you have an instability, it saturates it by moderate by modifying the distribution function to bring it back to marginal stability.
08:52:07 So, if the anisotropy adjusts to stabilize that most unstable wave. All the other waves are damped, you only have one wave.
08:52:18 No other waves. So, a situation like that is ineffective for scattering the cosmic rays and modifying the distribution function.
08:52:29 So, with apologies to Jonathan Swift. I'm here is what I currently think
08:52:38 so.
08:52:40 Without the pressure anisotropy instability, the cosmic rays in a bottleneck would drift at the minimum elfin speed along their flux tube, they don't excite the waves, and they don't coupled to the gas.
08:52:53 But the over pressure that accompanies the bottleneck bulges the magnetic field, and it doesn't have to bulge it to an extent that's visible to the naked eye, the ratio of the elfin speed to the speed of light, you know, could be tend to minus four.
08:53:07 And that's all you need. That's, that's all the bold you need to start driving and unstable pressure and I saw it up.
08:53:16 But that pressure and I saw to be will be abetted by the sub authentic drift.
08:53:23 It will increase that it will, it will destabilize the way of going in one direction, and it will damp, the wave going in the other direction. So there's one unstable wave and scattering by that most unstable wave, and I proposed will reduce the drift,
08:53:42 and allow the pressure and I saw it up once the drift is reduced to drive the other circular polarization.
08:53:50 And so I think the only situation where you have way, you have enough waves to scatter the cosmic rays, and they have the same growth rate is when there's no drift.
08:54:03 You just have a drift plus bottleneck. Now that doesn't mean that the system is completely static because there's a gas dynamic response so there's this acoustic pulse or whatever your situation is, but that the cosmic rays are not moving, did not have
08:54:17 a bulk drift, with respect to the fluid.
08:54:21 And so now we can calculate the scattering rate at which the pressure and I softer be is marginally stable, and if you were sort of tentatively congratulate.
08:54:30 She got through the talk without a whole lot of equations. Sorry.
08:54:34 I felt I had to do this.
08:54:36 So, this is a diffusion equation in momentum space, which we can use to estimate the.
08:54:45 How much scattering we need to balance this term which is driving anisotropy.
08:54:52 So we balance this term against this term balance the warping against the scattering. And what we find is that the scattering frequency is of order, speed of light, divided by the magnetic radiant life scale.
08:55:06 And the mean free path is of order, the gradient, like scale.
08:55:13 So, this relatively weak level of scattering relatively long mean free path will be enough to restore the coupling to the gas, but it's more defensive and weaker than the streaming instability.
08:55:29 That would be a claim.
08:55:32 And so let me summarize this. Okay, so first of all, this classical self confinement picture breaks down and predicts decoupling when the cosmic ray pressure gradient, and the density gradients in the gas are anti parallel, and at at the level of structure
08:55:52 in the interstellar medium or CGM or Halo. This must happen all the time.
08:56:00 And the result is a highly intermittent simulation, a situation where you have high pressure bottlenecks with very little pressure, essentially no pressure gradient in between these sources and the density maxima or in between density maximum and Chad
08:56:20 has tested this accounting for parsley ionized clouds fully ionized clouds, allowing diffusion not allowing diffusion. And although the, you require kind of a highly resolved simulation to really do these things accurately, they seem to be very robust,
08:56:39 they persistent clumpy medium single cloud. What, whatever.
08:56:45 But this picture might be modified by pressure anisotropy instability. So the outcome of the pressure anisotropy instability, could be this, this drip list state in which the scattering mean free path is is pretty long it's awarded the magnetic radiant
08:57:01 light scale. And I can't help wondering if this could give a better agreement with the gamma ray observations Could this be a physical mechanism for giving us a large cosmic rate if you 70.
08:57:15 So, with that, I will stop and very happy to take questions.
08:57:22 Excellent, thank you so much, Ellen. That was awesome.
08:57:27 Excellent, thank you so much, Ellen. That was awesome. I'm just in will give everyone a few minutes to process everything to go through the slack discussion there have been, there's been a variety of different questions that were brought up and discussion
08:57:39 topics, and we will reconvene here with our whole panel to start addressing some of the questions from the audience. In, we'll, we'll start back at 905 so in about seven eight minutes, so everyone can take a take a break and catch up on everything, and
08:57:57 then we'll start dealing with, with questions from the audience and our panel. Thank you.