08:05:06 So I'm going to give you a short, a very brief introduction, so it's not to take away from critiques time, but this is tutorial Wednesday. And if you have not already please join the halo 21 tutorials Slack channel. 08:05:24 That's where I'm going to ask all of the tutorial speakers to upload their slides and any kind of slack discussion that arises from the tutorials can happen on the halo 21 tutorials channel. 08:05:35 I am opening all four breakout rooms right now and you should all have the ability to join whichever room you desire. So after critiques tutorial there is a precipitation tutorial room, which people who want to go and continue that discussion, can just 08:05:56 join that room they can leave that will come back to the main room where all of the other tutorials will be happening. OK, so the schedule today is. 08:06:07 Okay. The schedule is Prateek is up, and then we'll have Jane Charlton giving the multifamily phase cloudy modeling tutorial starting at 830, starting at 9am. 08:06:20 As Biden is being sworn in, will get a tutorial on the multi-phase turbulent ASM analogies with the CGM by Shmuel Bialy and I'm so sorry if I pronounced your name and Crow was small l swell, shoo, shoo, l do you say it like two syllables well yes OLULB 08:06:37 Alley, and at 930 will get Ben Oppenheimer and John's new home to talk about sin synthetic X ray observations. So, if you have any questions about the breakout rooms just, you can let me know you can DM me on chat I can try to direct you but you should 08:06:54 be able to see that there are four breakout rooms that you can join and leave at well as you want to participate in these discussions. So, with that said, I'm going to stop sharing my screen and hand it over to Prateek. 08:07:33 So I shouldn't be talking about these precipitation type models and the significance and understanding dashes ELO's across masquerades. 08:07:46 And I thank the organizer for organizing this meeting, such in such a wonderful manner that everyone has, you know something to get out of it. I really thank them for putting in all the hard work and arranging it beautifully. 08:08:01 And this is our institute where I work. 08:08:05 So, you're all welcome to visit us. 08:08:08 As soon as it is possible. 08:08:10 Okay. 08:08:13 So, I'll be talking about a very simple and stripped down model of the second galactic medium. And so here you sort of my cartoon. 08:08:22 And this is mostly motivated from cool code clusters because that's where the observations of the volume filling phase of the heart phase is easily done. 08:08:35 So we know that the hot phase in galaxy clusters. 08:08:49 And even in cool course is in rough hydrostatic balance, and in the cold calls at the center the cooling time is shorter than the Hubble time. So that means, 08:08:53 as I, and we don't see any signatures of cooling flows in the sense of young stars and stop high star formation date so that means feedback heating due to eg and jets is somehow, preventing the central gas with short cooling time from cooling catastrophic 08:09:15 Lee, so. 08:09:19 So these are sort of the main elements of of CGM halos and, you know, mostly motivated from interact Lester medium. You have gravity, you know, dark matter gravitational potential you have hydrostatic volume filling phase, and you have cooling and heating 08:09:39 due to feedback. 08:09:42 Now, so this is these are sort of the simple equation so this is the hydrostatic equilibrium in an in a dark matter gravity which applies for the background diffuse gas and thermodynamics is extremely important. 08:09:58 Okay, and this is the entropy equation for the fluid element, which shows that the entropy can be lost because of radiative cooling, which is this term. 08:10:10 And, you know, you can increase the entropy, or internal energy, because of the subject of heating irreversible heating, which is represented here by this Q plus term. 08:10:22 And it's important to note that this is not a state function. Unlike the cooling function, which is a function of density and temperature alone. This can be a function of space and time right we, you know, when we studied thermodynamics. 08:10:37 We like debug q equals du plus pdv right the BBQ is important, which means that you cannot write Q as a state function. Here I'm showing a typical collision the line ization equilibrium, cooling, and it's useful to keep this in mind, because this applies 08:10:55 to you know most of the topics that we are going to hear about in this conference so here at very high temperatures, so this is long term long tea. 08:11:06 And this is technically it came into the seven side very high temperatures all the gases ionized you have free free cooling at lower temperatures ions are not fully ionized and you can have an atomic transitions of oxygen and so on. 08:11:22 So, and below 10 to the four Kelvin. Hydrogen starts recombining and you cannot excite atomic transitions and you know there is a steep follow in the cooling code around that tend to the full Kelman. 08:11:40 So, and you know, at at this temperature, there is also photo heating, which sort of imposes floor of 10 to the fourth element, which is sort of more, which is the motivation for imposing this clothing, and a lot of simulations that we have heard about. 08:11:55 Now one thing to note here is that all these temperature regimes are formerly thermal the unstable to small temperature perturbations. 08:12:07 Now, I already mentioned that you can, you know, the cluster crews should be thought of in rough thermal balance, the balance between cooling of the ICM due to these atomic and atomic and plasma processes, and also heating you to feedback. 08:12:29 So this idea of thermal instability is not very new and it goes, you know, long back. 08:12:36 But most of the older analysis was in the context of a background cooling flow in which the background gas. 08:12:45 cold and flu towards you know and sort of flow towards the center. 08:12:50 And in such a background, which is evolving. 08:12:54 On the cooling time. The, the density perturbations do not grow, and these are the papers that sort of. 08:13:02 We're using this model. 08:13:05 But the presence of these bubbles aging bubbles show that, you know, heating is also very very important in galaxy clusters. And because of the lack of cooling flow, one should consider thermal balance as the state at big on around with Jupiter, their 08:13:23 system. 08:13:26 Right, so that the earlier modules will perturbing the wrong equilibrium, basically, and an equilibrium with thermal balance is more motivated, at least for galaxy clusters. 08:13:36 So here is actually a simple one the simulations carried out about 10 years ago now, which shows, development of thermal instability in a periodic box. 08:13:50 And in this this black line shows the initial density perturbations, and this dotted red line shows its linear growth. And this is basically the entropy mode, which is commonly unstable. 08:14:04 And these scales of interests are isostatic, that is the sound crossing time across the modes is much shorter than the cooling time. So this actually applies to the galaxy cluster goes very relevant. 08:14:17 You also see this dash blue line, which has thermal conduction in it. The role of thermal conduction is to wipe out perturbations at small scales and the scale, below which perturbations are wiped out is called the fields length. 08:14:33 Now this is the linear state and nonlinear Lee This is what happens. These dense density and so these are ice robotics so whenever you have high temperature you have low density. 08:14:43 So these high density peaks, low temperature peaks become nonlinear they have shorter cooling time. And, you know, you get these nonlinear structure so this is hot, diffuse background phase and this is dense phase and this is with thermal conduction, 08:15:02 but without conduction you have many more small clouds as shown here. 08:15:09 Okay, so in this setup with periodic boundary conditions condition, you always have multi phase gas. After a thermal instability timescale which is a hoarder. 08:15:21 in a comparable to the cooling time. 08:15:23 And since the density. Since the plasma is compressing in the dense cool phase discovery phase is likely magnetically dominated in reality in these simulations we are actually imposing a temperature flow that like around 10 to the six Kelvin so that's 08:15:41 why this is not at tend to the full Kelvin but at a higher temperature, but that was just to just so that we can resolve the cooler phase A BIT bit better. 08:15:52 Okay so this setup did not have any gravity. Now the question is what happens if you have gravity. Can you explain these, these magnificent HL filaments that you see in Perseus cluster, by, by invoking local thermal instability in global thermal balance. 08:16:11 So here is actually a toy model in which we have included gravity so this is like a dark matter Halo. 08:16:19 You have gravity acting towards the center, and in every Shelby are balancing heating and cooling. Right. 08:16:25 But this thermal balance is not point by point. 08:16:30 It does not apply to every point but only insurance so the slightly dense regions in the shells can cool faster than their surroundings and it can in principle, become multi phase. 08:16:41 So this is one of the assets, which is motivated from observations of course, and we have hydrostatic equilibrium the gravity is due to dark matter. So the question is, what does this model give us. 08:16:52 does this also give us multi-phase gas as our periodic model. 08:17:02 So what we see in this model is right so here is actually a galaxy cluster, a model galaxy cluster with small perturbation shown on the left. This is density log density in CGS in it. 08:17:19 And you see the central central portion of the cluster is dense and cool. 08:17:27 cool. And we let this thermal balanced model run. And what we see is that there is a very very important parameter that we sort of noticed that the ratio of the schooling time to the free fall time in the background determines whether this simple and 08:17:44 sets of shell balance. 08:17:47 Shall Thurman balance can give rise to multi-phase gas or not. So whenever the cooling time to the free fall time is less than around 10, the dense regions condense, and form these nuggets, which are at tend to the full Calvinist the at the temperature 08:18:05 of the stable phase. 08:18:07 Okay, so these condense out there isn't the other case the cooling time to the free fall time is big, greater than 10 like 2030, then we don't see this condensation, even if we wait for many many many cooling times. 08:18:21 So this suggests that there can be some sort of self regulation going on in such systems where were D cool over tff with cooling time is measured in the background or gas is maintained in this state build a cooling down to the free four times greater 08:18:41 than 10. 08:18:43 And otherwise what would happen is this gas would become multi phase and result in condenses condensation and these cold clouds will sort of slowly fall towards the center on of order the free fall time and give rise to feedback fueled by cold gassed. 08:19:03 Now, this is actually a very very simple experiment, but it has far reaching consequences. 08:19:09 So this suggestion and salads, for the state of the heart CGM that the ancestors the following that at largely di, the halo should have a cosmological profile, like some sort of add to the minus 2.5 or something like that, in density. 08:19:29 And as soon as one reaches a radius. So you start constructing these models from outer boundary, and you impose hydrostatic equilibrium with a given density profile so you can actually start building it. 08:19:49 But at some point, you will hit radius, at which the ratio of the cooling time to the freefall time is hits 10, and this is the radius where you expect the hot gas density to be regulated. 08:20:01 And here, we put an ad says that within this radius there is a core, and you can make a choice for this goal. 08:20:09 Like you can have an entropy corridor, or a TT cooler tff of 10 core. And so these are actually models constructed for different halos ranging from a milky way mass Halo here at the bottom two or three times 10 to the 14 solar mass cluster here. 08:20:25 So these lines. 08:20:28 The dotted lines correspond to a Tq lower tff of 10 core and the solid line corresponds to an entropy code, and what they suggest is that the more massive halos like clusters, should have denser hot gas in the center. 08:20:44 So this is partly the reason that galaxy clusters image so profusely an X rays, whereas lower mass halos like the Milky Way. Or like, or even groups do not get as much because they are densities. 08:21:00 The hot gas densities are lower, of course they have their volumes and masses are also lower, but the density is also low. 08:21:08 So, so this is actually very very profound and it actually is based on a very simple model, which is this de cooler tff, the significance of this threshold. 08:21:19 So this is actually the original precipitation model and this. There has been a lot of work on this type of models. 08:21:28 Notably, my mom point and his collaborators. 08:21:32 And in fact for the Milky Way. The whole CGM is the core basically the cooling time to the free fall time ratio even at the video radius is smaller than 10 so the full CGM density has to be modified. 08:21:48 And this is what happens in these, the bottom lines here then dot the dotted line and in the solid line. 08:21:56 And this sort of an argument should apply to even other GORANI like AGN and the solo Corona in fact. 08:22:05 So what about observations. So here, I'm I have actually put together this graph from from marks 2015 paper here on x axis I show radius and the y axis shows the cooling time. 08:22:22 And this magenta ban shows this cooling time to the free fall time ratio between five to 20 so this is the zone, where you expect. 08:22:33 multi-phase gas to be present, according to this precipitation type models. And indeed, So what is shown here, profiles. 08:22:41 Data from except sample. And these blue ones. 08:22:46 Indeed show evidence for coal, gas in HL for all in far infrared. 08:22:52 Okay. Where is the red ones which are high, longer cooling times. Do not show multi-phase gas, so there is some evidence that something like a tea cooler tff of 10 is respected by real systems. 08:23:11 So in fact there is much more work by done by Mark, which shows observational comparisons across the masses. 08:23:22 Now, one of the questions is why, why did why thermal instability does not lead to multi-phase gas for large cooling time to the free fall time ratio, and it's a fundamental in the subtle effect. 08:23:33 Okay so here it is like a toy atmosphere, you know, which is it static, and it has gravity so you consider a blob here. Right, so you can you can consider to sort of limits, one where the background atmosphere is strongly stratified. 08:23:52 So these this blob is actually oscillating very very rapidly at the local branch Isla timescale so what these oscillations do, is they excite gravity waves in the neighborhood of this blob and limit the amplitude of this perturbation. 08:24:13 So the diving by thermal instability terminal instability wants to make this multi phase, but this diving of into gravity waves in the name, you know, in the surrounding medium balances this driving. 08:24:25 So this system can actually saturate at small amplitude Delta row by row less than one. So you never see multi-phase gas, even if you made for very many cooling times. 08:24:39 On the other hand, you know, we can also consider this scenario, where the background is not very strongly stratified. that is the brand Vizsla timescale is law, even in this case, as the blog falls, even though there are no restoring forces, you have 08:24:53 like local shedding of this blob, because it's moving relative to its surrounding. So this is sort of like a local cloud crushing setup where the density perturbations of smart. 08:25:05 Okay. In both cases, you can suppress formation of multi phase gas with, if the background cooling down or the freefall time is larger than this threshold. 08:25:16 So Mark has actually worked on this aspect a lot as well to elucidate what's going on and get and you can actually check out his latest work that he is just now posted on on the precipitation channel. 08:25:30 Now what about more complicated situation right for example in cosmological simulations. So there you know this, and sides of tumbling balance and shells and so on is of course, clearly not valid. 08:25:44 So here, actually is a snapshot of magnesium to column density from Dylan Nelson's work. 08:25:54 Recently, and it shows a lot of like tiny clouds. and this month is so this is this is dense gold gas and origin, you know this multiples gas has multiple origin, some of them are associated with weeks of galaxies and some are like long lived dense things, 08:26:11 which was stripped off from cosmological filaments, and so on. But what you see here is that the goal gas is actually ubiquitous. And as a very large area covering faction, you know, comparable to observations. 08:26:24 Similarly here, you have a situation from you on these jet simulations which show like an early phases, the multi phase gas can actually be stimulated along the jet directions. 08:26:39 Now, so this is actually a complicated complication that has to be incorporated in multi phase condensation. So this was a little numerical experiment that was done by people Chaudhry. 08:26:52 There she is. So in addition to those thermal balancing shells. She seeds, density perturbations. Okay, and what is shown here are a series of numerical experiments, the x axis is the amplitude of density perturbations, and the y axis is the minimum of 08:27:11 cooling down to the free full time in the diffuse gas profile, and it so this is sort of like a threshold for condensation so if you're above this threshold, you will have no condensation and if you're below this threshold, you have a tendency to become 08:27:25 multi phase the atmosphere can become a multi phase. So the key point to notice is that it has this hockey stick shape. So when your delta is smaller than one so when the perturbations are linear, then, then you sort of recover the, the cooling down to 08:27:45 the freefall time threshold of order, 10, but if you're density perturbations of nonlinear, then you know you can have multi phase condensation, even when the cooling down to the three full time is larger. 08:27:55 And this is what we see in in some of these cosmological simulations, and in a gn simulations that I showed from, you know, here you know here is actually the x axis here this time, or five Eagle us. 08:28:14 So what Shown here are some important quantities, from a gn Jetson so some from 08:28:25 ICM simulations with kinetic age feedback jets. And what you see is the presence of these cycles so this magenta is the ratio of cooling time to the freefall time measured in the hot face. 08:28:40 So if. So when this when this cooling down to three four time threshold drops right you have a lot of gas, coal, gas form that sort of funnels coal, gas to the AGM, and you have jet, an increase in the jet power. 08:28:56 Right. So you have these episodes of cooling and heating. And so for example here at this time, the cooling down with a free fall time is greater than 10, and you don't have any coal and gas. 08:29:07 So there are cycles in more realistic systems you expect cycles of cooling and heating. 08:29:13 And you critique I have to stop you here. And so I think we need to continue your discussion over in the precipitation workout room. And so, it sounds like you know this is an incredibly rich subject and that was a really great tutorial thank you I know 08:29:32 you had two slides left but I think that that was, you know, a wonderful. 08:29:39 That's fine. 08:29:39 And so the precipitation tutorial room is open, and so Prateek I'm going to ask that you join it I know Mark Boyd is going to head over there and I am going to introduce Jane Charlton who's up next.